The French Time Devices Revisited

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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 Feuillet’s
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 Sauveur’s clockwork measurement system (1701) by
Michel L’Affilard (1705) and Louis-Léon Pajot, comte d’Onzembray (1732) completely
out of range from the one tempo number that Sauveur himself supplied and also from
those of Étienne Loulié (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, Eugène Borrel, ‘Les indications métronomiques laissées par les auteurs français du XVIIIe
siècle’, 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 LouisLéon Pajot 1735’, in: Nils Schiørring, 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.
dutch journal of music theory, volume 15, number 3 (2010)
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Figure 1
Loulié, Chronomètre.
Measurement by Pendulum Length
Loulié’s chronomètre (Figure 1), a simple pendulum, stood
over six feet high. As Loulié 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 number360of pouces . Despite the device’s 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 Feuillet’s 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 chronomètre
(Figure 2), which had tempo numbers for seventeen French
dances and Entrées (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
chronomètre 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 entrée 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 5½ feet long and marked with
a scale of unevenly spaced sections (thus an improvement
over Loulié’s 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. Uffenbach’s drawing in Figure 2 shows
front and side views of a simple pendulum with graduated
Étienne Loulié, Éléments 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 Jürgen Kroemer, ‘“Le Cronomètre de Monsieur Feuillet”: Absolute Tempoangaben eines barocken
Tanzmeisters’, Österreichische 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 Niedersächsische Staats- und Universitätsbibliothek Göttingen. Uffenbach’s handwriting
is in old German script, a transcription of which is in the Appendix at the end of this article.
2
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Example 1
Loulié, Sonata incipits.
a.
c.
b.
d.
Incipit
a.
b.
c.
d.
Two beats lents Four beats légèrs Très lents A final movement Time signature Beats/ bar
Loulié’s number
Metronome mark
C-barré C 3/2
6/4 40 8
30 16
57
127
66
90
2
4
3
2
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 chronomètre, Uffenbach’s 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 L’Affilard (1705):6
•
•
•
•
•
No crescents = one beat/bar
A crescent above = two beats/bar
A crescent on the left = three beats/bar
Crescents above and below = four beats/bar
Crescents on both sides = six beats/bar (in L’Affilard only)
Without a clockwork mechanism, Feuillet’s numbers must be interpreted as pendulum
lengths instead of tierces. Those in Figure 3 produce reasonable metronome derivations
(Table 1). Corresponding almost exactly to Feuillet’s 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 Cronomètre’, 25f. and Miehling, Das Tempo, 59.
6 Michel L’Affilard, Principes très-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 Feuillet’s 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.
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Figure 2
Uffenbach’s drawing of Feuillet’s chronomètre.
Figure 3
Feuillet’s tempo numbers.
Since the highest number of the chronomètre described by Uffenbach is 60, it cannot be
an exact replica of Feuillet’s, 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 Feuillet’s 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
device’s range, as with 74 for the Entrée lente. While workable for this dance – because
it is in duple metre – this approach cannot be used with the compound-metre forms.
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Table 1
Metronome marks from Feuillet’s pendulum.
Dance
Time
signature
Beats/bar
Feuillet’s
number
Metronome
mark
Menuet
Passepied
Gaillarde
Gavotte
Entrée vite
Entrée lente
Entrée lente
Bourrée
Rigaudon
Sarabande
Passacaille
Courante
Chaconne
Chique lente
Loure
Gigue vite
Canary
3
3/8
C-barré
C-barré
C-barré
2
C
2
2
3
3
3/2
3
6/4
6/4
6/4
6/8
1
1
2
2
2
2
4
2
2
3
3
3
3
2
2
2
2
48
40
40
37
37
74
37
30
27
38
36
36
24
90
78
30
26
52
57
57
59
59
42
59
66
69
58
60
60
73
38
41
66
71
Table 2
Metronome marks from Feuillet’s numbers in scores.
Dance
Entrée de paysant
Gigue de Mr Feuillet
(gigue de thetis et pellee)
Gigue de Mr Feuillet
(gigue de polixenne)
Entrée de Mr Feuillet
Chaconne de Mr Feuillet
Sarabande de Mr Feuillet
Time
signature
Beats/bar
Feuillet’s
number
Metronome
mark
2
6/8
2
2
30
30
66
66
6/4
2
30
66
C-barré
3
3
2
3
3
30
24
38
66
73
58
Uffenbach obtained his chronomètre some five years after Feuillet’s 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 François Raguenet’s comparison of French and Italian music (1702). In response to
Raguenet’s remarks about assembling the various elements at the Paris Opéra:
How many times must we practice an opera before it’s 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.
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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 Lully’s premature demise
in 1687 when a blow to his toe became infected. Nevertheless, to the chagrin of critics,
distracting conducting continued at the Paris Opéra 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-barré signature, for example,
can have either two slow or four faster beats (depending on the piece’s 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 Chapelle’s numbers, mainly those in duple metre,
is what has produced untoward tempos. On the other hand, a crotchet beat unit is often
satisfactory when the signature is 3. And for the signature of 3/2, La Chapelle includes
an incipit of two voices comprising crotchets and minims, which is assigned a moderate
tempo of minim = M 54. A Rondeau in compound-metre 6/8, composed of crotchets and
quavers, is marked as dotted crotchet = M 66.13 Thus the extreme tempos occur principally
8
9
10
11
12
13
François Raguenet, Parallèle des Italiens et des Français en ce que regarde la musique et les opéras, Paris: Jean
Moreau, 1702; facsim. edn, Geneva: Minkoff, 1976, 96f. English translation in A Comparison between the
French and Italian Musick and Opera’s, London: W. Lewis, 1709, 42f. Reprinted in The Musical Quarterly 32/3
(1946), 428f.
Jean-Jacques Rousseau, Dictionnaire de musique, Paris: Vve. Duchesne, 1768, ‘Baton de mesure’.
Jacques-Alexandre de La Chapelle, Les vrais principes de la musique, Paris: l’auteur, la veuve Boivin, 1736-1752,
vol. 2, 41-56. His examples are supplied in Miehling, Das Tempo, 85-91.
Jacques Hotteterre, L’Art de préluder, Paris: l’auteur, Boivin, 1719; facsim. edn, Geneva: Minkoff, 1978, 57.
Pascal Boyer, Lettre à Monsieur Diderot sur le projet de l’unité de clef dans la musique. Et la réforme des mesures,
Amsterdam; Paris: Vente, 1767, 52-54, note.
La Chapelle, Les vrais principes, ‘Leçons à 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
Rousseau’s Le Devin du village is assigned a pendulum length of 24 pouces, or minim = M
73. The vocal line moves in crotchets, accompanied by quavers in the upper strings, and
the piece’s marking of Gai is the fastest one in Choquel’s examples.15
One of Choquel’s 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 Lully’s opera Thésée, specified to be a gigue; and a duet
having a Mouvement du Menuet.17 In sum, Choquel’s 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 L’Affilard 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 échomètre.
Sauveur furnished no diagram of his device, but it had to have included a clockwork
mechanism to measure fractions of seconds. Sauveur’s contemporary Chapotot, a Paris
instrument maker, built échomètres, and one survives in the collection of the Paris
Conservatoire des Arts et des Métiers. Since Sauveur’s 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
Lully’s Atys (Example 2).18 With a conversion formula of M = number360oof tierces , his number of
70 translates to a plausible minim = M 51.To achieve this tempo with Loulié’s chronomètre,
he specifies a pendulum length of 42 pouces, which produces M = 55.5.19 The absence of
a graduated scale in Loulié’s pendulum accounts for some discrepancy in metronome
derivations. Sauveur’s 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 méchanique, 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 tragédies lyriques in facsimile, New York: Broude International, 1998-2007.
Reproduced with kind permission.
19 Joseph Sauveur, Principes d’acoustique et de musique:ou Système général 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 échomètre at the Paris Conservatoire des Arts et des Métiers. Sauveur measures
Lully’s piece also in twelfths of a second (14); the conversion formula is M = 720/n.
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Example 2
Lully, Atys, ‘Allons, allons, accourez tous’, Act 1, Scene 2.
Four years later, L’Affilard attributed tempo numbers for various pieces in his Principes
très-faciles pour bien apprendre la musique to Sauveur’s system.20 These astonishingly rapid
tempos, which differ greatly from Sauveur’s 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.
• For slow forms such as sarabande and courante, L’Affilard’s numbers do not permit
an expressive performance. A tempo of crotchet = 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 L’Affilard identifies as ‘la mesure à six tems graves’, the
metronome marks derived range from 120 to 150 per crotchet, and do not qualify
as ‘very slow’. When each crotchet = 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
L’Affilard called his pieces appropriate for (social) dancing, which implies moderate
tempos. The abundant ornamentation, too, requires adequate time for its execution.
Example 3a
L’Affilard, Gigue.
Example 3b
L’Affilard, Passacaille.
20 L’Affilard, Principes, 52-151.
21 L’Affilard, Principes, 105, 89, 125-138. Talsma, Wiedergeburt, 154-169 and Miehling, Das Tempo, Anhang 2,
present L’Affilard’s pieces in modern notation.
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In 1974 Erich Schwandt proposed that the scaling of L’Affilard’s pendulum differed
from Sauveur’s, thus making modern translations of L’Affilard’s numbers ‘twice too
fast’.22 With some exceptions, Schwandt’s corrected numbers correspond more closely to
contemporary descriptions of the dance forms.23 Yet there may be a way to bring nearly
all of L’Affilard’s numbers within a plausible range. While he believed that he was using
Sauveur’s system, he was not a mathematician. The numbers supplied are more consistent
with Loulié’s scaling for pendulum lengths in pouces. Table 3 provides metronome marks
for L’Affilard’s pieces as derived from measurement in both tierces and pouces.
Table 3
L’Affilard’s numbers measured in Tierces and Pouces.
Beats/bar
Metronome
mark from
tierces
Metronome
mark from
pouces
C
2
2
2
2
2
4
2
2
2
2
2
120
120
120
120
90
106
66
66
66
66
57
62
50
45
74 ?
40
3/2
3/2
3/2
3/2
3
3
3
3
72
80
49
90
51
54
42
57
PAR LE TRIPLE SIMPLE
Sarabande en Rondeau
Passacaille
Chaconne
Menuet
42
34
23
51
3
3
3
3
3
3
3
1
86
106
157
71
56
62
75
50
PAR LE TRIPLE MINEUR
Passepied
Gigue
Air fort leger
42
31
31
3/8
3/8
3/8
1
1
1
86
116
116
56
65
65
A SIX TEMS GRAVES
Leçon
Sarabande
Marche en Rondeau
Air grave en Rondeau
24
27
24
30
6/4
6/4
6/4
6/4
6
6
6
6
150
133
150
120
73
69
73
66
A SIX TEMS LEGERS
Canaries en Rondeau
Menuet
Gigue
34
48
36
6/8
6/8
6/8
2
2
2
106
75
100
62
52
60
L’Affilard’s
number
Time
signature
A DEUX TEMS
Marche
Gavotte
Rigaudon
Bourrée
Pavane
Branle en Rondeau
30
30
30
30
40
34
PAR LE TRIPLE DOUBLE
Sarabande tendre
Air tendre
Air, fort grave
Courante
22 Erich Schwandt, ‘L’Affilard on the French Court Dances’, The Musical Quarterly 63 (1974), 395.
23 Erich Schwandt, ‘L’Affilard’, in: Stanley Sadie and John Tyrrell (eds), The New Grove Dictionary of Music and
Musicians, second edition, London: Macmillan, 2001, vol. 14, 109.
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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 Feuillet’s. One of L’Affilard’s 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
Sauveur’s system, and then converted to pendulum-length measurement, for Sauveur’s
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 L’Affilard prepared the
purported tierce numbers himself. More probably, he enlisted the aid of a mathematician,
who then failed to communicate the change to him. Loulié, who may have been the only
musician capable of catching the error, had died three years earlier.
Example 4
L’Affilard, ‘Air, fort grave’.
L’Affilard’s misattribution of his numbers to Sauveur’s tierce measurement might explain
why most of Choquel’s 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 L’Affilard’s
numbers from the assumed tierces into pendulum pouces, making slight adjustments.
The last set of numbers is found in Pajot’s ‘Description et usage d’un métromètre’, where he
calls his machine an improvement of Loulié’s chronomètre 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 Pajot’s ‘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 L’Affilard, Principes, 77ff.
25 Louis-Léon Pajot, comte d’Onzembray, ‘Description et usage d’un métromètre, ou machine pour battre les
mesures & les temps de toutes sortes d’airs’, in: Histoire de l’Académie Royale des Sciences, 1732, Paris, 1735,
‘Mémoires’, 182-196.
26 Pajot, ‘Description’, 183: ‘& nous y joindrons une Table de toutes les longueurs du Pendule, en pieds, pouces,
lignes & points, pour les différents durées des vibrations de demi-tierce en demi-tierce jusqu’à 180 demitierces, ou une seconde & demie.’
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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 division for what we propose. It is also known that a pendulum must have a length of 3 pieds
and 8½ lignes, for each vibration to last a second or 60 tierces.27
His full chart of pendulum lengths runs from ½ to 90 tierces, and its unprecedented
mathematical exactitude is the most probable reason that his work was accepted by the
Académie 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 8½ lignes, the correct length for a
second.
Figure 4
Pajot, Table for pendulum lengths (fragment).
27 Pajot, ‘Description’, 187f.: ‘Tout le monde sçait qu’une 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 sçait aussi que la longueur que doit avoir un Pendule, pour que
chaque vibration soit d’une seconde ou de 60 tierces, doit être de 3 pieds 8 lignes et demi.’
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Figure 5
Pajot, Métromètre.
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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, André Campra, AndréCardinal 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
L’Affilard’s numbers, Pajot’s numbers are amazingly rapid.
Figure 6
Pajot, Chart of tempos.
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 l’oreille le commencement & la fin de chaque vibration. … l’on a fait des trous pour
marquer 76 demi-tierces, sçavoir depuis 30 jusqu’à 68 tierces.’
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According to Pajot’s 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 Pajot’s tierce numbers for pieces in
Figure 6 do not appear to correlate with his machine’s description.
After Loulié’s death in 1702, Pajot acquired his chronomètre. In 1696, Loulié 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 Loulié’s 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 Loulié’s chronomètre, 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 Loulié’s lifetime. As has
been proposed, these numbers may have derived from Loulié’s missing ones.30
Just as L’Affilard 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 Lully’s Atys (Act 3, Scene 4) has a time signature of 3/2.31 Yet Pajot divides the bar
into two parts (thus 6/4) instead of three.
Even though Pajot’s chart specifies that ‘Les Démons’ (actually ‘Feste Infernale’; Act
4, Scene 3) from Lully’s 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
‘à 4 temps’ likely derives from a notation in a list that Loulié compiled, for it would be
unnecessary 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 Collasse’s Thetis & Pelée in Pajot’s chart is included
in Hotteterre’s description (1719) of the 6/4 signature. Calling its tempo grave, he
recommends four unequal beats (two minim/crotchet units).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 Pajot’s table include:
• A Gigue from Lully’s Amadis is misattributed to Collasse.
• The Menuet from Campra’s l’Europe galante has an incorrect time signature of 2.
• Lully’s Fêtes de l’amour 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 Feuillet’s chaconne.
• Although Pajot lists a ‘Divinités de la terre’ from Lully’s Persée, none exists in this
opera. Scholars have inferred that it must be the ‘Entrée de divinitez infernales’, but
29 Loulié, Éléments, 88.
30 See Patricia M. Ranum, ‘“Mr de Lully en trio”: Etienne Loulié, the Foucaults, and the Transcription of the
Works of Jean-Baptiste Lully (1673-1702)’, in: Jérome 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, L’Art de préluder, 59. Until corrected in Miehling’s 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
Louré.
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this is speculative. Perhaps Pajot listed the wrong piece or opera.
• Multiple possibilities exist for ‘Les Démons’ from Lully’s Psyché: the Prélude in Act 4,
Scene 1, where the demons enter and begin to terrify Psyché; the next piece (Scene 2)
with the three Furies and Psyché; the ‘Air des Démons’ that follows; and the Prélude to
Act 4, Scene 3, which involves the three Furies, two Nymphes of Acheron, and Psyché
(writers today have chosen the latter).
• For the first ‘Air des Songes funestes’ from Lully’s Atys, different possibilities have been
presented today.33
• The Courante nearly always had a time signature of 3/2, so the beat unit of Matho’s
unidentified Courante is probably a minim.
These discrepancies indicate that the chart was not completely Pajot’s own work. It is more
likely that he compiled it from Loulié’s 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 Pajot’s chart (Figure 6) contains
Loulié’s numbers. When this column is blank, Loulié’s number includes an entire bar in
triple metre and is found in the preceding column. The one exception – ‘Le Printemps
de Phaëton’ – 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
Loulié’s 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 Loulié
meant. Moreover, handwriting can easily be misread. Table 4 provides Pajot’s original
number for a beat (or bar when indicated), and the metronome marks derived from both
tierce and pouce measurement.
Pajot’s 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
Loulié’s work, and the highest number on his machine is nearly the same as on Loulié’s
chronomètre.
In contrast to the questionable identity of some free forms in Pajot’s chart, that of the
dance forms is more certain. When the numbers from L’Affilard, Pajot, and Feuillet are all
interpreted as pendulum lengths, as Feuillet’s 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. For example, the pace of L’Affilard’s Sarabande in 6/4 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 piece’s 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 the Menuet in 6/4
instead of 3, because the Pas de Menuet comprises two bars of 3, each of which has one
step. Thus the Maîtres à 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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Table 4
Pajot’s numbers measured in Tierces and Pouces.
Beats/bar*
Metronome
mark from
tierces
Metronome
mark from
pouces
32
34
2
?
112
106
64
62
68 (full bar)
37
45
63
32
??
2
??
??
3
106
98
80
58
112
44
59
54
45
64
30
38
48
361/2½
68 (full bar)
2
3
4
??
??
120
95
76
100
53
66
58
52
60
44
32
32?
2
?
112
112
64
64
56
45
2
2
64
80
48
54
Campra
Passepied de l’Europe galante
Rigaudon de l’Europe galante
Menuet de l’Europe galante
36 (full bar)
31
51 (full bar)
1
2
1
100
116
71
60
65
50
Destouches
Sarabande d’Issé
Bourée d’Omphale
Menuet de Marthésie
49
30
51 (full bar)
3
2
1
72
120
71
51
66
50
Matho
Courante
44
3
79
54
Lully
Bourée de Phaëton
La Mariée des Fêtes de Bacchus &
de l’Amour
Le Printemps de Phaëton
Gavotte de Roland
Les Démons de Psiché
1.er Air des Songes funestes d’Atis
2.d Air des Songes funestes d’Atis
Les Démons du 4.me acte de Proserpine
Passacaille de Persée
Les Démons d’Alceste à 4 temps
Les Divinités de la terre de Persée
La Chaconne des Arlequins des Fêtes de
Bacchus & de l’Amour
Collasse
Gigue d’Amadis [actually Lully]
Loure de Thétis & Pelée
L’Ouverture de Thétis & Pelée,
Le Commencement
Et la Reprise
Pajot’s
number
* ? indicates a questionable beat unit, and ?? an uncertain piece.
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Table 5
A comparison of numbers for dance forms.
Metronome marks derived from numbers interpreted as pouces instead of tierces.
Time signature
Beats/bar
L’Affilard
Pajot
Feuillet
Bourrée
2
2
66
Phaëton, 64
Omphale, 66
66
Gavotte
2
C-barré
2
2
66
Roland, 59
Rigaudon
2
2
66
L’Europe, 65
69
Sarabande
3/2
3
6/4
3
3
2
51
56
69
Issé, 51
58
Passacaille
3
3
62
Persée, 58
60
Chaconne
3
3
75
?
73
Menuet
3
1
50
L’Europe, 50
Marthésie, 50
52
6/8
2
52
3/8
6/8
6/4
1
2
2
65
60
Amadis, 64
66
Passepied
3/8
1
56
L’Europe, 60
57
Courante
3/2
3
57
54
60
Canaries
6/8
2
62
Loure
6/4
2
Gigue
59
71
?
41
moves too quickly for the hand to beat it comfortably in three.35 His remarks fit with
Table 5’s 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 L’Affilard’s
and Pajot’s numbers were based not on Sauveur’s system of tierce measurement, but on
the same pendulum-length measurement that was required for Feuillet’s device. The
35 Choquel, La Musique, 127: ‘Je crois qu’il vaut mieux appliquer cette mesure 6 & 4 au Menuet que celle du
triple simple; car le Pas de Menuet absorbant deux mesures à trois temps simples, puisque les Maîtres à
Danser font battre le Menuet à deux temps dont chacun emporte une mesure triple simple par chaque Pas,
il seroit beaucoup mieux de se réunir sur ce point avec eux. … La mesure à trois temps simples est dailleurs
si pressée pour le vrai mouvement du Menuet que la main n’a pas tout le temps nécessaire pour marquer
chaque temps suivant le triangle que forme cette sorte de mesure.’
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many discrepancies in Pajot’s chart indicate that he constructed it from Loulié’s missing
pendulum numbers.
Views from Contemporaries
According to Rousseau, Pajot’s machine succeeded in neither one tempo, nor another.36
Nicolas Framery’s comment on Rousseau’s article reveals that none of these timemeasuring 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, Loulié’s chronomètre 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 Feuillet’s. Perhaps more scores with tempo numbers for the dances await
discovery.
Instead of setting tempo with a chronomètre 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 Lalande’s Te
Deum (between 1715 and 1726). At the end of most versets is an annotation with the
performance length, which totals 29½ 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 Loulié, Sauveur, Feuillet, most of Choquel’s vocal
pieces, and L’Affilard’s and Pajot’s numbers when interpreted as pendulum pouces instead
of tierces. Choquel’s few extreme numbers for dance forms appear to derive from assuming
that L’Affilard’s numbers were tierces. For lack of a beat unit, La Chapelle’s 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, ‘Chronomètre’, 99: ‘Il y a une trentaine d’années qu’on vit paroître le projet d’un
Instrument semblable, sous le nom de Métromètre, qui battoit la Mesure tout seul; mais il n’a réussi ni dans
un tems, ni dans l’autre.’
37 Nicolas Framery, ‘Chronomètre’, in: Dictionnaire méthodique. Musique, Nicolas Framery and Pierre Ginguené
(eds), Paris: Panckoucke, 1791, vol. 1, 280: ‘Plusieurs méchaniciens ont exécuté & proposé différentes
machines, qui avoient pour but de marquer & surtout de conserver le véritable mouvement de chaque
morceau, tel qu’il a été conçu par l’auteur; mais trop compliquées dans leurs moyens, & trop bornées dans
leur objet, aucune n’a été adoptée.’
38 Jean-Philippe Rameau, Traité de l’harmonie, Paris: Jean-Baptiste-Christophe Ballard, 1722, 158.
39 Johann Joachim Quantz, Versuch einer Anweisung die Flöte traversière zu spielen, Berlin: J. F. Voss, 1752, XVII/
vii/46, 261.
40 Denis Diderot, Mémoires sur différens sujets de mathématique, Paris: Durant et Pissot, 1748, 195f.
41 See Lionel Sawkins, ‘Doucement and légèrement: Tempo in French Baroque Music’, Early Music 21 (1993),
365-374. The manuscript (F-Pn H400D) is described by Geneviève Thibault, ‘Le “Te Deum” de Lalande:
Minutage de l’époque’, 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 chronomètre 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, Mémoires, 193f.: ‘Ils objecteront contre tout Chronomètre en général, qu’il n’y a peut-être pas dans
un air quatre mesures qui soient exactement de la même durée… . Un Musicien qui sçait son art … chante ou
jouë plus ou moins lentement d’une mesure à un autre & même d’un tems & d’un quart de tems à celui qui
le suit. Le seul bon Chronomètre que l’on puisse avoir, c’est un habile Musicien qui ait du goût, qui ait bien
lû la Musique qu’il doit faire exécuter, & 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 Uffenbach’s handwritten text in old German script.1*
[249] Nach dießem hergeleßenen und an dem Weltmodell erläuterten beyden Aufsätzen,
zeigte ich der Gesellschafft eine gewiße zu der Music dienliche Machine, so ehedeßen auf
Befehl König Ludwig des XIV. von einem Mitglied der Königlichen Academie, Feuillet,
erfunden worden, inmaßen er sowohl in der Music als insonderheit denen Opern
keine Stimmen der Instrumenten hören, noch einige Ungleichheit oder Unordnung
vertragen konte, weilen es nun unter denen Täntzern und dem Orchester deren Opern
einen immerwährender Streit gesezet, ob man nehmlich ein Ballet entrée oder andern
Gesang nicht geschwind oder langsam genug vorgespiehlet, so hat der Erfinder ein Mittel
ausgesonnen, vermöge 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
Tänzer darnach zu richten. Es bestehet aber solches [250] in einem 5 ½ Schu langen und 2
Zoll im Quadrat dicken holzernen viereckenden Stabe, welcher nach Maßgebung des hin
und her schwenckens eines Senckels, der fornen an einer seidenen dünnen Schnur vibrirt,
viele ungleiche Abtheilungen auf einem aufgeklebeten langen Papier hat, worüber ein
meßinger viereckender Ring mit einem kleinen Arm, dadurch die Schnur gezogen, hoch
oder niederig gerutschet und gestellet werden kan, daß das centrum oscillationis oder die
Länge des Fadens an dem Perpendicul verändert werden könne, stellet man nun daßelbe
hoch oben hin und läßt den Faden lang, so giebt es langsame Vibrationes die mehr Zeit
wegnehmen, als wenn der Faden kurtz gelaßen wird, durch dießen Unterschied hat der
Erfinder einen Masstab formiren können, welcher die accurate Zeit eines Tacts, er seye
lang oder kurtz, bestimmen kan. Die äußere 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 meßingen Schieber vor, der durch den
hinter der Machine befindlichen Faden in die Höhe und hernieder gestellt werden kan,
angesehen derselbe oben und unten über kleine Rollen d, e gehet, und mit seinen beyden
Enden an einander fest geknüpfet 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 längst des holzernen Stabes eingehobelt worden, auf und
ab gerutschet werden können. Oben her bey f ist ein anderer unbeweglicher Arm mit 2
Löcher, wodurch der seidene Faden gezogen wird, feste eingeschraubet, über demselben
aber befindet sich ein Knopf g, der in einem Loch auf der Hirnseide des viereckenden
langen Stabes sich gedrange herumdrehen läßet, und um welchen der überflüßige
Seidenfaden gewickelt werden kan, angesehen das Bleygewichte oder der Senckel k, nicht
länger vor dem Stabe hangen muß als daß 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 würden und bey deßen Vorbeypassierung man jedes Mahl
den Tact schlagen und also die Geschwindigkeit des Tempo erkennen muß. Damit man
aber die eigendliche Einrichtung des beweglichen Schiebers desto beßer sehen könne, so
habe sie in nachfolgender Figur [Enlargement of K and C from Figure 2 - BJ] besonders
abgezeichnet.
Wie auch das Bleygewichte nach seiner nathürlichen Größe. Aus dem Masstabe, welcher
auf dem viereckenden Stock längst herunter stehet, siehet man übrigends wie die Mensur
sich immer verkürze, nachdem sie weiter herun[252]ter kommet, wie ich solche nach
eigendliche Verjüngung nach angeben eines besondern Maasstabes aufgetragen. In
*
Transcription courtesy of Dr. Paul Peucker, Archivist of the Moravian Church, Northern Province, Bethlehem,
Pennsylvania, USA.
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dutch journal of music theory
den runden Zirckel für welchem das Bleygewichte sonst zu vibriren pfleget, setzet man
Ziehrats wegen ein klein rund Spiegel Glas, damit man die Vibrationen desto beßer sehen
kan. Unter demselben aber stehet nachfolgendes Register von Täntzen, deren Tempo man
zu sehen verlanget, und weil der Raum in der Abzeichnung alhier zu klein geweßen, so
will sie folgendermaßen hier einrücken.
Verlangt man nun dießem nach das Tempo eines Tantzes, e.g. Menuets zu sehen, so
faßet man die Schnur so über beyde Rollen hinten an dem Instrumente gehet und den
untersten beweglichen Schieber anziehet, an, und stellet solchen über die Zahl wo 48 stehet,
siehet zu, daß das Bleygewichte nicht länger an seinem Faden als vor dem Spiegelgen,
wie auch nicht kürtzer hange, giebt demselben einen Stoß, oder läßt es seine Vibrationes
machen, und schlägt so offt der Senckel bey dem Spiegelgen vorbey fähret 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 übrigends aus denen Gesezen der Bewegung und
der Mechanic bekant, daß ein Senckel in seiner Schwenckung nicht mehr Zeit erfodere,
wenn er ein großes Zirckelstück fähret oder wenn er nur ein kleines anweißet, inmaßen
er in dem ersten Fall desto geschwinder, im lezten aber desto langsamer gehet, und wenn
anderst eine länge [253] von Faden, oder ein Centrum oscillationis behalten werden,
einerley Zeit Versaumung erfordert daß entwegen darff man also bey dießem Instrument,
so seyn Erfinder Mons. Feuillet, cronometre betittult, nicht fürchten, daß der Tact ungleich
werde angegeben werden, sintemahl die Schwenckung eben so viel Zeit wenn sie weit
ausgreiffet, oder wenn sie nur ein kleines Zirckelstück abschneidet und einen schwachen
Stoß bekommen, oder auch wenn sie in der Länge allmählig nachläßet, erfodert, und den
Tact immer einerley accurat angiebt biß der Senckel sich gar nicht mehr rühret, das doch
eine ziemliche Zeit währen kan. Es wird übrigends die Machine selbst in Paris von dem
Autore verfertigt, woran es gleichfalß 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] Daß man nun also mit dießer Machine die Tänzer und Musicos nicht allein
über 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 stärcken und das Geklopfe bey einer Music überhoben
zu seyn.
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