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beverly jerold
The French Time Devices Revisited
Much disparity exists among the metronome marks derived from the
tempo numbers for early eighteenth-century French time devices.
While some are reasonable, others are implausibly rapid. A newly
discovered source, which offers both Raoul Auger Feuillets numbers
for various forms and a drawing of the pendulum device for which
they were intended, solves the mystery of the conflicting numbers.
Because only a clockwork mechanism can measure fractions of
seconds, his numbers had to measure pendulum lengths (the simpler
and most frequent form of measurement). A comparison of his numbers
with those for the same dance forms from the two sources with
consistently extreme tempos indicates an almost exact correlation
when all are measured according to pendulum length, instead of the
presumed sixtieths of a second.
For some eighty years, the tempo numbers for French dance music
and certain vocal pieces, derived from time-measuring devices and
presented principally in a few French writings from 1696 to 1762,
have been a topic of lively discussion.1 When converted into
metronome marks, many of these numbers for the same form are
significantly inconsistent. Although the very rapid tempos have
often been considered valid, the conflict between these and the
other much slower tempos for the same forms has not been explained
adequately. Why are the numbers attributed to Joseph Sauveurs
clockwork measurement system (1701) by Michel LAffilard (1705) and
Louis-Lon Pajot, comte dOnzembray (1732) completely out of range
from the one tempo number that Sauveur himself supplied and also
from those of tienne Louli (1696)? Why do Jacques-Alexandre de La
Chapelle (1737) and Henri-Louis Choquel (1762) provide some numbers
of very modest speed, but others that are extraordinarily rapid?
Because all of these writers numbers are readily available in the
modern literature (note 1), they will not be repeated again, except
when relevant to material in a recently discovered source that
illustrates and describes the pendulum designed by the Paris
dancing master Raoul Auger Feuillet (d.1710). His numbers for
various dance forms provide the most accurate and plausible large
body of information to date about tempo of the period. At this
time, two principal forms of measurement existed: one based on
pendulum length in inches (pouces) and the other on sixtieths of a
second (tierces). The latter, however, requires a complex clockwork
mechanism. It was the confusion between these two measurement
systems that produced unusually rapid tempos in two sources. The
disparities in the other two sets of numbers can be attributed to
other factors. Throughout this article, the term metronome,
identified by an M, refers only to the modern device, whose
mechanism bears no relation to its forerunners.
1 See, for example, Eugne Borrel, Les indications mtronomiques
laisses par les auteurs franais du XVIIIe
sicle, Revue de musicologie 9 (1928), 149-153; Ralph
Kirkpatrick, Eighteenth-Century Metronomic Indications,
Papers of the American Musicological Society (1938), 30-50;
Hellmuth Christian Wolff, Das Metronom des Louis-
Lon Pajot 1735, in: Nils Schirring, Henrik Glahn, and Carsten E.
Hafling (eds), Festskrift Jens Peter Larsen,
Copenhagen: Wilhelm Hansen, 1972, 205-217; Willem Retze Talsma,
Wiedergeburt der Klassiker: Anleitung zur
Entmechanisierung der Musik, Innsbruck: Wort und Welt Verlag,
1980; Rebecca Harris-Warrick, Interpreting
Pendulum Markings for French Baroque Dance, Historical
Performance 6 (Spring 1993), 9-22; and Klaus
Miehling, Das Tempo in der Musik von Barock und Vorklassik,
second edn, Wilhelmshaven: F. Noetzel, 2003.
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Measurement by Pendulum LengthLoulis chronomtre (Figure 1), a
simple pendulum, stood over six feet high. As Louli specifies, the
measurement is according to the pied universel 33.12 cm. with a
pouce (royal French inch) of 27.6 mm. Thus the pendulum length for
one second of time is just slightly over 36 pouces, equivalent to
the English 39.1 inches. The formula for a metronome mark is
360number of pouces . Despite the devices lack of graduated
scaling, three of his numbers for four incipits of pieces from
sonatas by an unknown composer (Example 1) produce plausible
metronome derivations.2 An exception is Example 1b, whose pendulum
length of 8 pouces has vibrations too rapid for the eye to measure
accurately with ease, and may be a misprint. The shortest length
for a piece using Feuillets pendulum, to be discussed below, is 24
pouces. After visiting Paris in 1715-1716, the German architect,
librettist, and intellectual Johann Friedrich Armand von Uffenbach
returned to Frankfurt with a Feuillet chronomtre (Figure 2), which
had tempo numbers for seventeen French dances and Entres (Figure 3)
affixed to the bottom of its post. As the journal of his travel
experiences states: Eine Maschine den Tact in der Musik anzugeben,
von der Erfindung des Hr Feuillets zu Paris.3 In 1728, Uffenbach
gave a presentation about this device (included in his papers) to a
learned society in Frankfurt.4 According to his text, Feuillet
invented the chronomtre at the behest of King Louis XIV because he
could not hear any harmony (Stimmen) among the instruments in music
performances, particularly in operas, and could not bear disharmony
or disorder. Because there was perpetual strife between the dancers
and the opera orchestra concerning whether a ballet entre or other
song was played quickly or slowly enough, the inventor constructed
a small device by which the beat or tempo could always be the same,
and thus guide both the orchestra and the dancers on stage. It
consists of a 2-inch square post that is 5 feet long and marked
with a scale of unevenly spaced sections (thus an improvement over
Loulis device, which did not use graduated scaling). When the bob
moves in front of the circular mirror on the post, it casts a
shadow that enables the eye to grasp the beat more precisely.
Uffenbachs drawing in Figure 2 shows front and side views of a
simple pendulum with graduated
2 tienne Louli, lments ou principes de la musique, Paris:
Ballard, 1696; facsim. edn, Geneva: Minkoff, 1971,
86ff. The note value placed above the pendulum length in pouces
designates the beat unit.
3 Jrgen Kroemer, Le Cronomtre de Monsieur Feuillet: Absolute
Tempoangaben eines barocken
Tanzmeisters, sterreichische Musikzeitung 56/7 (2001),
23-28.
4 D-Gs, Cod. Ms. Uffenbach 13/II, 249-254. Figures 2 and 3 from
this manuscript are reproduced with the kind
permission of the Niederschsische Staats- und
Universittsbibliothek Gttingen. Uffenbachs handwriting
is in old German script, a transcription of which is in the
Appendix at the end of this article.
Figure 1Louli, Chronomtre.
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scaling. Therefore, the tempo numbers cannot be in the tierce
(sixtieths of a second) time measurement proposed today5 because
this requires a clockwork mechanism. Quoting from the French text
included with the chronomtre, Uffenbachs commentary explains the
crescents surrounding the number for each dance form in Figure 3.
Except for one omission, the beat unit corresponds to the system
described by Michel LAffilard (1705):6
Nocrescents=onebeat/bar Acrescentabove=twobeats/bar
Acrescentontheleft=threebeats/bar
Crescentsaboveandbelow=fourbeats/bar
Crescentsonbothsides=sixbeats/bar(inLAffilardonly)
Without a clockwork mechanism, Feuillets numbers must be
interpreted as pendulum lengths instead of tierces. Those in Figure
3 produce reasonable metronome derivations (Table 1). Corresponding
almost exactly to Feuillets numbers in Table 1 are the six for
dances in an early eighteenth-century manuscript of choreographies
in Feuillet notation, which likewise utilize crescents to indicate
the beat unit (Table 2).7 The numbers appear to be contemporaneous
with the manuscript and may be from the same hand as the
dances.
5 Kroemer, Le Cronomtre, 25f. and Miehling, Das Tempo, 59.
6 Michel LAffilard, Principes trs-faciles pour bien apprendre la
musique, fifth edn, Paris: Christophe Ballard,
1705; facsim. edn, Geneva: Minkoff, 1971. Directions for
interpreting the beat units are on folding plate II
(inserted by p.55). His instructions are also reprinted in
Rosamond E. M. Harding, Origins of Musical Time
and Expression, London: Oxford University Press, 1938, plate
10.
7 F-Po ms. 817. See Harris-Warrick, Interpreting pendulum
markings, 21f. For Feuillets Sarabande, the
number is uncertain. Of the four possibilities, 38 duplicates
that specified in Figure 3 for this dance. This
manuscript is described by Meredith Ellis Little and Carol G.
Marsh, La Danse Noble: An Inventory of Dances
and Sources, Williamstown, Mass.: Broude Brothers, 1992,
132f.
Example 1 Louli, Sonata incipits.
Incipit Time signature Beats/ bar Loulis number Metronome
mark
a. Two beats lents C-barr 2 40 57b. Four beats lgrs C 4 8 127c.
Trs lents 3/2 3 30 66d. A final movement 6/4 2 16 90
a. c.
b. d.
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Since the highest number of the chronomtre described by
Uffenbach is 60, it cannot be an exact replica of Feuillets, for
his numbers extend to 90. Nevertheless, its form had to be similar.
Uffenbach probably purchased it from the Atelier chez Feuillet,
continued by Jacques Dezais after Feuillets death, which would have
found a more ready market for a device of less imposing dimensions
than the one Feuillet needed for his own use with dancers. Because
it is difficult to gauge tempo visually by a rapidly moving
pendulum lacking an audible signal, it was advantageous to have one
of sufficient size to measure a slow compound metre, as in the
Chique lente in Table 1. The French text quoted by Uffenbach
advises the user to subdivide the beat when the number extends
beyond the devices range, as with 74 for the Entre lente. While
workable for this dance because it is in duple metre this approach
cannot be used with the compound-metre forms.
Figure 2Uffenbachs drawing of Feuillets chronomtre.
Figure 3Feuillets tempo numbers.
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Uffenbach obtained his chronomtre some five years after
Feuillets death, so the French writer probably overlooked the
difference between duple and compound metres. In closing his
presentation, Uffenbach observes that this machine not only enables
conformity between dancers and musicians, but also lessens the
arguments about correct tempo. Moreover, it helps those who are not
yet strong in keeping a steady beat, thereby relieving the (loudly
audible) time beating (Geklopfe) during the music. The form of this
time beating is clarified by a footnote in an anonymous English
translation (1709) of Franois Raguenets comparison of French and
Italian music (1702). In response to Raguenets remarks about
assembling the various elements at the Paris Opra:
How many times must we practice an opera before its fit to be
performed; this man begins too soon, that too slow; one sings out
of tune, another out of time; in the meanwhile the composer labors
with hand and voice and screws his body into a thousand contortions
and finds all little enough to his purpose.
Dance
MenuetPassepiedGaillardeGavotteEntre viteEntre lenteEntre
lenteBourreRigaudonSarabandePassacailleCouranteChaconneChique
lenteLoureGigue viteCanary
Timesignature
33/8C-barrC-barrC-barr2C22333/236/46/46/46/8
Beats/bar
11222242233332222
Feuilletsnumber
4840403737743730273836362490783026
Metronome mark
5257575959425966695860607338416671
Table 1Metronome marks from Feuillets pendulum.
Time signature
26/8
6/4
C-barr33
Beats/bar
22
2
233
Feuillets number
3030
30
302438
Metronome mark
6666
66
667358
Table 2Metronome marks from Feuillets numbers in scores.
Dance
Entre de paysantGigue de Mr Feuillet (gigue de thetis et
pellee)Gigue de Mr Feuillet (gigue de polixenne)Entre de Mr
FeuilletChaconne de Mr FeuilletSarabande de Mr Feuillet
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the translator observes:
Some years since, the master of the music in the opera at Paris
had an elbow chair and desk placed on the stage, where, with the
score in one hand and a stick in the other, he beat time on a table
put there for that purpose so loud that he made a greater noise
than the whole band, on purpose to be heard by the performer. By
degrees they removed this abuse from the stage to the music room
[probably the orchestra pit], where the composer beats the time in
the same manner and as loud as ever.8
An accident while beating time with a rod led to Jean-Baptiste
Lullys premature demise in 1687 when a blow to his toe became
infected. Nevertheless, to the chagrin of critics, distracting
conducting continued at the Paris Opra for much of the eighteenth
century. According to Jean-Jacques Rousseau (1768), the French did
not use a roll of paper for beating time, as commonly done
elsewhere, but a large baton of hard wood, which was struck
forcefully to be heard from afar.9
The musicien inconnu La Chapelle, too, used pendulum measurement
for many incipits of unknown pieces in his primer, but the
metronome marks derived from his numbers are widely disparate.10
While some are plausible, others are so extremely fast as to have
no relation to the others. La Chapelle provides no beat unit for
any of his numbers, and it is likely that the extreme tempos should
have a smaller beat unit than has been calculated. Because he
applies the time signature 2 indiscriminately for all forms of
duple movement (even the allemande, to which early sources nearly
always assign four slow beats and a signature of C), the beat unit
is uncertain. According to writers such as Jacques Hotteterre
(1719), the C-barr signature, for example, can have either two slow
or four faster beats (depending on the pieces texture and
predominating note values).11 In 1767, the critic Pascal Boyer
observed that time signatures were never intended to tell the
musician what to do with his body: When beating the measure of two
beats, several music masters make four hand movements, while others
make eight motions for the measure of four beats, etc., without
anyone ever accusing them of not knowing how to beat time.12 A
further complicating factor is that some composers (such as
Jean-Philippe Rameau) did not apply the signatures in the
conventional manner. Using an incorrect beat unit with La Chapelles
numbers, mainly those in duple metre, is what has produced untoward
tempos. On the other hand, a crotchet beat unit is often
satisfactorywhenthesignatureis3.Andforthesignatureof3/2,LaChapelleincludesan
incipit of two voices comprising crotchets and minims, which is
assigned a moderate tempoofminim=M54.ARondeauincompound-metre6/8,
composed of crotchets and quavers,ismarkedasdottedcrotchet=M 66.13
Thus the extreme tempos occur principally
8 Franois Raguenet, Parallle des Italiens et des Franais en ce
que regarde la musique et les opras, Paris: Jean
Moreau, 1702; facsim. edn, Geneva: Minkoff, 1976, 96f. English
translation in A Comparison between the
French and Italian Musick and Operas, London: W. Lewis, 1709,
42f. Reprinted in The Musical Quarterly 32/3
(1946), 428f.
9 Jean-Jacques Rousseau, Dictionnaire de musique, Paris: Vve.
Duchesne, 1768, Baton de mesure.
10 Jacques-Alexandre de La Chapelle, Les vrais principes de la
musique, Paris: lauteur, la veuve Boivin, 1736-1752,
vol. 2, 41-56. His examples are supplied in Miehling, Das Tempo,
85-91.
11 Jacques Hotteterre, LArt de prluder, Paris: lauteur, Boivin,
1719; facsim. edn, Geneva: Minkoff, 1978, 57.
12 Pascal Boyer, Lettre Monsieur Diderot sur le projet de lunit
de clef dans la musique. Et la rforme des mesures,
Amsterdam; Paris: Vente, 1767, 52-54, note.
13 La Chapelle, Les vrais principes, Leons deux parties, voix
egalles, vol. 3, 1-3. For examples, see Miehling,
Das Tempo, 90, nos. 43, 45.
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with duple metre, indicating that the probable beat unit for
most of these pieces should be smaller than assumed today. Another
writer using pendulum-length measurement was the attorney Choquel,
whose book includes numbers for five dance forms and eleven pieces
from sacred and secular vocal works.14 While the dances have
extreme tempos, most of the vocal pieces are moderate. For example,
Si des Galants de la ville (signature of 2) from Jean-Jacques
Rousseaus Le Devin du village is assigned a pendulum length of 24
pouces,orminim=M 73. The vocal line moves in crotchets, accompanied
by quavers in the upper strings, and the pieces marking of Gai is
the fastest one in Choquels examples.15
One of Choquels vocal pieces with a questionable tempo an
excerpt in duple metre from an unnamed motet by Michel-Richard de
Lalande lacks a beat-unit indication.16 Two other vocal pieces with
unusually rapid tempos are based on dance forms: an Air en Rondeau
from Jean-Baptiste Lullys opera Thse, specified to be a gigue; and
a duet having a Mouvement du Menuet.17 In sum, Choquels numbers are
reasonable for eight vocal pieces, questionable for three vocal
pieces, and extreme for five dance forms. We may find an
explanation below.
Measurement by Time The other writers offering many tempo
numbers are the court singer LAffilard and the scientist Pajot.
Unlike those of La Chapelle and Choquel, their numbers seem fairly
consistent within each set of pieces, but are much more rapid than
contemporary verbal descriptions imply. They purport to follow a
scaling based on sixtieths of a second (or tierces), as presented
by the mathematician Joseph Sauveur (1701) for his chomtre. Sauveur
furnished no diagram of his device, but it had to have included a
clockwork mechanism to measure fractions of seconds. Sauveurs
contemporary Chapotot, a Paris instrument maker, built chomtres,
and one survives in the collection of the Paris Conservatoire des
Arts et des Mtiers. Since Sauveurs pendulum cord was environ de 8
pieds (106 English inches) in length, the massive device could not
have been widely used. He provides a tempo number for just one
piece Allons, allons, accourez tous from Lullys Atys (Example 2).18
With a conversion formula of M =
360o
number of tierces , his number of
70translatestoaplausibleminim=M 51.To achieve this tempo with
Loulis chronomtre, he specifies a pendulum length of 42 pouces,
which produces M=55.5.19 The absence of a graduated scale in Loulis
pendulum accounts for some discrepancy in metronome derivations.
Sauveurs device, too, might not have been quite accurate, or he may
have used one of the differing measurements for the pied.
14 Henri-Louis Choquel, La musique rendue sensible par la
mchanique, second edn, Paris: Christophe Ballard,
1762; facsim. edn, Geneva: Minkoff, 1972, 115-213.
15 Choquel, La musique, 180ff.
16 Choquel, La musique, 201f.
17 Choquel, La musique, 186ff., 207ff.
18 From Jean-Baptiste Lully, The tragdies lyriques in facsimile,
New York: Broude International, 1998-2007.
Reproduced with kind permission.
19 Joseph Sauveur, Principes dacoustique et de musique:ou Systme
gnral des intervalles des sons, [Paris: s.n.,
1701]; facsim. edn, Geneva: Minkoff, 1973, 49f.; also in Joseph
Sauveur, Collected Writings on Musical Acoustics
(Paris 1700-1713), ed. Rudolf Rasch, Utrecht: The Diapason
Press, 1984, 147f. The latter (p. 40) includes a
photograph of the Chapotot chomtre at the Paris Conservatoire
des Arts et des Mtiers. Sauveur measures
Lullys piece also in twelfths of a second (14); the conversion
formula is M = 720/n.
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Four years later, LAffilard attributed tempo numbers for various
pieces in his Principes trs-faciles pour bien apprendre la musique
to Sauveurs system.20 These astonishingly rapid tempos, which
differ greatly from Sauveurs own tempo number, appear in a primer
for beginning vocal pupils. Since vocal agility takes many years to
develop and never attains the speed of which instruments are
capable, this requires further investigation; for example: The text
of a Gigue in 3/8 (Example 3a), whose tempo number of 31 per bar
is
translated as M 116, cannot be enunciated at this tempo.
Forslowformssuchassarabandeandcourante,LAffilardsnumbersdonotpermit
anexpressiveperformance.Atempoofcrotchet=M 106 is assigned to
his Passacaille (Example 3b), but it contains successive
semiquavers with separate syllables; his previous edition marks it
as Fort gravement. The text is a lament of spurned love: How many
tears have I shed without moving you?
For the four pieces that LAffilard identifies as la mesure six
tems graves, themetronome marks derived range from 120 to 150 per
crotchet, and do not qualify asveryslow.Wheneachcrotchet=M 150, the
correct beat unit has to be two beats of compound metre. Yet he
specified six very slow beats per bar, as spelled out by his system
of enclosing the tempo number with a crescent on both sides.21
LAffilard called his pieces appropriate for (social) dancing,
which implies moderate tempos. The abundant ornamentation, too,
requires adequate time for its execution.
20 LAffilard, Principes, 52-151.
21 LAffilard, Principes, 105, 89, 125-138. Talsma, Wiedergeburt,
154-169 and Miehling, Das Tempo, Anhang 2,
present LAffilards pieces in modern notation.
Example 2Lully, Atys, Allons, allons, accourez tous, Act 1,
Scene 2.
Example 3aLAffilard, Gigue.
Example 3b LAffilard, Passacaille.
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In 1974 Erich Schwandt proposed that the scaling of LAffilards
pendulum differed from Sauveurs, thus making modern translations of
LAffilards numbers twice too fast.22 With some exceptions,
Schwandts corrected numbers correspond more closely to contemporary
descriptions of the dance forms.23 Yet there may be a way to bring
nearly all of LAffilards numbers within a plausible range. While he
believed that he was using Sauveurs system, he was not a
mathematician. The numbers supplied are more consistent with Loulis
scaling for pendulum lengths in pouces. Table 3 provides metronome
marks for LAffilards pieces as derived from measurement in both
tierces and pouces.
22 Erich Schwandt, LAffilard on the French Court Dances, The
Musical Quarterly 63 (1974), 395.
23 Erich Schwandt, LAffilard, in: Stanley Sadie and John Tyrrell
(eds), The New Grove Dictionary of Music and
Musicians, second edition, London: Macmillan, 2001, vol. 14,
109.
A DEUX TEMSMarcheGavotteRigaudonBourrePavaneBranle en
Rondeau
PAR LE TRIPLE DOUBLESarabande tendreAir tendreAir, fort
graveCourante
PAR LE TRIPLE SIMPLESarabande en
RondeauPassacailleChaconneMenuet
PAR LE TRIPLE MINEURPassepiedGigueAir fort leger
A SIX TEMS GRAVESLeonSarabandeMarche en RondeauAir grave en
Rondeau
A SIX TEMS LEGERSCanaries en RondeauMenuetGigue
LAffilards number
303030304034
504574 ?40
42342351
423131
24272430
344836
Time signature
C22222
3/23/23/23/2
3333
3/83/83/8
6/46/46/46/4
6/86/86/8
Beats/bar
422222
3333
3331
111
6666
222
Metronome mark from tierces
12012012012090106
72804990
8610615771
86116116
150133150120
10675100
Metronome mark from pouces
666666665762
51544257
56627550
566565
73697366
625260
Table 3LAffilards numbers measured in Tierces and Pouces.
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With one possible exception, none of the tempos derived from
pendulum lengths is unusual. They are, in fact, quite similar to
Feuillets. One of LAffilards numbers is out of range from the rest:
the 74 for an Air, fort grave (Example 4), which is a reasonable
tierce number for this piece.24 Perhaps the tempo measurement was
first undertaken with Sauveurs system, and then converted to
pendulum-length measurement, for Sauveurs device must have been too
large and expensive to find a market. In the changeover, the number
74 was overlooked. Because practicing musicians rarely had access
to more than the most rudimentary general education, it is unlikely
that LAffilard prepared the purported tierce numbers himself. More
probably, he enlisted the aid of a mathematician, who then failed
to communicate the change to him. Louli, who may have been the only
musician capable of catching the error, had died three years
earlier.
LAffilards misattribution of his numbers to Sauveurs tierce
measurement might explain why most of Choquels numbers for vocal
pieces are reasonable, while those for dance forms (which include
two other vocal pieces) are excessively fast. For the dance forms
(Gavotte, Rigaudon, Menuet, Passepied, and Gigue), Choquel simply
converted LAffilards numbers from the assumed tierces into pendulum
pouces, making slight adjustments.
The last set of numbers is found in Pajots Description et usage
dun mtromtre, where he calls his machine an improvement of Loulis
chronomtre because it is measured in parts of a second instead of
pendulum pouces, uses an aural signal to identify the beginning and
last part of each pendulum swing, and has a graduated scale.25
Pajots Table of pendulum lengths (partially supplied in Figure 4)
comprises those for the different durations of vibrations from
demi-tierce to demi-tierce up to 180 demi-tierces, or a second and
a half ,26 using these values:
Pied [foot 331 mm.].Pouce [royal French inch], the twelfth part
of a pied.Ligne, the twelfth part of a pouce.Point, presumably the
twelfth part of a ligne.
The fundamental measurements are as follows:
24 LAffilard, Principes, 77ff.
25 Louis-Lon Pajot, comte dOnzembray, Description et usage dun
mtromtre, ou machine pour battre les
mesures & les temps de toutes sortes dairs, in: Histoire de
lAcadmie Royale des Sciences, 1732, Paris, 1735,
Mmoires, 182-196.
26 Pajot, Description, 183: & nous y joindrons une Table de
toutes les longueurs du Pendule, en pieds, pouces,
lignes & points, pour les diffrents dures des vibrations de
demi-tierce en demi-tierce jusqu 180 demi-
tierces, ou une seconde & demie.
Example 4LAffilard, Air, fort grave.
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Everyone knows that an hour is divided into 60 minutes ['], 1
minute into 60 seconds [''], and 1 second into 60 tierces ['''] or
120 half-tierces; this will give us a sufficiently small divi-sion
for what we propose. It is also known that a pendulum must have a
length of 3 pieds and 8 lignes, for each vibration to last a second
or 60 tierces.27
His full chart of pendulum lengths runs from to 90 tierces, and
its unprecedented mathematical exactitude is the most probable
reason that his work was accepted by the Acadmie Royale des
Sciences. The column headed Nombre des demi-tierces contains
tierces, with the demi-tierces inserted between each tierce. Thus
the number 60 in this column requires a pendulum length of 3 pieds
and 8 lignes, the correct length for a second.
27 Pajot, Description, 187f.: Tout le monde sait quune heure se
divise en 60 minutes, 1 minute en 60
secondes, et 1 seconde en 60 tierces ou 120 demi-tierces; cela
nous donnera une division suffisamment
petite pour ce que nous proposons. On sait aussi que la longueur
que doit avoir un Pendule, pour que
chaque vibration soit dune seconde ou de 60 tierces, doit tre de
3 pieds 8 lignes et demi.
Figure 4Pajot, Table for pendulum lengths (fragment).
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the french time devices revisited
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Figure 5Pajot, Mtromtre.
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dutch journal of music theory
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Pajot describes his machine (Figure 5, which includes a simple
pendulum in between front and side views of his own device) as
follows:
The two vertical pieces A, B, and C, D are each about five feet
in length . On top of these two pieces is a pendulum E, whose beats
of the bob are heard distinctly; thus one hears the beginning and
end [part] of each vibration. There are holes to mark 76
demi-tierces; in other words, from 30 to 68 tierces.28
In his chart of tempo numbers for pieces from Lully, Pascal
Collasse, Andr Campra, Andr-Cardinal Destouches, and Jean-Baptiste
Matho (Figure 6), the third column supplies the time signature; the
fourth, the number of beats per bar; the fifth, the number of
tierces per bar; and the sixth, the number of tierces per beat. As
with the tierce interpretation of LAffilards numbers, Pajots
numbers are amazingly rapid.
28 Pajot, Description, 184ff.: Les deux montants verticaux A,B,
& C, D, ont chacun environ 5 pieds de hauteur
. Sur ces deux montant est une Pendule E, dont les battements du
rocher se sont entendre distinctement,
ainsi on connoit par loreille le commencement & la fin de
chaque vibration. lon a fait des trous pour
marquer 76 demi-tierces, savoir depuis 30 jusqu 68 tierces.
Figure 6Pajot, Chart of tempos.
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the french time devices revisited
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According to Pajots text, his machine has an aural signal to
mark both the beginning of each pendulum swing and its return (a
period). A period lasting one second (60''') would therefore have
audible signals spaced a half second apart (or M 120). For the
fastest tempo on his machine (30'''), these signals would be at
quarter-second intervals (or M 240). But it is doubtful that
technology existed for attaining an audible signal at such speed.
Moreover, the ear cannot distinguish individual components moving
so rapidly, making the machine useless for determining tempo. Thus
Pajots tierce numbers for pieces in Figure 6 do not appear to
correlate with his machines description. After Loulis death in
1702, Pajot acquired his chronomtre. In 1696, Louli noted that he
had consulted with musicians who had performed under Lully, after
which he calculated tempo numbers for various pieces.29 These
numbers may have been inserted into Loulis personal copies of
scores in his extensive library, which was apparently dispersed
after his death, or they may have existed in a master list. No
trace of them has come to light. When obtaining Loulis chronomtre,
the collector Pajot may also have acquired some of his library or a
list of his tempo numbers. All of the pieces for which Pajot
provided tierce numbers in Figure 6 were composed during Loulis
lifetime. As has been proposed, these numbers may have derived from
Loulis missing ones.30
Just as LAffilard was not a mathematician, Pajot had no music
credentials, as can be verified by certain items in his chart. For
instance, the second Air des songes funestes from Lullys
Atys(Act3,Scene4)hasatimesignatureof3/2.31 Yet Pajot divides the
bar intotwoparts(thus6/4)insteadofthree. Even though Pajots chart
specifies that Les Dmons (actually Feste Infernale; Act 4, Scene 3)
from Lullys Alceste has 4 temps, he divides the C signature into
two parts, instead of four. Therefore, he did not himself provide
the four-beat description. This signature conveyed four beats,
normally slow unless indicated otherwise. The designation
4tempslikelyderivesfromanotationinalistthatLoulicompiled,foritwouldbeunnecessary
in the edition itself. Since the other pieces in this scene have
different time signatures, it served to identify the one intended.
An incipit for the Loure from Collasses Thetis & Pele in Pajots
chart is included in Hotteterres description (1719) of the 6/4
signature. Calling its tempo grave, he
recommendsfourunequalbeats(twominim/crotchetunits).32 Since Pajot
implausibly assigns the Loure the same tempo as the rapid Gigue,
the tempo number itself is probably incorrect. Further errors or
questionable aspects of Pajots table include:
AGiguefromLullysAmadis is misattributed to Collasse.
TheMenuetfromCampraslEurope galante has an incorrect time signature
of 2. LullysFtes de lamour et de Bacchus has no Chaconne des
Arlequins. Its purported
number 68 for a full bar measured in tierces would produce a
tempo almost twice as fast as Feuillets chaconne.
AlthoughPajot lists aDivinits de la terre fromLullysPerse, none
exists in this opera. Scholars have inferred that it must be the
Entre de divinitez infernales, but
29 Louli, lments, 88.
30 See Patricia M. Ranum, Mr de Lully en trio: Etienne Louli,
the Foucaults, and the Transcription of the
Works of Jean-Baptiste Lully (1673-1702), in: Jrome de La Gorce
and Herbert Schneider (eds), Jean-Baptiste
Lully: Actes du colloque = Kongressbericht:
Saint-Germain-en-Laye, Heidelberg 1987, Laaber: Laaber-Verlag,
1990, 314.
31 For this piece, Wolff, Das Metronom, 216, and Miehling, Das
Tempo, 80, select the preceding chorus, also
in 3/2.
32 Hotteterre, LArt de prluder, 59. Until corrected in Miehlings
second edition of Das Tempo (81), writers
have cited a different piece from this opera, which, however, is
not a Loure, but carries the expression mark
Lour.
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this is speculative. Perhaps Pajot listed the wrong piece or
opera. MultiplepossibilitiesexistforLesDmonsfromLullysPsych: the
Prlude in Act 4,
Scene 1, where the demons enter and begin to terrify Psych; the
next piece (Scene 2) with the three Furies and Psych; the Air des
Dmons that follows; and the Prlude to Act 4, Scene 3, which
involves the three Furies, two Nymphes of Acheron, and Psych
(writers today have chosen the latter).
ForthefirstAirdesSongesfunestesfromLullysAtys, different
possibilities have been presented today.33
TheCourantenearlyalwayshadatimesignatureof3/2,sothebeatunitofMathosunidentified
Courante is probably a minim.
These discrepancies indicate that the chart was not completely
Pajots own work. It is more likely that he compiled it from Loulis
numbers in a list incorporating abbreviations and notations. This
list may have comprised nothing more than a title for each piece
and its pendulum length. Using this thesis, the last column in
Pajots chart (Figure 6) contains Loulis numbers. When this column
is blank, Loulis number includes an entire bar in triple metre and
is found in the preceding column. The one exception Le Printemps de
Phaton may have an incorrect time signature (several possibilities
fit this title), for duple metre could be halved to obtain a number
for the last column. Pajot then misread Loulis numbers as tierces,
instead of pendulum pouces. He calculated the number of beats in
each bar and the resulting number of tierces. But in some instances
he may have misinterpreted the beat unit. Like us, he sometimes had
to guess which piece Louli meant. Moreover, handwriting can easily
be misread. Table 4 provides Pajots original number for a beat (or
bar when indicated), and the metronome marks derived from both
tierce and pouce measurement. Pajots chart appears to have been
prepared independently of his own machine, which, if its
description is accurate, would have produced audible signals too
rapid to be useful in most cases. While he clearly intended to
achieve tierce measurement, his machine may actually have been
based on pendulum length. He presents himself as building on Loulis
work, and the highest number on his machine is nearly the same as
on Loulis chronomtre. In contrast to the questionable identity of
some free forms in Pajots chart, that of the dance forms is more
certain. When the numbers from LAffilard, Pajot, and Feuillet are
all interpreted as pendulum lengths, as Feuillets must be, the
metronome derivations for each dance form are remarkably similar
(Table 5). Besides providing reasonable tempos, pouce measurement
removes the disparity found among some of the dances when measured
in tierces.Forexample,thepaceofLAffilardsSarabandein6/4 measured in
pouces is not greatly faster than the other Sarabandes; with tierce
measurement; on the other hand, the metronome marks are 72, 86, and
133. While early sources define the Chaconne as just somewhat
faster than the Passacaille, tierce measurement produces M 157 for
the former and 106 for the latter. None of the numbers in Table 5
should be regarded as a fixed tempo, but as an approximation to be
adjusted up or down according to the pieces texture. Some dances
existed in multiple forms: for example, Jean-Jacques Rousseau
describes the Gavotte as ordinarily graceful, often gai; also
sometimes tender and slow.34 Choquel makes an interesting point
when observing that it would be better to write theMenuet in 6/4
instead of 3, because the Pas de Menuet comprises two bars of 3,
each of which has one step. Thus the Matres Danser beat the Menuet
in two one beat for each bar of 3, which
33 See Miehling, Das Tempo, 79; and Wolff, Das Metronom,
216.
34 J.-J. Rousseau, Dictionnaire, Gavotte.
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the french time devices revisited
184
LuLLy
Boure de Phaton
La Marie des Ftes de Bacchus &
de lAmour
Le Printemps de Phaton
Gavotte de Roland
Les Dmons de Psich
1.er Air des Songes funestes dAtis
2.d Air des Songes funestes dAtis
Les Dmons du 4.me acte de Proserpine
Passacaille de Perse
Les Dmons dAlceste 4 temps
Les Divinits de la terre de Perse
La Chaconne des Arlequins des Ftes de
Bacchus & de lAmour
COLLASSe
Gigue dAmadis [actually Lully]
Loure de Thtis & Pele
LOuverture de Thtis & Pele,
Le Commencement
Et la Reprise
CAMPRA
Passepied de lEurope galante
Rigaudon de lEurope galante
Menuet de lEurope galante
DeSTOuCHeS
Sarabande dIss
Boure dOmphale
Menuet de Marthsie
MATHO
Courante
Pajots
number
32
34
68 (full bar)
37
45
63
32
30
38
48
361/2
68 (full bar)
32
32?
56
45
36 (full bar)
31
51 (full bar)
49
30
51 (full bar)
44
Beats/bar*
2
?
??
2
??
??
3
2
3
4
??
??
2
?
2
2
1
2
1
3
2
1
3
Metronome
mark from
tierces
112
106
106
98
80
58
112
120
95
76
100
53
112
112
64
80
100
116
71
72
120
71
79
Metronome
mark from
pouces
64
62
44
59
54
45
64
66
58
52
60
44
64
64
48
54
60
65
50
51
66
50
54
Table 4Pajots numbers measured in Tierces and Pouces.
* ? indicates a questionable beat unit, and ?? an uncertain
piece.
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dutch journal of music theory
185
moves too quickly for the hand to beat it comfortably in
three.35 His remarks fit with Table 5s Menuet metronome mark of 50
or 52 for one bar of 3; if the hand had to make three motions per
bar at this speed, it would shortly become fatiguing. From the
similar tempos for each dance form in Table 5, it can be seen that
LAffilards and Pajots numbers were based not on Sauveurs system of
tierce measurement, but on the same pendulum-length measurement
that was required for Feuillets device. The
35 Choquel, La Musique, 127: Je crois quil vaut mieux appliquer
cette mesure 6 & 4 au Menuet que celle du
triple simple; car le Pas de Menuet absorbant deux mesures trois
temps simples, puisque les Matres
Danser font battre le Menuet deux temps dont chacun emporte une
mesure triple simple par chaque Pas,
il seroit beaucoup mieux de se runir sur ce point avec eux. La
mesure trois temps simples est dailleurs
si presse pour le vrai mouvement du Menuet que la main na pas
tout le temps ncessaire pour marquer
chaque temps suivant le triangle que forme cette sorte de
mesure.
Bourre
Gavotte
Rigaudon
Sarabande
Passacaille
Chaconne
Menuet
Gigue
Passepied
Courante
Canaries
Loure
Time signature
2
2
C-barr
2
3/2
3
6/4
3
3
3
6/8
3/8
6/8
6/4
3/8
3/2
6/8
6/4
Beats/bar
2
2
2
2
3
3
2
3
3
1
2
1
2
2
1
3
2
2
LAffilard
66
66
66
51
56
69
62
75
50
52
65
60
56
57
62
Pajot
Phaton, 64
Omphale, 66
Roland, 59
LEurope, 65
Iss, 51
Perse, 58
?
LEurope, 50
Marthsie, 50
Amadis, 64
LEurope, 60
54
?
Feuillet
66
59
69
58
60
73
52
66
57
60
71
41
Table 5A comparison of numbers for dance forms. Metronome marks
derived from numbers interpreted as pouces instead of tierces.
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many discrepancies in Pajots chart indicate that he constructed
it from Loulis missing pendulum numbers.
Views from ContemporariesAccording to Rousseau, Pajots machine
succeeded in neither one tempo, nor another.36 Nicolas Framerys
comment on Rousseaus article reveals that none of these
time-measuring devices made an impact:
Several have built and proposed different machines, which were
aimed at marking and, in particular, conserving the true tempo of
each piece as conceived by the composer; but, too complicated in
their means and too limited [for achieving] their object, none has
been adopted.37
According to Jean-Philippe Rameau, Loulis chronomtre was
neglected because of its difficulty, although it was in other
respects an ingenious invention.38 Writing from the Berlin court in
1752, the flautist Johann Joachim Quantz had never known anyone who
used it.39 The one device that seems to have had practical
application (for use with dancing) was Feuillets. Perhaps more
scores with tempo numbers for the dances await discovery. Instead
of setting tempo with a chronomtre device, the encyclopedist Denis
Diderot suggested in 1748 that composers indicate the amount of
time needed to play their piece in its entirety.40 This method was
employed in an autograph manuscript of Lalandes Te Deum (between
1715 and 1726). At the end of most versets is an annotation with
the performance length, which totals 29 minutes or une bonne
demi-heure, written on the last page. The Te Deum had to fit within
the time frame specified by the king. While the tempo for some
movements cannot be established exactly because of different
versions, cuts, optional repeats, or internal metre changes, that
for eight movements with a single time signature and no
complicating factors is obtainable.41 All are moderate, and in
keeping with the tempos above from Louli, Sauveur, Feuillet, most
of Choquels vocal pieces, and LAffilards and Pajots numbers when
interpreted as pendulum pouces instead of tierces. Choquels few
extreme numbers for dance forms appear to derive from assuming that
LAffilards numbers were tierces. For lack of a beat unit, La
Chapelles numbers are unreliable for scientific inquiry. Because
their standards were not our standards, and their equipment not
ours, all of their numbers must be construed as approximations with
a greater or lesser degree of inaccuracy. They also are subject to
the same errors of misprints, mechanical malfunction,
36 J.-J. Rousseau, Dictionnaire, Chronomtre, 99: Il y a une
trentaine dannes quon vit parotre le projet dun
Instrument semblable, sous le nom de Mtromtre, qui battoit la
Mesure tout seul; mais il na russi ni dans
un tems, ni dans lautre.
37 Nicolas Framery, Chronomtre, in: Dictionnaire mthodique.
Musique, Nicolas Framery and Pierre Ginguen
(eds), Paris: Panckoucke, 1791, vol. 1, 280: Plusieurs
mchaniciens ont excut & propos diffrentes
machines, qui avoient pour but de marquer & surtout de
conserver le vritable mouvement de chaque
morceau, tel quil a t conu par lauteur; mais trop compliques
dans leurs moyens, & trop bornes dans
leur objet, aucune na t adopte.
38 Jean-Philippe Rameau, Trait de lharmonie, Paris:
Jean-Baptiste-Christophe Ballard, 1722, 158.
39 Johann Joachim Quantz, Versuch einer Anweisung die Flte
traversire zu spielen, Berlin: J. F. Voss, 1752, XVII/
vii/46, 261.
40 Denis Diderot, Mmoires sur diffrens sujets de mathmatique,
Paris: Durant et Pissot, 1748, 195f.
41 See Lionel Sawkins, Doucement and lgrement: Tempo in French
Baroque Music, Early Music 21 (1993),
365-374. The manuscript (F-Pn H400D) is described by Genevive
Thibault, Le Te Deum de Lalande:
Minutage de lpoque, Fontes artis musicae 12 (1965), 162-165.
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and human judgement we see today. Moreover, their lack of
metronome training for musicians led to what we would term rhythmic
inaccuracy, which was not entirely undesirable. As Diderot
comments:
Connoisseurs will object to the chronomtre because there are
perhaps not four bars in an air that have the same duration . A
musician who knows his art sings or plays more slowly or less
slowly from one bar to another, and even from one beat or
quarter-beat to the following.42
Rhythmic freedom was acceptable for soloists, but created havoc
in ensembles. This explains why leaders had to beat time audibly
and why tempos therefore had to be very moderate in comparison to
ours.43 If we had never undergone metronome training from
childhood, we, too, would perform as erratically as Diderot
describes. As for the numbers themselves, it is impossible to
obtain an accurate tempo measurement without first acquiring the
ability to maintain a perfectly steady tempo. The dancing master
Feuillet probably had as sound a rhythmic sense as anyone of the
period a further reason for the importance of his numbers. Together
with the visual evidence of the pendulum for which they were
intended, these numbers provide the key to interpreting the
questionable or ambiguous numbers of others. With few exceptions,
the various sources now present greater uniformity and plausibility
of tempo.
42 Diderot, Mmoires, 193f.: Ils objecteront contre tout
Chronomtre en gnral, quil ny a peut-tre pas dans
un air quatre mesures qui soient exactement de la mme dure . Un
Musicien qui sait son art chante ou
jou plus ou moins lentement dune mesure un autre & mme dun
tems & dun quart de tems celui qui
le suit. Le seul bon Chronomtre que lon puisse avoir, cest un
habile Musicien qui ait du got, qui ait bien
l la Musique quil doit faire excuter, & qui sache en battre
la mesure.
43 See, for example, J.-J. Rousseau, Dictionnaire, Battre la
mesure, 51.
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Appendix
The transcription of Uffenbachs handwritten text in old German
script.1*
[249] Nach dieem hergeleenen und an dem Weltmodell erluterten
beyden Aufstzen, zeigte ich der Gesellschafft eine gewie zu der
Music dienliche Machine, so ehedeen auf Befehl Knig Ludwig des XIV.
von einem Mitglied der Kniglichen Academie, Feuillet, erfunden
worden, inmaen er sowohl in der Music als insonderheit denen Opern
keine Stimmen der Instrumenten hren, noch einige Ungleichheit oder
Unordnung vertragen konte, weilen es nun unter denen Tntzern und
dem Orchester deren Opern einen immerwhrender Streit gesezet, ob
man nehmlich ein Ballet entre oder andern Gesang nicht geschwind
oder langsam genug vorgespiehlet, so hat der Erfinder ein Mittel
ausgesonnen, vermge eines kleinen Instrumentes den Tact Mensur oder
Tempo allemahl einerley zu haben und sich so wohl in dem Orchestere
als inter denen Scenen vor die Tnzer darnach zu richten. Es
bestehet aber solches [250] in einem 5 Schu langen und 2 Zoll im
Quadrat dicken holzernen viereckenden Stabe, welcher nach Magebung
des hin und her schwenckens eines Senckels, der fornen an einer
seidenen dnnen Schnur vibrirt, viele ungleiche Abtheilungen auf
einem aufgeklebeten langen Papier hat, worber ein meinger
viereckender Ring mit einem kleinen Arm, dadurch die Schnur
gezogen, hoch oder niederig gerutschet und gestellet werden kan, da
das centrum oscillationis oder die Lnge des Fadens an dem
Perpendicul verndert werden knne, stellet man nun daelbe hoch oben
hin und lt den Faden lang, so giebt es langsame Vibrationes die
mehr Zeit wegnehmen, als wenn der Faden kurtz gelaen wird, durch
dieen Unterschied hat der Erfinder einen Masstab formiren knnen,
welcher die accurate Zeit eines Tacts, er seye lang oder kurtz,
bestimmen kan. Die uere Gestalt von dem ganzen Werck kan man aus
beygesezter Zeichnung abnehmen, wo a, b der lange viereckende Stab
mit seinem Aufgeklebeten Masstabe ist, c aber stellet den meingen
Schieber vor, der durch den hinter der Machine befindlichen Faden
in die Hhe und hernieder gestellt werden kan, angesehen derselbe
oben und unten ber kleine Rollen d, e gehet, und mit seinen beyden
Enden an einander fest geknpfet ist. Damit aber besagter Schieber
allezeit fest auf dem Masstabe wieder gedruckt werde, so sind 2
eiserne Federn hinten [251] her an demselben gemacht, die in einer
Nuthe so lngst des holzernen Stabes eingehobelt worden, auf und ab
gerutschet werden knnen. Oben her bey f ist ein anderer
unbeweglicher Arm mit 2 Lcher, wodurch der seidene Faden gezogen
wird, feste eingeschraubet, ber demselben aber befindet sich ein
Knopf g, der in einem Loch auf der Hirnseide des viereckenden
langen Stabes sich gedrange herumdrehen let, und um welchen der
berflige Seidenfaden gewickelt werden kan, angesehen das
Bleygewichte oder der Senckel k, nicht lnger vor dem Stabe hangen
mu als da er juste in seinen Vibrationen bey dem Zirckel h, welcher
unten auf dem Masstabe gezeichnet ist, vorbey streiche, ohne
welches die Vibrationes nicht wichtig seyn wrden und bey deen
Vorbeypassierung man jedes Mahl den Tact schlagen und also die
Geschwindigkeit des Tempo erkennen mu. Damit man aber die
eigendliche Einrichtung des beweglichen Schiebers desto beer sehen
knne, so habe sie in nachfolgender Figur [Enlargement of K and C
from Figure 2 - BJ] besonders abgezeichnet.
Wie auch das Bleygewichte nach seiner nathrlichen Gre. Aus dem
Masstabe, welcher auf dem viereckenden Stock lngst herunter stehet,
siehet man brigends wie die Mensur sich immer verkrze, nachdem sie
weiter herun[252]ter kommet, wie ich solche nach eigendliche
Verjngung nach angeben eines besondern Maasstabes aufgetragen.
In
* Transcription courtesy of Dr. Paul Peucker, Archivist of the
Moravian Church, Northern Province, Bethlehem, Pennsylvania,
USA.
the french time devices revisited
188
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den runden Zirckel fr welchem das Bleygewichte sonst zu vibriren
pfleget, setzet man Ziehrats wegen ein klein rund Spiegel Glas,
damit man die Vibrationen desto beer sehen kan. Unter demselben
aber stehet nachfolgendes Register von Tntzen, deren Tempo man zu
sehen verlanget, und weil der Raum in der Abzeichnung alhier zu
klein geween, so will sie folgendermaen hier einrcken. Verlangt man
nun dieem nach das Tempo eines Tantzes, e.g. Menuets zu sehen, so
faet man die Schnur so ber beyde Rollen hinten an dem Instrumente
gehet und den untersten beweglichen Schieber anziehet, an, und
stellet solchen ber die Zahl wo 48 stehet, siehet zu, da das
Bleygewichte nicht lnger an seinem Faden als vor dem Spiegelgen,
wie auch nicht krtzer hange, giebt demselben einen Sto, oder lt es
seine Vibrationes machen, und schlgt so offt der Senckel bey dem
Spiegelgen vorbey fhret den Tact, so wird das rechte Tempo vor
einen solchen Tantz herauskommen, welches die Operisten so wohl als
Musicos in Ordnung und einer gleichen Mensur halten, auch sonsten
in der Music nicht wenig Nutzen kan. Es ist brigends aus denen
Gesezen der Bewegung und der Mechanic bekant, da ein Senckel in
seiner Schwenckung nicht mehr Zeit erfodere, wenn er ein groes
Zirckelstck fhret oder wenn er nur ein kleines anweiet, inmaen er
in dem ersten Fall desto geschwinder, im lezten aber desto
langsamer gehet, und wenn anderst eine lnge [253] von Faden, oder
ein Centrum oscillationis behalten werden, einerley Zeit Versaumung
erfordert da entwegen darff man also bey dieem Instrument, so seyn
Erfinder Mons. Feuillet, cronometre betittult, nicht frchten, da
der Tact ungleich werde angegeben werden, sintemahl die Schwenckung
eben so viel Zeit wenn sie weit ausgreiffet, oder wenn sie nur ein
kleines Zirckelstck abschneidet und einen schwachen Sto bekommen,
oder auch wenn sie in der Lnge allmhlig nachlet, erfodert, und den
Tact immer einerley accurat angiebt bi der Senckel sich gar nicht
mehr rhret, das doch eine ziemliche Zeit whren kan. Es wird
brigends die Machine selbst in Paris von dem Autore verfertigt,
woran es gleichfal bekommen, und welcher zu deutlicherm Unterricht
noch nachfolgende Beschreibung gemeiniglich mit bey leget:
[French text explaining the crescents that accompany the pouce
numbers in Figure 3.]
[254 bottom] Da man nun also mit dieer Machine die Tnzer und
Musicos nicht allein ber einen Kamm, auch ohne Abrede bringen kan,
sondern auch bey allen Concerten die Strittigkeiten wegen des
rechten Tempo vermindern werden, ein solches siehet man nicht nur
gar leichtlich aus der Beschreibung, es dienet aber auch diejenige,
so noch nicht gar feste und richtig im Tacte sind, zu strcken und
das Geklopfe bey einer Music berhoben zu seyn.
dutch journal of music theory
189
TvM_15_#3_nov_2010_7.indd 189 15-11-2010 12:27:57