A Performer's Investigation, Part 2

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

A Performer's Investigation, Part 2

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

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.

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.

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.

Gavin Black is Director of the Princeton Early Keyboard Center in Princeton, New Jersey. He can be reached by e-mail at [email protected].

Buxtehude BuxWV 141 – Part 3: Practicing the first fugal section
This month we return to the Buxtehude Praeludium in E Major, BuxWV 141, looking at the second section of the piece, which begins at m. 13 and goes through about m. 50. This—except for its last three measures or so, which are a transitional passage, cadential in nature, and which we will in the main discuss next month—is a contrapuntal, essentially fugal, section, a fact which has implications for studying, practicing, and learning the music. Much of what I will suggest here will involve revisiting the ideas that I discussed in the series of columns about counterpoint that began in September 2008, applying those ideas to this specific passage.
The fugal section that begins in m. 13 is in four voices. The musical text could by and large be written out on four staves, accounting for all of the notes, with each staff presenting a coherently “melodic” melody. (It departs from this briefly in mm. 32–33 with the addition of a few “extra” notes, and again in the transitional passage.) The voices behave like the voices of a contrapuntal piece: each of the four voices has a different compass, each of the voices is present most of the time but not all of the time, and, melodically, the voices do the same things at different times and different things at the same time. The section is “fugal” in that the voices enter one at a time, each with a version of the same theme, and that theme recurs a lot during the section.

Theme
This theme is as follows, in its first iteration:

It enters first in the top voice, and then in the other voices in descending order. It is present in 24 of the measures of the section, and a motive identical to the second half of this fugue subject is present in another 3½ or 4 measures. The longest stretch without any of this theme present—prior to the transitional/cadential section at the end—is about one measure.
(There is an interesting side note about this theme, one that in a sense is irrelevant to the piece on its own terms because of the chronology, but which should be intriguing to organists nonetheless. The first half of the theme is the same as the fugue subject of Bach’s Fugue in E-flat Major, BWV 552, and the second half of the Buxtehude theme is essentially the same as a recurrent pedal motive in the Prelude, BWV 552. This Buxtehude work seems like a more likely source of Bach’s inspiration for the so-called “St. Anne” Prelude and Fugue than is William Croft’s hymn tune, which Bach most likely never heard.)

Bass voice in pedal?
The first practical question about working on this section is whether or not the bass voice belongs in the pedal. This is often a question with Buxtehude, since the sources for his music do not often indicate pedal explicitly, and in any case are rather far removed in origin from the composer. In this section, there are several reasons to believe that the bass voice was indeed intended as a pedal part. First, it works on the pedal keyboard, and, in order to make it work, the composer has shaped it a little bit differently from any of the three other voices. That is, there is no scale-wise writing in the bass voice that is any faster than the eighth-note, whereas there is such writing in each of the other voices. Second, there are many places in this passage where it is awkward to play all four of the voices in the hands and where the fingering is much more natural without the lowest voice. (This is true, for example, in m. 33 or mm. 42–43.)
There is, as far as I can see, only one spot prior to the transitional/cadential section where it is actually impossible to play all four voices in the hands, namely the second eighth note of m. 44. Someone else might be able to find a clever way to make it work, and it is certainly possible to do so by fudging the duration of some of the longer notes. (Someone with larger hands than mine would have no trouble with it, but the stretch of a tenth is beyond what is normally found in music of this time.) Furthermore, the transitional section ending in m. 50 certainly requires pedal—really physically requires it—and there is no particularly good place to shift the bass line to the pedal if that line has been played in the hands from m. 20 on. So on balance this seems to me to be a section to be played with pedal.
(The closing fugue of the Praeludium in E Minor, BuxWV 142, presents an interestingly different picture. There the fingering is made dramatically easier, more natural, and more idiomatic to the organ playing of the time by not including the bass voice in what the hands are expected to play. However, at the same time the bass line itself is, if not unplayable in the pedal, still extraordinarily difficult and well outside what would have been the norm at the time.)

Learning protocol
The protocol for learning this fugal section starts with the approach that I outlined in the columns on counterpoint mentioned above; that is, playing through each voice separately and then playing pairs of voices. Here are some specific points about applying that approach to this passage:
1) The section that we are looking at is about 34 measures long—long enough that it should be broken up into smaller sections for this kind of practicing. It doesn’t really matter how it is broken up. It is fine to practice separate voices and pairs of voices in chunks of just a few measures, or in significantly larger chunks. One average way to do it would be to have breaks at around m. 23 and at around m. 36. Each voice will naturally break at a slightly different place. So, for example, it would make sense to play the soprano voice from m. 13 to m. 20, the alto from m. 15 to the middle of m. 23, the tenor from m. 17 through the first beat of m. 25, and the bass from m. 20 through m. 24. Then these sections of these voices can be combined in pairs.
2) When playing individual voices, it is fine to finger those voices in ways that will not be used when later putting the voices together. This is especially necessary and important with inner voices—typically the alto voice in a piece or passage that has three voices in the hands. Such an inner voice will almost certainly end up migrating from one hand to the other. However, at this stage it is important to play each voice in a way that is comfortable and natural, and that makes it as easy as possible to hear that voice as a coherent melody. It is also necessary to be flexible about playing inner voices in either hand. So, of course, when putting soprano and alto together it will be necessary to play the alto in the left hand, but when putting alto together with tenor it will be necessary to play the alto in the right hand.
3) At this stage, it is also not necessary to play the pedal part in the pedals. Practicing the pedal line as a pedal line (see below) can come later or can start in parallel with this process of getting to know the voices. However, for carrying out this approach to learning the voices, just as it doesn’t matter what fingering is used, it also doesn’t matter whether the feet play the bass voice or the left hand does. The important thing is that the student be able to listen carefully and hear the voices well while playing them.
4) In putting voices together in pairs it is a good idea some of the time to play the two voices on two manuals, in order to hear them with extra clarity. This is especially useful when voices cross or, as for example with the soprano and alto voices at mm. 38–39, come very close. The two sounds should be similar in volume and different in character.

Pedaling
While studying individual voices and pairs of voices, it is emphatically not a good idea also to finger and practice the manual part of the texture. That will come a little bit later. It is perfectly fine to practice the pedal part, however. It is interesting that in this piece the pedaling choices are more straightforward, and in fact the pedal part is probably easier overall, in the more active fugue subject and subject fragments, than in the measures in which the pedal is playing long-held notes.
The fugue subject can easily be played with alternate toes, starting with the right foot; the subject fragment that occurs in m. 33 and elsewhere can also be played with alternate toes, starting with the left foot. These pedalings are natural enough that I would expect essentially every student or player to use them. (There are other possibilities: for example, using the same foot to play some of the successive quarter notes, or occasionally using heel to play some of the sixteenth notes that are on white keys when the immediately prior note was on an adjacent black key. On the whole, I doubt that many players would find these variants easier or better, but perhaps some would. They could certainly be OK.) This consistent alternate toe pedaling implies nothing in particular about articulation, phrasing, timing, or other interpretive/performance matters.
However, when the pedal part moves more slowly, particularly from m. 43 on, pedaling choices both affect and depend on choices about articulation. To the extent that the player prefers or can accept spaces between these long notes, he or she can apply the principal of playing each note with whatever foot happens to lie most comfortably above that note. As an example that would lead me to the following succession of toes for the eleven pedal notes beginning with the first note of m. 44 and going to the end of m. 50:
l-r-r-l-l-r-l-l-r-r-l
For someone else it might be a little bit different. Creating more legato in this passage would involve different pedaling choices—for example, crossing the left foot under to play the E in m. 44, and then playing the C# in m. 45 with the right foot.
Of course, practicing the pedal line once pedaling choices have been made involves the usual things: keep it slow and accurate; look at the feet as little as possible—ideally not at all; repeat small-enough passages that the memory of the feeling of the passage does not fade before you get back to it. When the pedal part has become secure, join it first to the tenor voice, then to the left hand part as such—once that has also been practiced as outlined below—then to the hands together. (Of course, it is fine also to practice pedal with right hand alone. However, as always, left hand and pedal is most important. Usually if left hand and pedal has been practiced enough, then adding the right hand is something that feels natural and almost easy.)
And do not forget what might be the cardinal rule of practicing: if you hear yourself make a wrong note while practicing, do not stop or hesitate or go back and correct it. By the time that your ears have heard the wrong note, your mind should already have moved on to playing the next note. Next time through the passage you can make sure to adjust what needs to be adjusted to correct what was wrong.

Fingering choices
Once you have played through all of the voices and all of the pairs of voices, it is time to work out a fingering for the three voices that will be in the hands. And, as I discussed in the column from last July, the first task is to decide which notes belong in which hand. This must come before making specific fingering choices, and it must be done in such a way as to make those fingering choices as easy and natural as possible. As I wrote before: I have seen students waste a lot of time or even make a passage that could be fairly easy almost unplayable by assigning notes to hands in a way that was awkward. However, there is not always only one good answer, and the answer is not the same, necessarily, for any two players.
In any situation in which three voices are present and the notes of the alto voice can be reached by either hand—that is, generally, in which neither the soprano notes nor the tenor notes are more than an octave away from the alto notes—the player can, in a pinch, try it both ways. Generally it is nice to put “extra” notes with whichever other voice is less active. So, in m. 19, for example, I would play the first three notes of the alto voice in the right hand since the tenor voice has sixteenth notes, but then play the half note E in the left hand, since the soprano voice then has sixteenth notes. In m. 24 I would play the one alto voice (whole) note in the right hand, even though the soprano voice notes are a bit farther away, since the tenor voice is more active; in m. 25, however, I would shift the alto voice to the left hand since the soprano voice become much more active. Again, these choices are not right and other choices wrong. It is simply very important that each player—each student perhaps with the help of a teacher—work this out carefully and patiently, in a way that feels right.
After the “handing” and fingering have been worked out, it is possible to try an interesting challenge, namely to play the alto voice alone with the correct fingering. This involves letting that voice move from one hand to the other according to the plan that has been worked out. The goal is to play it in such a way that it sounds as natural and cantabile as it would sound played in one hand. It is simultaneously harder to do this outside the cushion of the other voices and good practice for playing that voice well when it is partly obscured by the other voices.

Practice procedures
Practicing the three-voice manual texture of course follows the usual pattern for any practicing. Each hand should be practiced separately, slowly, until it seems easy. The tempo should be allowed to rise only according to a pace that is comfortable: once a passage is learned well at one tempo, it can be played a little bit faster; playing it much faster will often lead to its falling apart. Once each hand is solid at a given tempo, the two hands can be put together at a slower tempo. This can then also be allowed to speed up gradually. The rule about not stopping or hesitating when you hear yourself make a wrong note is always utterly important.
After a player or student has carried out all of the above—individual voices, pairs of voices, pedal part, individual hands, left hand with pedal, and all the rest—there is an interesting exercise to try. Play the section—well learned, all parts together—and consciously listen only to one voice at a time. This is easiest with the soprano voice, next easiest with whichever voice is the lowest at a given time, quite hard with a real inner voice. The ability to do this and also keep the whole thing going accurately and with a feeling of ease will help to reveal the fruits of studying the voices thoroughly and also test the solidity of the overall practicing of the notes.
Next month I will discuss both the transition measures 47–50 and the free section that follows, beginning in m. 51. ■

Gavin Black is the Director of the Princeton Early Keyboard Center in Princeton, New Jersey. He can be reached by e-mail at [email protected]

Buxtehude BuxWV 141 – Part 1: Getting to know the piece
This month we begin the process of working on the Praeludium in E major, BuxWV 141, by Dietrich Buxtehude. As I mentioned last month, there is a good edition available online for free at http://imslp.info/files/imglnks/usimg/1/1e/IMSLP29682-PMLP06429-BuxWV136-154.pdf, pages 21–26. This is a reprint of the edition first published in the 1870s by Breitkopf & Härtel, edited by Phillip Spitta, and frequently reprinted, later on with revisions by Max Seiffert. It is also available in a 1988 Dover reprint and in Kalmus editions. There are several subsequent editions available through music dealers and at libraries. Small differences in these editions will not in any way interfere with the discussion of the process of working on the piece. Any one of them will serve this purpose very well.
The first step in working on a piece is to make sure that there are measure numbers, and if there are not—as in the edition referred to above—to put them in. This is worth doing! It will save time later and help in getting to know the piece. Even though the measure is somewhat of an arbitrary construct (and I feel pretty sure that as a matter of performance and listening nothing would change in the least if all of the bar lines in the notated music were erased), the act of going through and writing in measure numbers is a good first step in exploring what a piece seems to be about on the broadest level. The Buxtehude Praeludium has 110 measures. Going through the piece counting measures, I notice the following, among other things:
• three measures are whole notes;
• three tempo markings appear along the way, each of which apparently occurring at a place where there is also a noticeable change in texture;
• quite a few measures or passages are in only one voice;
• pedal is present almost exactly half the time (though this can be an artifact of the edition rather than the piece);
• several changes in time signature.
None of this is exactly earth shaking, and of course most of what there is to notice about a piece is not noticed casually while counting measures. However, I want to introduce the idea that noticing anything and everything about a piece is the first and an important step towards learning how to play it. I am not talking specifically—or only—about the things that constitute a formal analysis—harmonic or motivic/contrapuntal—such as might be done in a theory class. This might overlap with what I am talking about, and that kind of rigorous academic analysis has several important purposes, only some of which bear upon the act of learning a piece or actually performing it. However, noticing things about a piece—simple or complex, superficial (even, for example, things about font and layout in the page) or “deep” (contrapuntal structure, harmonic intricacies)—can increase ultimate performing security by increasing the extent to which a player simply knows what is coming up next. This is analogous to the fact that it is easier to drive around a town whose streets you know well, or to walk around a building where you know all of the corridors and staircases. It is also part of the process of making a non-memorized piece as well-learned and secure as a memorized piece is supposed to be. (A piece that is memorized mostly by feel is often not particularly secure.) Of course, working out fingerings and pedalings and then practicing them is by far the most important component of learning a piece and becoming comfortable playing it. However, the more consciously familiar you are with the landscape of a piece, the more your mind will be able to help you, as you practice and perform the work, with the task of remembering what is coming up next in time to execute it serenely and securely. Such things as “the next subject entry is in the tenor” or “there’s a surprising chord coming up” or “the first thing on the next page is a D-major chord” or “the font on page 4 is larger, because there are fewer lines” all serve this function. Some of these things might also contribute to an analysis of the piece and perhaps to a greater artistic understanding of the piece as well. However, the point right now is that they make the basic learning of the piece more solid and secure.
The first thing to explore about a piece is what sections the piece falls into. Sometimes sections are delineated by double bars or (of course) movement breaks, or flagged by words—tempo indications, usually. Sometimes they are not. It is also possible to be unsure whether two adjacent areas within a piece should be considered different sections or simply somewhat different parts of the same section. This almost always does not matter at all. Exploring the issue and describing for yourself what is going on is all that is necessary.
In this Praeludium, there are quite a few spots where something changes, that is, where one kind of writing gives way to another. These spots seem to be as follows: after m. 12; the beginning of m. 51; after m. 59; after m. 72; after the first beat of m. 75; after m. 86; and after m. 90. This suggests that there are eight different sections. The nature of the writing in the second, and longest, of these sections changes in the last three and a half measures, that is, from the middle of m. 47 through m. 50. There is no clear break leading into this change, so perhaps it isn’t quite a new section, but simply a different kind of passage. As I pointed out above, it does not matter what we call it as long as we notice what is happening.
So, if these passages or sections are different from one another, then how are they different and what can this tell us about how to work on the piece? Keyboard writing has a tendency to mix contrapuntal and non-contrapuntal textures. Therefore it is always useful in looking over a piece to notice which passages, if any, are written in a thoroughgoing contrapuntal texture and which are not. There may also be passages that seem to be somewhere in between. Of course one can assume that, in general, Renaissance and Baroque keyboard music will have a large proportion of formally worked out counterpoint, later music rather less.
In the case of this piece, the following sections seem to be fully contrapuntal, in the sense that they have a set number of voices and they treat recognizable motives imitatively: the section beginning at m. 13, excluding the last few measures; the section beginning at m. 60; the section beginning in m. 75; and the final section, which begins at m. 91. Each of these sections is more or less fugal—that is, in addition to their being contrapuntal in the sense described above, they have at least one theme or motive that is heard one or more times in each voice. These themes are first heard as follows: 1) mm. 13–15 in the soprano voice; 2) m. 60 in the alto voice; 3) m. 75 in the tenor voice; and 4) m. 91 in the alto voice. It is important to go through and find each and every occurrence of each of these themes. This is certainly part of understanding the rhetoric of the work, and of analyzing the work for achieving an intellectual understanding of the piece and of the mind of the composer. But it is also a very practical step in learning how to get the notes right and how to make the piece secure in performance. As noted above, the more you simply know what’s coming up, the more familiar you are with what is in the piece, the more likely you are to recall it in time to play it easily and securely. The most natural thing to remember is any kind of pattern, and a recurrent theme is a pattern.
Motives or themes, including themes functioning as fugue subjects, are of course not the only recurring patterns that can (and should) be noticed; we will get to some others just below. However, fugue subjects and similar recurring motives are easy to notice and to identify, and are therefore a good starting point. So it is a good idea to highlight them on a copy of the work. I find twelve instances of the theme introduced in m. 13—four in the soprano voice, three in the alto, two in the tenor, and three in the bass. There are also many instances of the second half of this theme occurring without the first half, as in, for example, measures 33 and 34. The theme introduced in m. 60, if we take it to be the full measure in the alto voice, occurs six times: three in the soprano voice, two in the alto, one in the tenor. (This section is in three voices.) However, each half of the theme occurs separately quite a few more times. Does it make sense to call this a measure-long theme, or is it really two separate four-note motives, which may or may not follow one another in the same voice? It doesn’t matter! As long as you notice what the notes and patterns are, either of those concepts will do very nicely to describe the situation. The theme introduced in m. 75 occurs six times, two in each of the three voices. Again, fragments of this theme also occur. The theme introduced in m. 91 seems to occur eleven times, though it would be possible to argue that a couple of them are not quite exactly that theme, but rather a close variant. Each half of the theme also occurs separately many times.
Turning for a moment to the four remaining sections of the piece, what is there to notice about them? First of all, they are short, occupying 27 of the piece’s 110 measures. Of course, this does not necessarily mean that they take up a proportionately small amount of time: that depends on tempo. One of these sections—mm. 87–90—is in a set number of voices (four), with a homophonic, somewhat hymn-like, texture: fully worked-out counterpoint, but with no imitation or motivic development. The other three (at mm. 1, 51, and 73) are not in any fixed number of voices or, really, in voices at all. They include passage work, trills and trill-like writing, fairly long one-voice passages, occasional abrupt changes in texture—the most noticeable of which is near the beginning, where a long solo passage ends in a four-note chord—and some unprepared dissonance. Two of these sections have written comments associated with them: trillo longo in mm. 51 and 53, and con discrezione in m. 73. Both of these might suggest rhythmic freedom at a fairly broad level. This is obvious with con discrezione. It also makes sense that trillo longo, written over a very brief trill-like passage, would suggest that the trill can be made to occupy more time than is notated for it.
Getting to know a piece in order to perform it securely involves simply noticing things, even things whose significance isn’t clear—indeed, even things that are not really significant except in that they form part of the process of getting to know the piece. It is most important to notice anything that happens more than once. There is a good chance that anything that happens more than once is important compositionally, that the composer did it on purpose. However, even if this is not the case, the act of noticing helps with learning. By “anything” in this context I mean, probably, anything except individual pitches. It is probably not fruitful to notice that, for example, the note “a above middle c” occurs in this measure, and then occurs again in that measure. Once in a while this might matter, but usually not. Anything more involved than an individual note, however, is worth paying attention to.
Here are some things—other than the well-defined motives discussed above—that I notice in looking over this piece. The upward leap of a step in the pedal part occurs five times in a row near the beginning; it is possible that the rising quarter-note line in the lowest voice (not shared with the other voices) in the section beginning at m. 60 could be heard as related to this, an extension of it. The countersubject fragment in m. 16 and again m. 18—four notes in the soprano voice beginning just after the downbeat—comes in again somewhat prominently in the final section beginning at m. 103, and ends up being the final gesture of the piece. It also occurs in m. 72, but in a way that is interrupted: it does not resolve, and it leads into the con discrezione section. The phenomenon of two voices playing together—that is, in a way that is in sync rhythmically and more or less parallel—is characteristic of the beginning (mm. 4–6) and the end (mm. 99 on) of the piece, but not, except fleetingly, the middle. The one instance of this that I notice in the middle of the piece is at m. 57 and seems to foreshadow the fugue subject that governs the final section of the piece beginning at m. 91.
The most interesting recurrence of a compositional element in this piece is the first four notes—that is, the rising scale fragment B–C#–D#–E—which keep coming back at crucial moments. To start with, it is the germ from which the rest of the opening section is, at least partly, built up. This is most explicit in mm. 3, 4, and 9. Then this opening gesture is quoted directly as the last notes of the fugue subject that is introduced in m. 13. Also, the second half of that subject is essentially an ornamented inversion of this motive. When the long fugal section that begins in m. 13 is coming to an end and gives way to non-fugal passage work, the four-note motive or a close variant of it is present throughout, as it also is in the following section. The final fugue subject, which enters in m. 91, is made up of the ornamented inversion of this motive, followed by the motive itself. From m. 94 on, the motive occurs in parallel or contrary motion in two or three voices at once repeatedly, and the flourish that gives energy to the ending of the work in mm. 106 and 109 is made up of two iterations in a row of this four-note motive in diminution.
I have posted a copy of the score of BuxWV 141 with various motives and other aspects of the text of the piece highlighted at http://www.gavinblack-baroque.com. Next month we will continue with this piece, and I will discuss how to break the work up into units for practicing. Then, in the August column, we will turn to the Boëllmann Suite Gothique.