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John Bull: Ut, re, mi, fa, sol, la

A Performer's Investigation, Part 2

Gary Verkade
Default

An anomaly here means something unusual, a musical passage
that does not conform to contemporary rules of counterpoint or otherwise
deviates from the norm. It also entails any incongruities or inconsistencies in
melody, harmony, counterpoint, or texture. The concept thus entails
interpretation and assumes some knowledge of historical musical practice. In a
piece with the rigorous formal construction of the one under consideration, we
might expect the voice leading, the treatment of harmony, the handling of
texture, etc. to be just as rigorous. Yet there are a number of ambiguities
that are noteworthy and curious.

The hexachord theme wanders from voice to voice. This is
unusual for the simple reason that the theme is treated as a cantus firmus;
cantus firmi, as a rule, do not wander. It is especially peculiar that the
wandering takes place in the middle of thematic statements. Only once does it
happen at the beginning of the theme (at unit 79) and that is remarkable for
another reason. The hexachord theme first begins as the soprano voice. It
wanders to the alto voice at unit 10 (see Example 14).

The theme only remains in the alto voice for the duration of
nine units before returning to the soprano (see Example 15). Only four units
later it wanders again to the alto (see Example 15). The switch in voices takes
place on paper at unit 22 where the upper two voices use the same pitch,
however it is not audible until unit 23.

The cantus firmus theme returns to the soprano beginning at
unit 31, where the ambiguity of which notes represent which of the two upper
voices is extended until unit 33 (see Example 16).

Another switch to the alto voice occurs during the space of
units 37-38 (see Example 17).

During the first four statements the hexachord theme wanders
between the soprano and the alto six times; one hears the theme moving through
the fabric of the composition. The return to the soprano, the last until the
final section of the piece, is effected at unit 43 (see Example 18).

The shift, at unit 79, of the hexachord theme from the
soprano voice to the bass voice, the leap from f1 to A-flat, is one of the more
dramatic shifts of the piece, moving very audibly from one outer voice to the
other. As we have noted above, the leap occurs as a result of the transposition
scheme. After that, the theme continues to wander somewhat. It moves to the
tenor at unit 133 (see Example 19). It also moves to the alto voice at unit
163, but that voice crossing is as good as inaudible and is accentuated by Bull
in another manner discussed below.

Anomalies II: texture/harmony

Example 20 shows how the hexachord theme, for the space of
two and one half whole notes, audibly becomes the highest voice without
actually leaving the alto voice on the page. Bull draws attention to this fact
by leaving the leading tone, b-natural0 of the cadence on C, hanging without
resolution; the soprano voice does not end, but is suddenly abandoned in
mid-cadence. This is an abruptio, the sudden cessation of a musical thought.
Right at that point, unit 13 of the piece, the effect of being left hanging at
the cadence is further emphasized by the open sonority of the fifth, C-G, an
anachronism, sounding for an instant in two-voiced texture due to the voice
leading of the bass and tenor voices. The effect is one of a hole in the music,
and it is one that allows, for a few moments, the theme to sound as if it were
the soprano voice.

Example 21 shows another curious passage. One can see that
the half-note e-flat1 in the alto at unit 100 is followed by a rest and that
the alto proper doesn't reenter until the second half of unit 102. There is,
however, right at unit 101, the entrance of an extra voice in the left hand,
f0, which sounds for the duration of a whole note only and then disappears. It
can only be the alto voice which suddenly plunges down into the tenor area,
crossing below the actual tenor at unit 101. The open space between the tenor
c1 (which, at unit 101, sounds like the alto voice) and soprano f2 disobeys the
rules of counterpoint which stipulate that there be no more than an octave
between upper neighboring voices. Not only does the space call attention to
itself, but the apparent extra voice, f0, does so as well. The
musical-rhetorical figure signified by the space, called longinqua distancia,
continues into unit 102 and is found between tenor and soprano (b-flat0 to
e-flat2) and then between alto and soprano (c1 to e-flat2).

Example 22 shows, at unit 144, the 12th entrance of the
hexachord theme, beginning on f-sharp0. The sonority is unusual, to say the
least, and eminently avoidable. First, the natural movement of the soprano
voice would be to a1 at unit 144, completing the cadential figure begun around
unit 141. The bass voice is expected to drop to A at unit 144 for the same
reason, but it does the unexpected also. The alto voice withdraws itself from
the affair with a rest, leaving the other voices to form the unusual harmony:
octave f-sharps over an e0 in the bass. I have no doubt that Bull knew that the
12th entrance of the theme, using the 12th pitch of the scale, was taking place
at the 144th (12 x 12) unit of the piece.

Example 23 illustrates a passage set audibly apart at unit
151 by the manipulation of texture. The four-voiced texture found at the first unit
of the example, the alto having first a half-note rest, is thinned out as the
soprano drops out at unit 150, while the bass drops out right at unit 151
leaving just a two-voiced texture. This is a unique moment for two reasons. The
two-voiced texture is the thinnest used by Bull in this work, and rarely used
at that. But that fact alone is not enough. What makes this striking is the
open sound of the fifth occurring right at the point where the texture is
thinnest. The listener cannot miss the anachronistic sonority; Bull literally
diverts our attention away from everything else directly to it as he also did
at unit 13 (see Example 20).

Example 24 shows another voice crossing, but one that does
not belong to the more audible events of the work.  However, beginning at unit 163, we have an occurrence which
acts as an accent and thus draws the ear to it. The alto voice here carries the
hexachord theme. One can observe how Bull accentuates this particular event.
First, the thematic note, e1, is only a half-note long; this is the only
passage in the work which has a thematic note which is not a whole note.
Second, the chord played at this point has an added voice in the right hand
making it five-voiced; at no other point, excepting the final chord of the work,
do more than four voices sound simultaneously. Third, the three inner voices
have the same length, a half note, and all are followed by a half-note rest;
i.e. the thickest texture is immediately followed by the thinnest texture used
by Bull in this piece. Fourth, the five-voiced texture is further emphasized
rhythmically by the quarter-note A found in both of the outer voices; the outer
voices are the most audible and the A found here presages the cadence on A
found across the next bar line. Fifth, the five-voiced texture is restored for
the brief period of a half note one unit later. It is an e1 in the right hand,
the only tone found both in the A (tonic) and E (dominant) triads which are
here forming a cadence--the d1 of the hexachord theme is the seventh of the
dominant-seventh chord--though E is conspicuously missing from the a-minor
sonority of unit 165.

Order

Hexachord

John Bull uses the hexachord as a cantus firmus. It is not a
theme that is developed as the theme of a fugue might be and does not itself
undergo transformation. It is a building block with which Bull constructs the
framework of his piece. It goes through a number of statements, but each
statement is clearly identifiable as a hexachord. The hexachord system reckons
with hexachords on G, C, and F although it is clearly a system based on
flexible pitch, i.e. it is the relation between each of the hexachord members
which remains inviolate; a particular ut may have any G, C, or F pitch. Bull,
however, seemingly drawing the consequences of a movable ut, places the
hexachord on all 12 chromatic tones, establishing a comprehensive system of
relative pitch. Mutation from one hexachord to the next, by way of a pivot
tone, a tone which has a function in two successive hexachords and facilitates
the transition of one hexachord to the next, does not occur here. Rather, each
hexachord stands on its own and demands its unique right to existence
independent of the previous hexachord. By setting up his piece in this manner,
Bull does away with the entire hexachord theory. The hexachord is used as a
tool to dismantle the theory based upon it.

Modulation

Having done away with mutation, Bull employs transposition.
Each of the first 12 entrances of the hexachord theme thus demands a harmonic
response, a modulation. Bull forces himself to write a music which touches on
12 keys. If we regard major and minor as modes, the entire gamut of keys in the
tonal system of the common practice period is utilized--all in one piece of
music. And his use of the whole-tone scale in transposing the hexachord theme
is truly astounding and sets this piece apart from anything else in the
keyboard literature of the time. So, too, did Debussy use the whole-tone scale
when, at the turn of the 20th century, traditional tonality was increasingly
becoming problematic as a system and composers were experimenting with new
systems of harmonic organization.

 

13

The hexachord theme, used as a cantus firmus in this
composition, i.e. unchanged, though transposed, is organized into a 13-unit phrase.
The transposition scheme of the piece requires 13 statements of the theme in
order to include all of the 12 tones and return to the starting point. The
correspondence of the length of the theme and the number of repetitions it
undergoes in the transposition scheme represents order on the highest level.
This produces a first section of 169 whole-note units (13 x 13).

 

17

After the transposition scheme has run its course, there are
four more statements of the hexachord theme in the soprano voice, bringing the
total number of thematic statements to 17. However, the total number of
whole-note units which comprise this second section of the work is not 52 (4 x
13). The 13th unit of the last thematic statement is omitted. That leaves us
with one unit fewer than anticipated. But 51 = 3 x 17.

 

11

The two main sections of the work, comprising all of the
statements of the hexachord theme, make up the body of the piece. It contains
220 whole-note units of music, instead of the 221 (17 x 13) units it would have
had, had the last statement of the hexachord theme contained its 13th unit. 220
(20 x 11 or 2 x 2 x 5 x 11 or 5 x 44) contains no factor of 13 or 17. However,
we know that at this period, as part of a very long history, gematria, the
theory of numbers and their meanings, was a branch of knowledge in which
artists not only dabbled, but used with impunity. One of the common uses of
numbers was the representation of names: A = 1, B = 2, C = 3, etc.
("I" and "J" were considered one letter, as were
"U" and "V"). Both "John" and "Bull"
are represented by the number 44 (4 x 11). By leaving out the final rest of the
final statement of the hexachord theme, Bull changes 52 to 51, thus relating
the second section of the work to the number 17, but also changing 221 to 220,
bringing the body of the piece into relationship with his own name through the
common factor of 11.

Almost as an aside I would also like to mention that the
number of anomalies, both of voice-leading and of texture-harmony, is 11. In
other words, the entire work is regularly constructed employing the accepted
rules of counterpoint/composition except those passages which Bull has given
his personal stamp by deviating from the norm. His personal stamp also extends
to the number of those stamps.

 

7

The peroration (or coda) comes last. It is extra, the icing
on the cake, the statement that ends the oration. It is fitting that it has its
own identity. The number seven has great significance in many cultures of the
world. It is traditionally related to the length of the week and thus also to
creation and the concept of completeness. It has even been maintained that the
number seven is responsible for bringing everything into existence, a thought
not necessarily misplaced in this context since Bull is calling a new system of
musical order into existence. The seven units of peroration bring the total
length of the composition to 227 whole-note units.

Primes

The structural numbers of the composition, 7, 11, 13, 17,
227, are all prime numbers. In addition, most of the anomalies take place at or
are centered on whole-note units which are prime (10, 13, 23, 31, 37, 43, 101,
133, 144, 151, 163). The only exceptions are units 10 (example 14) and 144
(example 22). Unit 144 has been related to the fact that the 12th statement of
the hexachord theme is taking place using the 12th member of the chromatic
scale. The passage at unit 10 is the first one in the series of those that
appear unusual. It is in fact the case that the numbers 10, 100 and 1000 have
an intimate relationship to the number 1. As beginnings of new orders of
numbers (the tens, the hundreds, the thousands) they have the same function as
the number 1 itself, the beginning of all numbers. Music theorists/philosophers
from all over Europe, from Italy to north-Germany, from Zarlino to Kircher to
Descartes, recognize in 1 not a number, but rather the concept of unity from
which all numbers, indeed all existence has its origin. Even as late as 1722,
Rameau makes the statement that the number 2 is the first number, not the
second. Observed from this point of view it is not inappropriate that the first
of the anomalies should occur at unit 10. Given the nature of music, both the
fact that it occurs in time and that it is context-bound--i.e. a context needs
to be established before events can be perceived--unit 10 is the first point at
which a unique event could occur "at the beginning" without simply
being perceived as the beginning of the music. Though the numbers 10 and 144
are not prime, I don't think that one can deny Bull's interest in prime numbers
(see Table 1.)

The whole-tone scale

One additional aspect of the piece remains to be mentioned,
one that is for me a particularly savory morsel. The whole-tone scale is made up
of just that: whole tones. How does the use of this scale tie in with the order
found in the rest of the composition? The whole tone is mathematically
represented by the proportion 9:8. We can now answer the question why there are
four concluding statements of the hexachordum durum, instead of three or five,
bringing the total number of statements of the hexachord theme to 17 (13 + 4).
The connection between the overall form of the work, which consists of 17
statements of the hexachord theme, and the transposition scheme is given by the
whole-tone scale itself: 9 + 8  =
17.

This composition is not to be disposed of as a mere
curiosity. It is a clear statement by a serious composer. Ut, re, mi, fa, sol,
la: a treatise on a system of music which it methodically, through the
organization of its discourse, declares obsolete and actively replaces,
utilizing admirable intellectual rigor, with a new order.
style='mso-tab-count:1'>         
n

Related Content

John Bull: Ut, re, mi, fa, sol, la

A Performer's Investigation, Part 2

Gary Verkade
Default

Anomalies I: voice leading

An anomaly here means something unusual, a musical passage that does not conform to contemporary rules of counterpoint or otherwise deviates from the norm. It also entails any incongruities or inconsistencies in melody, harmony, counterpoint, or texture. The concept thus entails interpretation and assumes some knowledge of historical musical practice. In a piece with the rigorous formal construction of the one under consideration, we might expect the voice leading, the treatment of harmony, the handling of texture, etc. to be just as rigorous. Yet there are a number of ambiguities that are noteworthy and curious.

The hexachord theme wanders from voice to voice. This is unusual for the simple reason that the theme is treated as a cantus firmus; cantus firmi, as a rule, do not wander. It is especially peculiar that the wandering takes place in the middle of thematic statements. Only once does it happen at the beginning of the theme (at unit 79) and that is remarkable for another reason. The hexachord theme first begins as the soprano voice. It wanders to the alto voice at unit 10 (see Example 14).

The theme only remains in the alto voice for the duration of nine units before returning to the soprano (see Example 15). Only four units later it wanders again to the alto (see Example 15). The switch in voices takes place on paper at unit 22 where the upper two voices use the same pitch, however it is not audible until unit 23.

The cantus firmus theme returns to the soprano beginning at unit 31, where the ambiguity of which notes represent which of the two upper voices is extended until unit 33 (see Example 16).

Another switch to the alto voice occurs during the space of units 37-38 (see Example 17).

During the first four statements the hexachord theme wanders between the soprano and the alto six times; one hears the theme moving through the fabric of the composition. The return to the soprano, the last until the final section of the piece, is effected at unit 43 (see Example 18).

The shift, at unit 79, of the hexachord theme from the soprano voice to the bass voice, the leap from f1 to A-flat, is one of the more dramatic shifts of the piece, moving very audibly from one outer voice to the other. As we have noted above, the leap occurs as a result of the transposition scheme. After that, the theme continues to wander somewhat. It moves to the tenor at unit 133 (see Example 19). It also moves to the alto voice at unit 163, but that voice crossing is as good as inaudible and is accentuated by Bull in another manner discussed below.

Anomalies II: texture/harmony

Example 20 shows how the hexachord theme, for the space of two and one half whole notes, audibly becomes the highest voice without actually leaving the alto voice on the page. Bull draws attention to this fact by leaving the leading tone, b-natural0 of the cadence on C, hanging without resolution; the soprano voice does not end, but is suddenly abandoned in mid-cadence. This is an abruptio, the sudden cessation of a musical thought. Right at that point, unit 13 of the piece, the effect of being left hanging at the cadence is further emphasized by the open sonority of the fifth, C-G, an anachronism, sounding for an instant in two-voiced texture due to the voice leading of the bass and tenor voices. The effect is one of a hole in the music, and it is one that allows, for a few moments, the theme to sound as if it were the soprano voice.

Example 21 shows another curious passage. One can see that the half-note e-flat1 in the alto at unit 100 is followed by a rest and that the alto proper doesn't reenter until the second half of unit 102. There is, however, right at unit 101, the entrance of an extra voice in the left hand, f0, which sounds for the duration of a whole note only and then disappears. It can only be the alto voice which suddenly plunges down into the tenor area, crossing below the actual tenor at unit 101. The open space between the tenor c1 (which, at unit 101, sounds like the alto voice) and soprano f2 disobeys the rules of counterpoint which stipulate that there be no more than an octave between upper neighboring voices. Not only does the space call attention to itself, but the apparent extra voice, f0, does so as well. The musical-rhetorical figure signified by the space, called longinqua distancia, continues into unit 102 and is found between tenor and soprano (b-flat0 to e-flat2) and then between alto and soprano (c1 to e-flat2).

Example 22 shows, at unit 144, the 12th entrance of the hexachord theme, beginning on f-sharp0. The sonority is unusual, to say the least, and eminently avoidable. First, the natural movement of the soprano voice would be to a1 at unit 144, completing the cadential figure begun around unit 141. The bass voice is expected to drop to A at unit 144 for the same reason, but it does the unexpected also. The alto voice withdraws itself from the affair with a rest, leaving the other voices to form the unusual harmony: octave f-sharps over an e0 in the bass. I have no doubt that Bull knew that the 12th entrance of the theme, using the 12th pitch of the scale, was taking place at the 144th (12 x 12) unit of the piece.

Example 23 illustrates a passage set audibly apart at unit 151 by the manipulation of texture. The four-voiced texture found at the first unit of the example, the alto having first a half-note rest, is thinned out as the soprano drops out at unit 150, while the bass drops out right at unit 151 leaving just a two-voiced texture. This is a unique moment for two reasons. The two-voiced texture is the thinnest used by Bull in this work, and rarely used at that. But that fact alone is not enough. What makes this striking is the open sound of the fifth occurring right at the point where the texture is thinnest. The listener cannot miss the anachronistic sonority; Bull literally diverts our attention away from everything else directly to it as he also did at unit 13 (see Example 20).

Example 24 shows another voice crossing, but one that does not belong to the more audible events of the work.  However, beginning at unit 163, we have an occurrence which acts as an accent and thus draws the ear to it. The alto voice here carries the hexachord theme. One can observe how Bull accentuates this particular event. First, the thematic note, e1, is only a half-note long; this is the only passage in the work which has a thematic note which is not a whole note. Second, the chord played at this point has an added voice in the right hand making it five-voiced; at no other point, excepting the final chord of the work, do more than four voices sound simultaneously. Third, the three inner voices have the same length, a half note, and all are followed by a half-note rest; i.e. the thickest texture is immediately followed by the thinnest texture used by Bull in this piece. Fourth, the five-voiced texture is further emphasized rhythmically by the quarter-note A found in both of the outer voices; the outer voices are the most audible and the A found here presages the cadence on A found across the next bar line. Fifth, the five-voiced texture is restored for the brief period of a half note one unit later. It is an e1 in the right hand, the only tone found both in the A (tonic) and E (dominant) triads which are here forming a cadence--the d1 of the hexachord theme is the seventh of the dominant-seventh chord--though E is conspicuously missing from the a-minor sonority of unit 165.

Order

Hexachord

John Bull uses the hexachord as a cantus firmus. It is not a theme that is developed as the theme of a fugue might be and does not itself undergo transformation. It is a building block with which Bull constructs the framework of his piece. It goes through a number of statements, but each statement is clearly identifiable as a hexachord. The hexachord system reckons with hexachords on G, C, and F although it is clearly a system based on flexible pitch, i.e. it is the relation between each of the hexachord members which remains inviolate; a particular ut may have any G, C, or F pitch. Bull, however, seemingly drawing the consequences of a movable ut, places the hexachord on all 12 chromatic tones, establishing a comprehensive system of relative pitch. Mutation from one hexachord to the next, by way of a pivot tone, a tone which has a function in two successive hexachords and facilitates the transition of one hexachord to the next, does not occur here. Rather, each hexachord stands on its own and demands its unique right to existence independent of the previous hexachord. By setting up his piece in this manner, Bull does away with the entire hexachord theory. The hexachord is used as a tool to dismantle the theory based upon it.

Modulation

Having done away with mutation, Bull employs transposition. Each of the first 12 entrances of the hexachord theme thus demands a harmonic response, a modulation. Bull forces himself to write a music which touches on 12 keys. If we regard major and minor as modes, the entire gamut of keys in the tonal system of the common practice period is utilized--all in one piece of music. And his use of the whole-tone scale in transposing the hexachord theme is truly astounding and sets this piece apart from anything else in the keyboard literature of the time. So, too, did Debussy use the whole-tone scale when, at the turn of the 20th century, traditional tonality was increasingly becoming problematic as a system and composers were experimenting with new systems of harmonic organization.

13

The hexachord theme, used as a cantus firmus in this composition, i.e. unchanged, though transposed, is organized into a 13-unit phrase. The transposition scheme of the piece requires 13 statements of the theme in order to include all of the 12 tones and return to the starting point. The correspondence of the length of the theme and the number of repetitions it undergoes in the transposition scheme represents order on the highest level. This produces a first section of 169 whole-note units (13 x 13).

17

After the transposition scheme has run its course, there are four more statements of the hexachord theme in the soprano voice, bringing the total number of thematic statements to 17. However, the total number of whole-note units which comprise this second section of the work is not 52 (4 x 13). The 13th unit of the last thematic statement is omitted. That leaves us with one unit fewer than anticipated. But 51 = 3 x 17.

11

The two main sections of the work, comprising all of the statements of the hexachord theme, make up the body of the piece. It contains 220 whole-note units of music, instead of the 221 (17 x 13) units it would have had, had the last statement of the hexachord theme contained its 13th unit. 220 (20 x 11 or 2 x 2 x 5 x 11 or 5 x 44) contains no factor of 13 or 17. However, we know that at this period, as part of a very long history, gematria, the theory of numbers and their meanings, was a branch of knowledge in which artists not only dabbled, but used with impunity. One of the common uses of numbers was the representation of names: A = 1, B = 2, C = 3, etc. ("I" and "J" were considered one letter, as were "U" and "V"). Both "John" and "Bull" are represented by the number 44 (4 x 11). By leaving out the final rest of the final statement of the hexachord theme, Bull changes 52 to 51, thus relating the second section of the work to the number 17, but also changing 221 to 220, bringing the body of the piece into relationship with his own name through the common factor of 11.

Almost as an aside I would also like to mention that the number of anomalies, both of voice-leading and of texture-harmony, is 11. In other words, the entire work is regularly constructed employing the accepted rules of counterpoint/composition except those passages which Bull has given his personal stamp by deviating from the norm. His personal stamp also extends to the number of those stamps.

7

The peroration (or coda) comes last. It is extra, the icing on the cake, the statement that ends the oration. It is fitting that it has its own identity. The number seven has great significance in many cultures of the world. It is traditionally related to the length of the week and thus also to creation and the concept of completeness. It has even been maintained that the number seven is responsible for bringing everything into existence, a thought not necessarily misplaced in this context since Bull is calling a new system of musical order into existence. The seven units of peroration bring the total length of the composition to 227 whole-note units.

Primes

The structural numbers of the composition, 7, 11, 13, 17, 227, are all prime numbers. In addition, most of the anomalies take place at or are centered on whole-note units which are prime (10, 13, 23, 31, 37, 43, 101, 133, 144, 151, 163). The only exceptions are units 10 (example 14) and 144 (example 22). Unit 144 has been related to the fact that the 12th statement of the hexachord theme is taking place using the 12th member of the chromatic scale. The passage at unit 10 is the first one in the series of those that appear unusual. It is in fact the case that the numbers 10, 100 and 1000 have an intimate relationship to the number 1. As beginnings of new orders of numbers (the tens, the hundreds, the thousands) they have the same function as the number 1 itself, the beginning of all numbers. Music theorists/philosophers from all over Europe, from Italy to north-Germany, from Zarlino to Kircher to Descartes, recognize in 1 not a number, but rather the concept of unity from which all numbers, indeed all existence has its origin. Even as late as 1722, Rameau makes the statement that the number 2 is the first number, not the second. Observed from this point of view it is not inappropriate that the first of the anomalies should occur at unit 10. Given the nature of music, both the fact that it occurs in time and that it is context-bound--i.e. a context needs to be established before events can be perceived--unit 10 is the first point at which a unique event could occur "at the beginning" without simply being perceived as the beginning of the music. Though the numbers 10 and 144 are not prime, I don't think that one can deny Bull's interest in prime numbers (see Table 1.)

The whole-tone scale

One additional aspect of the piece remains to be mentioned, one that is for me a particularly savory morsel. The whole-tone scale is made up of just that: whole tones. How does the use of this scale tie in with the order found in the rest of the composition? The whole tone is mathematically represented by the proportion 9:8. We can now answer the question why there are four concluding statements of the hexachordum durum, instead of three or five, bringing the total number of statements of the hexachord theme to 17 (13 + 4). The connection between the overall form of the work, which consists of 17 statements of the hexachord theme, and the transposition scheme is given by the whole-tone scale itself: 9 + 8  = 17.

This composition is not to be disposed of as a mere curiosity. It is a clear statement by a serious composer. Ut, re, mi, fa, sol, la: a treatise on a system of music which it methodically, through the organization of its discourse, declares obsolete and actively replaces, utilizing admirable intellectual rigor, with a new order.          n

John Bull: Ut, re, mi, fa, sol, la

A Performer’s Investigation, Part 1

by Gary Verkade
Default

Knowledge

In order to acquire knowledge about John Bull’s work, it is important to know a little bit about what knowledge actually meant at the time the work was created. Here we are dealing with the late Renaissance–early Baroque, the exact date of the composition itself, as far as I have been able to determine, being unknown. Michel Foucault in his book, The Order of Things: An Archaeology of the Human Sciences, states:

Up to the end of the sixteenth century, resemblance played a constructive role in the knowledge of Western culture. It was resemblance that largely guided exegesis and the interpretation of texts; it was resemblance that organized the play of symbols, made possible knowledge of things visible and invisible, and controlled the art of representing them. The universe was folded in upon itself: the earth echoing the sky, faces seeing themselves reflected in the stars, and plants holding within their stems the secrets that were of use to man (p. 17) . . . To search for a meaning is to bring to light a resemblance (p. 29) . . . There is no difference between the visible marks that God has stamped upon the surface of the earth, so that we may know its inner secrets, and the legible words that the Scriptures, or the sages of Antiquity, have set down in the books preserved for us by tradition. The relation to these texts is of the same nature as the relation to things: in both cases these are signs that must be discovered (p. 33) . . . Knowledge therefore consisted in relating one form of language to another form of language; in restoring the great, unbroken plain of words and things; in making everything speak. That is, in bringing into being, at a level above that of all marks, the secondary discourse of commentary. The function proper to knowledge is not seeing or demonstrating; it is interpreting (p. 40).

If knowledge in the Renaissance and Baroque is interpretation and uncovering order, then knowledge about a work of art created in this transition time at the end of the Renaissance and the beginning of the Baroque can only be about discovering an order and an interpretation. I do not believe that the impossibility of total certainty of the results of such inquiry should deter one from the attempt to understand a work in the sense the maker might have understood that concept of “understanding.” One thing is certainly true. Understanding, in this sense, for a musician cannot simply mean hearing and/or playing a work and responding with “like” or “dislike.” Our response must go deeper. “It is not enough to feel the effects of a science or an art. One must conceptualize these effects in order to render them intelligible” (Rameau, p. xxxv). We must dig in order to uncover what might be hidden from cursory view. We must, as Frescobaldi demands, “endeavour in the first place to discover the character of the passages, the tonal effect intended by the composer  . . . ”(Notes).

John Bull

 

John Bull (1562–1628) had his feet in the Renaissance and his head in the Baroque. In other words, he was a child of the Renaissance and experienced the beginnings of the new era as a grown man. He was the student of John  Blitheman. John is known as William in the Fitzwilliam Virginal Book, which contains an In nomine of his immediately preceding the Ut, re, mi, fa, sol, la of Bull’s which is the subject of the present essay. Blitheman was known for his cantus firmus compositions, which occasionally demanded great virtuosity of the player. Bull’s education, grounded in Renaissance teaching as it must have been, certainly did not end with his formal studies. He was elected first Public Reader in Music at Gresham College, London in March of 1597 where he remained, except for a year’s leave of absence, until 1607, the year which saw his necessary marriage to one Elizabeth Walter, who was pregnant with his child. During his period at Gresham, the College was a hotbed of discussion of new ideas, inventions and discoveries from all over Europe.

For example, during the last quarter of the sixteenth century the ideas of Copernicus became more widely disseminated among the general public, the world view which stood the previous view of the universe on its head. What was formerly immovable, the earth, now was realized to be hurtling through space at unheard-of speeds. Bull must have been well-informed as to the revolutions in scientific thought in which learned men all across Europe were engaged. He was part of the established intellectual community; the universities did not ignore these new, ground-breaking ideas. He must have known about the fierce debates between the followers of Copernicus and those of Aristotle at Cambridge during the 1580s. For “we find Gresham College was, throughout the first half of the seventeenth century, a general clearinghouse for information concerning the latest scientific discoveries. Its professors of astronomy and geometry were among the ablest scientists of their day, and the college’s central location in London made their rooms a convenient rendezvous for all those who were actually contributing to the advancement of science in England” (Johnson, p. 263).

There is no need to go into the relevance of science to music in either the Renaissance or Baroque eras. That relationship has been amply discussed in a plethora of publications. What is important to note here is that the age in which Bull lived and worked was one of adventurous discovery, one in which science was revolutionizing the view of the world, as well as one in which, first in Italy and then in the rest of Europe, music, too, was undergoing revolutionary change. It is important to note that revolution, new ways of thinking, were part and parcel of Elizabethan life. Bull was no stranger to the new.

The hexachord

The hexachord was first described, but not named, in Guido of Arezzo’s treatise Micrologus of 1025–28. There are three hexachords, all of which have the same intervallic structure: the hexachordum naturale (C - D - E - F - G - A); the hexachordum molle, so-called because it included b molle, i.e., b-flat (F - G - A - B-flat - C - D); and the hexachordum durum, so-called because it included b durum, i.e. b-natural (G - A - B - C - D - E). Since medieval theory did not consider pitches of higher or lower octaves to be identical, seven hexachords were differentiated in the scale from G to e2, all of them beginning on C, F, or G. There was no concept of modulation. A melody exceeding the compass of a single hexachord was considered to be in transition from one hexachord to another. This movement was referred to as mutation. Tonal centers were not established by such movement, but rather the compass of a particular melody simply shifted from one area to another by making use of a pivot tone, a tone which belonged to both hexachords. Thus, for example, the tone sol in one hexachord could at the same time function as the tone ut in another. Yet, because the hexachord has the same construction whether based on C, F, or G, it has one interesting similarity to the major-minor tonal system: it has the potential to form the basis of a relative pitch system.

Guido’s treatise was referred to throughout the ensuing centuries, though the term “hexachord” itself apparently does not appear until about the 16th century. Although Masses based on the hexachord were composed, keyboard composers of the late Renaissance and the early Baroque seem to have been particularly fascinated by the musical possibilities offered by this theme. Pieces based on the hexachord were written by such important composers as Girolamo Frescobaldi (2) and Gregorio Strozzi in Italy, Johann Jakob Froberger in Austria, Pieter Cornet (the piece survives only as a fragment) and Jan Pieterszoon Sweelinck in the Low Countries, Samuel Scheidt in North Germany, Pablo Bruna in Spain, and William Byrd (2), Thomas Tomkins (7!), John Lugge, and John Bull (3) in England.

John Bull and the hexachord

Thomas Morley, as Master Gnorimus in A Plaine and Easie Introdvction to Practicall Mvsick (1597) which is organized in dialogue form, spends at the beginning of that treatise a considerable amount of time explaining musical notation to Philomathes, a student in the dialogue. He does this by using the hexachord and the syllables ut, re, mi, fa, sol, la. Morley’s art of teaching music was not unique in England and musicians must have been familiar with this system.

 The adventurous John Bull composed three very different pieces on the hexachord. One, Ut, re, mi, fa, sol, la [II], is an extended composition (292 measures in the Musica Brittanica edition, 237 irregularly-barred measures in the Fitzwilliam Virginal Book) in which, after the second statement, the hexachord theme is treated principally as a cantus firmus in the soprano in long notes accompanied by figurations which become in the course of the piece quite virtuosic. Beginning with a long section in two voices, Bull introduces a third voice for a similarly long section, and then a fourth voice, the piece remaining four-voiced to the end. The subdivision of the beat changes a number of times in the course of this work and in addition to the metric two-against-three which occurs in the juxtaposition of duple and triple times, rhythmic two-against-three is also found in this composition, a favorite Bull device.

Another is the more contrapuntal, 188-measure Ut, re, mi, fa, sol, la [III] (not found in the Fitzwilliam Virginal Book) composition. The more sustained polyphonic nature of the five-part texture and the avoidance of metric and rhythmic variety (the piece moves principally in halves, quarters and eighths with some dotting of values) starkly differentiate this piece from the preceding one. In addition, the hexachord theme itself is found in several rhythmic forms, principally varying combinations of halves and quarters with some tied notes, dotted values and an occasional eighth-note.

The piece which is the subject of this essay is the shortest of the three hexachord compositions by Bull.

Ut, re, mi, fa, sol, la [I]

Editions

I made the decision to use the version of the piece found in the Fitzwilliam Virginal Book since it is clearly closer to the actual score of the piece as Bull himself might have written it. The version found in the Musica Brittanica edition, with its regularly-barred measures and its conformity to 20th-century notational practices, leads one to think that the piece may be in common time. Whereas I would like, as much as is possible for a musician living very much with both feet planted in the 21st century, to get into the musical mind of Bull as it manifests itself in this composition. One must assume that whoever copied the music in the 17th century had an understanding of the music he was copying and, especially, was closer to the manner in which it was notated than editors in the mid-20th century could have been. And it is the notation which provides the only clues we have directly from the composer, clues we need in order to reach some understanding of the work, without which appropriate interpretive decisions cannot be made. The importance of the manuscript and the collection in general speaks for going to the Fitzwilliam Virginal Book as primary source.

The theme

The theme (see Example 1) has two parts, which mirror each other, consisting of the ascending and descending hexachord. The highest note (at the first appearance of the theme an e1) is always repeated.

As do the other two compositions on this theme, the present work begins not only with the hexachordum durum, but also with the very same note: g0, although it is the soprano voice (not bass or tenor as in the other pieces) which here begins the work in this low register.

Meter

Since the irregular measures of 1/1, 2/1, 3/1, 4/1, 5/1, 9/2, and 12/2 do not seem to indicate any regular occurrence of accent, my attention was brought to the consideration of meter in terms of the theme as a whole. The whole note is the value at which the regular occurrence of the tactus takes place. The piece floats in an unaccentuated flow of regular beats of that tactus. The entrance of the hexachord theme every 13 whole-note units is the important, regularly occurring event in the work. The unit of measure is not the bar line, wherever it is drawn, but rather the whole note itself and we will subsequently refer to whole-note units rather than any measure numbers. The six ascending and six descending notes give us the duration of twelve whole-notes. Except for the first three statements and one curious half note during the 13th statement, the entire theme consists of 12 unvaried note values throughout.  The final pitches of the first two statements consist of two whole notes: two g0’s and two a0’s respectively. The final pitch of the third statement is one b0 whole note tied to another. After that, the final pitch of the theme is always a whole note separated from the following thematic statement by a whole-note rest. This makes the entire theme, the ascending and descending hexachord and the unit of rest, one phrase measuring 13 units (whole notes).

We can think of the hexachord theme as beginning with a downbeat and spanning the duration of 13 whole notes. A secondary accent occurs, perhaps, at the repetition of the highest note of the theme, which results in two units of six whole notes each. The 13th whole note of the first statement repeats the final note, that of the second statement repeats the final note with an ornament, that of the third is tied to the previous whole note. After that, the 13th whole note is a rest. The 13th unit of the hexachord theme functions, especially beginning with the fourth statement, as a breath, a metrical breath if you will, a moment of rest, of gathering energy, before continuing with the next statement. This music breathes in 13-unit phrases with a consistency unbroken until the end.

Transposition

The second statement of the hexachord theme begins a whole-step higher than the first statement; and the third statement begins another whole step higher. This transposition of the theme upwards by whole step is pursued rigorously up to f1, at which point the next statement would appear again on a G (g1, an octave above the first note of the piece). This Bull does not do, but rather jumps down almost two octaves to A-flat and begins the process of transposition by whole step upwards all over again, using the remaining pitches of the twelve-note chromatic scale.

Example 2 gives the initial notes of all 17 statements of the hexachord theme, the last 4 statements of which are all on the same pitch, g1. Thus we see that the cycle of whole-step transposition, beginning on g0, interrupted once at f1 and leaping down to A-flat instead and then continuing the cycle in order to return to g0, involves 13 statements of the hexachord theme.

Modulation

With the transposition of the hexachord theme Bull is forced to modulate to new keys at every single entrance of the theme. The composition manifests remarkable instances of modulatory prowess and enharmonic ambivalence. Consider Example 3.

The E-major chord at the beginning of Example 3 includes b0, the last note of the previous statement of the theme.  D-flat1 is the first note of the fourth entrance of the theme and it appears here immediately as D-flat and not as C-sharp, as might be expected from the previous harmony. The enharmonic modulation must take place somewhere and Bull chooses to do it here. Apparently, in spite of what the Musica Brittanica edition has done here (namely first spell c-sharp1, then tie to d-flat1), Bull is not interested in making a smooth, a plausible, enharmonic modulation (see Example 4).

We can see that Bull has not written a piece concerned with modulating to as many keys as possible, thereby enabling the hexachord theme to appear in those keys. The plan of his work is to transpose, to shift the hexachord theme; he shifts the theme and afterwards draws the harmonic consequences. The transposition of the hexachord theme is the given, leading to necessary modulation—not modulation leading to transposition of the theme. The transposition of the hexachord theme is the postulate which implies the stipulation of key, not vice versa.  In other words: the form is a priori and precipitates the harmony; the harmony does not precipitate the form.

Form

We have noted above that after 12 shifts or transpositions of the hexachord theme, i.e. with the 13th transposition, Bull returns, comes full circle transpositionally, to the g0 with which he started the piece, though here it is the bass voice and not the soprano as at the beginning. Here Ut, re, mi, fa, sol, la could conceivably end. Bull has traversed the entire gamut of pitches available to him in the chromatic scale and returned back to where he had started. This disregards, however, the psychological strain through which he has put his listener. Bull must draw the consequences of going so far afield harmonically. He must first establish conclusively for the listener that one has arrived “home.” And that is not achieved by a single statement on G.

There follow four more statements of the hexachord theme, all on G, all on the same g1, all in the soprano voice. However, just as Bull begins to anchor the listener in the hexachordum durum, he changes what has up to that point been a duple to a triple division of the beat. Now this is a common device found at the ends of many compositions of this period and others: triple subdivision as ecstatic conclusion. Statement 14 consists of three half notes per whole note. Occasionally the half notes are subdivided into duple quarters which sound against the (now dotted) whole notes. Statement 15 contains both duple and triple subdivisions of the beat; the quarter notes here are ambiguously either triple subdivisions of the duple half notes or duple subdivisions of the triplet half notes. This rhythmic ambiguity occurs exactly at the point where Bull is interested in being unambiguous harmonically, i.e., he can now afford to be ambiguous on the rhythmic level now that the harmonic level has become more stable. Statements 16 and 17 return to duple subdivisions on all levels, as had been the case from statements 1 to 13.

So at the end of the composition there are five statements of the hexachordum durum. The first of these five statements (on g0) occurs at the end of the transposition process begun at the outset of the piece and belongs to that process. It rounds off that section of the piece. The final four statements (on g1) are no longer part of that process, but provide the necessary anchoring in G in order for the piece to come to a satisfactory close.

Counterpoint I: beginning and end

The hexachord appears as a cantus firmus, it does not take part in any imitative counterpoint. Three of the four voices are, then, not predetermined by the form. The opening of Ut, re, mi, fa, sol, la is instructive (see Example 5) and merits a close look. It is not marked by strict imitation carried through the three free voices.

The soprano begins, opening with the hexachordum durum on g0. The bass enters one half note later on the same g0, before the soprano moves to its second note. The two voices sound together for the duration of one half note with the same pitch, thus obscuring the two-voiced texture. The bass continues stepwise downwards through the fourth unit. At unit three the alto enters with a motive different from both the hexachord in the soprano and the descending motive in the bass. It enters on the only available note between soprano and bass: g0. The tenor enters one unit later with the descending motive first heard at the bass entrance. However, the entrance of the tenor is obscured by the fact that at that same moment the alto and the soprano sound the same note together: c1. In other words, at the entrance of the fourth voice one hears only three voices. This obscures not only the texture again, but the imitation between bass and tenor as well. Significant, and genial, about the beginning of the work is that all four voices start from exactly the same point, exactly the same pitch: the final of the hexachordum durum, g0.

The descending fifth motive, found in the bass and tenor voices, does not reappear as such throughout the rest of the work until the very last measures. The motive is given one prefix note and is found here in all three free voices. This reminiscence of the beginning provides a fitting and appropriate close to the work (see Example 6).

Counterpoint II: alto motive

At the beginning of the work (see example 5) the soprano has the hexachord as cantus firmus and the bass and tenor voices imitate each other, in fact the first five pitches are exactly the same. The alto voice is here unique, free. It proves to have a more productive motive than that shared by tenor and bass, and, indeed, we find that it is not imitation which is most significant here or in the work as a whole. There are scattered passages which employ imitation in one form or another, more or less strictly, between two or three voices. There seems to be no overall formal principle which dictates when and where imitation between the voices takes place. It is one of the compositional means at Bull’s disposal and he uses it without ever losing the prevailing sense of freedom which the three voices have in the face of the strict formal construction of the transposition scheme of the hexachord.

The emphasis is not on imitative counterpoint, but rather on a free development of the concept of imitation. One can see this on the freedom with which Bull treats the alto motive, heard at the outset (see Example 7) and referred to henceforth as the alto motive no matter in which voice it is found.

During the course of the second statement of the hexachord theme, we hear this motive in different guises in three of the four voices (see Example 8).

Rhythm and intervals are altered, and inversion is heard in the alto and bass as well as retrograde in the bass voice. Just a few units later, during the third statement of the hexachord theme, the alto motive is found using a passing tone (see Example 9).

The part of the motive which is found at units 33–34, using the quarter-note passing tone, is one that is found in all the three free voices at that point and plays a role through the fourth entrance of the hexachord theme. The alteration of the alto motive thus generates a further motive that is used contrapuntally in these passages.

In Example 10, taken from the fourth statement of the hexachord theme, we find an interesting canon, interesting in the fact that it is not strict. The bass voice leads, followed by the alto voice one whole note later with a rhythmically enlivened version of the bass voice. Also noteworthy is how the same note takes on different harmonic functions. This is due, of course, to the fact that one of the voices is the bass and the other the alto. It also has to do with the fact that, although the entrance of the d-flat1 in the alto is rhythmically analogous to the entrance of the d-flat0 in the bass, namely mid-unit, the d-flat1 enters with the length of a whole note and obscures the fact that the alto voice is, contrary to the bass, placed on the unit (beat). Thus the g-flat0 in the bass becomes dissonant at unit 44, whereas the g-flat1 in the alto at unit 45 is consonant for its entire duration. So, too, the e-flat0 in the bass is consonant for its duration, but, the e-flat1 in the alto at unit 47 becomes dissonant.

This last example demonstrates the developmental possibilities of the alto motive. Given its construction (see Example 7), the small ambitus of a perfect fourth, the prominent interval of the third, and the half step at the end, it is a motive that is related to any other motive using those intervals. It is possible to recognize in example 10 that the alto line is directly derived from the alto motive in the bass voice. In other cases it is more difficult to assert that other motives with similar constructions were consciously fashioned from the alto motive. Nevertheless, many of the passages contain motives constructed with thirds and fourths, or often end with a half step, which fact is not surprising in music that is articulated with cadences.

From units 86–93 (see Example 11), the end of the seventh and the beginning of the eighth statement of the hexachord theme, we find the alto motive used in free imitative fashion between soprano, alto and tenor. Interesting is the alto voice which mirrors itself beginning at unit 89 and then tacks on a cadential e-flat1 - d1 - e-flat1.

Example 12, from the tenth statement of the hexachord theme, demonstrates a still freer treatment of the alto motive or, if you will, those primary intervals of which the alto motive is constructed. The passage does not illustrate imitative counterpoint, but rather a free development of the alto motive. Notice particularly the alto voice which, as in the previous example, mirrors itself and pivots around f-sharp1.

Immediately following this passage, at the end of the tenth and the beginning of the eleventh statement of the hexachord theme, the soprano states two versions of the alto motive successively, the first descending (i.e, inverted), the second ascending (see Example 13).

There are further passages in which the alto motive or fragments thereof play a role in the contrapuntal texture of the work. Often, just as is the case in a number of the above examples, they are worked into phrases which are much longer. The motive shines forth suddenly from within the context of something larger than itself and contributes to the unity of the work.          

Gary Verkade was born in Chicago and grew up in the south suburbs. He studied music at Calvin College and the University of Iowa in the United States, and in 1978 he received a Fulbright grant to study at the Folkwang-Hochschule in Essen, Germany, and lived in Germany for 17 years. He has performed much new music throughout Europe and the United States and is the composer of music for organ, electronics, chamber and improvisational ensembles.Verkade has been a guest professor/lecturer/performer at universities in Europe and the United States; he served on the music faculty of Carthage College, Kenosha, Wisconsin, from 1995–2000. He is presently on the faculty of the Musikhögskolan i Pitea, Sweden, where he continues to teach, perform, compose, record, and write about music.

Dieterich Buxtehude, <i>Vater unser im Himmelreich</i>: A Study in Expressive Content

Gary Verkade

Gary Verkade is an influential and sought after interpreter of new music throughout Europe and the United States in addition to his established reputation as an analyst and performer of the traditional literature. His extensive experience with music of past eras has led to the publication of essays and articles on a variety of subjects relating to organ performance, early music performance practice, and composition. An organist, composer, and co-founder of the Essen, Germany-based improvisation ensemble SYNTHESE, he has been a leader in bringing forth serious new music for the organ, commissioning new works and working in a collaborative capacity with several well-known composers. He has a particular interest in performing music for organ and electronics. Verkade’s own compositions range among music for organ, electronics, chamber and improvisation ensembles. As a player of improvised music, he has worked together with dancers, photographers and painters, on projects that bring the arts together in a complementary and fructuous manner. Dr. Verkade has been on the faculty of the Musikögskolan i Piteå, Sweden since 2000 as Professor of Organ. He has recorded with the Innova and Mode labels, most recently Winded, an album of works for organ and electronics, and Luciano Berio’s “Fa-Si” on Berio: The Complete Sequenzas, Alternate Sequenzas & Works for Solo Instruments, a collection of performances by the premier contemporary interpreters of new music.

Default

Motto

The noblest desire, the desire to know, imposes on us the duty to investigate.
--Arnold Schoenberg, Harmonielehre (Vienna, 1922)

Beginnings
Composition is the science of putting together consonance and dissonance in such a way that good counterpoint occurs.
Form consists in the artful variety and combination of such consonance and dissonance, in other words in the observation of the general and special rules of counterpoint, so that according to different usage and natural effect it happens that one composition is good, whereas another is better, pleasing the listener more and making its author famous.
--Christoph Bernhard, Tractatus compositionis augmentatus (Dresden, after 1657)

Yes, I readily admit that the rules are to some extent useless and unnecessary. However one sees how carefully they have been used in building harmony. And therefore the ignoramus should not fancy that it makes no difference and one can compose what his fantasy dictates. Oh, no!
--Andreas Werckmeister, Cribrum Musicum (Quedlinburg, 1700)

In sum: the work must be so rich that one must wonder in the extreme, and would have to be an idiot or an atheist (o, the poor, stubborn hearts), who would not be therefore moved to praise the creator.
--Andreas Werckmeister, Harmonologia Musica (Frankfurt and Leipzig, 1702)

Music is a heavenly-philosophical science, especially grounded in mathematics, which deals with sonority insofar as it produces concurrence and good and artful harmony.
--Johann Gottfried Walther, Praecepta der Musicalischen Composition (1708)

It must be looked into what art in music actually is. In my opinion it is as follows: through the use of harmony to awaken in the minds (Gemütern) of man a variety of emotions and, at the same time, through such orderly and sensible harmony to delight the understanding of connoisseurs.
--Georg Philipp Telemann

My goal has been to remind those who want to study music that they cannot get very far in this inexhaustible science without great effort.
--Georg Philipp Telemann, Letter to Johann Mattheson (1718)

All sciences and arts are bound together into a circle by a linked chain. Whoever understands only his own craft, understands nothing; rather, he is a pedant . . . .
--Johann Mattheson, Der vollkommene Capellmeister (Hamburg, 1739)

Introduction
In the Introduction of the new critical edition of Dieterich Buxtehude’s keyboard music, Christoph Wolff writes: “To a considerable extent, Buxtehude’s position in the history of music has been defined by his extraordinary reputation as an organist and by the widespread and continued popularity of his organ compositions.” Wolff continues to explain that Buxtehude’s reputation is based primarily on the free works, the Praeludia, especially those which are pedaliter. I, on the other hand, wish to spend some time with chorale-based works, in particular the chorale prelude Vater unser im Himmelreich, and I will endeavor to demonstrate that Buxtehude’s reputation as a master of organ music could rest on the chorale-based repertoire equally well. I will take as my starting point an historical perspective. I will attempt to listen to this composition with the ears of Buxtehude; in other words, I will keep in mind Baroque, especially German Baroque musical theory and practice.
Peter Reichert, in his article “Musikalische Rhetorik in den Choralvorspielen von Dietrich Buxtehude,” makes the point that our understanding of the chorale-based works by Buxtehude is colored by how much we do not understand about the musical tradition out of which these works arise. He states: “Our pleasure in listening to this music has become, so to speak, a purely culinary one in that we find delight in the beautiful appearance, the surface of the music . . . To the extent that real understanding of the inner content of this music has disappeared, we have devoted ourselves to the sonority of the music, the outer clothing as it were, taking care of the façade of a deserted building.” All those who believe along with the musicians of the Baroque that music is a discipline from which one can both learn and derive pleasure, must ask, along with me: What is there to hear in this composition? In other words: What is there to learn here, what is present here to enrich my experience?
The answers to these questions are, and to a certain extent can only be, personal. However, there is no doubt that some of what I hope to convey here has relevance to others. I would like to concentrate on two specific aspects of the composition, especially: 1) the harmonic and contrapuntal aspect and 2) the relationship of the music to the text and the chorale. It is clear that a composition based on a particular melody and a particular text concerns itself with both that melody and that text. So therefore the two aspects just mentioned are really one. The composition as a whole, the form and the details, will indeed be Buxtehude’s interpretation of that melody and text, expressed harmonically and contrapuntally, musically, which we, in turn, as players, perform at the organ. In order to adequately and appropriately perform we need to hear our way into music which is so far removed from us in time. The fact that this music may in some sense be familiar to us doesn’t necessarily mean that we automatically know what is going on. Familiarity does not necessarily breed understanding. What is it about familiar music, and what is it about unfamiliar music that is unique, unusual? Is there anything in Buxtehude’s composition which awakens our curiosity, strikes us as unexpected? These are the things from which we can learn. What is unusual about Vater unser im Himmelreich, both in the detail and in the form?
The following notes on Vater unser im Himmelreich do not intend to be exhaustive. I have chosen to consider what I deem to be essential to an understanding of the piece as a performer. Many interesting details regarding counterpoint, the handling of dissonance, rhythmic matters, variety in the composition of diminutions and ornaments, etc. have been consciously omitted.
In order to begin, we must attempt to review some history. For learning how to listen to Buxtehude by coming from today and moving back in time to Buxtehude’s day will not reveal to us the interesting and unusual aspects of his compositions. We must start before Buxtehude and move towards him chronologically.

Style
First, let us look at a simple, four-voiced arrangement of the chorale. The harmonization is taken from the chorale prelude itself, distilled out of the richer composition, reduced to the bare essentials. (Example 1) This is one possible harmonization of the chorale, written in a style reminiscent of the chorales found in Samuel Scheidt’s Görlitzer Tabulaturbuch of 1650, though still simpler, in fact positively boring. Yet, it might be suitable as a simple accompaniment to congregational singing.
Buxtehude’s chorale prelude is much more complicated. For example, it has interludes between the chorale phrases that employ imitation. The second example I would like to present consists of the previous simple setting enriched with interludes. However, these interludes are not given as found in Buxtehude, but are likewise distilled out of what is found there. It is again a simplified version—much simplified, though more complex than the preceding example. The harmony is basically the same, but now employs some passing tones and some suspensions in keeping with the simple style. None of the interesting figures, the daring voice leading, or the liberal dissonances of the original are used. In other words, there is no art here. (Example 2)
Playing and listening to these simplified versions of Buxtehude’s work serves to sensitize our ears to hear the art in Vater unser im Himmelreich and to make clear to us why these pieces are so worthy of study. Let us now turn to the chorale prelude itself.

Phrase One (Example 3)
The first thing to notice is that the piece begins with one single voice, a1. The other voices are heard throughout the rest of measure one, but again in the second measure the a1 is heard alone again. This accents those two notes which, significantly, belong to the word Vater, thus accenting that word. We must remember that anyone listening to works of this type in the Baroque knew the chorales they were based upon, not only the melodies, but also the texts. In fact, in chorales such as Vater unser im Himmelreich, i.e., chorales associated with only one particular melody, I think we can be reasonably sure that the melody was 1) recognizable if not too heavily ornamented and 2) the recognized melody automatically called to mind the associated text. That a single note begins this piece is significant for another reason. The single note, the unison, is the unitas, or “one.” In the Baroque, one was not considered to be a number, but was rather the beginning, the source of all number. The unitas was, of course, God, the Father.
The rest in the manuals and pedal is known as an aposiopesis, or abruptio, signifying the more or less abrupt cessation of a musical thought. This is most clearly seen in the pedal, where the typical cadential motive is missing its final note, namely a d on the first beat of measure 2. The motive and the harmony break off suddenly, leaving the a1 in the soprano to carry all of the weight of what is missing on beat one of measure two. In addition, the pedal, when it reenters, late, on beat two, in measure two, still does not bring the expected d, but rather enters on c-sharp. We hear, not the expected d-minor, but an A-major chord in first inversion, a chord that in the Baroque was considered to be particularly expressive.
The pedal continues with a figure known as passus duriusculus, or “a difficult step,” the chromatic sequence of notes: c-sharp, d, c-natural, B-flat. Shortly after the end of the passus duriusculus the alto voice has a quarter note a, which is tied over to the longer half note a in the following measure. This tying of a shorter note to a longer one goes against the rules of counterpoint and is known as a prolongatio. If one hears this note as occurring too soon and sounding too long, it has the effect of slowing down the music. Coupled with the word “Himmelreich” it could be a reference to the concept of eternity, which lasts a longer time than the imagination can fathom.
This happens just before the climax of the first phrase, the second half of measure four. There we find a parrhesia, “liberty of speech,” “candidness,” also known as licentia, “licence.” Traditional theory tells us that the e1 in the soprano is a dissonant note over a g-minor chord. In fact, however, the e1 is definitely consonant: it is the cantus firmus, which is the measure of all things consonant and dissonant. And, indeed, the A-major chord on beat four of that measure acts as a resolution of the preceding dissonance, the c-sharp (tenor) and e1 (soprano) of which, in turn, conclude the cadence on the first beat of the following measure. Before that happens, the tenor note, d, is repeated, emphasized, a reduplicatio: the repetition of a dissonant note. The entire first phrase, beginning with the emphasis on the word Vater, moves towards this goal: the great tension found in measure four and its resolution in measure five. It is indeed a whole phrase and must be played as such.

Phrase Two (Example 4)
With the upbeat to measure six an interlude or, more properly, a prelude to the second phrase of the chorale begins. It is a short fugal introduction, using strict imitation of a motive directly derived from the second chorale phrase, called a fuga realis, of which there are countless examples in Baroque organ literature. This kind of fugal writing is, in other words, the usual case, the norm. The chorale enters with the upbeat to measure eight. With the movement to g1 in measure eight, the chorale leaps up an entire octave to g2. This figure is the hyperbaton, the ascent of a voice out of its normal range. First and foremost, g1 is the chorale tone, not g2. Second, and as important, the leap up of an octave causes a second figure to occur, that of the longinqua distancia, in traditional counterpoint the forbidden separation of upper voices beyond that of an octave, here: d1–g2. Third, the g2 is found outside the staff of the soprano clef, middle c on the bottom line, very often used at this time. J. S. Bach still used the soprano clef for the notation of the Orgelbüchlein. Whether or not Buxtehude used this form of notation in his original manuscript does not change the fact that composers much before him and after him used those clefs in the notation of polyphonic music in Germany and elsewhere. One way or another Buxtehude knew that g2 was out of the traditional range of the soprano voice, which went from b-flat to e2, the range of the soprano clef without the use of ledger lines above or below the staff.
From the high g2 the line descends through the rest of that measure and the next, a catabasis. The pedal line descends also, from the beginning of measure nine through the end of the phrase, a catabasis spanning exactly the interval of an octave. The soprano descends just over the span of the octave. The tenor descends also, beginning in the middle of measure nine to the middle of measure ten. This explains the ellipsis, the lack of something necessary, found in those measures: the alto voice drops out. It is at this point more important for the alto voice to rest than for the polyphony to continue in four voices. Descending music in four voices is awkward to write. It is much more elegant to do it in three voices—which Buxtehude chooses to do here. He draws attention to this fact by allowing the alto to re-enter in measure ten with a dissonance, a cercar della nota, the entrance of a voice one step below the one that is consonant and meant. The soprano and bass voices, descending together in tenths in measure 9, form the figure of the gradatio. Although not defined identically by many authors, the gradatio is understood here to be the parallel movement between two voices.
The hyperbaton in connection with the longinqua distancia and the catabasis in the pedal are the principal carriers of musical meaning in this phrase. The hyperbaton / longinqua distancia, right at the words du and uns, meaning “you” (God) and “us” (mankind), with the emphasis on the great separation (an eleventh), points out with poignancy the space, both spiritual and physical, separating the Godhead from humankind. After the octave leap up, the soprano must descend. The situation is different in the pedal: there is no musical reason for the pedal to descend the octave a to A here. A different pedal line is certainly conceivable just as there is no necessity dictating that the soprano must leap up to g2. These are choices Buxtehude made, recognizable ones. The octave represents the entire gamut of music (the hyperbaton belongs here also): there are no notes that exist that are not found within its confines. The pedal catabasis begins at the word alle, “all,” a fitting representation of that important word. Or better: it is the word Buxtehude has interpreted as important in this phrase, that and the contrast of du and uns.

Phrase Three (Example 5)
Phrase three of the chorale is also introduced by a fuga realis based on the first part of that phrase. The motive is reworked to form a passus duriusculus, which is used throughout the entire chorale phrase. One observes it, somewhat modified in the alto voice in measure 15 and 16 as well as in the pedal in measure 16. The alto in the first part of measure 17 brings the related figure, like an intensification, of the saltus duriusculus, or difficult leap. Interestingly, the chorale itself, in the soprano, appears as a changed version of the fugal theme, as it takes over the chromaticism of the fuga realis motive with the c-sharp2 in measure 14. This is a polyptoton, a changed repetition of a theme, though compositionally the theme or motive has its origin in the chorale melody. Significantly, the chromaticism occurs just at the point the text speaks of being brothers (Brüder sein)—according to the musical interpretation of this (according to Buxtehude, if you will), evidently a difficult undertaking. However, it could also refer to the difficulty of “dich rufen an,” or in general be understood as a reference to prayer as lamentation.
The chorale melody has an extensio, the extension of a note beyond its expected length, on the word dich, “you,” referring to God, giving that word emphasis. Dich ru-fen an now has the rhythm: half note tied to quarter note–quarter note–eighth note–whole note, a syncopatio, or syncopation. The tenor voice is silent throughout most of the phrase, a very long ellipsis. And when the pedal is silent on the third beat of measure 15, the word dich receives an additional accent through the unusual texture, which is suddenly reduced to only two voices. The ellipsis in the tenor allows Buxtehude to make the three remaining voices as like each other as possible while still retaining the melody/accompaniment texture. The phrase ends with a pathopoeia, another chromatically altered note (f-sharp instead of f-natural).

Phrase Four (Example 6)
The prelude to the fourth chorale phrase is not a fuga realis although it utilizes imitation (each entrance an imitatio). The motive, drawn from the last few notes of the chorale phrase, is thrown from voice to voice: bass (m. 17), alto (m. 18), tenor (m. 19), alto (m. 20), tenor (m. 21), soprano (m. 22). However, the organization of this chorale phrase is the strictest yet. The text, und willst das Beten von uns han (literally: and wants prayer from us), expresses the will of God through the word “want,” which in German comes from the same word as “will.” It is God’s will that we pray to him. God’s will is, of course, a command, the law.
This will, this law of God, is expressed, not atypically for the era, through a fuga imaginaria, a specious, fictitious, or imaginary fugue: here, a canon. There is a strict canon between the pedal, which enters first, with the upbeat to measure 19, and the soprano, on the third beat of measure 20. The last notes of the soprano are ornamented using the motive first heard in measure 17. However, there is also a third voice to the canon hidden in the tenor which is unable to quite finish before the end of the chorale phrase. If the imitative motive is reduced to its principal notes, the three-part canon can be clearly seen. (Example 7)
The attention of the listener is drawn particularly to the strong cadence at the end of this phrase. It is the phrase in which the naming of God, through the use of attributes, comes to an end. The actual petition has yet to come. The b-natural1, tied into measure 22, is not properly resolved. Only through licence, catachresis, the leap first to e1, does the dissonance reach a1. The other voices are silent for a moment, aposiopesis, before the cadence on A follows in four voices.

Phrase Five (Example 8)
The next chorale phrase is introduced again by a fuga realis, though here not immediately recognizable due to the mistakenly printed e1 instead of the g1, which is demanded by the conception of the piece. (This realization I owe to Gerd Zacher.) Such mistakes of a third were often made; one needs only to consult the critical apparatus of any number of publications of Baroque keyboard music. The g1 is a dissonance, in fact a saltus duriusculus (a difficult leap, coming from c-sharp1) and a heterolepsis (a note that could come from another voice as passing tone, i.e., coming from the soprano a1). This phrase deals with the petition of the verse, “grant that the mouth not pray alone, help that it come from the depths of the heart.” It begins in this serious manner, the alto voice leaping up close to and sounding a dissonant g1 against the a1 of the cantus firmus in the soprano.
These measures are ruled by the syncopatio in the pedal (mm. 25–26), the ellipsis in the tenor (mm. 27–29), and the catachresis (m. 28). The syncopatio, with its attendant dissonances, encumbers the phrase somewhat, keeping it from getting underway, perhaps pointing out the difficulty of both the petition and the act of petitioning. The first point of relative rest and first real accent after the melody enters is the downbeat of measure 27, on the word bet’ (pray). The words allein der Mund are set in relief in two ways. First the catachresis occurs in conjunction with the passus duriusculus in the pedal: the licence used in handling the dissonances, a1 in the soprano against B-flat in the pedal resolving to the dissonant chord B-natural, e1, g1 on beat two. Second, the ellipsis in the tenor allows Buxtehude to make the cadence on F in three voices, all of which sound the tone F to the exclusion of all else: a musical picture of allein der Mund, “the mouth alone.”

Phrase Six (Example 9)
The prelude to the last chorale phrase is marked by imitation at the fifth between tenor and bass, the normal case in the fuga realis. The alto voice, however, does not participate in the imitation. It begins in parallel thirds (a gradatio) with the tenor and then goes parallel to the bass voice. It is a voice that helps out in the texture. What better picture could there be for the first word of the phrase: hilf’.
The use of musical-rhetorical figures in the music of the North Germans during the Baroque has been established without a doubt, as well as the use of specific forms and compositional techniques based on the expression of text. Connecting specific contrapuntal devices to expression is certainly not unprecedented in Buxtehude. As one example, in Komm, heiliger Geist, Herre Gott, BuxWV 200, Buxtehude employs no vorimitation at all, except preceding the sixth phrase: zu dem Glauben versammelt hast (gathered to the faith). Here Buxtehude composes a fuga realis, which, though it is the normal, preferred method of contrapuntal composition in general, plays the role of the unusual at this point, the exceptional, because it is the only case of such imitation in the entire chorale prelude, and thus receives expressive significance. Here, the gathering of the voices in the fuga realis, first one voice, then a second voice, then the third, is a musical picture of the gathering of the believers (German: versammeln).
This sixth phrase has the most ornamented melody of the piece and is governed by the hyperbole (descending into the range of a lower voice) in the soprano, the abruptio in alto, tenor and bass, the parrhesia on beat four of measure 33, and the circulatio (circular figure) in the soprano in measure 34. The word geh’ (go) is expressed by fast notes including the fastest of the piece (32nds) which descend into the alto and tenor range of the voice: Herzensgrund, depths of the heart. The entrance of the unprepared dissonant chord on beat four (parrhesia) underscores the difficulty of the entire procedure. The circulatio is an unambiguous depiction of the heart, the center of the circulatory system, described by William Harvey in 1628 in his famous book “On the Motion of the Heart and Blood in Animals,” a book about which Buxtehude must have known. The phrase ends with a pathopoeia: f-sharp instead of f-natural, a tone filled with passion “which cannot fail to move the listener” (Burmeister, 1599).

Cadences
It is important for the interpretation of this work to note the various ways Buxtehude deals with the cadences. The cadence in four voices at the end of phrase one is marked by the soprano and tenor: e1 makes tenor d dissonant, which moves to c-sharp, then d1 (soprano) and d (tenor). At the end of phrase two we find the a-mi cadence in four voices, i.e., a Phrygian cadence on a1—A is treated as E would be in modes 3 and 4—formed between the soprano and the bass. Phrase three ends with a cadence in three voices on d2 (soprano) with f-sharp instead of f-natural (pathopoeia), by which the bass note d is missing during the first moment. At the end of phrase four the soprano and the tenor again make the cadence in four voices, this time on A: tenor b making soprano a1 dissonant, which moves to g-sharp1, then a1 (soprano) and a (tenor). Phrase five ends with a cadence in three voices on F, supplying the third scale degree in the cadence scheme: d, a, and now f of the d-minor triad. Phrase six ends in four voices with a cadence formed again by soprano and tenor using the same basic scheme as the cadence at the end of phrase one, but this time utilizing more ornamentation. Here, as opposed to phrase one, the pedal has the root of the chord from the beginning and, different from phrase one, the alto voice has f-sharp instead of f-natural (pathopoeia). Each cadence is audibly different and the performance of each demands of the player a sensibility that takes this into account.

Coda (Example 10)
The work ends with one of Buxtehude’s characteristic codas: a florid melody line over a pedal point. This coda is, in effect, an ornamentation of the final chord. It has, however, its own expression not unrelated to the chorale text. In my opinion it is not the leap of an octave in the soprano voice at the beginning of measure 35 that symbolizes the rising of prayer to heaven. Nor is it the rising scale passage in the second half of measure 36, for both figures are followed by descents. One needs to see, and to hear, that the passage as a whole rises (anabasis): in the soprano first from d1 to d2, followed by a descent to f-sharp1, followed by another rise to a2, and followed again by a descent to d2. The ascending passages win over the descending passages: it ends higher than it began. This is, in fact, true of all of the voices except for the pedal. Both alto and tenor voices ascend farther than they descend over the space of those three measures. A number of the musical-rhetorical figures found in this chorale prelude are found in the final three measures including the hyperbaton, the longinqua distancia, the parrhesia, and the passus duriusculus. It is a succinct and effective summary of the work. The pedal anchors all, the low note, the one that hasn’t been heard since measure 5 and has been all but forgotten, perhaps the depths of the heart (from which prayer comes), perhaps simply pedal point and tonic note, the longest note of the composition.

Performance
The purpose here is not to go into basic performance techniques of North German Baroque music or Buxtehude in particular. That is a given regarding playing this music at all. Beyond that, the player must understand that proper Baroque playing technique is not enough. The fact must be taken into consideration that at no level of the composition does Buxtehude simply “write music.” Therefore the player cannot “simply play” the music. Compositional decisions were made on the basis of the chorale text, both on the local level of single notes and words, as well as on a more global level of form and compositional techniques. The text is the source of a great number of the musical ideas found here. Therefore performance decisions must be made with an ear towards the audibility of these musical features.
The registration cannot be simply “melody and accompaniment”, i.e., forte – mezzo piano. The melody must be clearly melody, yet the accompaniment must not be relegated to the background. The alto, tenor and bass voices simply have too much to express. The possibilities are otherwise almost endless, given this basic premise of the equality of importance of melody and accompaniment.
Tempo must be flexible. Buxtehude took the words of the text into careful consideration—the soprano is, in a very real sense, a sung musical line. Or better: it is the spoken oration, the declamation and, at the same time, an exegesis of the text. One must be able to linger on the words (= musical ideas) Buxtehude considers important.
Perhaps performance cannot pay attention to every detail found in this piece or any other. There is so much to which to listen in this very short composition that there is a real danger of becoming bogged down with details. And maybe from day to day one’s ear is drawn to different aspects of the composition. However, a performance that takes no notice at all of any of the richness found here is inadequate. Important aspects of the composition, aspects that can only be approached first rationally through knowledge of the text and not purely aesthetically (i.e., aurally), should not be ignored. In fact, performance in the Baroque belongs to the rational ordering of music in general. The pronunciatio, or delivery, is the final part of musica rhetorica. Without an adequate delivery, even the best music will fail to produce an effect in the listener. Without some rational thought, which I would like to call practice, some passages will not be recognized as unusual, there will be no contour, no shape to the composition, because these passages will never be heard. Frescobaldi admonishes: “ . . . one should endeavor in the first place to discover the character of the passages, the tonal effect intended by the composer, and the desired manner of performance . . . ” (italics are mine).
Performance is perspective, a way of listening. Performance is understanding, not interpretation. And yet, performance is individual. I would like to close with a remark by Hans Heinrich Eggebrecht made at the end of “Mythos Bach,” found in his book Geheimnis Bach. I will only substitute, for the word Bach, the word Buxtehude. “Understanding needs perspective, calls for the Ego. In other words, in speaking about Buxtehude, be it ever so scientific, we speak also about ourselves because understanding cannot exist without the Subject, without the Ego, and concerning Buxtehude we are called again and again to find a perspective, while at the same time attempting to find ourselves.”■

This article was first published as a chapter in the book Horizonte des Hörens Gerd Zacher, ed. Matthias Geuting (ISBN 3-89727-322-5, ISBN 978-3-89727-322-1, PFAU-Verlag, 2006), pp. 245–258.

 

Clavierübung III of J. S. Bach: Theology in Notes and Numbers, Part 2

Alexander Fiseisky
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Part 1 was published in the October issue of The Diapason, pp. 22–25.

Wir glauben all’ an einen Gott
[We all believe in one God]
(BWV 680–681)

The arrangement of the chorale Wir glauben all’ an einen Gott, the Protestant version of the Credo, opens a series of dramatic chorale preludes in the Clavierübung III. Their themes are built on the minor keys and gravitate around the interval of the fifth.
In this piece the fugal upper voices are contrasted against a melodic line in the bass that occurs seven times. (Example 9) This melody is based on a leap of a fourth followed by a downward move within the octave and displays a structural similarity to the theme of the so-called Dorian Fugue (BWV 538).55 The ostinato motif appears altogether six times in the pedal; once (the sixth appearance) in modified form on the manuals: there only the beginning of the motif appears, repeated three times.
Not just the relationship (6 + 1) in the use of this striking melody is important, but also the fact that its form is changed in the one time it is used on the manuals. Naturally, this begs the question as to the purpose of this change. We have here possibly an allusion to the Old Testament injunction: Six days you shall labor and do all your work, but one day must be reserved for prayer and spiritual needs. From here stem the characteristics of one of the developments: an elevation of the tessitura, the use of only upward leaps, the softening of the harshness of the harmonic minor, and finally the heterolepsis figure used in the upper voices.
The manual voices are developed out of the beginning of the melody of the chorale Wir glauben all’ an einen Gott. The first four notes of this motif in a tonal answer form a musical rhetorical figure, often encountered in the works of Bach, which Boleslav Javorsky called the predestination motif.56 The origin of this motif lies in the chorale melody Was mein Gott will, das g’scheh’ allzeit [What my God wills may always happen] and is usually used by the composer as a culminant, dramatic or recapitulating figure (Fugue in G Minor, BWV 542, Fugue in A Minor, BWV 543, etc.). The whole musical fabric of this chorale prelude is shot through with this predestination motif.
Towards the end of the composition, Bach quotes in the tenor, first in its entirety, the first line of the cantus firmus (bars 89–98). Typically, the subsequent figure in the pedal that accompanies the chorale melody is enlarged, not only in its range (two octaves), but also in the number of notes (to 43—CREDO). One can also hardly describe it as a coincidence that the work has 100 bars: Bach could not have found a better numerological symbol to underscore the idea of “We all believe in one God.”
If we had the task of finding within Bach’s output a work for organ where the dramatic element was more pronounced, we could, paradoxically, hardly do better than choose the small 15-bar manualiter fughetta on the chorale melody Wir glauben all’ an einen Gott in the Clavierübung III. Written in Handelian style,57 it is very chromatic. The traditional double dotting, the richly ornamented musical fabric, the use of characteristic rhetorical figures—tiratas—all combine to sharpen up the harmonic impact of this three-voice fughetta to the highest degree.
The high point of the piece comes in the 12th bar, which results in the interesting proportions of 4:5.58 The density of chords in this bar is a rare example in Bach’s organ works. (Example 10) The diminished seventh on the strong beat contains seven notes. The following diminished seventh from D sharp–C contains six notes, which together makes 13 notes—most certainly another numerological symbol and one that needs no explanation. The impact of the intensive harmonies is strengthened by “talking pauses” and the declamatory answers on the “weak” beats of the bars. The intonations from the introduction (viola da gamba solo) of the aria Es ist vollbracht from the St. John Passion (BWV 245) can be heard in the music. (Example 11)
The descending seconds in Lombardic rhythm, with articulation marks written out in full by the composer (bar 11), the key role of the striking diminished seventh from D sharp–C at the high point of the work, and the key chosen—this is by no means a complete list of the methods the composer has used to create a smooth transition to the subsequent part of the composition.

Vater unser im Himmelreich
[Our Father in Heaven]
(BWV 682–683)

In the extensive arrangement of the chorale melody Vater unser im Himmelreich we encounter an example of a trio that is from time to time expanded to five voices by means of the cantus firmus in canon. This is one of the rare works of Bach full of articulation marks. Thoroughness of articulation shows how important this aspect of organ playing was for the Leipzig cantor.
Already, the choice of key says a great deal about the associative structure of this music. E minor is the key of the opening chorus of the St. Matthew Passion (BWV 244), the Crucifixus from the Mass in B Minor (BWV 232), the Prelude and Fugue for organ (BWV 548), the chorale prelude Da Jesus an dem Kreuze stund (BWV 621) from the Orgelbüchlein, and many other works in which Bach created an atmosphere of grief, sorrow, and misfortune.
The narrative flow of the music in the greater chorale Vater unser im Himmelreich creates an atmosphere of stillness and calm, and invites the hearer to intense prayer. The movement in seconds in Lombardic rhythm59 is akin to the sighs of a humble soul turned towards God. Time moves gently, so as not to disturb the state of intimate prayer.
This composition is literally suffused with thematic symbolism. Allow me to name just a few (following B. Javorsky): the descending third – a symbol of grief; a smooth chromatic movement of 5 to 7 notes – pain; a progression in triplets – fatigue, weariness; a movement along the notes of a first inversion – a symbol of inevitable realization; and so on.
The musical fabric of the composition resembles the tenor aria Wo wird in diesem Jammertale für meinen Geist die Zuflucht sein? [Where will my spirit find its refuge in this vale of tears?] from the cantata Ach, lieben Christen, seid getrost [Ah dear Christians, be comforted] (BWV 114), which Bach completed in Leipzig in 1724. Without a doubt there is an inner connection between the two works. The text of the aria, especially the treatment of the key word “Jammertal” [“vale of tears“ in German] can give the performer the right feeling for the interpretation of the greater chorale prelude Vater unser im Himmelreich.
Another interesting detail of the work is the movement in seconds in Lombardic rhythm in the pedal. This occurs only once in the whole work, at bar 41
(JSBACH), an allusion to the composer’s unseen participation in the prayer to God the Father. (Example 12)
The intricately crafted rhythms of the greater chorale prelude Vater unser im Himmelreich give way in the manual version to flowing linear movement in sextuplets. This sharp contrast has not gone unnoticed by scholars. “As complicated as the rhythms in the large Our-Father prelude may be, so simple is the calm flow of the 16th notes in the manuals version . . .” wrote Christoph Albrecht.60 An interesting explanation for this contrast has been put forward by Albert Clement, who connects the greater chorale prelude with the text of the fourth verse of Luther’s chorale Vater unser im Himmelreich,61 and the smaller prelude with the following verses (5–8). The fourth verse appeals to God’s patience in a time of sorrow, while verses 5–8 speak of trust in His compassion and assistance.62
The placid wave motion of the accompanying voices in the manuals version of the chorale prelude Vater unser im Himmelreich gently prepares us for the stormy motion of the 16th notes in the greater chorale prelude Christ, unser Herr, zum Jordan kam [Christ, our Lord, to Jordan came] as the following section of the Clavierübung III.

Christ, unser Herr, zum Jordan kam [Christ, our Lord, to Jordan came] (BWV 684–685)
The greater chorale prelude Christ, unser Herr, zum Jordan kam presents us once again with something quite out of the ordinary. This is the first occurrence in the whole work of the cantus firmus being transferred to the pedal in a high register. The composer indulges here in musical picture painting: the 16th-note runs produce a sort of perpetuum mobile and create the impression of waves on the Jordan. The music is dominated by an atmosphere of waiting for the miracle of God’s appearance and with it, the forgiveness of sins through the ritual of baptism. (Example 13)
Attempts have been made by various authors to see in the upper voices a dialogue between the Savior and St. John the Baptist,63 a view that I personally do not find very convincing. Built on the symbolic motifs of the Cross and Willingness to Sacrifice,64 the dialogue in the upper voices is often syncopated or transformed into a typical Bachian motion. It does not seem in the least to be associated with the dialogue between God’s Incarnation and His forerunner, but rather serves, as does the stormy motion of the bass, to create a state of what I would call “joyful excitement”—an atmosphere that is typical of many iconographic depictions of the Feast of the Baptism of the Lord.
The appearance of the Holy Trinity—as the Spirit in the form of a dove descending from heaven and as the supernatural light surrounding Christ at His baptism in the waters of the Jordan—is present in this prelude at the deeper level of mystical numerological symbolism. The cantus firmus appears nine times against the three-voiced accompaniment (9×3 = 27), while the total number of bars in the prelude is 81 (27×3).
Each appearance of the cantus firmus is built on a particular number of notes: in four cases it is nine notes, in the other five cases it is eight. And they occur in a strict sequence: 9 + 8 + 9 + 8; 8 + 9 + 8 + 9 + 8. The symbolism of the numbers 3, 9, 27, 81 focuses our attention on the picture of the Holy Trinity, while the number 8 is associated with the heavenly chronos or with the Coming of the Messiah.65
The legitimacy of the numerical proportions in the greater chorale prelude is borne out by the numerological symbolism of the manual fugato in three voices on Christ, unser Herr, zum Jordan kam. The fugato is written in simple triple time and has 27 bars (27×3 = 81). The main theme—the first line of the chorale—occurs three times in the original and three times in the inversion, and each time it is accompanied by a counter-melody based on thematic material in diminution, which forms a kind of canon. (Example 14)
In the opinion of Christoph Albrecht, this is a musical representation of the Gospel words of St. John the Baptist: “He [Jesus] must increase, but I must decrease” (John 3:30).66 It is worth mentioning that the bridges in the fugato (bars 8–10 and 18–20) have an evident three-part structure containing the countersubject (= the diminished theme).
All in all, the composer introduces the theme a total of 14 times (three times the original theme, three times inverted, and eight times diminished).67 The concluding development of the theme in its original form (bass in bar 20) has been slightly altered through the introduction of the Willingness to Sacrifice motif as an anacrusis. This results in interesting proportions for the presentation of the thematic material: 2 + 1 + 3 + 8. It is not difficult to see that these numbers represent a numerical version of the name of the composer (BACH).

Aus tiefer Not schrei’ ich zu dir
[Out of the depths have I cried unto Thee] (BWV 686–687)

The only organ work of Bach written in true six parts with double pedal is the chorale prelude on Psalm 130 (129) Aus tiefer Not schrei’ ich zu dir—a further example of the stile antico in his work. Each verse of this monumental penitential chorale,68 welling up out of the depths of the heart, is introduced in the fugal-like exposition that concludes each time with the cantus firmus in the upper pedal voice. This gives the work, written in the best tradition of J. Pachelbel, the form of an unbroken chain of seven fugues, corresponding to the number of verses of the chorale.
Albert Schweitzer’s attention had already been drawn to the “motif (rhythm) of joy” that first greets one in the initial phrases of the countersubject. As the music develops, this symbolic motif is further elaborated and at the end totally dominates the musical fabric. (Example 15) Schweitzer proposed a dogmatic interpretation for its presence: “Bach . . . is trying to represent the Lutheran doctrine of repentance, according to which all true repentance leads of itself to the joyful certainty of salvation.”69
Schweitzer’s observation is, of course, interesting and not without subtlety, but in my opinion one is dealing here less with joy, but rather with the cleansing power of repentance and the resulting confidence of the penitent in his own future. The motif under consideration conveys just this feeling of confidence.
What motives led Bach to introduce the chorale prelude Aus tiefer Not schrei’ ich zu dir into the Clavierübung III at all? Penance was not a component of the Ordinary of the old Mass, although it had been included in the liturgy in Saxony since 1601. Neither was penance dealt with by Luther in his Great Catechism, although he sometimes mentioned it along with Baptism and the Eucharist as one of the Sacraments. This was apparently the decisive argument for Bach to place two fantasies on Aus tiefer Not schrei’ ich zu dir between the parts relating to Baptism and the Eucharist.
Numerological symbolism plays an important role in both works. As has already been said, the seven fugues that make up this work correspond to each of the seven verses of the chorale. The cantus firmus that crowns each fugue always consists of nine notes, whereas it is interesting to note that it first occurs in the ninth bar. In addition, the length of the cantus firmus from its first to last note always has the same length of eight half-bars.
This changelessness of the cantus firmus, with its connection to the numbers nine, eight, and seven is obviously meant to signify the objective, almost unearthly quality of the beneficial cleansing power that flows over the penitent sinner. An additional indication can be found in the fact that at each occurrence the cantus firmus is first woven into the musical structure only after the completion of the exposition with its five voices. (We recall that the number five symbolizes “sensual Mankind.”)
Our attention is also drawn to the relationship between the number seven (seven verses of the chorale and the seven fugues) and the number five (the five-part musical structure70). These two numbers have an interesting internal proportion: 7:5 = 1.4 (BACH). One could probably regard this as pure chance, were it not that these two numbers occur again within this work. The chorale prelude has 75 bars, where the number 75 is the numerological expression of the word ELEISON (5 + 11 + 5 + 9 + 18 + 14 + 13). The relevance of this cry for mercy in a work dealing with remorse can hardly be doubted.
It is characteristic that the manualiter version of the chorale Aus tiefer Not schrei’ ich zu dir displays the same numerological symbolism as the greater version. A slight change in the rhythmical structure makes the initial motif of the theme correspond to the eighth fugue of the Ariadne Musica Neo-Organoedum Per Viginti by Johann Caspar Ferdinand Fischer (ca. 1660–1746).
Bach’s work impresses us by its architecture. Just as in the first chorale prelude, we encounter an unbroken chain of fugues that treat the seven verses of the chorale one after the other, both in its tonic form and its inversion, where each is brought to a close by the statement of the cantus firmus in the soprano. This results in seven fugues. Six of them are of the same length. The cantus firmus occurs after the fifth bar and lasts for eight bars. But here we encounter an interesting new development: after the cantus firmus has run its course, Bach does not immediately begin with the following fugato, but each time inserts an extra bar as a sort of résumé. Thus the six units have the following structure: 5 + 8 + 1. It is not difficult to see that the résumé thus occurs in the 14th (BACH) bar of the appropriate unit.71
The last and seventh unit differs in its structure from the preceding six, and introduces a proportion that we have already encountered in the greater choral prelude on Credo (6+1). After it has started as all the preceding units (five bars of fugato without the cantus firmus, followed by eight bars with the cantus firmus), this seventh unit has instead of the “Bach résumé” an extension of the second cantus part for a further five bars, resulting in the new proportion of 5 + (8 + 5). It is not difficult to see that this new proportion brings us close to the Golden Rule: 8:5 = 1.6 whereas 13:8 = 1.625. This is not altogether surprising. Thus when the composer understood the combination 6 + 1 as the biblical command to labor for six days, but to keep the seventh as a Sabbath for your God, then it was appropriate that this “special” seventh day be not simply adorned with ordinary music, but be bejewelled with golden tones!

Jesus Christus unser Heiland
[Jesus Christ our Savior]
(BWV 688–689)

The last two chorale preludes in the Clavierübung III deal with the events surrounding the Last Supper. Viewed from a cultural perspective, the iconography of this subject centers around two key moments. The first is the Transubstantiation of the bread and wine into the Body and Blood of Christ. The second moment concerns the circumstances of Judas’s betrayal.
The greater chorale prelude Jesus Christus unser Heiland is woven out of three voices. The cantus firmus, based on an intonation of fifth, is written out in long notes and appears in the pedal. The lively duet in the upper voices simultaneously spins out the three-note stepwise motif (according to Javorsky, a motif of reconciliation), both in its tonic form and its inversion. (Example 16)
We have already encountered this characteristic method in the Clavierübung III: in the greater chorale prelude on Kyrie, Gott heiliger Geist. Its use with quickened tempi produces a mood of agitation and worried concern. A special feature of the musical language is the frequent use of unprepared dissonances that heighten the sense of drama. Speaking personally, this music always conjures up for me Leonardo da Vinci’s famous Milanese fresco of the Last Supper, where the disciples of Christ, unsettled by his prophecy of betrayal, turn to the Savior with just one question “Surely not I, Lord?” (St. Matthew 26:22).
The cantus firmus appears altogether four times in the pedal as the embodiment of Christ’s serenity and his willingness to drink the Cup of his Passion. Its 44 notes are arranged as a pattern of 10 + 12 + 10 + 12. It would appear that the composer has applied this numerical pattern to emphasize the union of the Old Testament (the Law) and the New Testament (the Testament of Christ). Obviously, it is appropriate to remember at this point that St. Augustine considered the number twelve to be a symbol of the Church of Christ. The universal, catholic character of the Church is portrayed by the numerical symbol 144 (= 12×12). Note that the three-note motif of reconciliation in the manuals occurs exactly this many times in the musical texture of this composition.72
Another mysterious symbol is embedded in the score. When one connects the first and the sixth notes of the first bar, and the second and fifth notes, and the third and fourth notes (d1-d2, f2-f1, e1-e2) with a straight line, one produces a graphic figure which resembles the Greek letters X (Chi) and I (Iota) superimposed on each other. (Example 17)
This figure is the emblem of God made Man (Ιησυ Χριστ – Iesus Christos), and one must assume that the composer intentionally built this motif into the structure of the chorale prelude, a chorale that begins with the words “Jesus Christus unser Heiland” [Jesus Christ our Savior]. Typically this emblem occurs 72 times within the work, something that can hardly be attributed to chance. In accordance with tradition, this symbolic number corresponds to the 72 biblical names of the Lord, 72 biblical angels, the 72 nations of the ancient world, and the 72 disciples that Jesus sent out to preach his gospel. The Old Testament book of Numbers tells of 72 elders who received the gift of prophecy from God (Numbers 11:24, 26).73
The manualiter version of Jesus Christus unser Heiland (an extensive fugal composition in four voices) displays a very interesting feature—the placement of the theme does not match the metrical structure. The use of such a technique in the final chorale work of the Clavierübung III undoubtedly has good reasons. Perhaps Bach wanted to underline that the teachings of Christ have an eternal relevance that is not bound by the confines of physical time.
The theme of this fugue displays a striking structure. It consists of 13 notes74 and is based on two elements, which have a significant structural function in the whole cycle: a leap over a fifth and a stepwise motif over a third. The first notes of the tonal answer replicate exactly the final cadence of the chorale Was mein Gott will, das g’scheh’ allzeit, which (following Javorsky) we have interpreted as a predestination motif. (Example 18)
The countersubject is worked out with a circulatio figure that represents the Cup of Sorrows. The theme occurs 17 times altogether, with the final statement in augmentation. Bach undoubtedly considers the number 17 to be the union of ten and seven, especially as the eleventh statement is introduced by a longer bridge passage. The number ten is associated with the Law of the Old Testament (The Decalogue), while according to Werckmeister, the number seven is the symbol for purity and peace.
Thus one can summarize the conjunction of all these symbols as follows: The predestination from above (predestination motif) and the reconciliation prophesied in the Old Testament (reconciliation motif) through the suffering of Christ on the Cross (the Cup of Sorrows motif) purifies the fallen world (13) and gives it eternal peace and bliss (7).

Four Duets: E minor, F major,
G major, A minor

Scholars agree that the four duets of the Clavierübung III are very difficult indeed to interpret. As Hermann Keller remarked, the duets are “so unique and in part so difficult to understand that one must almost be led to believe that Bach wished to express something very special, but no one has yet found the key to them.”75 And in fact the opinions of the experts concerning both the content and the meaning of these works are indeed very contradictory. Some of them are of the opinion that they should be played during the Eucharist, while others see them as symbolic representation of the four Gospels.76 Albert Schweitzer is most probably the furthest removed from the truth with his opinion that they have only found their way into the Clavierübung III by mistake. He thus underestimates the significance of numerical symbolism within this work. Above all he did not “notice” that with the addition of the four duets the total number of works in the Clavierübung III reached the “cosmic” number of 27.
How does this music present itself?
All four pieces are highly individual and represent the highest achievement within the development of the genre of keyboard music for two voices known as inventions. They display no direct connection to the church chorales, but one is aware that while they have an element of tone painting it would not be illogical to interpret them as representations of the four material elements of this world: fire, air, water, and earth. Indeed, just this sort of interpretation was first suggested by Rudolf Steglich.77
Let us now look at the musical design of the duets.
The duet in E minor (BWV 802) is pure energy. Whole rivers of fire flow in the rapid succession of 32nd notes and the broken line of the syncopated motif recalls tongues of fire. The jagged melisma, the semitone movement within the range of diminished thirds: all reinforce a pervading feeling of tension. An almost pagan cult of fire dominates this music. (Example 19)
The F major duet (BWV 803) is built on the idea of contrast. The sphere of air is represented as a contrast of light and dark elements. The main theme, the embodiment of light, occurs in a major key in both the exposition and the recapitulation. The central part gives the impression of sudden twilight, which shrouds all life and transforms everything into a ghostly world of shadows. The contrast of major and minor suggests conflict—the elements of light struggle to free themselves from the chains of the mythological shadow world. (Example 20)
The G major duet (BWV 804) paints a picture of a body of water sparkling in the rays of the morning sun. Murmuring and iridescent flowing passages stirred by a light breeze create the impression of an unending stream of flowing water, magically calling to us by its freshness and purity. (Example 21) The musical texture of this work shows a high degree of similarity to the aria Von der Welt verlang ich nichts [From the world I nought desire] as the seventh part of the cantata Sehet, welch eine Liebe hat uns der Vater erzeiget [See what love the Father has bestowed on us], 1 John 3:1 (BWV 64). (Example 22)

The duet in A minor (BWV 805) has a different character. Behind the slow unfolding of its ideas, behind the gravity of its utterances one can discern an unbending internal force that holds everything in its thrall and directs all things. The extended, epically expanding theme strives to embrace all earthly things. The rocklike solidity of this musical picture calls to mind the immovable foundation of the earth. (Example 23)
Unlike Rudolf Steglich, Albert Clement suggested another approach. He sees in the duets a connection to the tradition of home prayer.78 In the opinion of this expert, the four duets serve as a musical illustration of the 194th chapter of the book Geistliche Erquick-Stunden Oder Dreyhundert Haus- und Tisch-Andachten79 [Hours of Spiritual Refreshments, or 300 Prayers for Home and Table] by the renowned theologian Heinrich Müller (1631–1675). Entitled “Von vier süßen Dingen” [On Four Sweet Things], this part of Müller’s monograph is devoted to the interpretation of the religious essentials: the Word of God, the Cross, Death and heavenly Bliss.
Let us now look at the structure of the duets in detail (Figure 1). One’s attention is immediately drawn to the emphasized strictness in the handling of the meter and the thematic material in all four duets. This is especially apparent in the first and second duets.
In the third duet, the length of the bridge-passages creates an interesting relationship (Figure 2).
The theme of the fourth duet is exceptionally long (48 notes) and consists of two parts: the first part has 11 notes, while the second contains 37 notes. All three numbers have clear sacred connotations: 11 is the symbol for sin, 37 for the monogram of Christ, and 48 is the numerical equivalent of the abbreviation INRI (Iesus Nazarenus Rex Iudaeorum).80
The first duets contain not only the numbers 11 and 37 but also other numbers that are relevant to the theme of Golgotha: 13 (death), 17 (symbol of spirituality), 31 (the numerical equivalent of PNC as the abbreviation of Pro Nobis Crucifixus). It is remarkable that these are simply different combinations of just three numbers—one, three, and seven—and that 137 is itself the numerical equivalent of DOMINUS DEUS.
It is also noteworthy that the sum of 22 + 15 (first duet) and 18 + 13 (second duet) lead us again to the symbols 37 and 31. Moreover, the combination of the pairs 17 (first duet) and 31 (second duet), as well as the pairs 11 (first duet) and 37 (second duet) both lead to the above-mentioned key number 48. The same number results from the addition of 11, 31 (third duet), and 6 (fourth duet).
It is clear that Bach wove the numerical symbolism into the duets to illustrate the content of these works. The numerology leaves no doubt as to the subject of these works: the music of the duets revolves around the theme of the Passion.
The idea that the four duets in the Clavierübung III symbolize the Cross was first suggested by Gerhard Friedemann.81 His work contained a number of highly original ideas about numerical significance within these pieces, but also many valuable observations concerning the biblical symbolism present in the other sections of the Clavierübung III.
Unfortunately it would be beyond the scope of this article to discuss further in depth the many other interesting details that are to be found in the four duets. So I would like to confine myself to bringing just a few salient points to the attention of the reader. The total number of bars in all four pieces is 369, which is in itself an indication of the association of these works with the Passion.82 The number 16 (4×4), which forms the basis of the A minor duet, is a numerical representation of the Cross. 112 (the sum of the numbers of bars in the E minor and G major duets) is the equivalent of CHRISTUS (3 + 8 + 17 + 9 + 18 + 19 + 20 + 18), and 149 (the number of bars in the F major duet) represents RESURREXIT (17 + 5 + 18 + 20 + 17 + 17 + 5 + 22 + 9 + 19).83
It is difficult to deny the validity of Gerhard Friedmann’s conclusions, based as they are on the analysis of the numerical structure of the duets. But this raises a further question: Is there a connection between, on the one hand, the hidden numerological references to the Cross in the four duets of the Clavierübung III and on the other hand the obvious descriptive character of the music?
Yes, one can indeed find such a connection! It is well known that in earlier times the cross was used as a symbolic representation of the four elements. But with the coming of Christendom, it became an object of adoration and so lost the association with the pagan worship of fire, air, water, and earth.
So now we wish to put ourselves in the shoes of the composer and try to answer the following question: How is it possible to portray musically a Cross, the product of human hands, soaked with the divine Blood of the Savior and transformed by the divine Will into an object of salvation? The answer is obvious. The best way to accomplish this is that chosen by Bach in the four duets of the Clavierübung III.

Prelude and Fugue in E-flat Major
The Prelude and Fugue in E-flat Major forms an overreaching arch that encloses the whole cycle. It is a work on a truly symphonic scale and is in this respect without parallel in the world’s organ literature. Its epic stature is complemented by the vividness and the passion of the musical language.
In both the prelude and the fugue the composer introduces three different musical spheres nevertheless bound together by such characteristics as common key and thematic material. The work is most commonly thought of as being an expression of the Holy Trinity. But no one to date has been able to produce a truly convincing proof for this view. As a result a number of unresolved controversies exist: which part of the fugue, the second or the third part, represents the Holy Spirit, and which Jesus Christ?
The very existence of these controversies should suggest to us that the work has not yet been sufficiently examined. To say nothing of the “echoes” episodes of the prelude, which most experts have associated with the Son of Man. How should we understand this embellished fluttering “in the spirit of the Rococo” to be a picture of the Savior?
In my opinion one should not view this music as one would a picture on a wall.
It is indeed Bach’s purpose to sing the praises of the Triune God, but it is not his intention to paint a musical picture of God. Three parts that are characterized through changes in the musical texture—in both the prelude and the fugue—are always the same God, the One, the Indivisible, the Holy and Consubstantial Trinity.
With what means does the composer accomplish this task? Let us first examine the prelude.

This article will be continued.

 

Bach and Die Kunst der Fuge

by Jan Overduin
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Jan Overduin is Professor of Music at Wilfrid Laurier University in Waterloo, Ontario, where he teaches organ and church music. He began studies in The Netherlands, where he was born, and continued in Canada at the University of Western Ontario, where he received the Masters degree in performance. The list of his teachers includes Marie-Claire Alain, Peter Hurford, and Jean Langlais. He has directed many choirs including the Wilfrid Laurier University Choir and Chapel Choir, the Niagara Chamber Choir (which he founded), the Menno Singers, the Mennonite Mass Choir. He has been actively involved in church music for over 40 years, most recently as director of music at St. Matthew's Lutheran Church in Kitchener, Ontario from 1985 to 1997. As organ soloist, he has recorded numerous broadcasts for radio and has played concerts in Europe, North America, and the Far East. His discography includes nine CDs with trumpeter Eric Schultz (on the German labels 'ebs' and 'Arte Nova Classics'), a solo album recorded at Ottobeuren, Germany (on 'ebs'), and a recent CD with recorder virtuoso Matthew Jones. Forthcoming is a book on improvisation for organists, published by Oxford University Press, and a new organ edition of the Art of Fugue. Jan Overduin may be contacted at [email protected] and welcomes visitors at his website http://info.wlu.ca/ ~wwwmusic/overduin/index.htm

The Kunst der Fuge, BWV 1080, a work consisting of 14 fugues and 4 canons all on one theme, is Bach's farewell, his testament. It is a very solemn and personal work, and ends with Bach's only fugue on his name, the notes B-flat, A, C, and B-natural (B, A, C, and H in German). Never before did he use this chromatic theme on such a grand scale or with such clarity as here at the end of Contrapunctus XIV. It is as if he puts his signature not only to the KdF, but also to his life's work. In fact it is uncanny, this very clear reference to his own name. The aural effect is almost dizzying, as is the visual appearance of the last page, with C.P.E. Bach's handwritten note about his father's death: "In this fugue, where the name BACH appears as a countersubject, the composer died." Like Shakespeare in the character of Prospero in The Tempest, Bach himself appears on stage, but it is to say "good-bye."

It is fitting that Bach reserved the 14th fugue for the use of the plain theme in clearest form, because of the relationship between the number 14 and his name. By allowing each letter of the alphabet a number (a=1, b=2, c=3, d=4 and so on), Bach's name adds up to 14 (2 + 1 + 3 + 8). Moreover, the name J.S. Bach adds up to its retrograde 41 (9 + 18 + 14). Though Bach's familiarity with numbers is not documented, the cabalistic numerical ideas were common knowledge.1 The work may have been intended as his third and final offering to the Mizler Society, which he had joined in June 1747, waiting until he was the 14th member to join. He also had his portrait painted for this society with 14 buttons on his jacket. Perhaps his aim was to finish the KdF by June 1749, as his third and final offering, since a condition of membership obliged him to submit a published "scientific" work every year until the age of 65.2

The more I play this work, the more aware I become of how saturated it is with personal references or "signatures." The B-A-C-H theme in the obvious four-note form or more subtly through the use of themes that contain 14 or 41 notes permeates the entire KdF. A casual listener or player is not likely to be conscious of some of these allusions, but the fact that they are there in such abundance imbues the work with a personal intensity and warmth that can easily be felt. While some or even many of the "B-A-C-H's" may occur spontaneously as a result of Bach's use of chromatic language, there are reasons to suspect that their incorporation is part of the overall design of the work and intention of the composer. Bach is not merely scribbling his name all over the score or playing numerological games. The chromatic language itself, the use of the key of D minor, the shape of theme and its inversion with its hymn-tunes analogies, the dramatic use of silence, various other motifs--it is all these and more, together with the "signatures," that give the work its deeply personal flavor.

The following examples include only appearances of the B-A-C-H theme that use the four actual notes B-flat, A, C, and B-natural. Excluded are all transpositions of the motif, e.g. E-flat, D, F, E etc., of which there are numerous examples. All examples have the four notes in the same octave.  Again, by relaxing this restriction, the list could be greatly expanded. Included however are those statements of the motif that are decorated with unessential notes, especially between the second and third notes; the unessential notes may serve to hide the visual but usually do not obscure the aural impact of the motif. These observations do not pretend to be profound, but are merely the result of a growing familiarity with and fondness for this stupendous work. If they have any validity, it is in underlining the deeply personal nature of the KdF.

Immediately in Contrapunctus I, in the most obvious voice, i.e. the soprano, in measures 10-12 Bach features the four-note name theme. Bach "hides" the eighth-note E by having it dip below the alto note G, so that even though the soprano part by itself really spells B-E-A-C-H (not a word in German), the ear perceives it as B-A-C-H. (Example 1)

The B-A-C-H motif is more hidden in Contrapunctus II, though increasing chromaticism causes it to occur more frequently. It appears twice in measures 35 to 37, both times in the dotted note motif that dominates this fugue. Though the first two notes are separated from the third and fourth by a complete measure, they occur in adjacent statements of the dotted note motif, and therefore appear related and connected. (Example 2)

Measures 22-23 of Contrapunctus III contain a very clear statement of B-A-C-H, shared between the upper two voices (B-A in the soprano, C-H in the alto).  While this sharing serves on the one hand to hide the motif, it also underlines it, since the effect is that of an ornamented version: the B-A-C-H motif beautified in a flowery way. (Example 3)

One of the most poignant of all references to the name of Bach occurs in Contrapunctus IV. The shape of the regular inverted theme is such that there is a noticeable high point on the notes B-flat and its "resolution" to the semitone below. There is also a marked similarity to the hymn-tune "Aus tiefer Noth schrei ich zu dir," a hymn paraphrase of Psalm 130 (De profundis). The resemblance in fact is too obvious to ignore.3 In Contrapunctus IV, and only here, Bach transposes the second half of the theme up a whole tone, so that the high point of the theme now is C-H (C and B-natural) instead of B-A (B-flat and A). This causes a sudden modulation to another key, the dominant of the dominant, a rather wrenching and quite dramatic shift of key. It happens first in bar 61, and thereafter four more times (in other words, not every time the theme is heard). The change from the expected high point B-A to C-H may not be exactly an obvious reference to Bach's name, but certainly for the player, the alteration of the climax of the theme is all the more dramatic and personal, especially when the personal nature of the hymn "Aus tiefer Noth schrei ich zu dir" is taken into consideration as well. Not only the personal pronoun is emphasized by this veiled reference to B-A-C-H, but also the idea of "calling" (schreien).   (Examples 4a and 4b) 

"Calling" is also happening constantly throughout this fugue through the use of the pervading "call-motif" of the descending minor third. Towards the end of Contrapunctus IV occurs another and much more traditional example of the use of the B-A-C-H motif: in bars 135-136 it is slipped in once into the tenor voice, like a hardly noticeable signature. (Example 4c)

In Contrapunctus V, the KdF theme appears consistently in 14-note form, as it will continue to do in much of the rest of the KdF, with the two descending thirds smoothed out with passing notes. Thus the theme itself is being identified with the name of Bach. Moreover, it is especially interesting that the B-A-C-H motif is heard quite plainly and in the most obvious voice (soprano) exactly in bar 41. (Examples 5a and 5b)

Contrapunctus VI states the B-A-C-H motif near the beginning, in measures 4 and 5 in the soprano. Again the first two notes are separated by a measure from the third and fourth, but they are perceived to be related to each other through their rhythmic emphasis. (Example 6)

Contrapunctus VII features the B-A-C-H motif in much the same way, for example in the tenor part of measures 17-19. Within the context of a statement of the KdF theme in 14-note form (and in diminution), the notes B-A are again separated from C-H by a measure, but each pair of notes comes at a similar point, i.e. the end of two parallel phrases. (Example 7)

With the introduction of a new theme that is rather chromatic, numerous instances of B-A-C-H occur in Contrapunctus VIII. In measure 11 a very clear statement of B-A-C-H is shared between the two lower voices (Example 8a). In measures 85-86, the motif is featured in the soprano and in measure 112 in the bass (Examples 8b and 8c). The main KdF theme (inverted), which occurs as theme III in this fugue (beginning in measure 95, in the alto), consists always of exactly 14 notes. More noticeably, each measure begins with a quarter rest (Example 8d). The use of silence on the downbeat is a technique often used by Bach to symbolize eternity and/or death.4 Thus the form of the theme in this fugue forms associations not only with the name "Bach" (14 notes), but also with "death" (silence on the downbeats). A convincing example of this technique to express longing for death is often encountered in Bach's chorales, such as at the end of Cantata #56 (Ich will den Kreuzstab gerne tragen). (Example 8e)

In Contrapunctus IX, in bars 84-85, the B-A-C-H motif is shared between the soprano (B-flat, A) and alto (C, B-natural), but because the voices cross, the motif appears to remain in the same voice, the alto. (Example 9)

In Contrapunctus X, again exactly in bar 40-41, the B-A-C-H motif makes an appearance in the two upper voices. (Example 10)

The 14-note version of the main KdF theme, with rests on every downbeat, now  "rectus," boldly opens Contrapunctus XI (Example 11a). The inversion of the second theme of Contrapunctus VIII, which in this fugue appears as theme III, very clearly spells B-A-C-H. Donald Tovey rejects this allusion to the name of Bach, since strictly speaking the theme misspells his name as B-A-C-C-C-H, yet to a listener (as opposed to a mere score-reader) this is almost as obvious an allusion to the name of Bach as in the final fugue.  (Example 11b) The B-A-C-H motif occurs frequently, not only in connection with the third theme, but elsewhere as well. An example is found in measure 144, with the motif shared between the alto (B-flat, A) and the soprano (C, B-natural).  (Example 11c)     

Contrapunctus XII and XIII, the two completely invertible "mirror" fugues, leave the composer with very little room to maneuver.  The listener has no idea of the strict rules behind these wonderful pieces, especially the playful Contrapunctus XIII. Even here the B-A-C-H motif pervades everything, though not as overtly as elsewhere in the KdF. The descending semitones B-A and C-H permeate the texture, but the four notes never occur together, and seldom within the same octave. One reason that Bach chose D minor as the key for this work may well have been that it allowed him to "season" fugues like Contrapunctus XII and XIII with these notes.  For example, C-H (the more unusual of the two pairs of notes) is used six times in measures 25-26 of Contrapunctus XIIb, just after several highly exposed B-A's. Appearances of the motif within one voice and within the compass of a minor third also occur (though somewhat more separated than usual) in measures 14-16 of Contrapunctus XIIa (bass) and measures 46-47 of Contrapunctus XIIb (bass). Similar concentrations of B-A and C-H occur in Contrapunctus XIII, imbuing the whole with the flavor of the BACH motif (e.g. in Contrapunctus XIIIa: eight times B-A in measures 32-35, followed by eight times C-H in measures 37-41).

Theme II of Contrapunctus XIV consists of exactly 41 notes, as if in direct preparation for the next theme, that of B-A-C-H itself (Example 12). There are also numerous examples of the B-A-C-H motif in the earlier part(s) of this fugue, again as if to prepare us for the plain statement of Theme III in measure 183. To list just three examples: measures 16-17 (tenor), 59-60 (alto/soprano), and 133-134 (alto).  (Examples 13, 14, and 15)

The evolution of the B-A-C-H motif is but one of many marvels of the KdF.  A constant companion in the background, like a quietly-flowing underground stream,5 in Contrapunctus XIV it finally appears quite alone and "naked," like a new-born babe. It is a paradoxical moment of loneliness and pity, sadness and comfort, weakness and strength. Almost immediately it is used in stretto and inversion, and "with the boldest and most mysterious harmonies"6 that are wrenching in their effect on us. It is at this point that this great composer, for whom nothing seemed impossible, especially in this work, leaves us forever. But the unfinished ending in which the composer is "called by name" also contains the promise of what "eye has not seen, nor ear heard." (I Cor. 2:9)

Notes

                        1.                  William Wright, The Organ--The Instrument and Its Literature (University of Toronto: private publ., 1994) 96.

                        2.                  J.S. Bach, Die Kunst der Fuge, ed. Davitt Moroney (Muenchen: G. Henle, 1989) vii.

                        3.                  The main theme in "rectus" form vaguely hints at "Vater unser" (Lord's Prayer). The descending thirds in Contrapunctus IV are also striking characteristics in some chorales, e.g., "Wie schön leuchtet der Morgenstern" (How lovely shines the morning star) and "Wer weiss, wie nahe mir mein Ende" (Who knows how near is my life's end). The most ornamented of all versions of the theme, as found in the Canon per Augmentationem in contrario Motu shows a striking resemblance to the "Agnus Dei" from the Mass in B minor.

                        4.                  Many of the more ornate chorale settings such as those in Schemelli's Gesangbuch illustrate this, e.g., "Lasset uns mit Jesu ziehen," "Es ist vollbracht," and "Liebster Gott, wann werd ich sterben?"  Examples in Das Orgelbüchlein include "Alle Menschen müssen sterben," and "Wir danken dir, Herr Jesu Christ, dass du für uns gestorben bist" (BWV 623 and 643).

                        5.                  In other words, like a Bach (German: brook).

                        6.                  Donald Francis Tovey, Essays in Musical Analysis: Chamber Music (first published in 1944; London: O.U.P., 1972) 88.

Fugal Improvisation in the Baroque Era—Revisited

Maxim Serebrennikov
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But the basis for all improvisation must be preparation. If I haven’t prepared, I can’t improvise. If I’ve made careful preparations I can always improvise. 

—Ingmar Bergman, 1968

 

The question of fugal improvisation in the Baroque era has been raised in the pages of musicology literature more than once.2 It still remains topical today; yet in the practice of Baroque improvisation, the improvisation of fugue has rarely become an object of independent study. Besides William Renwick’s book, The Langloz Manuscript: Fugal Improvisation through Figured Bass (2001), it is difficult to name any widely known work that is specifically dedicated to the art of fugal improvisation in the Baroque era.3 Much valuable and interesting information about this performance practice of baroque musicians is scattered throughout various books and articles, whose subject matter is not even directly related to improvisation.

The present article therefore aims: 

1) to summarize the existing research on partimento practice;

2) to describe all the stages of fugal improvisation, beginning with the mastery of separate elements and finishing with an organization of the whole, as recorded in German sources of the first half of the 18th century.

 

Introduction 

Today the ability of an academically trained musician to create “on-the-fly” is thought of as exceptional—for the gifted only. Yet it is well known that in the Baroque era every professional musician was expected to possess this “gift.” Within the rich diversity of improvisational genres and forms that made up the standard set for which a Baroque improviser was to be prepared, fugue held the greatest place of honor.

At that time it was not just the great musicians who were skilled at improvisation; every church organist had to be able to improvise a fugue on a given theme. . . . The ability to improvise fugue was considered a requirement for every serious musician to such a degree then that the lack of that skill could serve as reason for ridicule. . . . And, although the testing of organists did not always include fugue improvisation, both Mattheson and Adlung think that no one should be taken as an organist who has not proved his right to such a post through the improvisation of fugue.4

In the 18th century if you couldn’t improvise you couldn’t call yourself a keyboard player. Worse than that, you couldn’t get a job, since all organist auditions required extemporaneous performance of a fugue on a given subject.5

Truly, the ability to improvise fugue was a necessary skill for organists, because a fugal statement of musical material was stipulated by the very program of the liturgical service. Beginning in the second half of the 17th century, the role of the organist, on whose shoulders rested the burden of the musical life of the church, grew remarkably.6 The organ, which had at one time humbly accompanied church ritual, became a most important attribute of the church service—almost its main participant. This was especially true in the northern regions of Germany, where the organ gained such acoustic strength and richness of register that it became like “a second minister,” and the musical compositions that it “delivered” were self-contained “texts” addressed to the congregants. Mattheson emphasized that fugal presentation of the chorale subject on the organ helped “to arouse reverence within the listeners.”7

For musicians in the secular sphere, fugal improvisation as a skill was not as necessary as it was for church organists, but the ability, nevertheless, was always appreciated. In the circle of experts and enlightened amateurs, fugal improvisation on a subject proposed by someone among those present could become one of the most intriguing and entertaining elements of a musical program. Success in such improvisation provided the performer with the established reputation of master of the highest order (a reputation that could help in a further promotion).

Although fugal improvisation was a widespread practice among Baroque musicians, we are forced to gather information on its technique literally in bits and pieces. As early as 1702, Andreas Werckmeister, in his treatise Harmonologia musica, points out the reason: “many musicians are secretive and reticent with their knowledge.”8 Possibly, musicians divulged their knowledge about improvisation very unwillingly because they considered it a unique commodity, providing a constant supply of students. Perhaps they did not wish to destroy the myth of the divine origin of the gift of improvisation. In any case, even in treatises that are dedicated specifically to improvisation and fantasieren, there are no concrete instructions that would allow us today to understand how fugue was improvised.9

Nonetheless, some secrets of Baroque fugal improvisation have already been revealed by scholars. David Ledbetter writes about one of them:

By the early eighteenth century, instruction in fugue in Bach’s tradition grew out of the figured bass, rather than contrapuntal treatises, and so was approached as an improvised genre. The technique of this was practised by using fugato movements expressed as figured basses, called in Italian partimento fugues.10

To the uninitiated musician such a statement may seem paradoxical, since according to our notion fugue and figured bass represent distinct types of musical thinking and observe a different tradition of notation. However, the discovery during the last decade of a large number of examples of so-called partimento fugue or thoroughbass fugue shows that improvisation of fugue during the Baroque epoch—just like the improvisation of homophonic forms—actually had its foundation in the practice of figured bass.11 The detailed study and comparison of these examples, strengthened by the testimony of contemporary treatises, allow us to take another step forward on the path to understanding the Baroque technique of fugue ex tempore.

That the overwhelming majority of improvised fugues during the Baroque epoch were thoroughbass fugues can be explained from the point of view of psychology. The texture of a “contrapuntal fugue” (i.e., polyphonic texture) is formed by combining individualized melodic lines, each vying for our attention. In contrast, the texture of thoroughbass fugue is predominantly two-dimensional—that is, it can be clearly divided into the leading voice and a complex of accompanying voices. Consequently, improvisation of a multi-part “contrapuntal fugue” necessitates the division of attention into three or more channels, whereas performance of a multi-part thoroughbass fugue demands division into just two. Experience shows that the attention of even a well-prepared musician is capable of maintaining control over only two (a maximum of three) simultaneously proceeding streams of information.12 As such, for objective (psycho-physiological) reasons, improvisation of thoroughbass fugue is attainable for a broad mass of musicians, whereas improvisation of a multi-part “contrapuntal fugue” is negotiable to a rare few.13 

Having touched on the issue of the limits of human attention, which is so relevant to musical improvisation, it would be remiss to ignore the opportunity to quote Sergey Prokofiev, in an interview published by the New York Times in 1930:

Three melodies remain about the limit that the average ear can grasp and follow at one time. This can be done when the melodies are clearly sounded and contrasted in pitch and tone color. For a short time the ear may perceive and assimilate the effect of four different parts, but this will not be long continued, if the four parts, or melodies, are of equal importance. Listening to a four or five or even six-part fugue, the ear is conscious, possibly, of the presence of all the voices, but it only perceives and follows precisely the most important of the melodies being sounded. The other parts fill in, enrich the musical background and harmony, but they become as blurred lines of the picture. They are not clearly recorded in the listener’s consciousness as separate melodic strands in the tonal fabric. This being true, it behooves the composer to realize that in the polyphonic as well as in the structural sense he must keep within certain bounds.14

Such is the point of view of a professional musician who possessed extraordinary musical faculties. As for specialists in the fields of psychology and physiology, they have yet to come to a single opinion concerning the volume and capabilities of human attention.

Analysis

The modern theory of improvisation is based on these principles: 1) “improvisation is based on memory” and “the improviser does not create the material, but builds it from prepared blocks, from long-memorized musical segments”;15 and 2) the improviser always works from a given model.16 

What were the building blocks that Baroque performers utilized in the process of fugue improvisation? In what sequence could they combine them? To answer these questions, let us turn to concrete musical material.17

The overwhelming majority of German samples of thoroughbass fugue follow strophic form in their composition.18 In addition, organization of the musical material inside the strophes is very often based on the typical Baroque-era structure of “head and tail,” where the role of the “head” is played by a group of statements (more rarely by a single statement) of the subject and the role of the “tail” by sequence based on standard harmonic formulae of thoroughbass. The conclusion of each strophe is marked by a cadence. Such is the method used by Kirchhoff, for example, in his C-major fugue from L’A.B.C. Musical (c. 1734), which clearly presents three strophes (Example 1):

Strophe 1 includes five statements of the subject (bars 1–9), a 2–6 sequence (bars 9–11), and a 7–6 cadence (bar 12);

Strophe 2 includes two statements of the subject in the upper part in immediate succession (bars 12–15), a statement in the bass (bars 16–17) and the 2–6 sequence already used in strophe I (bars 18–20), and a 7–6 cadence (bars 20–21);

Strophe 3 contains a statement of the subject in the bass (bars 21–22), a 2–6 sequence that shifts to 7–7 (bars 22–25), and the more explicit 5–6/4–5/3 cadence (bars 25–26).

The structural similarity among the strophes is evidence of the improvisatory nature of thoroughbass fugue, the result of work that uses a single model. It was specifically the strophe that served as the universal compositional unit, by which through duplication the improviser assembled his fugue. The number of strophes was varied, according to how long the improvisation should last. The structure of the strophe, though, did not vary. In this way the improviser’s task was to quickly and neatly fill out this preassembled structure with concrete musical material.

Obviously, the improvisation of a fugue had as its starting point the harmonization of the chosen or suggested subject. A harmony, as a rule, was kept for all multi-part statements of the subject, becoming, might we say, a retained “counter-harmony” (Gegenharmonie).19 Changes to the harmonization were made only in cases where a tonal answer was necessary. Frequently, even the counterpoint to the answer (the first countersubject) was drawn out of this same “counter-harmony.” This is easily affirmed by noting the numeral for the harmonic intervals between the answer and countersubject and then comparing the result to the author’s own figures for analogous multi-part statements (Example 2).20 

In many samples of thoroughbass fugue, all entries of the subject are concentrated at the beginning of a strophe. Following one after another without dividing episodes, the statements form a compact thematic group that serves as an entire syntactic unit larger than just a single statement. The tendency toward an increase in the hierarchical degree of unit complexity is another specific quality of improvisatory technique. The combination of smaller syntactic units into larger ones helps to expand the general volume of information accessible within short-term memory.21

The similarity among the strophes of thoroughbass fugue is also increased by the uniformity of the order of entries. In all strophes, a descending order of entries of the parts predominates as the most convenient and intrinsic with respect to technical considerations and notation of thoroughbass.22

The next syntactic unit of the strophe, following the group of statements, is the episode. This section of the fugue was the most comfortable for the improviser, since here he could use patterns that he had learned. Judging from extant samples of thoroughbass fugue, episodes most often consisted of sequential repetition of one, more rarely two, harmonic formulae stereotypical to thoroughbass. This observation is supported by the theoretical works of that time. As such, to attain success in the improvisation of fugue, Philipp Christoph Hartung, in Musicus Theoretico-Practicus (1749), recommends learning entire musical progressions, which one should be able to freely and confidently play from memory, and not just read from sheet-music.23 Many of the fragments he suggests are nothing more than textural elaborations of standard thoroughbass sequences. The thoroughbass nature of Hartung’s sequences appears especially clear if we extract their harmonic scheme and supply it by figures (Example 3).

Playing sequences had to become an automatic skill, something that was simply “in the hands” of the performer. The automation of playing skills allowed the improviser to free his attention considerably so as to be directed instead to solving upcoming tasks. In other words, while the hands played out the episode, the mind could be planning out the next set of operations. Given this, the hands had to be able to play for as long as was necessary for thinking out. For this reason, the inert nature of sequential development was not a detriment to fugue played ex tempore. The existing unspoken rule in musical practice that the number of segments in a sequence (in the case of exact repetition) should not exceed three was not observed too strictly during the fugue improvisation. Theoretically, there could be any number of segments in a sequence, as it was defined less by artistic needs than by technical ones. In practice, episodes, composed of sequences made of four to five segments, were the norm for thoroughbass fugue.

The unity of thematic material was not also a problem for thoroughbass fugue. The episode could smoothly continue the subject, but could also introduce  new musical material. In any case, the primary task of the improviser in moving from one syntactic unit to another was to transition as naturally as possible. It follows then that the greater the active memory capacity of the performer and the more formulae he could recall and have “in his hands,” then the higher the likelihood of attaining agreement of intonation between the suggested subject and episodes selected from among those prepared during the process of his musical training. The ability to competently use these preparations from “homework assignments” was very likely a basic craft known to the improviser.

The degree to which the improviser relied upon such materials prepared in advance can be judged by examining, for example, the B-flat-major fugue from Johann Caspar Simon’s collection Leichte Præludia und Fugen (1746). Of its total 37 bars, 20.5 bars (i.e., more than half) are based on material connected neither with the fugue subject, nor with its countersubject. The especially obvious “home preparations” reveal themselves in the second half of the fugue, which is made up of four autonomous sections resembling, in their function, additions in the tonic key (Example 4). At first, Simon builds a sequence on the harmonic formula 7–7, embellishing the bass line with melodic figuration. He then builds a second sequence on the harmonic formula 2–6 in strict chordal texture. Further, he inserts a toccata-like fragment pulled from the fugue’s preceding prelude, a fragment that is also in its nature a sequence. Finally, he concludes the piece with a decisive cadence in solid chordal presentation (Grave). Comparing the “specific gravity” of thematic and non-thematic material in Simon’s fugue, the conclusion suggests itself. Essentially, if the improviser were not restricted by concrete devices of thematic work, then the entire fugue, excepting statements within the exposition, could be designed from elements prepared in advance.

Judging by some samples of thoroughbass fugue, the “stock” material could penetrate straight into the group of statements, replacing separate statements or pulling them out. For example, in Fugue no. 21 (F major) from the Langlo(t)z Manuscript, the second strophe begins not with the restatement of the subject, but with non-thematic counterpoint, and only the bass part enters with the theme (Example 5).

In the D-minor Fantasy from the Mylau Tabulaturbuch, a straightforward “home preparation” in the form of a typical sequence 6/5–5/3 appears in the first strophe between the fourth and fifth statements (Example 6a). Viewed separately, this fragment appears optional—since the other statements work successfully without it (Example 6b).

The energy expended by a performer for fugue improvisation could be conserved by using the same episode for various strophes. This repetition could be identical, but it could also be modified by means of various textural clichés. For example, the second and third episodes of the anonymous G-major Prelude (which is in fugue form) from the Mylau Tabulaturbuch are based on a single harmonic formula, the 7–7 progression, though the shapes of their texture are distinct. In the first case, the lower voice is diminished; in the second, the pair of upper voices (in regular imitative counterpoint). Incidentally, this prelude demonstrates direct application of Hartung’s aforementioned recommendations: the prelude’s second episode (Example 7a) differs from his sequence shown in Example 3a only by key.

The existence of a single stockpile of thoroughbass harmonic formulae inevitably led to the appearance of universal sequences that traverse the pages of thoroughbass literature from one composition to the next, regardless of authorship. Comparison of the episode sections of numerous thoroughbass fugues makes clear that of the great variety of harmonic formulae offered in contemporary thoroughbass treatises and manuals, a precious few sequential patterns predominate: 7–7, 6/5–5, 6–6, 4/2–6.

The manner of sequential motion also deserves special comment. In many samples of thoroughbass fugue, the episodes are based on diatonic sequences that descend stepwise down the scale. On one hand, descending motion step-by-step possesses a certain inertness, which under the conditions of improvisation (i.e., mental and psychological tension and temporal deficit) just plays into performer’s hands. On the other hand, diatonic motion step-by-step provides the sequence freedom in the selection of the target tonality. In reality, the great tonal mobility is hidden in diatonic sequence; a trajectory of such a sequence could be easily and organically turned at any moment into one of closely related keys. Here is a small experiment: the test of the key possibilities of a 2–6 sequence from the second strophe of the C-major fugue from Kirchhoff’s L’A.B.C. Musical (Example 8).

As these examples demonstrate, it is possible to conclude the sequence in any closely related key without applying much effort. Understandably, the target key will influence the length of the sequence. Here it is very important not to lose a sense of balance and good measure. Although the versions represented in Examples 8e and 8f are technically no different than the remaining ones, these two are much less suited to actual artistic use due to their extended monotony. Should Kirchhoff have needed, in the process of improvisation, to expand the fugue by adding another strophe, he likely would have followed version c) or d) in place of the cadence on the C-major tonic.24

Once the fugue’s continuation took a concrete shape in the mind of the improviser, he could stop the potentially endless development of a sequence via the most convenient cadential formula. The playing of cadences (as well as sequences) in any key of the instrument—literally, with closed eyes—was also a necessary skill for every professional keyboardist of the Baroque era. In the opinion of many 18th-century musicians, cadential formulae are the basis, the foundation of thoroughbass; it is specifically this skill that forms the starting point for practical study of the trade. The number and types of cadential formulae varies with each source. The Precepts and Principals (1738) attributed to Johann Sebastian Bach, for example, count seventeen patterns among the most frequently used (Example 9).

Immediately following the cadence, occasionally commencing upon its final tones, the new strophe begins and all events of the described process are repeated. The similarity of the strophes imparts to the unfolding of the fugue’s form a character of repeated expositions. The formal approach to realization of the strophic scheme inevitably aroused the feeling of monotony, which, naturally, stirred up criticism from contemporaries. Mattheson, who regularly attended testing of organists, wrote:

One should restrict oneself even less to the practice of some organists, who first quite respectably, without the slightest embellishment, perform the theme four times through on the entire keyboard in nothing but consonances and pastoral thirds; then begin again just as circumspectly with the consequent from its beginning; always producing the same tune; interposing nothing imitative or syncopating; but constantly only playing the naked chord, as if it were a thoroughbass.30

Here are the impressions produced on Marpurg by a certain organist who attempted to play fugue ex tempore:

Someone often has the good intention to make it better. But what does he do? He slams out the figured bass, and this is terrible to hear. There are no suspensions which make the harmony pleasant, fluent and coherent. It is a jolting harmony. One hears no stretto, no motivic development of the theme. There is no order, and the number of voices one can only surmise at the end, when as, per forma, it ought to be clear directly after the first exposition of the theme through different voices of the fugue. The theme is will never be wisely advised in the middle voices. You only ever hear it above or below—as one hand accompanies another as in an aria. One never hears the theme as comfortable, nor at the appropriate time, expressively and sensitively for the mind and the ear in a sustained and affecting way. It is but a senseless din and tumult—not to mention the discord within the harmony.31

The picture described by Mattheson and Marpurg was characteristic of improvisations by mediocre organists. The more talented and gifted performers avoided precise repetition of strophes and brought to each new strophe a certain degree of newness, to which extant samples of thoroughbass fugue eloquently testify. In addition to the aforementioned tonal reinvention of strophes, one can quite often find such methods of refashioning as introducing a new counterpoint to the subject, “register leap” (i.e., a skipping of two or more register pitches where the subject can enter), and the use of stretto in the final strophe.

Although the opinion does exist that “the part of the fugue related to statements of the subject was created during improvisation,”25 there is reason to suggest that even during these sections the performer could sometimes refer to prepared material. Judging from extant samples of thoroughbass fugue, the study of fugal improvisation included not just the regular practice of sequential progressions and cadences, but the development of a definite set of concrete approaches to working with the most common types of subjects. Describing the demands placed on candidates for the vacancy of organist at the Hamburg cathedral, Mattheson noted: 

I don’t consider it art to concern people [organists] with unknown themes; rather, it is better to take something well-known and flowing in order to work it out even better. That is what matters, and the listener will like it better than some chromatic piddling about.26

If one allows for the possibility that Mattheson was not alone in this opinion, then the chances of being tested on a subject built of familiar melodic patterns, or even on a known subject, were not so small, and thus the entire improvisation could come down to a combination of prepared materials.

Let us recall, for example, the subject that King Frederick the Great suggested to J. S. Bach for an improvised fugue in Potsdam (Example 10). It is not known with certainty whether Frederick himself composed this subject or borrowed it, but judging by its melodic profile, the monarch had chosen to demonstrate to Bach his knowledge in the “learned style” (gelehrter Stil).27 It must be noted that the subject contains four thematic elements, and all of them are conventional within Baroque style: a) movement in the tonic triad, b) a jump of a seventh (saltus duriusculus), c) descending chromatic movement (passus duriusculus), and d) melodic cadence. Any Baroque musician would certainly know these melodic patterns, along with the methods of their elaboration within a fugue. The elements listed here are well represented both in didactic and artistic samples of thoroughbass fugues, and what is especially important is that their musical realization (counterpoint, harmonization) often coincides.

Depending on the conditions of improvisation, “home preparations” could have various degrees of concretization. In those cases where a fugue was improvised on the occasion of a public challenge or competitive auditions, the performer had to hold his prepared materials in his memory. In everyday practice, however, it was acceptable to use the preparations written out on paper. We find examples of such preparations in a Daniel Magnus Gronau manuscript, which is held today in the Library of Polish Academy of the Sciences (Gdansk) as MS. Akc. 4125.28 This manuscript contains 517 (!) sets of preparatory sketches for fugue improvisation in all twenty-four keys. Each set holds three thematic records, written one below the next on individual staves (Example 11). On the upper staff in soprano clef, the subject with figures is written out, and the beginning of the answer with countersubject is outlined in small notes.29 On the second staff in bass clef, the counterpoint to the subject with figures is recorded. On the third staff, also in bass clef, the answer with figures is fixed. In this way, every set encompasses all necessary material for planning any statement of the subject, whether alone or with multiple voices, whether in the tonic or in the dominant.

Thanks to such preparations, the process of fugue improvisation is considerably simplified, since the need to search for a harmonization of the subject, a counterpoint to it, and a suitable answer is taken care of. Essentially, the performer must only care for the episode material, and the fugue, necessary for the church service, is ready.

In summary, the improvisation of fugue during the Baroque epoch was not necessarily the spontaneous nor extemporaneous fruit of inspired fancy. Much more often it was soundly prepared and planned on all levels: from the syntactic to the compositional. Even before the start of improvisation, the performer could clearly imagine the compositional structure that he must fill out using his musical material, the bulk of which could be prepared during “home” practice. One of the most widespread compositional models was strophic form, where the structure of each strophe had identical organization and included three syntactic units: the group of statements, the sequential unfolding, and the cadence. As a result, the entire improvisation could be boiled down to finding the right harmonization for the given subject and thinking up a tonal structure for the strophes; all the rest—textural formulae, cadences, sequences—the performer took from his memory practically in ready form.

 

Postscript

It stands to reason that the strophic form described in this article was not the only compositional model used for fugal improvisation during the Baroque. The discovery of this model, though, in other improvisatory genres of the Baroque era gives reason to consider it as universal within the improvisation practice of that time.

There is reliable evidence that the strophic form was purposefully worked out in the process of musical training. For example, Precepts and Principles contains a set of fourteen keyboard exercises for mastering the harmonic formulae most common to thoroughbass. Surprisingly, all these exercises are precisely identical in form—all are strophic (Example 12).

The outer strophes are in the tonic, while the central ones are in the closely related keys (in dominant and parallel). It is not difficult to imagine how many distinct figuration preludes could be created on the basis of only one model, varying merely harmonic content and textural formulae.32 If one involves methods of structural transformation (extension or compression of strophe), then the number of variants is multiplied.

Examples of such preludes can be found among the sources discussed in this article. Thus, in analyzing some pieces from the Langlo(t)z Manuscript or Kirchhoff’s L’A.B.C. Musical, one gets the impression that the authors had the structure of Bach’s exercises specifically in mind while they composed, so strong are the similarities. The C-minor Prelude from the Langlo(t)z Manuscript, for example, differs from Bach’s exercises due only to one additional strophe and short melodic links between the strophes (Example 13). The F-major Prelude from Kirchhoff’s L’A.B.C. Musical also contains an additional strophe, but the development within the third and fourth strophes is dynamicized thanks to structural transformations: the sequential development is truncated in the third, and the “head” motive is withdrawn in the fourth (Example 14).

The list of works of an improvisatory character that have strophic form with variations of its solutions can be further extended, but this would be a topic for a separate article. ν

 

The list of German sources, containing samples of thoroughbass fugue

“39. PRAELUDIA et FUGEN del Signor Johann Sebastian Bach” (Staatsbibliothek zu Berlin—Preussischer Kulturbesitz, Musikabteilung; shelf mark: Mus. ms. Bach P 296). Published in The Langloz Manuscript: Fugal Improvisation through Figured Bass, With Introductionary Essay and Performance Notes by William Renwick. (New York: 2001), pp. 35–187.

“Des König[lichen] Hoff-Compositeurs und Capellmeisters ingleichen Directoris Musices wie auch Cantoris der Thomas-Schule Herrn Johann Sebastian Bach zu Leipzig Vorschriften und Grundsätze zum vierstimmigen spielen des General-Bass oder Accompagnement. für seine Scholaren in der Music. 1738” (Brussels: Bibliothèque du Conservatoire royal; shelf mark: mr. FRW 27.244). Published in J. S. Bach’s Precepts and Principles for Playing the Thorough-Bass or Accompanying in Four Parts, Leipzig, 1738, translation with facsimile, introduction, and explanatory notes by Pamela L. Poulin. (Oxford, 1994), pp. 41–45.

Händel, Georg Friedrich. Aufzeichnungen zur Kompositionslehre: aus den Handschriften im Fitzwilliam Museum Cambridge (Composition Lessons: from the Autograph Collection in the Fitzwilliam Museum Cambridge), Hrsg. von Alfred Mann. Leipzig: Veb Deutscher Verlag für Musik, 1978. S. 53–70 (Hallische Händel-Ausgabe: Kritische Gesamtausgabe. Suppl. Bd. 1). Republished in Continuo Playing According to Handel: His Figured Bass Exercises, With a Commentary by David Ledbetter (Oxford: Clarendon Press, 1990), pp. 44–61.

Heinichen, Johann David. Der General-Bass in der Composition. Dresden, 1728, S. 516–520.

Kellner, Johann Christoph. Grundriss des Generalbasses. Op. XVI. Erster Theil. Cassel, [1783], S. 41–45.

Kirchhoff, Gottfried. L’A.B.C. Musical (Amsterdam [c. 1734]), 34 S. Republished as Kirchhoff, Gottfried, L’A.B.C. Musical, Hrsg., kommentiert und Generalbaß realiziert von Anatoly Milka (St. Petersburg: Musikverlag “Compozitor,” 2004), XXVIII, 104 S.

Niedt, Friedrich Erhardt. Musicalische Handleitung. Erster Theil. Handelt vom General-Bass, denselben schlecht weg zu spielen (Hamburg, 1700), Cap. X. Republished as Niedt, Friedrich Erhardt, The Musical Guide, Parts 1 (1700/10), 2 (1721), and 3 (1717), translated by Pamela L. Poulin and Irmgard C. Taylor; introduction and explanatory notes by Pamela L. Poulin (Oxford: Clarendon Press, 1989), pp. 48–49.

“Pral: Kirchhoff” (Staatsbibliothek zu Berlin—Preussischer Kulturbesitz, Musikabteilung, Mus. ms. 11605), published in Kirchhoff, Gottfried, Prelude and fugue for organ from the manuscript Mus. ms. 11605: first edition, edited and with a preface and commentaries by Maxim Serebrennikov (St. Petersburg: Polytechnical University Publishing House, 2009), 16 p.

Simon, Johann Caspar. Leichte Praeludia und Fugen durch die Tone: C. D. E. F. G. A. B. dur (Augsburg [1746]), 14 S.

Simon, Johann Caspar. Leichte und wohlklingende Praeludia und Fugen durch die Tone: C. D. E. F. G. A. H. moll (Augsburg [1747]), 14 S.

Simon, Johann Caspar. Musicalisches A. B. C. in kleinen und leichten Fugetten (Augsburg, 1749), 24 S.

“TABULATUR Buch 1750” (Mylau, Archiv der Evangelisch-lutherischen Kirchgemeinde; shelf mark: MS H 3a). Transcribed in Shannon, John R., The Mylauer Tabulaturbuch: a Study of the Preludial and Fugal Forms in the Hands of Bach’s Middle-German Precursors. Ph.D., Music, University of North Carolina at Chapel Hill, 1961. Vol. 2, iii, 184 p.

 

Notes

1. I wish to express my deep gratitude to Prof. David Ledbetter (Royal Northern College of Music), who read the final draft of this article and kindly provided me with helpful comments and constructive suggestions.

2. The topic has been actively discussed especially in the last two decades in connection with awakened interest in the Italian improvisational practice of partimento, which spread throughout Europe in the 18th century. Currently the study of partimento is gaining incredible momentum. The most comprehensive study of this field at the moment is Giorgio Sanguinetti’s book The Art of Partimento: History, Theory, and Practice (New York: Oxford University Press, 2012).

3. Although Renwick’s book contains a special subheading, Fugal Improvisation through Figured Bass, he does not treat the actual process of improvisation. His work is not a theoretical study about fugal improvisation, but an anthology of authentic musical samples for practical mastery of this skill. In fairness, the article “On the fugue improvisation” by the Russian musicologist Sergey Maltsev also should be mentioned: Sergey Maltsev, “Ob improvizacii i improvizacionnosti fugi,” in Teoriya fugi: sbornik nauchnish trudov, otv. red. A.P. Milka (Leningrad: Izd-vo LOLGR, 1986), pp. 59–60. Unfortunately, this work containing many valuable observations about the process of fugal improvisation, because of a language barrier, did not gain wide circulation.

4. Maltsev, “Ob improvizacii i improvizacionnosti fugi,” pp. 59–60.

5. David Yearsley, “Spontaneous fugue,” in Early Music, 2001, Vol. XXIX (3), p. 452.

6. See Marina Nasonova, “Prakticheskaya deyatelnost severonemetskogo organista XVII veka,” in Starinnaya muzyka: praktika, aranzhirovka, rekonstrukciya: Materialy nauchno-prakticheskoy konferencii (Moscow: Prest. 1999), pp. 117–128.

7. Johann Mattheson, Grundlage einer Ehren-Pforte (Hamburg, 1740), S. XXXIII, § 48. Based on the study of ecclesiastical protocols, Reinhard Schäfertöns concluded that the free prelude and the organ chorale prelude and fugue were central points of organ playing at the time of worship (Reinhard Schäfertöns, “Die Organistenprobe— Ein Beitrag zur Geschichte der Orgelmusik im 17. und 18. Jahrhundert,” in Die Musikforschung, 1996, 49, Jg. Hf. 2, S. 143).

8. “Denn viel Musici sind heimlich und rahr mit ihren Wissenschaften,” Andreas Werckmeister, Harmonologia musica (Franckfurth und Leipzig, 1702), S. 95.

9. In Part I of his Musicalische Handleitung (1700), F. E. Niedt promises to give a “proper instruction on how Fugues are to be improvised” in the next parts (Cap. X). Unfortunately, his death prevented him from fulfilling his intention.

10. David Ledbetter, Bach’s Well-tempered Clavier: The 48 Preludes and Fugues (New Haven and London: Yale University Press, 2002), p. 99.

11. For more details about the difference between the terms partimento fugue and thoroughbass fugue, see Maxim Serebrennikov, “From Partimento Fugue to Thoroughbass Fugue: New Perspectives,” in BACH: Journal of the Riemenschneider Bach Institute, vol. XL, no. 2 (2009), pp. 22–44.

12. It is also important to realize that there is a notable difference between the resources demanded for perception of information as opposed to its creation (which is precisely what improvisation requires). The latter takes much more energy, and therefore, resources for attention are more quickly expended.

13. One musician alive today who possesses a phenomenal gift for improvising in any style and genre is Richard Grayson. Some of his improvisations (including fugue) on a subject proposed by an audience can be viewed on YouTube.

14. From an interview with Olin Downes, in New York Times, February 2, 1930, Arts & Leisure, p. 112.

15. Mikhail Saponov, Iskusstvo improvizatsii: Improvizatsionnye vidy tvorchestva v zapadnoevropejskoj muzyke srednikh vekov i Vozrozhdeniya (Moscow, 1982), p. 57 [in Russian]. Similar statements can be found also in Maltsev, “Ob improvizacii i improvizacionnosti fugi,” p. 6; David Schulenberg, “Composition and Improvisation in the School of J. S. Bach,” in Bach Perspectives I, 1995, p. 5; William Renwick, Analyzing Fugue: A Schenkerian Approach (Stuyvesant, NY: Pendragon Press, 1995), p. 17; Pamela Ruiter-Feenstra, “J. S. Bach and Improvisation Pedagogy: Extemporaneous Composition,” in Keyboard Perspectives II (2009), ed. by Annette Richards, p. 43; Michael Richard Callahan, Techniques of Keyboard Improvisation in the German Baroque and their Implications for Today’s Pedagogy (Ph.D. dissertation, University of Rochester, Eastman School of Music, 2010), p. 10.

16. “The improviser, let us hypothesize, always has something given to work from—certain things that are at the base of the performance, that he uses as the ground on which he builds. We may call it his model.” Bruno Nettl, “Thoughts on Improvisation: A Comparative Approach,” in The Musical Quarterly, 1974, Vol. LX, No. 1, p. 11.

17. A list of German sources, containing samples of thoroughbass fugue, appears at the end of the article.

18. The strophic form of the thoroughbass fugue has roots in the verset fugues tradition and to the sectional structure of motets and ricercar. What we say about strophes of thoroughbass fugue is closely related to Joel Lester’s “parallel sections” and David Ledbetter’s “series of expositions.” See Joel Lester, “Heightening levels of activity in J. S. Bach’s parallel-section constructions,” in Journal of the American Musicological Society, Vol. 54, No. 1 (Spring 2001), p. 49–96; and Ledbetter, Bach’s Well-tempered Clavier, p. 100.

19. The term “Gegenharmonie” first appeared in Abhandlung von der Fuge by Friedrich Wilhelm Marpurg, where it is given the following definition: “Counterharmony. Thus is named the material in the remaining parts which is set against the subject.” (“Die Gegenharmonie. So heißt diejenige Komposition, die dem Fugensatze in den übrigen Stimmen entgegengesetzt wird.”) Friedrich Wilhelm Marpurg, Abhandlung von der Fuge (Berlin, 1753), S. 18.

20. Since all standard harmonic structures in thoroughbass are noted in shorthand, we have added to the original figuring (where necessary) those signatures within brackets, which were implied by default.

21. By way of numerous experiments, it has been shown that the capacity of short-term (active) memory, without which the process of improvisation is simply impossible, is limited to 7 ± 2 units of information (the so-called Miller’s number). This can be increased only by uniting disparate elements into groups. We refer to a very illustrative example from Maltsev’s article in order to demonstrate the activity of this mechanism: “For example, short-term memory can retain around seven different letters (perhaps, X, J, D, B, G, U, S), but the number of letters drastically increases if we try to remember seven words, and will increase even more drastically if we try to remember seven sentences.” (Maltsev, “Ob improvizacii,” p. 69.) As Michael Callahan emphasizes: “Experts recognize relevant patterns, and therefore perceive stimuli in larger and more meaningful units than novices do; expert improvisers notice patterns in music and conceive of musical units in large spans (e.g., entire voice-leading structures and phrases, rather than individual notes).” (Callahan, Techniques of Keyboard Improvisation, p. 22.)

22. We remind the reader that the harmonic vertical in thoroughbass is constructed upwards from a given note, therefore the part entering with the subject must always be the lowest one.

23. “Alle in bissherigen Numern muessen nicht nur vom Papier, sondern auch auswendig auf das fertigste und deutlichste gelernt werden,” in Philipp Christoph Hartung, Musicus Theoretico-Practicus, Zweyter Theil (Nuremberg, 1749), S. 12, § 42).

24. Sometimes the tasks that were given to organists for the purpose of testing were limited by a time-frame. For example, the testing of organists for the post at the Hamburg Cathedral (24 October 1725) included the presentation of an entire fugue “created for four minutes,” a prelude of “about two minutes,” a chaconne of “about six minutes,” etc. See Johann Mattheson, Grosse General-Baß-Schule (Hamburg, 1731), S. 33. It is very difficult to improvise a piece with continuous development and at the same time fit everything within a given time-frame. It is much easier to fill the established time limits with standard-size strophes, adding a necessary number.

25. Anatoliy Milka, Muzikalnoye prinosheniye I. S. Basha: k rekonstrukzii I interpretazii (Moscow, 1999), p. 151 [in Russian].

26. “Denn mit fremden Sätzen die Leute zu scheeren, halte ich für keine Kunst; lieber was bekanntes und fliessendes genommen, damit es desto besser bearbeitet werden möge. Darauf kommt es an, und es gefällt dem Zuhörer besser, als ein chromatisches Gezerre” in Mattheson, Grosse General-Baß-Schule, S. 34–35.

27. For more details on the authorship of Thema Regium see Milka, Muzikalnoye prinosheniye I. S. Basha, pp. 153–167.

28. For more details about the manuscript MS. Akc. 4125 see Andrzej Szadejko, “Daniel Magnus Gronau (1700–1747)—didaktische Aspekte in Orgelwerken am Beispiel der Signatur MS. Akc. 4125 aus der Danziger Bibliothek der Polnischen Akademie der Wissenschaften,” in Musica Baltica (Gdansk, 2010), S. 351–361. It is interesting that Szadejko views the given source solely from a didactic perspective: as exercises in counterpoint. In my opinion, considering its intended purpose, MS. Akc. 4125 has more in common with such collections as the Langlo(t)z Manuscript and the Mylau Tabulaturbuch; it is also an anthology containing musical material necessary for the church organist’s everyday activity.

29. Indeed, the written-out figures concern themselves not with the single-part statement at the beginning of a fugue, but to the latter (multi-part) statements.

30. “Vielweniger darff man sich an den Gebrauch einiger Organisten binden, die das Thema erst, ohne die geringste Verblümung, fein ehrbar und viermahl durchs gantze Clavier in lauter Consonantzien und Lämmer-Tertzien hören lassen; hernach wieder mit dem Gefährten eben so bescheidentlich von oben anfangen; immer einerley Leier treiben; nichts nachahmendes oder rückendes dazwischen bringen; sondern nur stets den blossen Accord, als ob es ein General-Baß wäre, dazu greiffen” in Johann Mattheson, Der Vollkommene Capellmeister (Hamburg, 1739), S. 388, § 97.

31. “Ein anderer hat öfters den guten Willen, es besser zu machen. Aber was thun er? Er dreschet den Generalbaß, und dieses ist sehr erbaulich anzuhören. Da sind keine Bindungen, die die Harmonie angenehm, fliessend und zusammenhängend machen. Es ist eine holperichte Harmonie. Da höret man keine enge Nachahmung, keine Zergliederung des Satzes. Da ist keine Ordnung, und die Anzahl der Stimmen erfähret man zur Noth am Ende, da man solche gleich nach der ersten Durchführung des Satzes durch die verschiedenen Stimmen hätte empfinden sollen. Dieser Satz wird niemahls in den Mittelstimmen klüglich angebracht. Man höret ihn nur immer oben oder unten wozu beständig die eine Hand die andere, so wie eine Arie, accompagnirt. Man hört das Thema niemahls bequem und zur rechten Zeit auf eine den Verstand und das Ohr nachdrücklich rührende Art eintreten. Es ist ein hanbüchenes Gelärme und Gepolter; der unharmonischen Gänge nicht zu gedenken” in Marpurg, Abhandlung von der Fuge, Theil II (Berlin, 1754), S. XXIII–XXIV).

32. About the use of ars combinatoria techniques in the 18th-century, see Leonard G. Ratner, “Ars Combinatoria: Chance and Choice in Eighteenth-Century music,” in Studies in Eighteenth-Century Music: A Tribute to Karl Geiringer on his Seventieth Birthday, ed. by H. C. Robbins Landon and Roger E. Chapman (New York: Da Capo Press), pp. 343–363.

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