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BACH: Journal of the Riemenschneider Bach Institute, Vol. 53, No. 2, 2022
Copyright © 2022 Baldwin Wallace University, Berea, OH
260
J. S. Bach, the Viola da Gamba, and Temperament
in the Early Eighteenth Century
LOREN LUDWIG
A
consideration of temperament in J. S. Bach’s music for viola
da gamba (or viol) sits at the intersection of three lines of
historical inquiry: the history of Bach as a composer, teacher,
music theorist, and liturgist; the history of the viol; and the history of
temperament. Bringing these three conversations into dialogue makes
visible two biases that have crept into their respective historiographies: 1) that tuning and temperament—particularly in the eighteenth century—was primarily the province of keyboard players; and
2) that by the early eighteenth century the historical trajectory toward
equal temperament (ET) had largely been charted (if not quite yet
reached), and that alternative approaches to tuning during the period
represent historical cul-de-sacs peripheral to the primary concerns of
performers and music historians.1
But, as is often the case, historical sources tell a richer story, one
that complicates narratives around the historical development of tuning and temperament strategies, the musical and scientific instruments used to study them, and the diverse aesthetic concerns
motivating the scholar-practitioners whose writings document this
history. As we will see, these writings bedevil convenient characterizations of the viol and non-ET systems as antiquated by the early
eighteenth century, versus well- and quasi-equal temperament as
formulated by keyboard players (Bach included) as forward looking
and “progressive.” In fact, the non-ET tunings described in this
article were developed—often using a viol in place of or in tandem
with a monochord—by musicians who saw themselves as participants
in the most cutting-edge European scientific communities and
I am indebted to the expertise of Yulia Frumer, Roland Hutchinson, Bettina
Hoffmann, John Moran, Ross W. Duffin, Bradley Lehman, and numerous other
friends and colleagues who provided insightful feedback and responded to draft
material with wisdom and patience.
1
This view is explicit in the most influential English-language history of tuning
and temperament, James Murray Barbour, Tuning and Temperament: A Historical
Survey (East Lansing: Michigan State College Press, 1951).
L UDWIG 261
institutions. Thus, this consideration of temperament in Bach’s
music for viola da gamba reveals an “occult” history of tuning, one
that unfolded alongside and in dialogue with the familiar development of circulating temperaments. This history privileges ease of
tuning and the quality of familiar diatonic intervals over the far
reaches of the circle of fifths and broadens the conversation to include
a community of scientist-musicians who resisted the purported emergent consensus around well- and quasi-equal temperaments. The viol
tunings discussed below include those that appear in the anonymous
Instruction Oder Eine Anweisung Auff Der Violadigamba (ca. 1730),
the “perfect and mathematical” tunings of Thomas Salmon (1647–
1706), the “true scale, or basis of musicke” of John Harrison (1693–
1776), as well as several tunings associated with Carl Friedrich Abel
(1723–1787) that have not yet received significant scholarly
attention.
Tuning the Viol in Eighteenth-Century Europe
By the early eighteenth century, the viola da gamba was nearly at
the end of a reign that had begun in early sixteenth-century Italy.2 As
portended by its emergence as an accessory to courtly intimacy in
Mantua and other northern cities, the viol would remain the favorite
bowed instrument of the aristocracy until the last embers of
the tradition cooled in mid-to-late eighteenth-century Germany,
England, and Hungary.3 In fact, one of the last virtuosi of the instrument, composer and viol player Carl Friedrich Abel, was closely
associated with the Bach family over the course of his career.4 Abel
is a good candidate to have premiered Bach’s three sonatas for viola da
gamba and harpsichord, BWV 1027–1029 (now that the pieces have
2
See Ian Woodfield, The Early History of the Viol (Cambridge: Cambridge
University Press, 1984); Annette Otterstedt, The Viol: History of an Instrument, trans.
Hans Reiners (Kassel: Bärenreiter, 2002); Peter Holman, Life after Death: The Viola
Da Gamba in Britain from Purcell to Dolmetsch (Woodbridge, Suffolk: Boydell Press,
2013); and Bettina Hoffmann, The Viola Da Gamba, trans. Paul Ferguson (London:
Routledge, 2018).
3
See Holman, Life after Death; and Michael O’Loghlin, Frederick the Great and
His Musicians: The Viola Da Gamba Music of the Berlin School (Aldershot, UK:
Ashgate, 2008).
4
Abel’s father Christian Ferdinand (ca. 1683–1737) performed with Bach’s
orchestra in Cöthen, and young Carl Friedrich would later study under Bach at the
Thomasschule in Leipzig, according to Charles Burney, where he would meet his
future business partner Johann Christian Bach. Holman, Life after Death, 170.
262
B ACH
been dated 1736–1741), and may have played the viol in the late
version of the St. Matthew Passion in 1742.5 This article concludes
with a discussion of tunings associated with Abel that may reflect the
arc of Abel’s career from Germany to England and that mediate
between the different approaches to tuning and temperament elucidated below.6 The first decades of the eighteenth century had seen the
virtuoso publications of Marin Marais and Jean-Baptiste Forqueray,
whose solo works represent something of a summit of the possibilities
of the instrument. Marais had served as a musicien du roi under Louis
XIV. Bach, who would have first encountered Marais’s music as
a teenager in compilations assembled by his older brother Johann
Christoph, would reference the royal French associations of the viol
in his last work to call for the instrument, the late version of the St.
Matthew Passion (1742).7 But in several of the cantatas Bach would
draw on a different set of valences entirely, seeking the instrument’s
quiet, intimate, and pastoral associations.8 Written for a funeral service,
the Actus tragicus (1707–1708) pairs viols and recorders to create what
Laurence Dreyfus calls a “solace of otherworldly instruments.”9 The
aching obbligato line in the alto aria “Es ist vollbracht” from the St.
John Passion (1724), as well as the viol’s appearance in the opening
tombeau of the Trauer Ode BWV 198 (1727), affirm Bach’s sense of
the viol as an accessory to tragedy.10
5
Holman, Life after Death, 170.
“The pure method of tuning the Harpsichord, according to Abel,” London,
British Library, Add MS 34007, described in Brian Capleton, “Carl Friedrich Abel, A
Gainsborough Painting, and Viol Temperament—Some Evidence and Enigmas,”
The Consort 59 (2003): 51–74.
7
Christoph Wolff, Johann Sebastian Bach: The Learned Musician (London: W.
W. Norton & Company, 2000), 46. Charles Medlam documents Bach’s familiarity
with the French viol school in Approaches to the Bach Cello Suites: A Hand-Book for
Cellists (Teddington: Fretwork Editions, 2013), 10.
8
As in Handel’s use of the instrument in Cleopatra’s aria “V’Adoro Pupille” in
Giulio Cesare (1724).
9
Laurence Dreyfus, Bach’s Continuo Group (Cambridge, MA: Harvard
University Press, 1987), 166.
10
This tradition had been well established over the course of the seventeenth
century, from Dowland’s “Lachrimae” pavans for viol consort early in the century
through Marin Mersenne’s comment in the Harmonie Universelle (Paris, 1636), 180,
that “l’on peut appeller le Ton, ou le mode du Violon, le mode gay & ioyeaux,
comme celuy de la Viole & de la Lyre, le mode triste & languissant” (the tone, or
mode, of the violin may be called gay and lively, as the mode of the viol and lyre is sad
and languid), to what Annette Otterstedt characterizes as the “überdurchschnittlich
6
L UDWIG 263
While the viol in England and France had become a virtuoso solo
instrument whose repertoire was idiomatic to the instrument itself,
German composers like Heinrich Schmelzer, Dietrich Buxtehude,
and Georg Philipp Telemann largely treated the viol as just another
tenor- or alto-range melody instrument.11 Nikolaus Harnoncourt
argues that it was the distinctive sound of the viol, as much as its
associations, that German composers, including Bach, sought.12 If in
the cantatas and passions Bach’s use of the viol evoked ancient pastoral and aristocratic (if not royal) associations, the Brandenburg
Concerto No. 6 (1721) and the three sonatas for viola da gamba and
harpsichord (none of which may have been originally scored for viol)
deployed the instrument in forward-looking instrumental chamber
music.13 These works, like Telemann’s so-called Paris Quartets, the
Quadri (1730) and Nouveaux Quatuors (1738), or Jean-Philippe
Rameau’s Pieces de Clavecin en Concert (1741), offer galanterie and
a modern vision of the viol quite independent of its historical cultural
associations.14
–
viele deutsche Trauerkompositionen mit einer Begleitung von tiefen Streichern, oft
einem Gambenensemble” (an above-average number of German funeral compositions with an accompaniment of low strings, often a viol ensemble). Otterstedt, “Die
Gambe am Ende des Barockzeitalters,” in Bachs Orchester- und Kammermusik: das
Handbuch, ed. Siegbert Rampe (Laaber: Laaber-Verlag, 2013), 172. Unless otherwise
indicated, all translations are mine.
11
The recent discovery of a single surviving copy of Telemann’s twelve unaccompanied fantasias for viol, TWV 40:26–37, notwithstanding.
12
Nikolas Harnoncourt, The Musical Dialogue: Thoughts on Monteverdi, Bach
and Mozart (Portland, OR: Amadeus Press, 1984), 49. Since Harnoncourt’s publication, we have learned about the substantial traffic of German viol players across the
Channel following the Restoration, and the related proliferation of works on the
continent for the English lyra viol (such as Carl Friedrich Abel’s grandfather Clamor
Heinrich’s Dritter Theil Musicalischer Blumen [1677]). See Richard Carter, “Clamor
Heinrich Abel’s Dritter Theil Musicalischer Blumen, 1677: A Lost Source of Lyra
Consort Music,” Viola Da Gamba Society Journal 3 (2009): 55–82.
13
See Hans Eppstein, Studien Über J. S. Bachs Sonaten für ein Melodienenstrument und obligates Cembalo (Uppsala: Acta Universitatis Upsaliensis, 1966).
14
Ultimately, however, such works were unable to sustain the continued use of
the instrument. As Otterstedt writes, “und so fristete die späte Gambe ein Zwischendasein aus überlieferter Praxis und einer neuen Ästhetik, die kurzfristig mit der
Generation der Bach-Söhne in Mode kam und für die Carl Friedrich Abel der
hervorragende Exponent war” (“and so the late viola da gamba straddled traditional
practices and a new aesthetic that came into fashion briefly with the generation of
Bach’s sons and for which Carl Friedrich Abel was the outstanding exponent”).
Otterstedt, “Die Gambe am Ende des Barockzeitalters,” 170.
264
B ACH
For the purposes of this essay, it is significant that none of Bach’s
works for the viol are unaccompanied. The viol’s appearances in the
cantatas and passions are accompanied by a continuo group anchored
by organ, while the Brandenburg Concerto No. 6 and obbligato
sonatas require a harpsichord. Thus, on the face of it, the question
of how viol players in Bach’s time might have tuned their instruments
when playing Bach’s music can be answered quite easily: they tuned
to reference pitches provided by the keyboard.15
Such an answer, while likely practically correct, offers little to
modern scholars and players of the viol. Instead, this essay offers an
account of a largely overlooked group of eighteenth-century tuning
strategies—several formulated using the viol itself. These strategies
were motivated by quite different priorities than the familiar desire to
make remote keys accessible to composers while preserving a distinct
“character” for each key, the panacea of eighteenth-century German
keyboard temperament theory. The question becomes, then, how
might viol players have had to adapt their native tuning and setup
practices to play Bach’s music? And what is revealed in the evident
friction between the temperament strategies pursued by Bach (as
representative of the move toward well- and quasi-equal temperaments), and the various flavors of unequal temperament promulgated
by the (largely) amateur viol players and musicians discussed below?
Of course, writings by viol players have been a home for theories
of tuning and temperament since the sixteenth century and treatises
by Hans Gerle, Sylvestro di Ganassi dal Fontego, and others.16 Before
the emergence of a range of competing “well” temperaments around
the turn of the eighteenth century, conventional wisdom held that
fretted instruments were tuned in ET (or a close approximation),
while keyboard instruments were tuned using some variety of Pythagorean or meantone tuning. As recently as 2002, Annette Otterstedt
made the familiar (and contested) claim that “there is not a single
15
For a detailed summary of the likely temperaments in which Bach worked
over the course of his career, see Siegbert Rampe, “Die Temperatur von Bachs
Orchestra und Kammermusik,” in Bachs Orchester- und Kammermusik: das Handbuch, 313–22.
16
See Woodfield, The Early History of the Viol; Mark Lindley, Lutes, Viols and
Temperaments (Cambridge: Cambridge University Press, 1984); David Dolata,
Meantone Temperaments on Lutes and Viols (Bloomington: Indiana University Press,
2016); and Hoffmann, The Viola Da Gamba.
L UDWIG 265
shred of incontrovertible evidence of the meantone temperament on
fretted instruments.”17 Though fretted, the viol is not a “fixed pitch”
instrument—skilled performers can “bend” fretted pitches by as
much as a quarter tone in either direction using various left-hand
techniques.18 Thus, historical accounts of fret placement suggest ET
must be read carefully, for unlike plucked instruments, viols can be
“set up” or calibrated in some approximation of ET but played so as
to produce pure (or purer) intervals.
Equally important to the history narrated here is the coincidence
of the viol and natural philosophy, a domain of inquiry responsible
for much of the early modern writing on musical temperament. The
centuries that saw the development of the viol and the related industries of luthiery, string making, composition, music printing, pedagogy, and performance were the same centuries that witnessed the
slow gestation of modern, experimental science in Europe.19 Like the
viol, natural philosophy was a gentleman’s pursuit. The aristocratic
associations of the instrument, combined with the ubiquity of musical training for gentlemen, meant that a viol would have been a frequent accessory to those with the leisure to consider arcane topics like
temperament. More than a few notable figures in this emergent
scientific community played the viol, from Constantijn Huygens,
who played consorts with his children, including Christian, to
Samuel Pepys, president of the Royal Society from 1684 to 1686,
who frequently mentioned his viol in his diary, to Isaac Newton, who
copied Christopher Simpson’s instructions on how to hold, tune,
and play the viol into his notebooks while a student at Cambridge,
to Benjamin Franklin, whose viol would be stolen by marauding
British troops in Philadelphia later in the century.20
17
Annette Otterstedt, The Viol: History of an Instrument (Kassel: Bärenreiter,
2002), 187. In fact, Dolata documents “incontrovertible evidence” for the use of
meantone temperaments on lutes and viols. Dolata, Meantone Temperaments.
18
In 1599 Italian Ercole Bottrigari would explain that “fixed but variable
instruments are those which, after they have been tuned by the conscientious player,
can partially change the intonation upwards or downwards by the player stopping the
string a little higher or lower at their discretion. This can be done on both the lute
and the viol, although these are both fixed instruments by virtue of their frets.”
Translated and quoted in Hoffmann, The Viola Da Gamba, 51.
19
See Rebecca Cypess, Curious and Modern Inventions: Instrumental Music as
Discovery in Galileo’s Italy (Chicago: University of Chicago Press, 2016).
20
On Huygens, see Tim Crawford, “Constantijn Huygens and the ‘Engelesche
Viool,’” Chelys 18 (1989): 41–60; on Newton, see Penelope Gouk, Music, Science,
266
B ACH
The tuning strategies described in this article were devised and
shared within this milieu of elite eighteenth-century natural philosophy. Music was a particular fascination, and, as in the previous century, the line between scientific and musical instruments was not
always possible to discern.21 By the eighteenth century, the priorities
of these empiricist musical amateurs often diverged from the mainstream of European musical development, as typified by expansion of
forms (and forces) and the systematic use of increasingly remote keys.
Yet, these theorists sought an alternative source of authority—the
nascent scientific establishment that included the Royal Society in
England and the French Encyclopédistes—and employed what they
understood to be the most forward-looking techniques and practices.
Clergyman and music theorist Thomas Salmon, for example, would
devise a complex mechanical solution to the problem of realizing just
intonation on a viol, and would describe his viol as a “monochord,”
an instrument with millennia of history as a musical research instrument.22 Clockmaker and inventor of the marine chronometer John
Harrison would also use his viol to “discover” a temperament, one
that he formulated using the logarithms and mathematics of circles,
recently revolutionized by the advent of calculus.23 While some
might discount these just, pi-based, or quasi-Pythagorean
–
and Natural Magic in Seventeenth-Century England (New Haven, CT: Yale University Press, 1999), 224–37; and on Franklin, see Loren Ludwig, “The Viola Da
Gamba in Eighteenth-Century Virginia and Maryland: New and Reconsidered
Evidence,” Journal of the Viola Da Gamba Society of America 51 (2019): 27–66.
21
See Cypess, Curious and Modern Inventions. For the overlap of the social
networks of amateur musicians and natural philosophers in seventeenth-century
Cambridge, see Gouk, Music, Science, and Natural Magic in Seventeenth-Century
England. See also Patrizio Barbieri, Enharmonic Instruments and Music 1470–1900
(Latina: Levante, 2008); and Alexander Rehding, “Instruments of Music Theory,”
Music Theory Online 22, no. 4 (2016): 1–22.
22
See, for example, Salmon’s manuscript treatise “The Division of the Monochord” (ca. 1702–1705), in which he initially describes interval calculations in
relation to a “monochord” but soon slips into a granular discussion of fret locations
and interval sizes on a viol that reveals that the two instruments are, in fact, one and
the same. For a transcription of “The Division of the Monochord,” see Benjamin
Wardhaugh, Thomas Salmon. Writings on Music (Farnham, Surrey: Ashgate, 2013),
2:145–60.
23
John Harrison, A Description Concerning Such Mechanism as Will Afford
a Nice, or True Mensuration of Time Together with Some Account of the Attempts for
the Discovery of the Longitude by the Moon as Also an Account of the Discovery of the
Scale of Musick (London, 1775).
L UDWIG 267
temperaments as historical and musical “dead ends,” this teleological
perspective would slight the rich complex of aesthetic, social, and
scientific discourses that were brought together during the eighteenth
century under the umbrella of “tuning and temperament.”
Crucial to these divergent tuning interests between early
eighteenth-century keyboard enthusiasts and the amateur viol players
discussed below is the viol’s peculiar identity somewhere between
a fixed-pitch and non-fixed-pitch instrument. This results in a particular relationship to the conceptualization and use of temperament.
Though viol players routinely temper the pitches of open strings and
frets, their ultimate goal is not to play in a particular temperament,
but rather to calibrate the instrument so as to be able to play in tune.
This distinction—how the instrument is calibrated versus how it is
played—results from the fact that a skilled player can “bend” any
fretted pitch by as much as a quarter tone in either direction. This
strategy was described as early as 1619 in Michael Praetorius’s Syntagma Musicum: “one also can help give to and take from the string
with one’s grip at the frets. This cannot be done at all with harpsichord strings or organ pipes[,] where nothing can be given or taken
away.”24 This pitch flexibility in relation to the physical location of
the fret on the fingerboard would be both theorized and utilized later
in the century by viol players such as Salmon and Dietrich Steffkin,
a seventeenth-century viol virtuoso and one of Salmon’s informants.
For unlike metal frets, the gut frets on most viols are not, by
themselves, determinant of pitch. Nor are they intended to be.
Rather, tied frets are primarily a timbral technology on the viol. When
used according to widely documented historical practices, the fret
“focuses” the timbre, in effect imbuing each fretted note with the
bright, overtone-rich qualities of the open string. When viol players
tune their frets by sliding them up or down the neck, they are aligning
the best timbral position of the fret with the location of the reference
pitch on the fingerboard. To maximize the “focusing” effect of the
fret, a player must position their finger so that it presses the string
firmly against the fret without muting the vibrating segment of the
string. Slight adjustments to the location of the finger on the fingerboard also affect pitch, so “tuning the frets” calibrates an instrument
such that a specific player’s finger positions will maximize the effect of
24
Transcription and translation from Lindley, Lutes, Viols & Temperaments, 36.
268
B ACH
the fret while playing in tune. Should a player need to alter the pitch
of a fretted note minutely, they might need to sacrifice timbral focus
for pitch accuracy by rolling the finger toward or away from the
bridge or “tugging” on the string either laterally or along its length,
the very practices referenced above by Ercole Bottrigari and
Praetorius.
How do these material and technical considerations affect the
choice of temperament in how a viol is tuned and played? When there
is no keyboard or other fixed-pitch instrument to which to tune,
players calibrate (“tune”) their open strings and frets with the knowledge that they will selectively micro-inflect certain notes as necessary
during performance. However, when a keyboard is present (as is true
in all of Bach’s works that include the viola da gamba), such a divergence is unnecessary and often undesirable. In such circumstances,
a viol becomes a fixed-pitch instrument, and micro-corrections that
diverge from the keyboard’s tempered references sound out of tune.
Thus, playing with keyboards is both a blessing and a curse. Much
less effort is required to play twelve fixed pitches in predicable locations on the fingerboard, but players must accept harmonies composed of tempered (as opposed to just) intervals.
The Instruction Oder Eine Anweisung Auff Der Violadigamba
Such an approach is suggested by the enharmonic equivalence
that appears “baked in” to the tuning described in the one extant
eighteenth-century German treatise on the viol, the anonymous
Instruction, oder eine Anweisung auff der Violadigamba (ca. 1730).25
Bettina Hoffmann, in the introduction to her recent edition of
the Anweisung, traces the treatise to the collection of a nineteenthcentury composer and organist at the Leipziger Nikolaikirche, Carl
Ferdinand Becker (1804–1877). According to Hoffmann, the manuscripts in Becker’s collection “are almost all connected with Saxon
cities—Leipzig, Dresden, Zschopau, and Weißenfels.”26 The Anweisung manuscript appears to be a fair copy or even the work of a professional copyist, while the contents reveal the influence of
a professional (and stylish) viol player. The roughly thirty pages of
25
Leipzig, Leipziger Stadtbibliothek, Becker/ 4 271, recently published in
Bettina Hoffmann, ed., Instruction Oder Eine Anweisung Auff Der Violadigamba,
trans. Michael O’Loghin (Heidelberg: Edition Güntersberg, 2014).
26
Hoffmann, Instruction Oder Eine Anweisung Auff Der Violadigamba, vii.
L UDWIG 269
the Anweisung include an introduction to music notation, a discussion
of “commonly used keys” and how they map to the viol, useful tables
showing options for how to execute chordal passages, and a thorough
discussion of ornamentation with notated examples. The treatise ends
with the statement “[w]en ein SCHOLAR dieße INSTRUCTION
verstehet Und im PRACCIM gebracht so hat er keine ferner INVERMATION nohtig, sondern er kan sich selbsten helffen” and Hoffmann concludes that the text “is to be understood as a complete
introduction to music, not just to the art of gamba playing.”27
The Anweisung’s temporal and geographic proximity to Bach
makes the treatise’s discussion of chromatic scales and “commonly
used and customary keys” particularly relevant to how a viol player
might have navigated tuning and temperament issues in Bach’s
music. Early in the treatise the author presents two chromatic scales,
one rendered with sharps and one with flats (fig. 1). Note names in
German appear beneath each scale. The author’s choice to use the
same name for multiple pairs of enharmonically equivalent pitches
(“Dir” for both D s and E f , “cis” for B s and C, etc.) strongly suggests
Figure 1. Enharmonic equivalence in Anon., Instruction oder eine Anweisung
auff der Violadigamba, 6–7. Leipzig, Stästische Bibliothek, Becker / 4 271,
http://digital.slub-dresden.de/id45404352X
27
“When a scholar has understood and put into practice these instructions, he
needs no further information, and can assist himself.” Hoffmann, Instruction Oder
Eine Anweisung Auff Der Violadigamba, ix. Translation by Michael O’Loghlin.
270
B ACH
that the author conceived of the instrument as having twelve fixed
pitches per octave. The Anweisung appears to represent the approach
of a professionally minded viol player seeking to navigate a musical
mainstream that assumed the presence of a keyboard tuned in a wellor quasi-equal temperament. This difference may also reflect the
practical priorities of the Anweisung’s intended readership.
Another hint about early eighteenth-century tuning/tempering
practices can be gleaned from the lists of “commonly used and customary keys” that appear in the Anweisung, first as arpeggios and then
as cadential formulae.28 These show, in order, the keys of A minor, A
major, B-flat minor, B-flat major, C minor, C major, D minor, D
major, E minor, E major, F minor, F major, G minor, G major, B
minor (“H.Mol”), and B major (“H: duhr”) (fig. 2). Following the
Figure 2. Anon., Instruction oder eine Anweisung auff der Violadigamba, 15.
Leipzig, Stästische Bibliothek, Becker / 4 271, http://digital.slub-dresden.
de/id45404352X
28
Hoffmann, Instruction Oder Eine Anweisung Auff Der Violadigamba, 15.
L UDWIG 271
cadential formulae, the author of the Anweisung lists the “very rarely
used” keys of C-sharp minor, C-sharp major, D-sharp minor,
D-sharp major, F-sharp minor, F-sharp major, G-sharp minor, and
G-sharp major.
A modern reader familiar with the high baroque solo repertoire
for viol might notice the absence of E-flat major, A-flat major, Csharp minor, and F-sharp minor among the “commonly used and
customary keys,” and the presence of C-sharp minor and F-sharp
minor among the “very rarely used” keys. The fact that the relative
majors of C-sharp minor and F-sharp minor (E and A, respectively)
do appear among the “commonly used keys” suggests that the Anweisung’s author was concerned about the comparatively wide major
third (G s -B s or C s -E s ) that would likely define the “dominant”
sonority in those minor keys in many contemporaneous keyboard
temperaments. The absence of E-flat major and A-flat major among
the commonly used keys is puzzling, considering the presence of their
relative minors on the same list. The recently discovered print of
Telemann’s twelve fantasias for unaccompanied viola da gamba TWV
40:26–37 (printed in the mid 1730s—nearly exactly contemporaneous with the Anweisung) contains movements in C-sharp minor and
F-sharp minor as well as an entire three-movement fantasia in E-flat
major.29 Thus, despite its topical, temporal, and geographic proximity, the Anweisung offers few definitive details beyond the confirmation of enharmonic equivalence and a tuning system in which certain
keys remained problematic enough that they were listed as “rarely
used.” Nevertheless, the Anweisung offers a menu of usable keys for
viol players that extends from five flats (B-flat minor) to five sharps (B
major), which was a much wider palette of potential keys than any of
the other eighteenth-century temperaments for viol considered
below.30
The Anweisung, with its enharmonic equivalence, wide range of
usable keys, and up-to-the-minute examples of ornaments, is a perfect
29
The middle movement of Fantasia No. 8 is in C-sharp minor, the middle
movement of Fantasia No. 10 is in F-sharp minor, and Fantasia No. 12 is in E-flat
major.
30
O’Loghlin’s thematic catalog of works for the viol associated with the midcentury Berlin School lists primarily pieces in zero to two sharps or flats, with a few
outliers in three signed sharps or flats. O’Loghlin, Frederick the Great and His
Musicians, 209.
272
B ACH
figure for the fashionable musical mainstream that included Bach’s
chamber music for viol, Telemann’s unaccompanied fantasias and
chamber music collections, and the over fifty surviving works for viol
by the mid-century Berlin School. This was an approach to the viol
that was aligned with a musical progressivism characterized by the
“mixed taste,” longer and more developed forms, and the increasing
importance of remote keys. That German composers and theorists of
the eighteenth century understood their circulating temperaments to
be state-of-the-art is revealed in, for example, Carl Philipp Emanuel
Bach’s description of his preferred temperament: “[d]urch diese neue
Art zu temperiren sind wir weiter gekommen als vor dem.”31
Viol Temperaments as Cutting-Edge Science
But Carl Philipp Emanuel’s “great advances,” even if they were
noticed and remarked upon by eighteenth-century writers, have
assumed a disproportionate centrality by virtue of nearly three centuries of repetition as the dominant narrative in the historiography of
eighteenth-century European music. Of course, there are various
ways of being “modern,” as any eighteenth-century amateur musician
with a finger on the pulse of institutions like the Royal Society of
London or the French Académie des sciences might have testified.
Unlike the professional composers, theorists, and performers of
the period who sought temperament solutions that would allow for
the use of all keys while preserving their distinct sonic identities, the
amateur musicians discussed in the next three sections—Thomas
Salmon, John Harrison, and Carl Friedrich Abel—developed temperaments that served an alternative set of values and showcased
cutting-edge scientific and technological theories and practices. These
values included the specific aesthetic qualities of diatonic intervals in
a few familiar keys, ease of tuning, and a legible connection to ancient
systems of tuning and their inherited authority.
All three temperaments relied on (and in some cases instigated)
groundbreaking developments in science and technology. Salmon’s
interchangeable fingerboards preceded by nearly a century the
widespread adoption of interchangeable parts in design and
31
“The new method of tuning marks a great advance over the old,” in Carl
Philipp Emanuel Bach, Essay on the True Art of Playing Keyboard Instruments, trans.
William J. Mitchell (New York: Norton, 1949), 37.
L UDWIG 273
manufacturing that would occur as a key phase of the industrial
revolution.32 Harrison’s use of logarithms and the geometry of circles
(recently reformulated to integrate calculus) brought to tuning and
temperament ideas he had developed while designing the extremely
accurate marine chronometers that would revolutionize timekeeping
and navigation. And the “pure method of tuning the Harpsichord,
according to Abel,” is preserved in the hand of the young Muzio
Clementi (1752–1832), who would transform and modernize the
culture of keyboard building and playing in England.
Thomas Salmon’s “ Perfect and Mathematical Proportions”
The earliest, most familiar, and perhaps most influential of these
three viol-linked temperaments was a “syntonic diatonic” just tuning
formulated by Thomas Salmon in
