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Francesco Gasparini's Twenty-One Keys: Do they reflect the use of meantone?

by Carl Sloane

Carl Sloane is a pharmacist by education, a freelance translator by vocation, and an amateur harpsichordist.

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In his famous treatise on continuo playing,1 Francesco Gasparini gives a table of twenty-one keys which the student could expect to encounter. The absence of certain keys proves that the contents of the table are determined by the tuning which Gasparini used, and because of his standing, it would be of particular interest if the precise nature of this tuning could be established.

There are immediate indications that Gasparini had in mind some type of regular meantone (RMT)2 with the usual range of Eb to G# and the wolf between G# and Eb. These indications, supported by substantial evidence that meantone was common in Italy well into the eight-eenth century,3 include the complete absence of Ab and the apparent expectation that the table would be universally applicable. However, the matter cannot be automatically considered settled, since the the book was written at a time when meantone was being discarded in favor of temperaments with no wolf. Tempérament ordinaire, which eliminated the wolf by spreading it over several fifths, had been in use in France for some time when it was described by d'Alembert,4 and Werckmeister's tunings,5 which usually solved the problem by reducing the number of tempered fifths, had been published at least by 1691. In addition, there are apparent inconsistencies in the table itself.

The keys are illustrated in the form of figured scales which begin on the tonic, rise to the sixth degree, descend a ninth to the dominant, then leap back to the tonic. They are divided into two groups, those of "great usefulness" (gran giovamento):

G, g, a, A, Bb, b, C, c, d, D, Eb, e, E, F, f, f#, and those used in modulations:

bb, B, c#, eb, F#.

Major keys in group 1 thus run from Eb to E around the circle of fifths, minor keys from F to F#.

Tagliavini6 argues against RMT, pointing out that the absence of Db major is difficult to understand when the more highly inflected Gb major (enharmonic F#) is present. To his rhetorical suggestion that this paradox may be due to the presence of the wolf in the dominant chord of Db, he replies that C# minor should then logically be absent as well. He does not attempt to establish the criterion used to exclude keys from group 1.

The composition of group 1 does not initially seem compatible with the use of RMT: F minor, with its poor tonic chord, and E and Eb majors, with a poor chord on V and IV respectively, would not be expected in this group. On the other hand, there is plenty of contemporary evidence showing that poorly tuned intervals were used regularly in practice (Ref. 3, 156-8, 193), and on this basis, the makeup of group 1 can be logically explained.

In RMT, the most complex major keys in group 1, Eb and E, each have a single note outside the range Eb to G#; the most complex minor keys, F and F#, each have two such notes, at least one of which is on the sixth or seventh degree (see Fig. 1). Accordingly, the keys in group 1 may have been chosen on the understanding that major keys were allowed a maximum of one unavailable note and minor keys a maximum of two, the greater freedom in the minor keys being due to the variable inflection of VI and VII.

It is worth noting that even in group 2, Gasparini's key signatures never have more than three flats or four sharps, thus staying within the same limits as the major keys in group 1. (The section on modulation--(pp. 111-114)--gives key signatures which exceed these limits, but it also illustrates keys not included in the table, so that Gasparini has here presumably sacrificed some degree of rigor.) In addition, the order within each pair of parallel keys in group 1 is obviously determined by the complexity of the key signature, suggesting a certain preoccupation with key complexity and unavailable notes.

 Owing to the manner in which unavailable notes enter as one moves around the circle of fifths, exact location in the scale was probably of secondary importance in group-1 keys. But ultimately position must have become of critical importance. From Fig. 1 it is apparent that the most elementary keys not in the table would have an unavailable note on at least one of I, II or V. Although the presence of the wolf on either I or V (an unavailable note on one member of either of the pairs I/V or II/V) may have been the underlying reason for outright rejection, I think that a more likely working criterion was the spelling of I, II and V, and that the presence of F# major does not imply the inclusion of Gb, any more than the presence of C major implies the inclusion of B#. It seems likely, especially in view of the more lenient treatment of minor keys in group 1, that the presence of the wolf on the dominant of C# minor (or the wrong spelling for II) was considered acceptable. This hypothesis is admittedly not as credible as it would be if Gasparini had not figured V with a major third, because some softening of the effects of the wolf would be expected in certain positions of the chord G#-B-D#, especially of the first inversion, by the presence at the relevant pitch of a partial from the B-natural.7

To the extent that RMT is established, Gasparini's table shows that, contrary to most modern opinion, G# was not retuned to Ab for compositions in F minor.7 In addition, the table gives a valuable clue to the tuning used by Domenico Scarlatti. There is almost nothing in the Venice and Parma codices to suggest that Scarlatti retuned for F minor, in which he wrote extensively (in the Parma codex, it occurs more often than any other minor key), but there is some rather pretty evidence    that he retuned for Ab major and several of the keys in group 2.8 One is therefore strongly tempted to conclude that Scarlatti used the same tuning as Gasparini.

Notes

                        1.                 Francesco Gasparini, L'Armonico Pratico al Cimbalo (1708; reissue, New York: Broude Bros., 1967), 83-6.

                        2.                 "Regular" means only that the eleven good fifths are the same size.

                        3.                 Patrizio Barbieri, Acustica, Accordatura e Temperamento nell'Illuminismo Veneto (Rome: Torre d'Orfeo, 1987), 152-8.

                        4.                 Jean-Le Rond d'Alembert, Elemens de Musique Theorique et Pratique (1752; reissue, New York: Broude Bros., 1966), 48-9.

                        5.                 Andreas Werckmeister, Musicalische Temperatur (1691; reissue, Utrecht: Diapason Press, 1983), 78-9.

                        6.                 Luigi Ferdinando Tagliavini, "L'Armonico Pratico al Cimbalo. Lettura Critica," in  Francesco Gasparini (1661-1727)--Atti del primo convegno internazionale (Comune di Camaiore) (Florence: Olschki, 1981), 133-55, at 149-51.

                        7.                 C. Sloane, "A Further Note on Tempered Minor Chords," Journal of Sound and Vibration 170, 2 (1994): 261-2.

                        8.                  Carl Sloane, "The Case for Meantone in Scarlatti," Continuo, 16, 6 (1992): 1516.

Related Content

Francesco Gasparini's Twenty-One Keys: Do they reflect the use of meantone?

by Carl Sloane

Carl Sloane is a pharmacist by education, a freelance translator by vocation, and an amateur harpsichordist.

Default

In his famous treatise on continuo playing,1 Francesco Gasparini gives a table of twenty-one keys which the student could expect to encounter. The absence of certain keys proves that the contents of the table are determined by the tuning which Gasparini used, and because of his standing, it would be of particular interest if the precise nature of this tuning could be established.

There are immediate indications that Gasparini had in mind some type of regular meantone (RMT)2 with the usual range of Eb to G# and the wolf between G# and Eb. These indications, supported by substantial evidence that meantone was common in Italy well into the eight-eenth century,3 include the complete absence of Ab and the apparent expectation that the table would be universally applicable. However, the matter cannot be automatically considered settled, since the the book was written at a time when meantone was being discarded in favor of temperaments with no wolf. Tempérament ordinaire, which eliminated the wolf by spreading it over several fifths, had been in use in France for some time when it was described by d'Alembert,4 and Werckmeister's tunings,5 which usually solved the problem by reducing the number of tempered fifths, had been published at least by 1691. In addition, there are apparent inconsistencies in the table itself.

The keys are illustrated in the form of figured scales which begin on the tonic, rise to the sixth degree, descend a ninth to the dominant, then leap back to the tonic. They are divided into two groups, those of "great usefulness" (gran giovamento):

G, g, a, A, Bb, b, C, c, d, D, Eb, e, E, F, f, f#, and those used in modulations:

bb, B, c#, eb, F#.

Major keys in group 1 thus run from Eb to E around the circle of fifths, minor keys from F to F#.

Tagliavini6 argues against RMT, pointing out that the absence of Db major is difficult to understand when the more highly inflected Gb major (enharmonic F#) is present. To his rhetorical suggestion that this paradox may be due to the presence of the wolf in the dominant chord of Db, he replies that C# minor should then logically be absent as well. He does not attempt to establish the criterion used to exclude keys from group 1.

The composition of group 1 does not initially seem compatible with the use of RMT: F minor, with its poor tonic chord, and E and Eb majors, with a poor chord on V and IV respectively, would not be expected in this group. On the other hand, there is plenty of contemporary evidence showing that poorly tuned intervals were used regularly in practice (Ref. 3, 156-8, 193), and on this basis, the makeup of group 1 can be logically explained.

In RMT, the most complex major keys in group 1, Eb and E, each have a single note outside the range Eb to G#; the most complex minor keys, F and F#, each have two such notes, at least one of which is on the sixth or seventh degree (see Fig. 1). Accordingly, the keys in group 1 may have been chosen on the understanding that major keys were allowed a maximum of one unavailable note and minor keys a maximum of two, the greater freedom in the minor keys being due to the variable inflection of VI and VII.

It is worth noting that even in group 2, Gasparini's key signatures never have more than three flats or four sharps, thus staying within the same limits as the major keys in group 1. (The section on modulation--(pp. 111-114)--gives key signatures which exceed these limits, but it also illustrates keys not included in the table, so that Gasparini has here presumably sacrificed some degree of rigor.) In addition, the order within each pair of parallel keys in group 1 is obviously determined by the complexity of the key signature, suggesting a certain preoccupation with key complexity and unavailable notes.

 Owing to the manner in which unavailable notes enter as one moves around the circle of fifths, exact location in the scale was probably of secondary importance in group-1 keys. But ultimately position must have become of critical importance. From Fig. 1 it is apparent that the most elementary keys not in the table would have an unavailable note on at least one of I, II or V. Although the presence of the wolf on either I or V (an unavailable note on one member of either of the pairs I/V or II/V) may have been the underlying reason for outright rejection, I think that a more likely working criterion was the spelling of I, II and V, and that the presence of F# major does not imply the inclusion of Gb, any more than the presence of C major implies the inclusion of B#. It seems likely, especially in view of the more lenient treatment of minor keys in group 1, that the presence of the wolf on the dominant of C# minor (or the wrong spelling for II) was considered acceptable. This hypothesis is admittedly not as credible as it would be if Gasparini had not figured V with a major third, because some softening of the effects of the wolf would be expected in certain positions of the chord G#-B-D#, especially of the first inversion, by the presence at the relevant pitch of a partial from the B-natural.7

To the extent that RMT is established, Gasparini's table shows that, contrary to most modern opinion, G# was not retuned to Ab for compositions in F minor.7 In addition, the table gives a valuable clue to the tuning used by Domenico Scarlatti. There is almost nothing in the Venice and Parma codices to suggest that Scarlatti retuned for F minor, in which he wrote extensively (in the Parma codex, it occurs more often than any other minor key), but there is some rather pretty evidence    that he retuned for Ab major and several of the keys in group 2.8 One is therefore strongly tempted to conclude that Scarlatti used the same tuning as Gasparini.

Creative Continuo: or

Examples of Enlivening a Figured Bass on the Harpsichord

by J. Bunker Clark
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Nothing is more dull in a performance of Baroque music than a continuo harpsichordist who mechanically plays a chord for every bass note in the score. Or who reverently plays a printed realization, which usually follows the same practice. Only rarely one hears a realization exhibiting some element of spark and imagination.

 

This "essay" consists of ten examples demonstrating various ways of treating a figured bass in a creative manner. The intended instrument is the harpsichord, not the organ, for the harpsichord is capable not only of furnishing chords, melodies, and polyphony, but is also--due to the noisy jacks--a percussive instrument, which quality may as well be exploited from time to time. Sometimes only jack-noise can be heard in an orchestral situation.

The most important advice is a) to be imaginative and do something different than a printed realization, and b) to be sensitive to the performance situation. These examples are intended for an orchestral continuo player, but some of the principles can be applied to chamber groups. (Continuo on the organ demands a different treatment.) All but the last example are from Handel's  Messiah, and include the printed realization available from Kalmus. I originally intended this article to be unencumbered with scholarly apparatus, but consultation with several colleagues prompted an annotated bibliography.

 

Bibliography/Notes

 

Arnold, Franck Thomas. The Art of Accompaniment from a Thorough-Bass, as Practised in the XVIIth & XVIIIth Centuries. Oxford: Oxford University Press, 1931; reprint, with introduction by Denis Stevens, in 2 vols., New York: Dover, 1965.  The title to ch. 4, "On Certain Niceties of the Accompaniment," is borrowed from C. P. E. Bach's chapter "Von gewissen Zierlichkeiten des Accompagnements" (Versuch, part 2, 1762, ch. 32; Mitchell trans., pp. 386-403). Arnold's book is the grand-daddy on the subject. Much of it, however, is about how to realize specific figures.

Ashworth, Jack. "How to Improve a Continuo Realization." American Recorder 26, no. 2 (May 1985): 62-65. P. 62: "The first axiom of playing continuo accompaniment from an editorially supplied part is that one must never hesitate to change it" (p. 62). Tips (p. 65): "1. Be sensitive to the frequent necessity of reducing the texture from four to three--or occasionally even to two--parts, depending on the volume of the solo instrument, the range in which it is playing, and the nature of the piece. 2. Do not feel compelled to play a chord on every bass note provided by the composer. In fact, don't even be tempted to. 3. Avoid doubling or going above the soloist's part in the realization. 4. Avoid playing full chords on bass notes taking the weak part of a beat unit. 5. Be sparing with ornamentation. 6. Above all, remain sensitive to the needs of the soloist, and accommodate those needs insofar as you can. Good continuo players must be as supportive as they are unobtrusive."

Bach, Carl Philipp Emanuel. Versuch über die wahre Art das Clavier zu spielen. Berlin, 1759, 1762. Trans. William J. Mitchell as Essay on the True Art of Playing Keyboard Instruments. New York: Norton, 1949. Ch. 6, "Accompaniment," is the most relevant, especially the section "Some Refinements of Accompaniment," pp. 386--403, a "must read" primary-source primer on the subject. There are many cross-references to Arnold's 1931 book in Mitchell's notes. Several valuable quotes: "Of all the instruments that are used in the playing of thorough bass the single-manual harpsichord is the most perplexing with regard to forte and piano.  To make amends for the imperfection of the instrument in this respect the number of parts must be increased or reduced" (p. 368). "It is often necessary to strike chords over short rests in advance of their bass notes, as a means of retaining order and winning variety" (p. 418, in a section "Chords that precede their bass notes"). For recitatives, see pp. 420--25, which includes, for the organ: "In recitatives with sustained accompanying instruments, the organ holds only the bass, the chords being quitted soon after they are struck."

Borgir, Tharald. The Performance of the Basso Continuo in Italian Baroque Music. Ann Arbor: UMI Research Press, 1987.  Ch. 19, "Neapolitan Continuo Practice: The Partimenti," 141--47, is the most important for this purpose. The term "partimenti" represents a bass needing realization in the treble, resulting in a piece that can serve as a keyboard solo. First developed by Gaetano Greco (ca. 1657--ca. 1728), it was further developed by Francesco Durante in a manuscript titled Partimenti, ossia intero studio di numerati, per ben suonare il cembalo. Durante's exercises consist of harmonizing ascending and descending scales (later called regola dell'ottave, rule of the octave). The advanced ones have written-out passages in the treble: scales or other motives in one hand imitating the other. Indeed, the third (and last) group of exercises is of fugues. Ch. 20 includes excerpts of written-out accompaniments, mostly in solo cantatas, by Francesco Gasparini (1695), Benedetto Marcello, Alessandro Scarlatti, and a sonata attributed to Handel for viola da gamba and "cembalo concertato."

Bötticher, Jörg-Andreas. "'Regeln des Generalbasses': Eine Berliner Handschrift des späten 18. Jahrhunderts." Basler Jahrbuch für Historische Musikpraxis 18 (1994): 87--114. This concerns a manuscript by "Herrn Musico Heering," dated 1771, which includes a realized edition of Largo and Vivace movements from a C-major sonata for two flutes by Johann Gottlieb Graun (pp. 111--13), with some examples of a right-hand chord on a beat where the bass part has a short rest. The issue also has these articles: Graham Sadler and Shirley Thompson, "Marc-Antoine Charpentier and the Basse Continue," 9--30; Arnaldo Morelli, "Basso Continuo on the Organ in Seventeenth-Century Italian Music," 31--45; George J. Buelow, "The Italian Influence in Heinichen's Der General-Bass in der Composition (1728)," 47--66; Regula Rapp, "Was der späte General-Baß?," 115--27; and see notes to the last item, below.

Buelow, George J. Thorough-Bass Accompaniment According to Johann David Heinichen. Berkeley: University of California Press, 1966. Rev. ed., Ann Arbor: UMI Research Press, 1986. An excellent guide to continuo playing by a highly respected scholar, based on the most important writer of the early 18th century (1711, 1728) on the subject. Heinichen took advantage of the publication of Gasparini (1708; see below). The most valuable section is ch. 6, "The 'Art' of Accompaniment: Specific Aspects of Style," pp. 175--218. Includes examples of changing right-hand realization in quarters or 8ths to 16th figuration; and even break up 8ths or quarters in the bass (pp. 194--202). But the reverse (pp. 202--03): change 16ths in bass to quarters or 8ths. There is a section (pp. 205--08) on imitating a solo voice in the right hand. Ch. 9 is a practical demonstration of realizing Alessandro Scarlatti cantata Lascia deh lascia al fine di tormentarmi più.

Daube, Johann Friedrich (1756), quoted in The Bach Reader, ed. Hans T. David and Arthur Mendel, rev. ed. (New York: Norton, 1966), 256:

For the complete practical application of thorough bass it is necessary to know three species: (1) the simple or common; (2) the natural, or that which comes closest to the character of a melody or a piece; (3) the intricate or compound.

The excellent Bach possessed this third species in the highest degree; when he played, the upper voice had to shine. By his exceedingly adroit accompaniment he gave it life when it had none. He knew how to imitate it so cleverly, with either the right hand or the left, and how to introduce an unexpected counter-theme against it, so that the listener would have sworn that everything had been conscientiously written out. At the same time, the regular accompaniment was very little curtailed. In general his accompanying was always like a concertante part most conscientiously worked out and added as a companion to the upper voice so that at the appropriate time the upper voice would shine. This right was even given at times to the bass, without slighting the upper voice. Suffice it to say that anyone who missed hearing him missed a great deal.

Daw, Brian A. "Alessandro Scarlatti's Continuo Realization of Da sventura a sventura (1690): An Analysis and Observations Relating to Late Seventeenth-Century Keyboard Practices." Early Keyboard Journal 4 (1985-86): 51--60. Shows (pp. 54--55) how Scarlatti anticipates or imitates motives in the solo voice; also keyboard textures a 3--7 (not necessarily the usual 4 parts), and distributing realization in both hands. Leaves out the 3rd in a cadence when it's sung by the voice. Main point: the continuo complements, not doubles, the voice.

Derr, Ellwood. "Concertante Passages in Keyboard Realizations in Handel: Some Guidelines." The Diapason, September 1985, 9--12. Liberally quotes Heinichen/Buelow. Subjects: arpeggiation; furnishing imitations, as explained by Heinichen, and with example from J. S. Bach; examples from Handel's "O thou tellest" (the descending scale, imitations by Handel). "What eighteenth-century writers have not commented upon is the matter of necessity, as occasions arise, for the treatment of the concerting harpsichord part to complete the musical surface. It is then the task of analysis to ferret out these details. While realizations of certain passages may be undertaken on the basis of examples in treatises, those made on the basis of contextual settings in real pieces by composers of stature are likely to be more successful still, especially in the hands of a capable continuo harpsichordist" (p. 12).

Donington, Robert. The Interpretation of Early Music. Rev. ed. New York: Norton, 1992. The section "Going Beyond the Figures," especially pp. 306--07, 313--15, is valuable, relevant, and includes quotes from 17--18th-century authors.

Dreyfus, Arthur. Bach's Continuo Group: Players and Practices in His Vocal Works. Cambridge: Harvard University Press, 1987. " . . . manuscripts . . . provide no evidence to indicate how keyboard players voiced the chords of the continuo realization. For this reason I have not discussed styles of continuo realization."

Gasparini, Francesco. L'armonico pratico al cimbalo: Regole, osservazione, ed avvertimenti per ben suonare il basso, e accompagnare sopra il cimbalo, spinetta, ed organo. Venice, 1708. Facsimile, New York: Broude Bros., 1967. Trans. Frank S. Stillings, ed. David L. Burrows, as The Practical Harmonist at the Harpsichord. New Haven: Yale University Press, 1963. Ch. 10, "Del diminuire, abbellire, or risiorire gli accompagnamenti" (diminution, embellishment, and adornment of the accompaniment) has examples of right-hand counter-melodies; ch. 11, "Del diminuire, ò risiorire il fondamento" (diminution, or adornment of the bass), has examples of breaking up or arpeggiating the continuo line.

Gudger, William D. "Playing Organ Continuo in Handel's Messiah." The American Organist 19, no. 2 (February 1985): 91--92. On use of organ vs. harpsichord, and how the organ was often used only to double bass line and imitative entries of the chorus. Handel normally had two harpsichords for oratorios--the first played by himself until the late 1730s, when he had a claviorganum (combination organ/harpsichord).

J. S. Bach's Precepts and Principles for Playing the Thorough-Bass or Accompanying in Four Parts. Trans. Pamela L. Poulin. Oxford: Clarendon Press, 1994. Dated 1738, much is adapted from Friederich Erhardt Niedt, Musicalische Handleitung oder Gründlicher Unterricht (Musical guide or fundamental instruction; Hamburg, 1700/10). How to realize the figures; nothing more creative.

Keller, Hermann. Thoroughbass Method: With Excerpts from the Theoretical Works of Praetorius, Niedt, Telemann, Mattheson, Heinichen, J. S. & C. P. E. Bach, Quantz, and Padre Mattei, and Numerous Examples from the Literature of the 17th and 18th Centuries. Trans. and ed. Carl Parrish. New York: Norton, 1965. From Mattheson, Grosse Generalbaß-Schule (Hamburg, 1731): break up right-hand chords like a pleasing toccata (p. 47). From Heinichen, Der Generalbass in der Composition (Dresden, 1728): instead of "poor kind of accompaniment" or "very plainly accompanied," "either 1) divide the accompaniment between both hands . . . or 2) undertake the full-voiced accompaniment with the left hand alone and thereby enable to the right hand with more ease to invent a separate song or melody to the bass, as far as our ideas, taste, and talent will allow" (p. 48).

Ledbetter, David, ed. Continuo Playing According to Handel: His Figured Bass Exercises. Oxford: Clarendon Press, 1990. Dated from 1724 and mid-30s, when he was teacher to daughters of George II, especially Princess Anne. Root, 6 chord, 6/4 chords, 6/5 chords, 2 chords, &c.; exercises in fugue, with models. Nothing especially creative.

Rogers, Patrick J. Continuo Realization in Handel's Vocal Music. Ann Arbor: UMI Research Press, 1989. The first part deals with figuring in the sources; it's the second part, "Realization Problems," that is of more use: unison textures (play realized or unrealized?), and problems of realization in recitatives. Ch. 8, "Short Rests in the Bass," deals with whether to play a chord over a bass rest, and supports doing so from examples. Theorists of the time also describe the practice--for example, see quote from C. P. E. Bach, above. Mattheson's Grosse General-Baß Schule (Hamburg, 1731): ". . . it must be observed that the right hand must necessarily sound first when a sixteenth rest occurs . . . because the empty space offends the ear, which wishes most of all that everything be orderly and continuous, complete, and not broken up. Striking first with the right hand can be used with such rests throughout in accompanying, except for a few instances where the composer's intentions must be regarded" (quoted p. 148). Cites Telemann's Singe-, Spiel- und Generalbass-Übungen (Hamburg, 1733--34)--of 48 short songs, figured rests are used in six. Ch. 9, on pedal points, concludes, backed up by Heinichen, Telemann, and C. P. E. Bach, that figured pedal points generally should be harmonized, but unfigured ones not. Includes (pp. 186--87) detailed figuring of the Messiah's Pifa, meas. 1--11.

Rogers, Patrick J. "A Neglected Source of Ornamentation and Continuo Realization in a Handel Aria." Early Music 18, no. 1 (February 1990): 83--89. 1st: 2-part arrangement Ms. (ca. 1725) at the Fitzwilliam Museum of "Molto voglio" from Rinaldo, is included in Chrysander's 2nd ed. (1894) of the opera. 2nd: "Sventurato, godi o core abbandonato" from Floridante. 3rd: "Cara sposa" from Radamisto. These arrangements: 1) frequently contain at least part of the aria text; 2) usually are not literal transcriptions, and segments are recomposed and improved; 3) they are effective idiomatic keyboard pieces; 4) either are simple 2-part versions, which may relate to Handel's teaching duties, or more elaborate arrangements in 3 or more parts; 5) some have extensive ornamentation of the original vocal line. "Cara sposa" is a continuo aria, with complete text between staves. Rogers concludes that it's really a keyboard piece, perhaps freely based on pre-existing vocal ornamentation--best example of such ornamentation--and includes a complete edition in the article.

Thieme, C. A. Treatise, "Some Most Necessary Rules of Thorough Bass by J. S. B." [1725], once owned by Johann Peter Kellner, trans. in Bach Reader, 390--98. Basically how to realize chords from the figures.

Towe, Teri Noel. "Messiah: Reduplication without Redundancy: Editions and Recordings Past and Present." The American Organist 19, no. 2 (February 1985): 74--90. Occasional references to continuo playing in recordings.

Williams, Peter. Figured Bass Accompaniment. 2 vols. Edinburgh University Press, 1970. The best modern book on the subject, with many quotes and examples from the treatises, and vol. 2 has many unrealized examples, with interspersed suggestions for completing them. "When the bass rests on the beat, play the chord in the right hand" (p. 31, from Bologna Ms., ca. 1730; C. P. E. Bach, ch. 37; Manfredini 1775, 59). "Not all quick repeated bass notes have to be played; they may be omitted or broken" (Türk 1822, 293).

Williams, Peter. "Johann Sebastian Bach and the Basso Continuo." Basler Jahrbuch für Historische Musikpraxis 18 (1994): 67--86. Includes (pp. 77--78) a realization by Heinrich Nikolaus Gerber (Bach's pupil) of Sonata no. 6 from Tomaso Giovanni Albinoni, Trattenimenti armonici per camera, op. 6 (Amsterdam, ca. 1712)--the realization (ca. 1724--25), according to Gerber, "durchcorrigirt von Sebastian Bach." Williams: ". . . at least a few ties between the upper parts are beginning to suggest an articulated part-writing." Also cites Bach's written-out accompaniment for the Largo of the Flute Sonata in B minor, BWV 1030, from the autograph score. "There is some evidence in Germany that players were sometimes encouraged to work towards a more 'künstlerisches' accompaniment than can easily be produced from a merely 'schulmeisterlich' harmonization in four parts" (p. 81). Bibliography, pp. 85--86.

 

Cover feature

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Taylor & Boody Organbuilders, Staunton, Virginia

Goshen College, Goshen, Indiana

About the organ.

Designing an organ for Rieth Hall at Goshen College was a
pleasure. The opportunity to place the organ in the traditional location, high
in the rear gallery, was ideal both visually and aurally. The form and
proportions of the hall, with its austere yet warm and inviting interior,
called the organbuilder to respond with similar clarity and restraint. The
ample height of the room suggested a plain, vertical configuration of the
instrument, on which natural light from the clerestory windows would fall
gently. Everything about the hall spoke of its solid construction and honesty
of materials, qualities that we strive to reflect in our organs. Likewise the
acoustical properties of the hall, so warm and reverberant and at the same time
intimate and clear, allowed the organ’s tone to develop freely without
being forced. The result is an endearing musical instrument that is
aesthetically inseparable from the space in which it stands.

Initial inspiration for the Goshen case came from the organ
built by David Tannenberg in 1774 for Trinity Lutheran Church in Lancaster,
Pennsylvania. While only the case and façade pipes of that lovely
instrument have survived, they constitute the finest example we have in our
country of south German case architecture from the 18th century.
Tannenberg’s use of the double impost, with its Oberwerk division
gracefully placed as a reflection of the Hauptwerk below, was typical of organs
in his native Saxony and Thuringia. Other exterior influences from that time
and place include the two swags that bracket the center tower, and the broad
lower case that supports the full width of the impost and omits the spandrels
common to earlier styles. Apart from its simple springboard moldings, the
Goshen case is relatively flat and plain by comparison with its historical
counterparts. Its only bold three-dimensional element is the polygonal center
tower. The small pointed towers in Tannenberg’s design are here merely
implied by the V-shaped arrangement of foot lengths in the tenor fields. The
use of six auxiliary panels to raise the smaller pipe feet above the impost
moldings adds interest to the design. The considerable height of the lower case
was determined by the need for a passageway over the 2-foot concrete riser
behind the organ. This height gave space between the console and impost for the
eventual inclusion of a small Brustwerk with several stops for continuo
accompaniment. Cabinets for music storage are built into the back on both sides
of the lower case.

Another aspect of the design reminiscent of 18th-century
south German traditions is the position of the windchests in relation to the
action. The two windchests of the Hauptwerk are spaced apart from the center of
the case by the width of the keyboards. This leaves room for trackers of the
Oberwerk to reach their rollerboard without blocking access to the Hauptwerk
action and its pallets. It also provides optimum space for 8’ bass pipes
at the sides and leaves room for tuning the tenor pipes of the Hauptwerk with
only minimal obstruction by the Oberwerk rollerboard. The windchests for the
Pedal are located behind the case at the level of the impost, a placement that
Tannenberg could also have used.

Both the playing action and stop action are mechanical. The
manual keys are hinged at the tail and suspended from their trackers. There are
no thumper rails to hold the keys down, so they are free to overshoot slightly
when released, as is the case in traditional suspended actions. Trackers,
squares and rollers are all made of wood. There is no felt in the action. Keys
are guided by pins at the sides. Together these details combine to give a
feeling of buoyancy and liveliness reminiscent of antique instruments. The aim
is not so much to provide a light action as to arrive at one having the mass
and friction appropriate to the size and character of the organ. Such an action
may need occasional minor adjustment of key levels with changes in humidity,
but this is a small price to pay for the advantages gained over more sterile
modern alternatives. 

Wind is supplied by two single-fold wedge bellows (3’ x
6’) fed by a blower located in a small room below the organ. Natural
fluctuations of the wind pressure in response to the playing contribute to the
lively, singing quality of the organ’s sound. A wind stabilizer can be
engaged when unusually heavy demands on the wind system call for damping of
these fluctuations. The organ’s single tremulant is made in the old-fashioned
beater form. On seeing a tremulant puffing away in one of our organs, a
Japanese friend remarked that the organ was laughing! It is useful to think of
an organ’s wind as its breath and the bellows as lungs, for the
instrument’s appeal is closely tied to our perception of its lifelike
qualities. 

The tonal character of an organ is rarely revealed by its
stoplist. This is particularly true in an instrument of only twenty-four stops.
Once the builder accepts the constraints of a given style and the essential
registers have been chosen, there is usually little room or money left to
include stops that would make a modest design appear unique on paper.
Fortunately for the art, the musicality of the organ is not bound by its
stoplist; rather, it is determined by a host of other complex factors. These
can be partially defined in the technical data of pipe scaling and
construction, general design parameters, materials and the like, but in reality
much more rests on the elusive criteria of experience, skill and taste of the
builder. Taken together this means that each new organ, albeit small, presents
fresh opportunities for artistic expression. It is important that all the pipes
speak promptly, be they reeds or flues, except in the case of strings, which
gain charm from their halting speech. It is less important that the pipes
produce precisely the same vowel sounds from note to note, for here variety
adds refreshing character and interest to the organ.

At Goshen we chose to voice the 8’ Principal to be
somewhat brighter and richer in overtones than has been our wont. This was
achieved by giving the pipes lower cutups than was customary in German and
Dutch organs of the 17th century and before. The five distinctly different
8’ flue stops on the manuals deserve special mention. Although all
followed scaling patterns we have used frequently in the past, when voiced they
proved to be unusually satisfying, particularly in combination with each other.
Whenever the 16’ Bordun is used with them a magical new dimension is added
to the sound. If, for example, one draws the Bordun with the Viol da Gamba, the
effect is that of a quiet 16’ Principal. Used with the Spillpfeife the
Bordun reverts to its role as a flute. In an organ of this size it is crucial
that every stop work as well as possible with every other. Following south
German practice, both 8’ and 4’ flutes on the Hauptwerk are made in
the same form. This duplication of flutes within the same family was not the
custom in the north, where lower pitched flutes were usually stopped and those
above them progressively more open. The Oberwerk configuration at Goshen with
its two stopped 8’ registers and partially open 4’ Rohrflöte is
typical of the northern tradition. We look forward to the day that the 16’
Violonbass with its cello-like speech can be added to the Pedal.
style="mso-spacerun: yes"> 

The distinctive musical effect of the Goshen organ is
strongly colored by the use of the recently released Bach-Lehman temperament
described in the accompanying article. Because the completion of the organ in
February coincided with the publication in Early Music of Bradley
Lehman’s treatise on J. S. Bach’s temperament, we chose to tune the
organ according to his plan. Here was the ideal opportunity to try the
temperament on an organ built in Germanic style and at the same time to honor
Dr. Lehman as a distinguished Goshen alumnus for his work in this field. The
experiment has been a fascinating one. It has provided a place to hear
Bach’s organ music as we have not heard it before. We are honored to have
played a part in translating the dry mathematical numbers of this temperament
into the vibrant sound of the organ. 

With few exceptions the many parts of the organ were
constructed from raw materials in our Virginia workshop. Through the skills of
each craftsman the design moved from an idea to paper and then through raw wood
and metal into a large and impressive object. Note by note the tonal picture
has been filled in by voicing and tuning until in the end we experience a new
instrument with an identity all its own. We hope that it will give pleasure to
those who play and hear it far into the future.

--George Taylor

The organ project at Goshen College

“Dienlich, Ordentlich, Schicklich, Dauerlich”

In 1999 we were asked by the organ consultant for Goshen
College, Roseann Penner Kaufman, to make a proposal for the new Goshen College
Music Center. As with any new project, I went to Goshen full of excitement at
the promise of participating in what was to be a spectacular project. My
enthusiasm was short-lived when I saw the design for the recital hall. It was a
standard fan-shaped, sloped-floor, small college recital hall, with theatre
seats and carpet in the aisles. The space for the organ was planned in a niche
at the back of the stage. The design would have been fine for small chamber
recitals, but it was not a proper home for an organ. The prospects for the
organ looked bleak. We would not have felt productive or inspired. We always
say that the room is more than half the organ. I took a deep breath and told
the Goshen committee what I thought of the plan. The committee listened and
asked us to offer suggestions on how the recital hall might be designed to work
best with the musical programs envisioned for this space.

I returned to Staunton eager to develop a plan. One of the
first things I did was to research the Mennonite Quarterly Review for articles
describing historical Anabaptist worship spaces. I hoped that the essence of
these rooms would lead me to an aesthetic that would tie the new hall to the
old tradition, which would, in turn, also be good for music, especially the
organ. My research acquainted me with four German words used to express the
qualities of the historical spaces: dienlich, ordentlich, schicklich and
dauerlich--serviceable, orderly, fitting and lasting. I also found prints
of the interiors of some of these churches. Rectangular in shape with open
truss timber roof framing, clear glass windows, galleries on several sides,
rough stone floors, moveable chairs, unadorned, honest and powerful, these
spaces had all the qualities that I was looking for. They also had enduring
musical-acoustical qualities and so many are used today for concerts.

The simple sketch that I made went first to the Goshen organ
committee who, led by Doyle Preheim and Chris Thogersen, embraced the plan.
Then the concept went to Rick Talaske and his team of acousticians. They
transformed the plan into practical geometry and surface treatments to make the
space an acoustical success. Mathes Brierre Architects took the acoustical plan
and translated it into a visual design that evokes the warehouse or
brewery-turned-church concept of the early Dutch Mennonite spaces. Schmidt
Associates worked through the technical details with Casteel Construction to
conceive the simple pre-cast concrete panels and graceful curved steel arches
that make the hall appealing in its architecture, superior in acoustical
performance and straightforward and durable in construction. There was creative
and sensitive work done by a Goshen group concerned with decor and furnishings.
The result is successful beyond our expectations. The collaboration of all the
partners made the project exceed the ability of any one of us.

Once the hall was underway, we scheduled a meeting at St.
Thomas Fifth Avenue in New York with a group from Goshen and Calvin and Janet
High from Lancaster, Pennsylvania. We had a great day in New York showing
everyone our organ in the gallery of St. Thomas. The Highs’ enthusiasm
for the St. Thomas organ and the Goshen Music Center paved the way for their
generous gift that underwrote the cost of the organ.

We realized that the floor area of Rieth Hall was small in
relation to the height. We saw that if there could be the addition of one more
bay to the length there would be significant improvement in the proportions of
the space and at least 50 more seats could be added. Again, the Goshen design
group supported our suggestion. At a time in the project when the building
committee was attempting to control costs and squeeze performance out of every
dime, they found the funds for this most important late addition.
style="mso-spacerun: yes"> 

I predicted at the time we were creating the designs for
Rieth Hall, that the unique qualities of this space would have something to say
to the Goshen students about music and worship. This prediction has been
realized. First, there is genuine enthusiasm for a cappella singing in Rieth
Hall, encouraging this wonderful Mennonite tradition. Second, there has been a
spontaneous seizing of the space by the students for their own student-directed
Sunday worship. In this age of searching for the right path in worship and
liturgy, of debating the influence and appropriateness of mass media and
popular music for worship, we have built something at Goshen College that
reaches across the span of time to those Mennonite roots. Led by the seemingly
old-fashioned qualities of dienlich, ordentlich, schicklich and dauerlich, we
have made a  music space and organ
that inspire and excite us to make music and to celebrate and serve our God and
Creator.

Wood and the Goshen organ

The traditional pipe organ is a wooden machine. Early on in
our careers as organ builders we realized that getting control over our
materials in both an aesthetic and technical sense was essential to our success
as organ makers. Our first path was to make friends with our neighborhood
sawmillers. One of these was an octogenarian whose experience reached back to
horse logging and steam power. He taught us the value of long, slow, air-drying
of lumber. He also knew the old traditions of sawing, how to take the tension
out of a log, how to saw through the middle of the log and keep the boards in
order so that the cabinetmaker could match the grain. He remembered the methods
of quarter sawing that impart the most dimensional stability to the boards and
in oak bring out the beautiful fleck of the medullary rays. We have built our
own sawmill based on a portable band saw. For quarter sawing, we have built a
double-ended chain saw that can split logs up to 60 inches in diameter. The
half logs (or quarters in extremely large timber) are then aligned on our band
saw and sawn in a radial fashion into boards. This lumber is then air-dried for
a number of years. At the end, we put the wood in our dry kiln and gently warm
it up to stabilize the moisture content at 8% to 10%.

Oak is the traditional wood of Northern European organ
building so it was natural for us to choose white oak for the Goshen organ. We
have long admired the Dutch and German organs dating back to the 16th century.
The earliest organs show only the natural patina of age and no finish; the
concept of finishing wood as in varnishing or oiling came well into the 18th
century. We followed this earlier practice for the Goshen organ. The oak has
been hand-planed to a smooth polish, much smoother than can ordinarily be
produced with sanding. The hand-planed wood will resist dirt. We feel there are
also musical benefits from using wood in its natural state. The case and
carvings together with all the interior parts transmit sound energy and reflect
and focus the sound of the pipes. Also, the open pores and surface
imperfections of the natural wood have an effect on the sound reflection.

Another aspect of wood use in historic organs is how
efficiently the old builders utilized their wood. Before the age of machinery,
cutting, transporting and converting timber to sawn, dried lumber ready for use
was costly. The best wood was always used for the keyboards, playing action,
wind chests and pipes. The next selection went to the most visible parts of the
case, especially the front of the organ. The rest was used for carvings, heavy
structural members, walkways, bellows framework and back panels. Some of this
wood shows knots, cracks and other defects that might offend our modern sense
of perfection. However, in addition to demonstrating good wood utilization, the
varying density and differences in surface texture of these so-called defects
may indeed benefit the music. How we perceive the sound of an organ is a very
complex and subtle equation. This is one of the wonderful aspects of the real
pipe organ that differentiates it from the sterile sound of the electronic
substitute. We feel it is good stewardship to apply the hierarchy of selection
as practiced by the old masters. We try to use all the wood, through careful
selection, with thoughtful conservation of a vanishing resource.

--John Boody

Acoustic design of Rieth Recital Hall at Goshen College

In 1998, the design team of design architect Mathes Group
(now Mathes Brierre Architects), architect of record Schmidt Associates and
acoustician The Talaske Group (now Talaske) began preliminary work on a new
music education and performance building for Goshen College’s campus.
This project was the College’s greatest building investment to date and
they were determined to do things right . . . with a very modest budget. The
Recital Hall (now Rieth Recital Hall) was slated to house a new tracker organ
of exceptional quality. As acousticians, we offered some general planning
recommendations--not the least of which was a 50-foot ceiling
height--and recommended that the organ builder be hired as soon as
possible.

Enter John Boody of Taylor & Boody, organ builders from
Virginia. John energized the subsequent meetings with some profound advice that
proved to set the final direction for the space. He moved our thinking from a
“fixed” seating configuration to a flexible arrangement based on a
flat floor where seats can face either end of the room. This unique concept
facilitated the accommodation of a conventional “recital hall” or
assembly arrangement with musicians or presenters on a small stage. The cleverness
of the concept is the seats can be turned to face the opposite direction in the
room, offering a classic organ recital arrangement. Furthermore, John
recommended that the proportions of the room would be better served if
lengthened by adding another bay of structure. These fundamental planning ideas
changed the direction of the design in perpetuity.

We embraced these new directions yes">  and identified the many other room acoustics design features
that would support the client’s needs. The 50-foot ceiling height remained,
and we worked with the architects and construction manager to render the room
as a sound-reflective concrete enclosure, embellished with wood. The goal was
to maintain the warmth of sound created by the organ. Within the “theatre
planning” process, we guided and exploited naturally occurring
opportunities for introducing sound diffusing shaping to reflect low- and
mid-pitched sound in all directions--by introducing one side balcony and a
rear balcony, recesses from circulation paths and recesses created by
deeply-set windows. We recommended deliberate articulation of the walls to
diffuse mid- and high-pitched sound. Wood surfaces were detailed to minimize
absorption of low-pitched sound. Retractable velour curtains and banners were
recommended in abundance and specified by Bob Davis, theatre consultant.
Architecturally, curtain and banner pockets were created so the sound-absorbing
materials could be retracted completely on demand. These features make possible
a broad “swing” of the sound of the room from very reverberant for
choral and organ performance to articulate for assembly events or amplified
music performance. Fundamental to the acoustic design was the need for silence.
This was accomplished by structural discontinuities in the building (acoustic
isolation joints) and the proper placement and design of heating and air
conditioning systems.

Within their mission statement, Goshen College states:
“Musical expression is a human manifestation of the divine impulse and,
as such, serves as a window into the individual soul, a bridge between human
beings and a means of corporate religious experience.” In light of the
students adopting the Rieth Recital Hall for their weekly convocations and the
many other uses, we are pleased to say the happy story continues!

--Rick Talaske

Bach temperament

This organ is the first since the 18th century to use Johann
Sebastian Bach’s tuning, as notated by him in 1722 on the title page of
the Well-Tempered Clavier. This tuning method is a 2004 discovery by Bradley
Lehman. The article about this discovery is published in the February and May
2005 issues of Early Music (Oxford University Press), and further details are
at <www.larips.com&gt;.

The layout, dividing the Pythagorean comma, is:

F-C-G-D-A-E = 1/6 comma narrow 5ths;

E-B-F#-C# = pure 5ths;

C#-G#-D#-A# = 1/12 comma narrow 5ths;

A#-F = a residual wide 1/12 comma 5th.

In this tuning, every major scale and minor scale sounds
different from every other, due to the subtle differences of size among the
tones and semitones. This allows music to project a different mood or character
in each melodic and harmonic context, with a pleasing range of expressive
variety as it goes along. It builds drama into musical modulations.
style="mso-spacerun: yes"> 

The result sounds almost like equal temperament, and it similarly
allows all keys to be used without problem, but it has much more personality
and color. In scales and triads it sounds plain and gentle around C major (most
like regular 1/6 comma temperament), mellower and warmer in the flat keys such
as A-flat major (most like equal temperament), and especially bright and
exciting in the sharp keys around E major (like Pythagorean tuning, with pure
fifths). Everything is smoothly blended from these three competing systems,
emerging with an emphasis on melodic suavity.

The following chart shows the relative size of each major
third, resulting from each series of the intervening four fifths. This system
of analysis is from the 1770s, published in the theoretical work of G. A. Sorge
who was a former colleague of Bach’s. The intervals having higher numbers
sound spicier, more restless. In this measurement, a value of 11 would indicate
a major third that is one syntonic comma too sharp (a “Pythagorean major
third,” having been generated by four pure fifths).
style="mso-spacerun: yes"> 
A pure major third would be represented
here as 0.

Bb-D    6
style='mso-tab-count:1'>            
D-F#
    7
style='mso-tab-count:1'>            
F#-A#
8

Eb-G    7
style='mso-tab-count:1'>            
G-B
      5
style='mso-tab-count:1'>            
B-D#
   9

Ab-C    8
style='mso-tab-count:1'>            
C-E
       3
style='mso-tab-count:1'>            
E-G#
   10

Db-F     9
             F-A
       3
style='mso-tab-count:1'>            
A-C#
   9

Equal temperament, as opposed to the variety shown here, has
a constant size of 7 in all twelve of the major thirds.

In functional harmony, the Bach tuning sets up especially
interesting contrasts within minor-key music. The key of A minor has the
plainest tonic juxtaposed with the most restless dominant. F minor, a major
third away, has the opposite relationship: troubled tonic, calm dominant. And
C# minor has the average character between these behaviors, where the tonic and
dominant are both moderately energetic. 

In major-key music, the tonics and dominants have characters
similar to one another. The sizes of major thirds change by only 1, 2, or 3
units from each key to its neighbors, moving by the circle of fifths (through
typical subdominant/tonic/dominant progressions). Any change of Affekt is
therefore gradual and subtle, as if we never really leave the home key
altogether but it feels a little more or less tense as we go along.

In any music that modulates more quickly by bypassing such a
normal circle-of-fifths cycle, the contrasts are momentarily startling. That
is, the music’s dramatic harmonic gestures become immediately noticeable,
where the major thirds have changed size suddenly from one harmony to the next.
This comes up for example in the Fantasia in G Minor (BWV 542), Gelobet seist
du, Jesu Christ (BWV 722), and the fourth Duetto (BWV 805), and especially in
music by the Bach sons.

This system turns out to be an excellent tuning solution to
play all music, both before and after Bach’s. It is moderate enough for
complete enharmonic freedom, but also unequal enough to sound directional and
exciting in the tensions and resolutions of tonal music.

A recording will be ready for release this summer, including
music by Bach, Fischer, Brahms, et al.

--Bradley Lehman

A brief history of the organ in the Mennonite Church

Some people might find it unusual to find such a remarkable
organ in a Mennonite college. Aren’t the Mennonites those folks with the
buggies and suspenders? It is true that some Mennonite congregations still take
literally founder Menno Simons’ caution against the organ as a
“worldly” invention, but most, especially in the last fifty years,
have embraced it as a vital contributor to the musical and worship life of the
community. 

The Mennonite Church has its beginnings in the 16th-century
Protestant Reformation. Because of persecution, most of the early worship
services were held secretly, in homes or out-of-the-way places. Mennonites also
believed that the true church existed in small, simple gatherings; therefore,
it was uncommon for early Mennonites to even set aside a separate building for
worship. 

Two hundred years after the beginning of the movement,
churches in Germany and the Netherlands had grown to the point of meeting in
dedicated buildings, and by the 1760s several in urban areas had installed pipe
organs. It was another two hundred years, however, before organs became common
in the Mennonite conference that supported Goshen College. Even now, the organ
is not necessarily assumed to support congregational singing, but contributes
other service music. Organ study is now offered at all of the Mennonite Church
USA-affiliated colleges, and the new Taylor & Boody organ at Goshen will
certainly have a profound impact on the future of worship and organ study
throughout the denomination.

--Roseann Penner Kaufman

Roseann Penner Kaufman, DMA, is adjunct instructor in organ
at Bethel College, N. Newton, Kansas, a four-year liberal arts college
affiliated with the Mennonite Church USA. She also serves as director of music
for Rainbow Mennonite Church in Kansas City, Kansas. Dr. Kaufman served as the
consultant to Goshen College for their organ project.

Specifications for Opus 41

Hauptwerk

16' Bordun (C-D# wood, rest metal*)

8' Principal (77% tin)

8' Spillpfeife

8' Viol da Gamba (77% tin)

4' Octave

4' Spitzflöte

3' Quinte

3' Nasat

2' Superoctave

IV-V Mixtur

8' Trompet

Oberwerk

8' Gedackt (99% lead)

8' Quintadena

4' Principal (77% tin)

4' Rohrflöte

2' Waldflöte

II Sesquialtera

IV Scharff

8' Dulcian

Pedal

16' Subbass (wood)

(16' Violonbass) space prepared

8' Octave

4' Octave

16' Posaune (C-B wood, rest 99% lead)

8' Trompet (99% lead)

Couplers

Oberwerk / Hauptwerk

Hauptwerk / Pedal

Oberwerk / Pedal

Tremulant to entire organ

Mechanical key and stop action

Compass: manual 56 notes C-g''', pedal 30 notes C-f'

Lehman-Bach temperament

Interior metal pipes of hammered alloys

*All unmarked metal alloys of 28% tin, 72% lead

Case of solid white oak

Windchests of solid oak, pine & poplar

Number of pipes: 1604

Wind pressure: 75mm

Wind stabilizer

The builders

George K. Taylor

John H. Boody

Bruce Shull

Emerson Willard

Christopher A. Bono

Kelley Blanton

Chris A. Peterson

Sarah Grove-Humphries

Robbie Lawson

Jeffrey M. Peterson

Larry J. Damico

Holly Regi

Thomas M. Karaffa

Bob Harris

Katie Masincup

Ryan M. Albashian

Kristin E. Boo

The Historical Italian Organ

Tradition and Development

by Francesco Ruffatti
Default

A concert by Luigi Ferdinando Tagliavini and Gustav Leonhardt at the Basilica of San Petronio in Bologna, held on October 27, 2000, provided the inspiration for  writing an article on the historical Italian organ, its tradition and development. My goal is to give a panoramic view of the subject, and anyone knows that when looking at a panoramic view much of the detail is lost. Still, such an attempt is worth carrying out because some general guidelines can in any case be drawn. To do so, it is necessary to go back a number of centuries and try to understand the original role of the organ in the musical world of Italian churches.

 

The Basilica of San Petronio is no ordinary place from the standpoint of organbuilding history. It enjoys the presence of two unique instruments: the oldest Italian organ in existence, built by Lorenzo da Prato between 1471 and 1475, roughly 20 years prior to the discovery of America by Columbus,1 and a later organ, built by Baldassarre Malamini in 1596. The instruments are located face to face in the area traditionally reserved for the choristers, behind the high altar.

The program notes for the Tagliavini-Leonhardt concert, written by Marc Vanscheevwijck, well explain the use for which organs of medieval and renaissance times were intended:

Alternatim performance practice, i.e., the performance of liturgical pieces alternating contrasting musical forces in the various versets of the sacred texts, originates in the old antiphonal singing of psalms of the first centuries A.D. In responsorial music a soloist or a small group of singers alternated with the larger choir. Sometimes they alternated plainchant with polyphonic settings of the text. Probably as early as the organ began to be used in church, the organist already improvised "versets," alternating with the choir singing the counter versets in Gregorian chant. Obviously, the schola never repeated the texts of the versets played by the organist, who improvised (and later composed) on the relative Gregorian melodies. The earliest source of such a practice is the Faenza Codex, compiled c.1420. During the following century this alternatim practice spread throughout Italy. Many alternatim settings, particularly of the mass proper, have been preserved, some of the most famous of which were composed by Girolamo Cavazzoni, Claudio Merulo, Andrea Gabrieli, and (in the 17th century) the Fiori Musicali of Girolamo Frescobaldi.2

 

Two aspects immediately come to mind:

1. The organ location, which for effective responsorial use had to be near the choir and not necessarily in a favorable position for the congregation,

2. A tonal structure suitable for dialogue with a small group of singers.

There was no need for a sound big enough to accompany the choir, simply because the organ was intended as a soloist. And accompanying the congregation was certainly not in the agenda, since people did not sing during liturgy in Italian Catholic churches until very recently.3

What effect did all of this have on the sound? Since power was not the issue, early Italian organbuilders developed their talents in other areas, and tonal quality became the priority. They created relatively small instruments, mostly with only one manual, with gentle, beautifully voiced stops. Wind pressures were in most cases quite low, down to 42-45 mm. at the water column, and the voicing techniques as well as the tonal design in general reflected such an approach.

Listening to music by Antegnati (also a famous Italian organbuilder), Segni, Veggio, Gabrieli and others performed on the beautiful organs of San Petronio gave me and the entire audience (a few hundred people all gathered in the large space behind the high altar, to be able to best hear the organs) a good perspective of the musical experience which was originally expected from such instruments.

It is my belief that the original DNA of ancient Italian pipe organs, as defined by their original use in the liturgy, played a decisive role in the subsequent evolution of the instruments. This was due to a strong sense of tradition among the vast majority of builders and to their reluctance to introduce changes to a practice which was considered successful. Examples to the contrary do exist, but any effort of generalizing, or extracting general rules from a complex reality, always ends up sacrificing notable exceptions.

In post-Renaissance times, organ use became widespread. All Italian churches had at least one organ and often one or two Positivo4  instruments in addition to the main organ. And a very significant change took place: in addition to being used as a solo instrument for improvisations and for the performance of written music, the organ also became an accompanimental instrument for the choir. Its location within the building also changed in most cases, taking into greater consideration the congregation as the beneficiary of musical performances: the preferred location for new instruments became a balcony facing the nave, which is still considered by many to be the ideal location for the best possible diffusion of sound within a building. Naturally, broader tonal resources had to be made available in order to accommodate this new function, but this did not cause a significant change in the original voicing practices. In other words, more stops were introduced and a Pedal division was added (normally consisting of one or two stops), but the basic tonal structure remained the same and no major changes took place in the sound: still low pressures and gentle voicing. After all, organs still did not need to be big or powerful, because they were not intended to support an entire congregation, just a choir.5

A further, major evolution took place as a result of the greater demands by the repertoire of the Romantic period. A great number of new stops were introduced: reeds of various types, more flutes, strings, even percussion: drums, cymbals, bells and the like. The organs built by the Serassi family of Bergamo towards the end of the eighteenth century and during the following century are a good example of the romantic Italian organ. The occupation of Bergamo by the troops of Napoleon (1796-1813) and subsequently by the Austrians (1814-1859) influenced organbuilding practices by introducing new musical models and, as a consequence, by contributing to the development of new devices and new sounds that would improve the performance of the music inspired by the teaching of Simon Mayr (1763-1845), by his pupil Gaetano Donizetti (1797-1848) and by Gioacchino Rossini.6 The famous composer Felice Moretti (also known as Father Davide da Bergamo), a Franciscan monk and a family friend of the Serassi, composed music that was deeply influenced by opera. Also, Giuseppe II Serassi, the most innovative member of the family, introduced new devices aimed at facilitating the dynamic control of sound: the third hand, or mechanical super coupler, the fourth hand, or sub coupler, the expression shades, pedals for pre-set combinations of stops, an easier system for the coupling of the manuals (by means of a pedal and no longer by the sliding of the upper manual into position), settable combinations of stops, and the Tiratutti or Tutti for the Ripieno ranks.7

In spite of all of this, the ancient core of the instrument and the basic tonal concept behind it remained virtually unchanged for a good part of the nineteenth century. Low wind pressures were still the rule, as well as unforced voicing, fairly open pipe toes, and few nicks at the languids. As a consequence,   there was a broad harmonic development in the sound, allowing a very effective use of each stop in combination with others and forming an ensemble of rare cohesion and beauty. Pressures of sometimes less than 50 mm. at the water column naturally presented a real challenge, particularly for the voicing of reed stops, but this had the effect of encouraging builders to find original design and voicing methods to overcome the difficulties.8

At this point, it is necessary to define the tonal core of the organ which I have indicated as an element of continuity in Italian organbuilding throughout the centuries. Its main component is the Ripieno. The term does not translate to Mixture, but rather it defines a series of individual Principal scaled ranks of pipes at various pitches, creating a system of sounds at harmonic intervals, normally beginning with 8' pitch as the foundation of the manual.

The composition of a typical Ripieno with its traditional nomenclature follows:

Principale (I) 8'

Ottava (VIII) 4'

Decimaquinta (XV) 2'

Decimanona (XIX) 11/3'

Vigesima seconda (XXII) 1'

Vigesima sesta (XXVI) 2/3'

Vigesima nona (XXIX) 1/2'

Trigesima terza (XXXIII) 1/3'

Trigesima sesta (XXXVI) 1/4'

And occasionally:

Quadragesima (XL) 1/6'

Quadragesima Terza (XLIII) 1/8'

The highest pitch in the entire Ripieno is in most cases the note C at 1/8'. Beyond this limit a ritornello or break begins with pipes double the length, or one full octave lower in pitch.9

Table 1 is intended to give a clear and comprehensive idea of the tonal composition of the Ripieno. The method I am utilizing is unconventional and it consists of identifying each pipe by a number corresponding to its place in an ideal succession of notes starting with number 1 as low C of the 8' Principal. Low C at 4' will consequently be numbered as 13, low C at 2' will be numbered as 25 and so on. The highest pitch pipe in the Ripieno will be number 73, corresponding to the pitch limit of 1/8'. Once a rank reaches note number 73 it will break back and start a ritornello with note C#62 (or one full octave lower). To simplify matters, I am showing the first octave as complete (12 notes). The most common arrangement in Italian historical organs calls for a short first octave (8 notes, with C#, D#, F# and G# missing). Notes are identified by octave number, according to the Italian system, by which C1 corresponds to note C of the first octave, F3 to note F of the third octave, and so on. The chosen compass for our example is of 49 keys, C1 to C5. This system, by numbers rather than by footage, is intended to provide a more immediate idea of the repetition of equal size pipes throughout the compass for the entire Ripieno. Equal number means equal size pipe.

The conventional method is shown in Table 2. The Ripieno here is comparable, in pure terms of number of pipes, to a Principal chorus with 8', 4' and 2' stops plus a six-rank mixture. But by looking at Table 2 one can immediately appreciate the vast difference from such an arrangement. At note C#2 the first doubling or double pitch appears: pipes from the 1/2' rank (XXIX) and 1/4' rank (XXXVI) become of identical size. Consequently, between notes C#2 and F2 the tonal effect is not that of a six-rank mixture but rather of a five-rank mixture with one of the ranks doubled. This aspect becomes more and more prominent as we move up the keyboard, to the point that at note C#4 (key number 38) with all ranks from Decimaquinta (2') up drawn, only two pitches can be heard: 2', repeated 4 times, and 11/3', repeated three times. As one can easily appreciate, such tonal structure cannot be compared with that of a Mixture, or Fourniture or any other multiple-rank stop designed as a single entity. The Ripieno is simply different. It is conceived as a sum of individual ranks at different pitches, each separately usable in combinations with any other rank and all usable at once as a pleno.10

Obviously, this feature provides a great deal of flexibility in the tonal palette. From an organbuilder"s practical standpoint, it has two effects:

1. It forces the voicer to be extremely scrupulous as to the tonal balance, regulation and speech adjustment of each pipe even in the highest pitched ranks, since each can be separately used;

2. It makes tuning more difficult, due to the drawing effect on the equal pitched pipes when they play together. Only a tuner who knows how to deal with such a problem can obtain a stable tuning of the Ripieno.11

Tuning with double pitches was nothing new to ancient builders. In fact, pre-Renaissance and Renaissance organs, in Italy as well as in other European countries, often had double or even triple notes of equal length in the treble of the Principal, the Octave and sometimes the Fifteenth, to enhance the singing qualities of the instrument in the treble. This practice strangely survived, in some areas of Italy, all the way to the beginning of the 19th century. This proves that the difficulties connected with the tuning of multiple equal-pitched pipes never bothered Italian organbuilders too much.12

Other traditional stops forming the original core of the historical Italian organ include the following:

Flauto in Ottava (4'), normally tapered or cylindrical, sometimes stopped

Flauto in Decimaquinta (2') in the earlier instruments

Flauto in Duodecima (22/3')

The Terzino, or Tierce flute (13/5') was later added and, in the nineteenth century, the Flauto Traverso or Fluta (8', normally in the treble only).

Early strings appeared in the eighteenth century, at 4' in the bass and occasionally over the entire compass, but such stops were vastly different from what we think of as a string today. They had no ears, no beards, no nicks at the languids. These characteristics, combined with a very narrow scale, contributed to produce a sound with a very prominent transient at the attach and a cutting sustained tone, strongly imitative of early string instruments.

The Voce Umana or Fiffaro, a Principal-scaled stop at 8' pitch (treble only) was also used in the Renaissance and became increasingly more common in the Baroque and later periods. Its pipes were normally tuned sharp against the 8' Principal, except in the Venetian tradition and among a few builders in the south of Italy, where flat tuning was preferred.

The above description, as I have said earlier, represents a simplification of a much more complicated subject, and many examples exist that do not follow the rule.13 Also, all of those who are familiar with ancient Italian organs will agree that the tonal experience that comes from a Callido or a Nacchini organ is vastly different from that of an Agati or a Catarinozzi. They were expressions of very different artistic environments and the builders were very faithful to their own local traditions.

What happened in nineteenth-century Italian organbuilding is worth investigating a bit more closely. Early signs of rejection of the Italian romantic organ appeared. In 1824 the Cardinal Vicar of Rome promulgated an edict stating: "Organists may not play on the organ music written for theater, or with profane character, but only music that can encourage meditation and devotion . . . "14 Still, many of the major builders in the north, as well as many in other parts of the country, continued in their tradition of building instruments without changing their style.15 But at some point, foreign influence became a strong factor16 and the "new inventions," the Barker lever first and then pneumatic and electric action, came into the picture.17 Pneumatic action in particular and the new sounds, such as the "modern strings" and harmonic stops demanded higher wind pressures, and the organ sound became stronger and aggressive. But, as we all know, pneumatic action represented only a relatively short transition period in organbuilding history, and a further evolution of the instrument was soon marked in the following century by a perfected electric action and by the rediscovery, in the mid 1960s, of tracker action. This movement was immediately promoted by some of the major Italian builders18 and it became stronger and stronger over the years. The neoclassical instrument was created, based on mechanical action and on the re-discovery of the traditional sounds and voicing techniques. But, as it is often the case, the intent was not that of copying the past but rather of preserving the best of tradition within a new context which was calling for a new use of the organ: the support of congregational singing.

One may get the impression that it is impossible to extract a general trend from this entire process of evolution. Still, I believe that one common denominator can be found: the unforced, pleasing singing quality that has survived unchanged for over five centuries, and which effectively represents, in musical form, the character of the Italian language.

 

Notes

                  1.              The instrument consists of one manual and short pedalboard, as follows. Manual: F1-A4 without F#1, G#1; divided keys G#1/Ab1, G#2/Ab2, G#3/Ab3; Pedal: F1-D2 directly connected to the corresponding manual keys. The stoplist follows:

Principale contrabasso (24', façade) - doubled from C#3

Principale (12', rear façade - doubled from C#3, triple from Bb3)

Flauto in VIII

Flauto in XII

Ottava (doubled from Bb3)

XII

XV

XIX

XXII

XXVI-XXIX

Spring windchest, A = 470 Hz, meantone temperament; restoration by Tamburini, 1974-1982. The above information is the courtesy of Liuwe Tamminga, recitalist and organist at the Basilica of San Petronio.

                  2.              Concerning earlier use of the organ in western world churches, see Peter Williams (Duke University, Durham, NC) in his essay "The origin of the Christian organ with some particular reference to Italy," Acts of the International Symposium on "I Serassi--L"arte organaria fra sette e ottocento," Ed. Carrara, Bergamo, 1999, p. 12. Referring to the early Middle Ages, he writes: "I don"t know any evidence that organs were brought into church in order to accompany singing--whether it was the celebrant singing at mass, the lay people responding with their own acclamations, or the monks chanting their daily office in private or in public. All that one can be certain about is that organs were there to provide sound, and whatever later music historians may have assumed, it is seldom if ever clear what kind of sound they made, or for what purpose and at what point they made it. Only from the thirteenth century onwards the picture is clear . . ."

                  3.              While the practice of congregational singing at celebrations in Italian churches may have had its first examples at the end of the nineteenth century, it was during the Second Vatican Council that this practice was actually encouraged.

                  4.              A Positivo can be described as a smaller size "cabinet" organ, self-contained, whose casework is normally divided in two sections: the lower case, containing the bellows (normally two multi-fold hinged bellows activated by levers), and the upper case, which sits on top and which holds the keyboard, the windchest and pipes. It was almost invariably built without independent pedal stops,  and its pedalboard, when present, consisted normally of one short octave, whose keys were connected to the corresponding keys of the first octave at the manual by means of strings or wires. Although easily movable (sometimes large handles on the sides of the two sections of the case indicate this possibility), it is different from a Portativo, an even smaller instrument whose primary function was that of providing music during outdoor processions.

                  5.              Larger instruments are not unknown to historical Italian organbuilding. I will mention two examples of rare complexity:

a.) The instrument at the church of San Nicolo L"Arena in Catania, by Donato del Piano (1698-1785), with a total of five keyboards, divided between three consoles attached to the case (1 manual - 3 manuals - 1 manual) with the larger console in the center and one pedalboard for the center console, plus a separate small automatic pipe instrument activated by a rotating drum. This enormous, beautiful instrument, now in a poor state of disrepair (among other things, the pipes have all been removed and stored), includes pipework of extremely unusual shape.

b.) The great organ at the Church of the Cavalieri di S. Stefano in Pisa, built between 1733 and 1738 by Azzolino Bernardino della Ciaia (1671-1755) with the help of other organbuilders from different parts of Italy, with four manuals plus a fifth manual activating a harpsichord. This organ was later converted into a pneumatic instrument and subsequently electrified. Only a portion of the original pipework survives.

                  6.              See Luigi Ferdinando Tagliavini, "Le risorse dell"organo Serassiano e il loro sfruttamento nella prassi organistica dell"epoca," in Acts of the International Symposium on "I Serassi--L"arte organaria fra sette e ottocento", Ed. Carrara, Bergamo, 1999, pp. 80-84.

                  7.              See Giosue Berbenni, Acts of the International Symposium on "I Serassi--L"arte organaria fra sette e ottocento," Ed. Carrara, Bergamo, 1999, pp. 22-24.

                  8.              The lower the wind pressure, the thinner the tongues must be to obtain promptness of speech. But thin tongues also produce undesirable side effects, notably:  a) A thinner timbre in general, with greater development of overtones and less fundamental; b) Uncontrollable sound at the bass register, where any reed naturally tends to become louder; c) Very weak trebles. To overcome these problems, a series of interesting methods were developed. I will mention a few:

a.) Wide and deep shallots to increase the volume of air excited by the tongue, with the effect of increasing the prominence of the fundamental in the tone;

b.) Double or even triple tongues at the low register, to control volume, timbre and stability;

c.) Variable tongue thickness at the treble, with the filing of the tip to obtain promptness while retaining a good volume of sound.

For a more complete description of voicing methods on low pressure reeds, with specific reference to the reeds of Serassi organs, see Francesco Ruffatti in "I registri ad ancia negli organi Serassi," Acts of the International Symposium on "I Serassi--L"arte organaria fra sette e ottocento," Ed. Carrara, Bergamo, 1999 pp. 144-150.

                  9.              When the lowest pitched stop on the manual is the Principal 16' the nomenclature remains the same, although all stops start one octave lower in pitch. The stoplist becomes:

Principale (16')

Ottava (8')

Decimaquinta (4')

Decimanona (22/3')

and so on. In essence, the organ is still seen as based on the 8' Principal, with the extension of a counter octave towards the bass (see my article on Gaetano Callido, December, 1999 issue of The Diapason, p. 17, Note 8).

                  10.           Luigi Ferdinando Tagliavini in his article "Il ripieno," L"organo, Year 1, No. 2, July-December, 1960, Ed. Patron, Bologna, points out the difference between the Italian Ripieno and the northern European mixtures as follows:

"a) The classical Italian ripieno is divided into its constitutive elements, corresponding to separate stops, while the foreign mixtures, starting from a certain pitch (from 4', from 22/3', from 2', from 11/3' etc.) are condensed into one stop;

b) Both in the ripieno and in the northern mixtures a gradual "compression" towards the treble takes place, a compression which is more limited in the German and northern European organ, greater in the Italian organ. In fact a ripieno will have a "compressed" extension in the treble, reduced from 8' to 2', while in the Mixtur-Scharf scheme the treble is extended between 8' and 1';

c) The "masking" of the jumps produced by the breaks is done differently in Italy from abroad; in Italy, by the division of breaks into two different points, one for the octave stops and one for the quint stops; abroad by the partial or complete substitution of the break in quint and fourth with the one in octave.

The northern European mixtures, through a particular interpretation of the break and without any fear of going beyond the pitch limits in the bass and the treble as imposed by the Italian ripieno, tend to make the tonal "density" more uniform, by reducing the difference between the tonal richness of the bass and the treble. Part of such uniformity is sacrificed by the Italian organbuilder in favor of tonal beauty. This is why the use of the Italian ripieno is mostly chordal and for toccatas, while the northern European organum plenum, especially the German, can also perform a polyphonic role."

In c) Tagliavini refers to alternation of quint and unison breaks within the same rank in all ranks of the mixture.

The pitch limit of northern European mixtures and related stops is often C at 1/16', close to the limit of human hearing, one full octave higher than the Ripieno and this factor alone determines a dramatic difference in the sound from the Ripieno.

                  11.           Drawing is an acoustical phenomena by which the sound of a pipe is drawn or pulled into tune by the sound of a second pipe which is playing an interval close to being pure or in tune. This effect is stronger between unison pipes; when tuning the second pipe to the first, its sound will slide into tune as soon as its frequency approaches that of the first pipe, but before it actually reaches the same value, thus determining an apparent tuning condition. Adding a third pipe and trying to tune it to the two previous sounds becomes impossible if the first two pipes are in a status of apparent unison, because each of the two sounds will react to the third pipe differently, according to their real frequency value. The difficulties increase exponentially from note C#4 up in the example shown, where two groups of 4 and 3 equal size pipes respectively play at once. The procedure to tune the Ripieno is consequently different and definitely more complicated than that of a regular mixture stop, as it must take into account the drawing of equal length pipes.

                  12.           I am here mentioning two organs, built in Tuscany by the Paoli family of Campi Bisenzio at the beginning of the 19th century, both restored by Fratelli Ruffatti in recent years:

a.) the organ in the Church of S. Francesco in Pontassieve, near Florence, built by Giacobbe Paoli, which includes doublings at the Principale starting with note Bb3, at the Ottava from note F3 and at the Decimaquinta also from note F3;

b.) the organ built by Michelangelo Paoli in the Basilica of S. Maria, Impruneta - Firenze, utilizing the pipes of a previous instrument by Bernardo d"Argenta, 1535, which has doublings at the Principale starting from note F#3, at the Ottava from note B3 and at the Decimaquinta from C4. Having re-built the windchest entirely, the builder could have easily eliminated the doublings had he not believed in the validity of such tonal approach.

                  13.           As an example, Sicilian organs in the 18th century were often built with multiple Ripieno ranks activated by a single stop control.

                  14.           See "La riforma dell"Organo Italiano" by Baggiani, Picchi, Tarrini, Ed. Pacini, Ospedaletto (Pisa), 1990, pp. 9-10.

                  15.           The largest instrument built by the Serassi family, the "Organum maximum" with three keyboards and over three thousand pipes, was built in the romantic style as late as in 1882. This instrument was restored by Fratelli Ruffatti between 1983 and 1985. It includes many of the effects which were rejected by liturgists, such as the drum, a bell and other percussion.

                  16.           Ferdinando Casamorata (1807-1881), musician and music scholar, introduced the work of Cavaillé-Coll to the Italian musical scene by making public the work of J. A. De La Fage "Orgue de l"Église Royale de Saint Dénis, construit par MM Cavaillé-Coll père et fils, Facteur d"orgues du Roi." Rapport. II edition, Paris, 1846. See "La riforma dell"Organo Italiano" by Baggiani, Picchi, Tarrini, Ed. Pacini, Ospedaletto (Pisa), 1990, p. 12. He gave explanations and favorable comments on some of the most remarkable characteristics of the instrument, notably the variety of wind pressures, the Barker lever, the "strength" of the upper registers, especially the reed stops, etc., and presenting them as valuable innovations worth imitating.

                  17.           An important role in this process was played by George William Trice (1848-1920), a British merchant who became an organbuilder and established a factory in Italy. He built the first electric action organ in 1888 for the Church of S. Andrea, Genoa. Other notable instruments followed, among which the three-manual instrument for the Church of the Immaculate Conception in Genoa, inaugurated in 1890 with concerts by Alexander Guilmant and Filippo Capocci.


18.               

Tamburini and Ruffatti were the first major Italian companies, in the early 1960s, to resume building mechanical action instruments.

 

Francesco Ruffatti has been a partner since 1968 of Fratelli Ruffatti, builders and restorers of pipe organs, in Padova, Italy. Besides being the tonal director of the firm, he is actively involved in the research on historical Italian organs and the supervision of the many historical restorations performed by the firm.

How BACH encoded his name into <i>Die Kunst der Fuge</i><span style='font-style:normal'> together with his tuning</span>

by Herbert Anton Kellner
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I read with very great interest and pleasure the recent contribution by Jan Overduin to The Diapason1, "Bach and Die Kunst der Fuge." Therein, the author presented about two dozen typical examples, illustrating how the composer has interwoven the musical texture of the oeuvre with the notes of his name b, a, c, h, within the various counterpoints. (In English nomenclature, the German b is designated b-flat.) By this procedure BACH has inscribed--so to speak--in many places his signature to his compositions. Beyond this most simple form, a variety of permutations of these four basic letters can also be found, or else, transpositions to other pitches, as shown by R. Kreft,2 a comprehensive special study printed in multicolor.

For the present article, three examples from Prof. Overduin's article will be extracted and discussed. Beyond the occurrence of the name BACH in these particular musical passages, possible simultaneous allusions by the composer to his mathematical system of unequal well-tempered tuning3 will be identified. This musical temperament--due to its intrinsic mathematical nature--is necessarily based on a certain set of numbers. The rationale for the present approach to study Die Kunst der Fuge is the fact that Bach has frequently structured the form of his compositions via numbers of a set belonging to the  wohltemperirt system. From this observation originated my "Vienna manifesto" of the Bach-year 1985: to analyze Bach's works with particular attention to the aspect of numbers pertaining to well-tempering.4 Utilizing this artifice, Bach attains an elaborate unity between features of the musical form and structuring in the widest sense and the harmony of tuning--initially and nominally the harpsichord. The most specific composition for this system was, of course, Das Wohltemperirte Clavier. A harpsichord can be well-tempered in not more than 19 elementary tuning-steps.5 This is the number for the closure of the circle, and the 19 intervals are 12 fifths followed by 7 octaves in the opposite direction.

In view of the essential occurrence of the name b, a, c, h for carrying out this study, the number alphabet and its gematrial correspondences needs first of all to be introduced. Thus, the letters are numbered along the Latin alphabet from A=1, B=2, C=3,  . . . I=9, J=9 [sic],  . . . K=10,  . . . U=20, V=20 [sic],  . . . X=22, Y=23, Z=24. Expressed via that numbering, B, A, C, H will appear as 2, 1, 3, 8. The adding-procedure as prescribed by the gematria, 2+1+3+8, yields the correspondence BACH=14. Likewise, J.S. BACH will be 41, the crab or inversion of the number 14.

Now the well-tempered system will be concisely laid out, putting special emphasis on the way it will be ultimately reflected here in Die Kunst der Fuge. This temperament comprises 7 perfect fifths and 5 well-tempered ones. It derives from the central key of tonality, C-major.6 In its triad C-E-G, the enlarged third beats at the same rate as the reduced fifth--an ideal mutual adaptation. To complete the description, four well-tempered fifths ascend from c and reach the second octave of the initial third e closing this chain of fifths c-g-d-a-e. From c downwards extends a chain of six perfect fifths, reaching g-flat (f-sharp). Of course, octave-transpositions must be applied in practical harpsichord tuning wherever necessary. The last tempered fifth of the system results as B-f-sharp, closing the circle. From the third e upwards ascends the seventh and last perfect fifth e-b.

The unique and distinguishing feature of wohltemperirt is its musico-theological foundation; no other tuning has anything similar to offer. Due to the beat-rates in the triad at the perfection of the unitas,7 the system is founded upon a tri-unitarian basis. The nucleus of baroque thoroughbass is the triad, itself a symbol of the Holy Trinity. Just hearing a triad, its three components merge suavely and smoothly into an agreeable, pleasant unity.8 Furthermore, the beat ratio of 1:1 of the constituent intervals can be considered as a profound symbol of the monotheistic principle--it is here where Werckmeister's ideas on the perfection of the baroque unitas are rooted.

Returning now from theological spiritualities and mathematical ratios to the music itself, by what means could Bach reflect in a composition the numbered alphabet and the gematria? A few such examples will follow now. As concerns the numbered alphabet, for the onset of its table A=1, one may refer to the well known A-major fugue of The Well-Tempered Clavier I. Its theme starts with an isolated note a, followed by three 8th-rests. Such an incipit is highly unusual, if not bizarre, and correlating with the table's A=1 appears natural and not far fetched. For the correspondence BACH=14, the C-major fugue's theme--as well as that of B-major--starts with 14 keystrokes.9 Within Die Kunst der Fuge itself, following the first four pieces, already the theme of contrapunctus 5 (and others) count 14 keystrokes. For the gematrial correspondence J. S. BACH=41, not later than the initial two keystrokes d, a, of Die Kunst der Fuge--set in d-minor--show 41 if juxtaposed.

Now it will be indicated how musical structures can convey hints or allusions to the well-tempered system. It is based upon the ratio of the unitas between the beats of the tempered third and fifth, 3 and 5 in thoroughbass. Therefore, immediately the number 135--in juxtaposition--may be used, for instance, within the bar numbered by 135. Other possibilities may be derived from the two sorts of fifths, 5 well-tempered, 7 perfect, such as in juxtaposition 57, 75 (75 could be made up via the tri-unity as 31+13+3110), or even 577. Finally, in terms of musical notation, 5 relates  to e, 7 to g, and 3 to c. As to the number 19 and concomitant abstract structuring, looking now as an example at the B-major prelude of WTC I, it counts 19 bars, starts at bar 1913 and ends at bar 1931.11

The first extract from Prof. Overduin's article is contrapunctus 4 (BWV 1080, 4), measures 135 to 138, page 15 in Davitt Moroney's edition from G. Henle.12 Starting from bar 135 (unitas-third-fifth) the tenor sounds BACH, rhythmically comparable to a sigh. The fugue terminates at 138, which incidentally corresponds to ACH, the final letters of the composer's name; in German a sighing exclamation. Perhaps the terminating pedal on d (D=4) through the last four bars may be related to the four letters of BACH. (See Example 1.)

The second example, page 46 in the Moroney/Henle edition (BWV 1080, 11), concerns contrapunctus 11, bars 90 and 91. (See Example 2.) As Prof. Overduin points out, the alto introduces by theme three the notes B, A, C, H, but he mentions that Tovey rejected this as an allusion to BACH because in fact, it is B-A-C-C-C-H sounding here. However, Tovey could at his time not be aware of Bach's tri-unitarian temperament and thus, necessarily failed to understand the significance of A,C,C,C: 1,3,3,3 in numbers. As much as within B-AC-H, 2-13-8, the number 28, secundus numerus perfectus is centered upon 13, unitas-trinitas, the present extended theme 2-1333-8 includes three times the number 3. The frame still remains B and H. An essential factorization holds, 1333=31*43: the prime numbers 31, trinitas-unitas and 43 = CREDO (3+17+5+4+14)--a tri-unitarian Credo! Starting with the second half of this bar and counting from the bass fundament upwards, presents the notes e, a, c, thus 513, nothing else than a permutation of 135. This is interpreted as fifth 5, unitas and third 3 in thoroughbass. The crucial bar in this example is 91--the crab or inversion of 19--by which number of elementary steps the circle of fifths will close. Working backward in this bar to the second quaver shows a, a, c, thus 113: a numerical triptych of unitas and trinitas. This measure 91 not only sounds BACH in the alto, but its onset reads d, g, b, converted to numbers 4,7,2.

As concerns 472, Bach was certainly intimately familiar with the notion of permutations, thinking for example, of his choral fugues or certain three-part inventions. Thus, just from a cyclical permutation of 472 results the number 247 (=13*19). According to the baroque gematria, 247=MUSICALISCHE TEMPERATUR which is the title of Werckmeister's classical treatise, 1691. Furthermore, 247=112+135 holds additively, but the implications of such observations cannot be detailed here and these results were published elsewhere already some time ago.13

The third example still deals with contrapunctus 11, bars 144 to 145, page 48 in the Moroney/Henle edition. (See Example 3.) There the alto and treble sound BA-CH and the bass and tenor in the second quaver of 144 present G, E, converting to 7 and 5, the numbers of perfect and well-tempered fifths. The bass, in fact, now sounds G,G,G,E, in numbers 7775. It may also be mentioned that contrapunctus 11 starts in a Trinitarian fashion by three bars identically structured, with eighth-note rests on the downbeat and 3 subsequent eighth notes; one has 3+3+3=9, trias trinitatis per additionem.

Finally, a typical manifestation of the unitas, a determining and crucial element in Bach's structuring of his compositions can be pointed out at this occasion. The contrapunctus 11 extends over 184 bars, an even number. The midpoint therefore falls upon the bars 92 and 93, see the preceding example. The bar 93 (=3*31, tri-unitary factorization!) sounds, from the fundament of the bass upwards, a, c, e; in numbers 1,3,5: unitas, third and fifth in thoroughbass--on  the dominant of d-minor. In the central triad of C-major of wohltemperirt, third and fifth beat at the unison! Hence, this piece is obviously pivoted symmetrically upon the very nucleus of the well-tempered musico-mathematical system.

The considerations above represent a corollary to the examples of the underlying article in The Diapason. As to the aspects described and analyzed, there is no pretension whatsoever to be exhaustive. Rather, the purpose is, hopefully, to be thought provoking, to stimulate and encourage further, more systematic and complete investigations into the direction outlined here--as much as the article published by Prof. Overduin has led to the present study.

After having reconstituted the well-tempered system Werckmeister/Bach initially in 1975,14 it was gratifying for me to see how organ builders have taken up and followed the ideas, appreciating the technological and musical qualities of this baroque temperament. These builders include Rudolf von Beckerath, John Brombaugh & Associates Inc., T. S. Buhr, Paul Fritts & Co., Gerhard Grenzing, Otto Hoffmann Organs, Claude Jaccard, Yves Koenig, Michael Korchonnoff, Dominique Lalmand, Gebr. Oberlinger, Martin Pasi, Richards, Fowkes & Co., Charles M. Ruggles, Taylor & Boody, George Westenfelder, Karl Wilhelm, Hellmuth Wolff and Munetaka Yokota.

On these organs, tuned accordingly, many distinguished musicians have performed and recorded, including Martin Balz, Luc Beauséjour, Jonathan Biggers, Gavin Black, Robert Clark, David Dahl, George Edward Damp, François Espinasse, Bernard Foccroulle, Martin Gester, André Isoir, Calvert Johnson, Donald Joyce, George Ritchie, David Rothe, Wolfgang Rübsam, Yasuko Uyama-Bouvard and others.

A discography as at that time I have published in The Tracker.15 Further references to analyses of Bach's compositions are contained--together with a heuristic derivation of the well-tempered system--in the Blankenburg-Michaelstein symposium proceedings.16 For those interested in more musicological details, a bibliography is also contained within my lecture publication on historical temperaments, held at the symposium in the Vienna Hochschule für Musik und Darstellende Kunst.17.

Johann Sebastian Bach and Die Kunst der Fuga

by Herbert Anton Kellner

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This article first takes up the question of the authentic title of Bach's last published work. Thereafter, this paper demonstrates a relation between the theme of the unfinished fugue of this composition and the well-tempered tuning "wohltemperirt". Already an earlier study1 in The Diapason identified possible allusions within Die Kunst der Fuga to the tuning Werckmeister/Bach for which Das Wohltemperirte Clavier was composed. Bach used the set of numbers belonging to the system "wohltemperirt" to arrange for the setup of his compositions, succeeding in this way to unify the musical harmony with architecture. Such structuring can be of a very abstract nature and concern even the melody of themes, number of keystrokes, or bar-lengths of movements, etc. The present case as well will show a rather complex and abstract means of structuring, but unambiguously recognizable.

 

Due to the way Die Kunst der Fuga was edited and published, there have always been some doubts and queries as to the exact intentions of the composer, including the authenticity of the title. It reads--in the printed edition--Die Kunst der Fuge. However, there also exists a manuscript version of the title page written by Bach's son-in-law, Johann Christoph Altnikol (Deutsche Staatsbibliothek Berlin, Mus. ms. Autogr. Bach P 200), that once belonged to the collection of Georg Poelchau. Altnikol, close to Bach, assisted the composer suffering from failing health and eyesight in preparing the publication. On Altnikol's manuscript, Figure 1, the title page reads Die Kunst der Fuga [sic]:

Now the gematria will be applied2, as commonly used by baroque composers and writers--even preceding Bach--such as Kuhnau3 or Werckmeister4. The title of Johann Sebastian Bach's last work, in Altnikol's spelling, shown together with the composer's full name thus reads:

Thanks to Altnikol's manuscript, the likely title in its authentic spelling is established, as it appears improbable that this gematrial equivalence represents a mere co-incidence. Within Bach's holograph of Das Wohltemperirte Clavier the composer himself always spelled "Fuga" and never "Fuge". On the contrary, the spelling of Die Kunst der Fuge [sic] results in 162=2x9x9. No gematrial significance whatsoever appears.

At Bach's time the most common numbering of the alphabet was from 1 to 24, A=1, I, J=9, U,V=20 and Z=24, as shown5 in Figure 2. It is this numbering that leads to the conclusion above.

However, the triangular alphabet was in use as well and also known to Bach, and both alphabets are tabulated in Figure 3, the triangular values follow from any Z of Dieben's alphabet via Zx(Z+1)/2:

The finality to present this table is, of course, to check Die Kunst der Fuga via this alternative, triangular alphabet. The latter converts Werckmeister's Musicalische Temperatur to the value of 19756 (whereas according to Henk Dieben the outcome is 247=13x19). With the number 1975 one may first recognize 19 as twelve fifths and seven octaves that close the circle, 19 intervals, 12+7. The remaining juxtaposition 75 shows the 7 perfect and the 5 well-tempered fifths of the system. Werckmeister's title thus allows the gematrial conversion via two distinct alphabets! After this introductory preparation, the supposedly authentic title will be now converted via the triangular alphabet as well. One finds Die Kunst der Fuga = 1225=(5x7)x(5x7) broken up into prime numbers. A double conversion yields a perceptible result in this case as well: 5 well-tempered fifths and 7 perfect ones of Werckmeister's and Bach's system "wohltemperirt". As 5x7=35, the figures 3=third and 5=fifth in thorough-bass appear--in the C-major triad these intervals beat in unison. The first prelude of Das Wohltemperirte Clavier comprises 35 bars. This title, Die Kunst der Fuga, can certainly be said to be scrupulously selected/constructed--and certainly not understood up to now.

 

The second part of this study will investigate the structure of the first theme of the last, unfinished fugue, in relation to the tuning Werckmeis-ter/Bach upon which Das Wohltemperirte Clavier is based. In this system wohltemperirt, 5 tempered fifths and 7 perfect ones close the circle of 7 octaves. This amounts to a division of the Pythagorean comma by five. Refining to more detail, there are the 4 usual well tempered fifths c-g-d-a-e, together with 1 tempering fifth B-f#, and the remaining 7 fifths are perfect7. A corresponding set of these numbers of fifths characterizing the musical temperament looks like 4, 1, 7.

At this stage, a small, but necessary, mathematical excursion follows. From Euclid and Greek mathematics, the "perfect numbers" were considered. These numbers are made up by the sum of their divisors, such as for the first perfect number, 6=1+2+3. Likewise, for the next one 28=1+2+4+7+14, being divisible in turn by 1, 2, 4, 7 and 14. It is remarkable that Werckmeister and other musicians as well8 were apparently fascinated by these numeri perfecti and in several of his treatises he quotes 6, 28, 496, 8128, 33550336. There exists an infinity of perfect numbers, but up to now it is unknown whether there are any odd perfect numbers--all perfect numbers known to date are even. These numbers considered perfect may be the reason that baroque and earlier composers grouped their works by numbers of 6 for publication.

Now the characteristic set of numbers 4, 1, 7 of "wohltemperirt", (4 well-tempered fifths, 1 tempering fifth B-f# and 7 perfect fifths), will be assembled with its crabwise permutation 7, 1, 4 and centered upon 6, primus numerus perfectus. The perfectly symmetrical constellation 4-1-7-6-7-1-4 results. Gematria-wise, letters are associated to these numbers. The outcome of this procedure is D-A-G-F-G-A-D. Here one recognizes the unfinished fugue's theme of the composition, Fig. 4.1 and 4.2.

In the final rhythmic layout of these notes, by the fourth note, a sudden ritardando halving of the tempo might be felt, giving to the theme its tragic austerity, Fig. 4.3.

As regards the significance of the digits within the set 1, 4, 7, it must be remembered that the prelude of the tempering tonality B-major in WTC I counts 417 keystrokes9. Within the Well-tempered Clavier I and II comprising an even number of 5750 bars--counting through the entire composition--the number of the two central bars are 2875 and 287610. Thus, the midpoint will be bar 741 of Part II (2876-2135=741), again with the digits 1, 4, 7: the numbers of fifths.

 

In conclusion, these considerations provide a clue to the "authentic" title of Bach's last composition printed. Also, the characteristic numbers specifying "wohltemperirt" were identified as the theme of the last, unfinished piece of Die Kunst der Fuga. At this occasion, two recent publications investigating the composition might be quoted, by Hans-Jörg Rechtsteiner11 and above all, Vincent Dequevauviller12, the latter distinguished by a remarkable originality of ideas, sadly missing in the Bachjahrbuch--due to the unfortunate publishing policy of the present editors.

This paper was written in commemoration of Bach's passing away 250 years ago on 28. 7. 1750. By that date, at the middle of the 18th century--written according to European usage--will look as 28.7.'50, the central bar of Das Wohltemperirte Clavier reappears. Likewise, Bach's birthday on 21.3.1685, late in the 17th century, appears as 21.3.'85. Here, reconverting via the number alphabet of Henk Dieben, 2138 appears: BACH.

 

 

Notes

                  1.              Kellner, Herbert Anton, "How Bach encoded his name into Die Kunst der Fuge together with his tuning." The Diapason, May 1999, 14-15.

                  2.              Kellner, H. A., "Le tempérament inégal de Werckmeister/Bach et l'alphabet numérique de Henk Dieben." Revue de Musicologie 80/2, 1994, 283-298.

                  3.              Kellner, H. A., "Welches Zahlenalphabet benutzte der Thomaskantor Kuhnau?" Musikforschung 33/1, 1980, 124-125.

                  4.              Hermann, Ursula, "Andreas Werckmeister--Lebensweg und geistiges Umfeld." In: Bericht über das Werckmeister-Kolloquium aus Anlaß des 340. Geburtstages von Andreas Werckmeister am 30. November 1985, Michaelstein/Blankenburg 1986, Studien zur Aufführungspraxis und Interpretation von Musik des 18. Jahrhunderts, Heft 30, p. 5.

                  5.              Harsdoerffer, Georg Philipp, Poetischer Trichter, Nürnberg, Wolffgang Endter MDCL. Faksimile Wissenschaftliche Buchgesellschaft Darmstadt, 1975.

                  6.              Duparcq, Jean-Jacques, private communication.

                  7.              Kellner, H. A., The Tuning of my Harpsichord. Schriftenreihe Heft 18. Verlag Das Musikinstrument, E. Bochinsky, Frankfurt/Main 1980.

                  8.              Werckmeister, A., Musicalische Temperatur, p. 14, 19; see also Walther, Johann Gottfried, Musicalisches Lexicon, oder, Musicalische Bibliothek. Leipzig, 1732, Ed. R. Schaal, Kassel 1953.

                  9.              Kellner, H. A., "Das wohltemperirte Clavier--Tuning and Musical Structure." English Harpsichord Magazine 2/6, April 1980, 137-140, in particular p. 139.

                  10.           Kellner, H. A., "Das wohltemperirte Clavier--Implications de l'accord inégal pour l'oeuvre et son autographe." Revue de Musicologie 71, 1985, 143-157.

                  11.           Rechtsteiner, Hans-Jörg, Alles geordnet mit Maß, Zahl und Gewicht. Der Idealplan von Johann Sebastian Bachs Kunst der Fuge. Peter Lang, Europäische Hochschulschriften, Reihe 36, Musikwissenschaft, Vol. 140, 1995. P. 44, Completing the unfinished fugue by 133 bars is absurd; Davitt Moroney's completion by 30 bars in his Henle-edition is much more reasonable.

                  12.           Vincent Dequevauviller, L'art de la fugue, un "problème algébrique," Etude sur les caractéristiques numériques et les raisons de l'inachèvement de la dernière oeuvre de Jean-Sébastien Bach. Association pour la Connaissance de la Musique Ancienne, 1998, ISBN 2-9513089-0-6. The proposed completion of the unfinished fugue by 37 bars is correct.

 

 

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