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 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 Louis- Léon 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.

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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 360 is number of 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

2 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.

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Example 1 Loulié, Sonata incipits.

a. c.

b. d.

Incipit Time signature Beats/ bar Loulié’s number Metronome mark

a. Two beats lents C-barré 2 40 57 b. Four beats légèrs C 4 8 127 c. Très lents 3/2 3 30 66 d. A final movement 6/4 2 16 90

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 Figure 3 Uffenbach’s drawing of Feuillet’s chronomètre. 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.

Time Feuillet’s Metronome Dance signature Beats/bar number mark

Menuet 3 1 48 52 Passepied 3/8 1 40 57 Gaillarde C-barré 2 40 57 Gavotte C-barré 2 37 59 Entrée vite C-barré 2 37 59 Entrée lente 2 2 74 42 Entrée lente C 4 37 59 Bourrée 2 2 30 66 Rigaudon 2 2 27 69 Sarabande 3 3 38 58 Passacaille 3 3 36 60 Courante 3/2 3 36 60 Chaconne 3 3 24 73 Chique lente 6/4 2 90 38 Loure 6/4 2 78 41 Gigue vite 6/4 2 30 66 Canary 6/8 2 26 71

Table 2 Metronome marks from Feuillet’s numbers in scores.

Time Feuillet’s Metronome Dance signature Beats/bar number mark

Entrée de paysant 2 2 30 66 Gigue de Mr Feuillet 6/8 2 30 66 (gigue de thetis et pellee) Gigue de Mr Feuillet 6/4 2 30 66 (gigue de polixenne) Entrée de Mr Feuillet C-barré 2 30 66 Chaconne de Mr Feuillet 3 3 24 73 Sarabande de Mr Feuillet 3 3 38 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 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. 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: l’auteur, la veuve Boivin, 1736-1752, vol. 2, 41-56. His examples are supplied in Miehling, Das Tempo, 85-91. 11 Jacques Hotteterre, L’Art de préluder, Paris: l’auteur, Boivin, 1719; facsim. edn, Geneva: Minkoff, 1978, 57. 12 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. 13 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 18 360o Lully’s Atys (Example 2). With a conversion formula of M = number of 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 hisPrincipes 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.

Metronome Metronome L’Affilard’s Time mark from mark from number signature Beats/bar tierces pouces A DEUX TEMS Marche 30 C 4 120 66 Gavotte 30 2 2 120 66 Rigaudon 30 2 2 120 66 Bourrée 30 2 2 120 66 Pavane 40 2 2 90 57 Branle en Rondeau 34 2 2 106 62

PAR LE TRIPLE DOUBLE Sarabande tendre 50 3/2 3 72 51 Air tendre 45 3/2 3 80 54 Air, fort grave 74 ? 3/2 3 49 42 Courante 40 3/2 3 90 57

PAR LE TRIPLE SIMPLE Sarabande en Rondeau 42 3 3 86 56 Passacaille 34 3 3 106 62 Chaconne 23 3 3 157 75 Menuet 51 3 1 71 50

PAR LE TRIPLE MINEUR Passepied 42 3/8 1 86 56 Gigue 31 3/8 1 116 65 Air fort leger 31 3/8 1 116 65

A SIX TEMS GRAVES Leçon 24 6/4 6 150 73 Sarabande 27 6/4 6 133 69 Marche en Rondeau 24 6/4 6 150 73 Air grave en Rondeau 30 6/4 6 120 66

A SIX TEMS LEGERS Canaries en Rondeau 34 6/8 2 106 62 Menuet 48 6/8 2 75 52 Gigue 36 6/8 2 100 60

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’stierce 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 demi- tierces, 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 divi- sion 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, André- 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 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.

Metronome Metronome Pajot’s mark from mark from number Beats/bar* tierces pouces Lully Bourée de Phaëton 32 2 112 64 La Mariée des Fêtes de Bacchus & 34 ? 106 62 de l’Amour Le Printemps de Phaëton 68 (full bar) ?? 106 44 Gavotte de Roland 37 2 98 59 Les Démons de Psiché 45 ?? 80 54 1.er Air des Songes funestes d’Atis 63 ?? 58 45 2.d Air des Songes funestes d’Atis 32 3 112 64 Les Démons du 4.me acte de Proserpine 30 2 120 66 Passacaille de Persée 38 3 95 58 Les Démons d’Alceste à 4 temps 48 4 76 52 1 Les Divinités de la terre de Persée 36 /2½ ?? 100 60 La Chaconne des Arlequins des Fêtes de 68 (full bar) ?? 53 44 Bacchus & de l’Amour

Collasse Gigue d’Amadis [actually Lully] 32 2 112 64 Loure de Thétis & Pelée 32? ? 112 64 L’Ouverture de Thétis & Pelée, Le Commencement 56 2 64 48 Et la Reprise 45 2 80 54

Campra Passepied de l’Europe galante 36 (full bar) 1 100 60 Rigaudon de l’Europe galante 31 2 116 65 Menuet de l’Europe galante 51 (full bar) 1 71 50

Destouches Sarabande d’Issé 49 3 72 51 Bourée d’Omphale 30 2 120 66 Menuet de Marthésie 51 (full bar) 1 71 50

Matho Courante 44 3 79 54

* ? 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 66 Omphale, 66

Gavotte 2 2 66 Roland, 59 C-barré 2 59

Rigaudon 2 2 66 L’Europe, 65 69

Sarabande 3/2 3 51 3 3 56 Issé, 51 58 6/4 2 69

Passacaille 3 3 62 Persée, 58 60

Chaconne 3 3 75 ? 73

Menuet 3 1 50 L’Europe, 50 52 Marthésie, 50 6/8 2 52

Gigue 3/8 1 65 6/8 2 60 6/4 2 Amadis, 64 66

Passepied 3/8 1 56 L’Europe, 60 57

Courante 3/2 3 57 54 60

Canaries 6/8 2 62 71

Loure 6/4 2 ? 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 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, 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 pendulumpouces 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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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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