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beverly jerold The French Time Devices Revisited Much disparity exists among the metronome marks derived from the tempo numbers for early eighteenth-century French time devices. While some are reasonable, others are implausibly rapid. A newly discovered source, which offers both Raoul Auger 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 XVIII e 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. 169 dutch journal of music theory, volume 15, number 3 (2010)
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  • beverly jerold

    The French Time Devices Revisited

    Much disparity exists among the metronome marks derived from the tempo numbers for early eighteenth-century French time devices. While some are reasonable, others are implausibly rapid. A newly discovered source, which offers both Raoul Auger Feuillets numbers for various forms and a drawing of the pendulum device for which they were intended, solves the mystery of the conflicting numbers. Because only a clockwork mechanism can measure fractions of seconds, his numbers had to measure pendulum lengths (the simpler and most frequent form of measurement). A comparison of his numbers with those for the same dance forms from the two sources with consistently extreme tempos indicates an almost exact correlation when all are measured according to pendulum length, instead of the presumed sixtieths of a second.

    For some eighty years, the tempo numbers for French dance music and certain vocal pieces, derived from time-measuring devices and presented principally in a few French writings from 1696 to 1762, have been a topic of lively discussion.1 When converted into metronome marks, many of these numbers for the same form are significantly inconsistent. Although the very rapid tempos have often been considered valid, the conflict between these and the other much slower tempos for the same forms has not been explained adequately. Why are the numbers attributed to Joseph Sauveurs clockwork measurement system (1701) by Michel LAffilard (1705) and Louis-Lon Pajot, comte dOnzembray (1732) completely out of range from the one tempo number that Sauveur himself supplied and also from those of tienne Louli (1696)? Why do Jacques-Alexandre de La Chapelle (1737) and Henri-Louis Choquel (1762) provide some numbers of very modest speed, but others that are extraordinarily rapid? Because all of these writers numbers are readily available in the modern literature (note 1), they will not be repeated again, except when relevant to material in a recently discovered source that illustrates and describes the pendulum designed by the Paris dancing master Raoul Auger Feuillet (d.1710). His numbers for various dance forms provide the most accurate and plausible large body of information to date about tempo of the period. At this time, two principal forms of measurement existed: one based on pendulum length in inches (pouces) and the other on sixtieths of a second (tierces). The latter, however, requires a complex clockwork mechanism. It was the confusion between these two measurement systems that produced unusually rapid tempos in two sources. The disparities in the other two sets of numbers can be attributed to other factors. Throughout this article, the term metronome, identified by an M, refers only to the modern device, whose mechanism bears no relation to its forerunners.

    1 See, for example, Eugne Borrel, Les indications mtronomiques laisses par les auteurs franais du XVIIIe

    sicle, Revue de musicologie 9 (1928), 149-153; Ralph Kirkpatrick, Eighteenth-Century Metronomic Indications,

    Papers of the American Musicological Society (1938), 30-50; Hellmuth Christian Wolff, Das Metronom des Louis-

    Lon Pajot 1735, in: Nils Schirring, Henrik Glahn, and Carsten E. Hafling (eds), Festskrift Jens Peter Larsen,

    Copenhagen: Wilhelm Hansen, 1972, 205-217; Willem Retze Talsma, Wiedergeburt der Klassiker: Anleitung zur

    Entmechanisierung der Musik, Innsbruck: Wort und Welt Verlag, 1980; Rebecca Harris-Warrick, Interpreting

    Pendulum Markings for French Baroque Dance, Historical Performance 6 (Spring 1993), 9-22; and Klaus

    Miehling, Das Tempo in der Musik von Barock und Vorklassik, second edn, Wilhelmshaven: F. Noetzel, 2003.

    169dutch journal of music theory, volume 15, number 3 (2010)

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  • the french time devices revisited

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    Measurement by Pendulum LengthLoulis chronomtre (Figure 1), a simple pendulum, stood over six feet high. As Louli specifies, the measurement is according to the pied universel 33.12 cm. with a pouce (royal French inch) of 27.6 mm. Thus the pendulum length for one second of time is just slightly over 36 pouces, equivalent to the English 39.1 inches. The formula for a metronome mark is 360number of pouces . Despite the devices lack of graduated scaling, three of his numbers for four incipits of pieces from sonatas by an unknown composer (Example 1) produce plausible metronome derivations.2 An exception is Example 1b, whose pendulum length of 8 pouces has vibrations too rapid for the eye to measure accurately with ease, and may be a misprint. The shortest length for a piece using Feuillets pendulum, to be discussed below, is 24 pouces. After visiting Paris in 1715-1716, the German architect, librettist, and intellectual Johann Friedrich Armand von Uffenbach returned to Frankfurt with a Feuillet chronomtre (Figure 2), which had tempo numbers for seventeen French dances and Entres (Figure 3) affixed to the bottom of its post. As the journal of his travel experiences states: Eine Maschine den Tact in der Musik anzugeben, von der Erfindung des Hr Feuillets zu Paris.3 In 1728, Uffenbach gave a presentation about this device (included in his papers) to a learned society in Frankfurt.4 According to his text, Feuillet invented the chronomtre at the behest of King Louis XIV because he could not hear any harmony (Stimmen) among the instruments in music performances, particularly in operas, and could not bear disharmony or disorder. Because there was perpetual strife between the dancers and the opera orchestra concerning whether a ballet entre or other song was played quickly or slowly enough, the inventor constructed a small device by which the beat or tempo could always be the same, and thus guide both the orchestra and the dancers on stage. It consists of a 2-inch square post that is 5 feet long and marked with a scale of unevenly spaced sections (thus an improvement over Loulis device, which did not use graduated scaling). When the bob moves in front of the circular mirror on the post, it casts a shadow that enables the eye to grasp the beat more precisely. Uffenbachs drawing in Figure 2 shows front and side views of a simple pendulum with graduated

    2 tienne Louli, lments ou principes de la musique, Paris: Ballard, 1696; facsim. edn, Geneva: Minkoff, 1971,

    86ff. The note value placed above the pendulum length in pouces designates the beat unit.

    3 Jrgen Kroemer, Le Cronomtre de Monsieur Feuillet: Absolute Tempoangaben eines barocken

    Tanzmeisters, sterreichische Musikzeitung 56/7 (2001), 23-28.

    4 D-Gs, Cod. Ms. Uffenbach 13/II, 249-254. Figures 2 and 3 from this manuscript are reproduced with the kind

    permission of the Niederschsische Staats- und Universittsbibliothek Gttingen. Uffenbachs handwriting

    is in old German script, a transcription of which is in the Appendix at the end of this article.

    Figure 1Louli, Chronomtre.

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    scaling. Therefore, the tempo numbers cannot be in the tierce (sixtieths of a second) time measurement proposed today5 because this requires a clockwork mechanism. Quoting from the French text included with the chronomtre, Uffenbachs commentary explains the crescents surrounding the number for each dance form in Figure 3. Except for one omission, the beat unit corresponds to the system described by Michel LAffilard (1705):6

    Nocrescents=onebeat/bar Acrescentabove=twobeats/bar Acrescentontheleft=threebeats/bar Crescentsaboveandbelow=fourbeats/bar Crescentsonbothsides=sixbeats/bar(inLAffilardonly)

    Without a clockwork mechanism, Feuillets numbers must be interpreted as pendulum lengths instead of tierces. Those in Figure 3 produce reasonable metronome derivations (Table 1). Corresponding almost exactly to Feuillets numbers in Table 1 are the six for dances in an early eighteenth-century manuscript of choreographies in Feuillet notation, which likewise utilize crescents to indicate the beat unit (Table 2).7 The numbers appear to be contemporaneous with the manuscript and may be from the same hand as the dances.

    5 Kroemer, Le Cronomtre, 25f. and Miehling, Das Tempo, 59.

    6 Michel LAffilard, Principes trs-faciles pour bien apprendre la musique, fifth edn, Paris: Christophe Ballard,

    1705; facsim. edn, Geneva: Minkoff, 1971. Directions for interpreting the beat units are on folding plate II

    (inserted by p.55). His instructions are also reprinted in Rosamond E. M. Harding, Origins of Musical Time

    and Expression, London: Oxford University Press, 1938, plate 10.

    7 F-Po ms. 817. See Harris-Warrick, Interpreting pendulum markings, 21f. For Feuillets Sarabande, the

    number is uncertain. Of the four possibilities, 38 duplicates that specified in Figure 3 for this dance. This

    manuscript is described by Meredith Ellis Little and Carol G. Marsh, La Danse Noble: An Inventory of Dances

    and Sources, Williamstown, Mass.: Broude Brothers, 1992, 132f.

    Example 1 Louli, Sonata incipits.

    Incipit Time signature Beats/ bar Loulis number Metronome mark

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

    a. c.

    b. d.

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    Since the highest number of the chronomtre described by Uffenbach is 60, it cannot be an exact replica of Feuillets, for his numbers extend to 90. Nevertheless, its form had to be similar. Uffenbach probably purchased it from the Atelier chez Feuillet, continued by Jacques Dezais after Feuillets death, which would have found a more ready market for a device of less imposing dimensions than the one Feuillet needed for his own use with dancers. Because it is difficult to gauge tempo visually by a rapidly moving pendulum lacking an audible signal, it was advantageous to have one of sufficient size to measure a slow compound metre, as in the Chique lente in Table 1. The French text quoted by Uffenbach advises the user to subdivide the beat when the number extends beyond the devices range, as with 74 for the Entre lente. While workable for this dance because it is in duple metre this approach cannot be used with the compound-metre forms.

    Figure 2Uffenbachs drawing of Feuillets chronomtre.

    Figure 3Feuillets tempo numbers.

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    Uffenbach obtained his chronomtre some five years after Feuillets death, so the French writer probably overlooked the difference between duple and compound metres. In closing his presentation, Uffenbach observes that this machine not only enables conformity between dancers and musicians, but also lessens the arguments about correct tempo. Moreover, it helps those who are not yet strong in keeping a steady beat, thereby relieving the (loudly audible) time beating (Geklopfe) during the music. The form of this time beating is clarified by a footnote in an anonymous English translation (1709) of Franois Raguenets comparison of French and Italian music (1702). In response to Raguenets remarks about assembling the various elements at the Paris Opra:

    How many times must we practice an opera before its fit to be performed; this man begins too soon, that too slow; one sings out of tune, another out of time; in the meanwhile the composer labors with hand and voice and screws his body into a thousand contortions and finds all little enough to his purpose.

    Dance

    MenuetPassepiedGaillardeGavotteEntre viteEntre lenteEntre lenteBourreRigaudonSarabandePassacailleCouranteChaconneChique lenteLoureGigue viteCanary

    Timesignature

    33/8C-barrC-barrC-barr2C22333/236/46/46/46/8

    Beats/bar

    11222242233332222

    Feuilletsnumber

    4840403737743730273836362490783026

    Metronome mark

    5257575959425966695860607338416671

    Table 1Metronome marks from Feuillets pendulum.

    Time signature

    26/8

    6/4

    C-barr33

    Beats/bar

    22

    2

    233

    Feuillets number

    3030

    30

    302438

    Metronome mark

    6666

    66

    667358

    Table 2Metronome marks from Feuillets numbers in scores.

    Dance

    Entre de paysantGigue de Mr Feuillet (gigue de thetis et pellee)Gigue de Mr Feuillet (gigue de polixenne)Entre de Mr FeuilletChaconne de Mr FeuilletSarabande de Mr Feuillet

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    the translator observes:

    Some years since, the master of the music in the opera at Paris had an elbow chair and desk placed on the stage, where, with the score in one hand and a stick in the other, he beat time on a table put there for that purpose so loud that he made a greater noise than the whole band, on purpose to be heard by the performer. By degrees they removed this abuse from the stage to the music room [probably the orchestra pit], where the composer beats the time in the same manner and as loud as ever.8

    An accident while beating time with a rod led to Jean-Baptiste Lullys premature demise in 1687 when a blow to his toe became infected. Nevertheless, to the chagrin of critics, distracting conducting continued at the Paris Opra for much of the eighteenth century. According to Jean-Jacques Rousseau (1768), the French did not use a roll of paper for beating time, as commonly done elsewhere, but a large baton of hard wood, which was struck forcefully to be heard from afar.9

    The musicien inconnu La Chapelle, too, used pendulum measurement for many incipits of unknown pieces in his primer, but the metronome marks derived from his numbers are widely disparate.10 While some are plausible, others are so extremely fast as to have no relation to the others. La Chapelle provides no beat unit for any of his numbers, and it is likely that the extreme tempos should have a smaller beat unit than has been calculated. Because he applies the time signature 2 indiscriminately for all forms of duple movement (even the allemande, to which early sources nearly always assign four slow beats and a signature of C), the beat unit is uncertain. According to writers such as Jacques Hotteterre (1719), the C-barr signature, for example, can have either two slow or four faster beats (depending on the pieces texture and predominating note values).11 In 1767, the critic Pascal Boyer observed that time signatures were never intended to tell the musician what to do with his body: When beating the measure of two beats, several music masters make four hand movements, while others make eight motions for the measure of four beats, etc., without anyone ever accusing them of not knowing how to beat time.12 A further complicating factor is that some composers (such as Jean-Philippe Rameau) did not apply the signatures in the conventional manner. Using an incorrect beat unit with La Chapelles numbers, mainly those in duple metre, is what has produced untoward tempos. On the other hand, a crotchet beat unit is often satisfactorywhenthesignatureis3.Andforthesignatureof3/2,LaChapelleincludesan incipit of two voices comprising crotchets and minims, which is assigned a moderate tempoofminim=M54.ARondeauincompound-metre6/8, composed of crotchets and quavers,ismarkedasdottedcrotchet=M 66.13 Thus the extreme tempos occur principally

    8 Franois Raguenet, Parallle des Italiens et des Franais en ce que regarde la musique et les opras, Paris: Jean

    Moreau, 1702; facsim. edn, Geneva: Minkoff, 1976, 96f. English translation in A Comparison between the

    French and Italian Musick and Operas, London: W. Lewis, 1709, 42f. Reprinted in The Musical Quarterly 32/3

    (1946), 428f.

    9 Jean-Jacques Rousseau, Dictionnaire de musique, Paris: Vve. Duchesne, 1768, Baton de mesure.

    10 Jacques-Alexandre de La Chapelle, Les vrais principes de la musique, Paris: lauteur, la veuve Boivin, 1736-1752,

    vol. 2, 41-56. His examples are supplied in Miehling, Das Tempo, 85-91.

    11 Jacques Hotteterre, LArt de prluder, Paris: lauteur, Boivin, 1719; facsim. edn, Geneva: Minkoff, 1978, 57.

    12 Pascal Boyer, Lettre Monsieur Diderot sur le projet de lunit de clef dans la musique. Et la rforme des mesures,

    Amsterdam; Paris: Vente, 1767, 52-54, note.

    13 La Chapelle, Les vrais principes, Leons deux parties, voix egalles, vol. 3, 1-3. For examples, see Miehling,

    Das Tempo, 90, nos. 43, 45.

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    with duple metre, indicating that the probable beat unit for most of these pieces should be smaller than assumed today. Another writer using pendulum-length measurement was the attorney Choquel, whose book includes numbers for five dance forms and eleven pieces from sacred and secular vocal works.14 While the dances have extreme tempos, most of the vocal pieces are moderate. For example, Si des Galants de la ville (signature of 2) from Jean-Jacques Rousseaus Le Devin du village is assigned a pendulum length of 24 pouces,orminim=M 73. The vocal line moves in crotchets, accompanied by quavers in the upper strings, and the pieces marking of Gai is the fastest one in Choquels examples.15

    One of Choquels vocal pieces with a questionable tempo an excerpt in duple metre from an unnamed motet by Michel-Richard de Lalande lacks a beat-unit indication.16 Two other vocal pieces with unusually rapid tempos are based on dance forms: an Air en Rondeau from Jean-Baptiste Lullys opera Thse, specified to be a gigue; and a duet having a Mouvement du Menuet.17 In sum, Choquels numbers are reasonable for eight vocal pieces, questionable for three vocal pieces, and extreme for five dance forms. We may find an explanation below.

    Measurement by Time The other writers offering many tempo numbers are the court singer LAffilard and the scientist Pajot. Unlike those of La Chapelle and Choquel, their numbers seem fairly consistent within each set of pieces, but are much more rapid than contemporary verbal descriptions imply. They purport to follow a scaling based on sixtieths of a second (or tierces), as presented by the mathematician Joseph Sauveur (1701) for his chomtre. Sauveur furnished no diagram of his device, but it had to have included a clockwork mechanism to measure fractions of seconds. Sauveurs contemporary Chapotot, a Paris instrument maker, built chomtres, and one survives in the collection of the Paris Conservatoire des Arts et des Mtiers. Since Sauveurs pendulum cord was environ de 8 pieds (106 English inches) in length, the massive device could not have been widely used. He provides a tempo number for just one piece Allons, allons, accourez tous from Lullys Atys (Example 2).18 With a conversion formula of M =

    360o

    number of tierces , his number of 70translatestoaplausibleminim=M 51.To achieve this tempo with Loulis chronomtre, he specifies a pendulum length of 42 pouces, which produces M=55.5.19 The absence of a graduated scale in Loulis pendulum accounts for some discrepancy in metronome derivations. Sauveurs device, too, might not have been quite accurate, or he may have used one of the differing measurements for the pied.

    14 Henri-Louis Choquel, La musique rendue sensible par la mchanique, second edn, Paris: Christophe Ballard,

    1762; facsim. edn, Geneva: Minkoff, 1972, 115-213.

    15 Choquel, La musique, 180ff.

    16 Choquel, La musique, 201f.

    17 Choquel, La musique, 186ff., 207ff.

    18 From Jean-Baptiste Lully, The tragdies lyriques in facsimile, New York: Broude International, 1998-2007.

    Reproduced with kind permission.

    19 Joseph Sauveur, Principes dacoustique et de musique:ou Systme gnral des intervalles des sons, [Paris: s.n.,

    1701]; facsim. edn, Geneva: Minkoff, 1973, 49f.; also in Joseph Sauveur, Collected Writings on Musical Acoustics

    (Paris 1700-1713), ed. Rudolf Rasch, Utrecht: The Diapason Press, 1984, 147f. The latter (p. 40) includes a

    photograph of the Chapotot chomtre at the Paris Conservatoire des Arts et des Mtiers. Sauveur measures

    Lullys piece also in twelfths of a second (14); the conversion formula is M = 720/n.

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    Four years later, LAffilard attributed tempo numbers for various pieces in his Principes trs-faciles pour bien apprendre la musique to Sauveurs system.20 These astonishingly rapid tempos, which differ greatly from Sauveurs own tempo number, appear in a primer for beginning vocal pupils. Since vocal agility takes many years to develop and never attains the speed of which instruments are capable, this requires further investigation; for example: The text of a Gigue in 3/8 (Example 3a), whose tempo number of 31 per bar is

    translated as M 116, cannot be enunciated at this tempo. Forslowformssuchassarabandeandcourante,LAffilardsnumbersdonotpermit

    anexpressiveperformance.Atempoofcrotchet=M 106 is assigned to his Passacaille (Example 3b), but it contains successive semiquavers with separate syllables; his previous edition marks it as Fort gravement. The text is a lament of spurned love: How many tears have I shed without moving you?

    For the four pieces that LAffilard identifies as la mesure six tems graves, themetronome marks derived range from 120 to 150 per crotchet, and do not qualify asveryslow.Wheneachcrotchet=M 150, the correct beat unit has to be two beats of compound metre. Yet he specified six very slow beats per bar, as spelled out by his system of enclosing the tempo number with a crescent on both sides.21

    LAffilard called his pieces appropriate for (social) dancing, which implies moderate tempos. The abundant ornamentation, too, requires adequate time for its execution.

    20 LAffilard, Principes, 52-151.

    21 LAffilard, Principes, 105, 89, 125-138. Talsma, Wiedergeburt, 154-169 and Miehling, Das Tempo, Anhang 2,

    present LAffilards pieces in modern notation.

    Example 2Lully, Atys, Allons, allons, accourez tous, Act 1, Scene 2.

    Example 3aLAffilard, Gigue.

    Example 3b LAffilard, Passacaille.

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    In 1974 Erich Schwandt proposed that the scaling of LAffilards pendulum differed from Sauveurs, thus making modern translations of LAffilards numbers twice too fast.22 With some exceptions, Schwandts corrected numbers correspond more closely to contemporary descriptions of the dance forms.23 Yet there may be a way to bring nearly all of LAffilards numbers within a plausible range. While he believed that he was using Sauveurs system, he was not a mathematician. The numbers supplied are more consistent with Loulis scaling for pendulum lengths in pouces. Table 3 provides metronome marks for LAffilards pieces as derived from measurement in both tierces and pouces.

    22 Erich Schwandt, LAffilard on the French Court Dances, The Musical Quarterly 63 (1974), 395.

    23 Erich Schwandt, LAffilard, in: Stanley Sadie and John Tyrrell (eds), The New Grove Dictionary of Music and

    Musicians, second edition, London: Macmillan, 2001, vol. 14, 109.

    A DEUX TEMSMarcheGavotteRigaudonBourrePavaneBranle en Rondeau

    PAR LE TRIPLE DOUBLESarabande tendreAir tendreAir, fort graveCourante

    PAR LE TRIPLE SIMPLESarabande en RondeauPassacailleChaconneMenuet

    PAR LE TRIPLE MINEURPassepiedGigueAir fort leger

    A SIX TEMS GRAVESLeonSarabandeMarche en RondeauAir grave en Rondeau

    A SIX TEMS LEGERSCanaries en RondeauMenuetGigue

    LAffilards number

    303030304034

    504574 ?40

    42342351

    423131

    24272430

    344836

    Time signature

    C22222

    3/23/23/23/2

    3333

    3/83/83/8

    6/46/46/46/4

    6/86/86/8

    Beats/bar

    422222

    3333

    3331

    111

    6666

    222

    Metronome mark from tierces

    12012012012090106

    72804990

    8610615771

    86116116

    150133150120

    10675100

    Metronome mark from pouces

    666666665762

    51544257

    56627550

    566565

    73697366

    625260

    Table 3LAffilards numbers measured in Tierces and Pouces.

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    With one possible exception, none of the tempos derived from pendulum lengths is unusual. They are, in fact, quite similar to Feuillets. One of LAffilards numbers is out of range from the rest: the 74 for an Air, fort grave (Example 4), which is a reasonable tierce number for this piece.24 Perhaps the tempo measurement was first undertaken with Sauveurs system, and then converted to pendulum-length measurement, for Sauveurs device must have been too large and expensive to find a market. In the changeover, the number 74 was overlooked. Because practicing musicians rarely had access to more than the most rudimentary general education, it is unlikely that LAffilard prepared the purported tierce numbers himself. More probably, he enlisted the aid of a mathematician, who then failed to communicate the change to him. Louli, who may have been the only musician capable of catching the error, had died three years earlier.

    LAffilards misattribution of his numbers to Sauveurs tierce measurement might explain why most of Choquels numbers for vocal pieces are reasonable, while those for dance forms (which include two other vocal pieces) are excessively fast. For the dance forms (Gavotte, Rigaudon, Menuet, Passepied, and Gigue), Choquel simply converted LAffilards numbers from the assumed tierces into pendulum pouces, making slight adjustments.

    The last set of numbers is found in Pajots Description et usage dun mtromtre, where he calls his machine an improvement of Loulis chronomtre because it is measured in parts of a second instead of pendulum pouces, uses an aural signal to identify the beginning and last part of each pendulum swing, and has a graduated scale.25 Pajots Table of pendulum lengths (partially supplied in Figure 4) comprises those for the different durations of vibrations from demi-tierce to demi-tierce up to 180 demi-tierces, or a second and a half ,26 using these values:

    Pied [foot 331 mm.].Pouce [royal French inch], the twelfth part of a pied.Ligne, the twelfth part of a pouce.Point, presumably the twelfth part of a ligne.

    The fundamental measurements are as follows:

    24 LAffilard, Principes, 77ff.

    25 Louis-Lon Pajot, comte dOnzembray, Description et usage dun mtromtre, ou machine pour battre les

    mesures & les temps de toutes sortes dairs, in: Histoire de lAcadmie Royale des Sciences, 1732, Paris, 1735,

    Mmoires, 182-196.

    26 Pajot, Description, 183: & nous y joindrons une Table de toutes les longueurs du Pendule, en pieds, pouces,

    lignes & points, pour les diffrents dures des vibrations de demi-tierce en demi-tierce jusqu 180 demi-

    tierces, ou une seconde & demie.

    Example 4LAffilard, Air, fort grave.

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    Everyone knows that an hour is divided into 60 minutes ['], 1 minute into 60 seconds [''], and 1 second into 60 tierces ['''] or 120 half-tierces; this will give us a sufficiently small divi-sion for what we propose. It is also known that a pendulum must have a length of 3 pieds and 8 lignes, for each vibration to last a second or 60 tierces.27

    His full chart of pendulum lengths runs from to 90 tierces, and its unprecedented mathematical exactitude is the most probable reason that his work was accepted by the Acadmie Royale des Sciences. The column headed Nombre des demi-tierces contains tierces, with the demi-tierces inserted between each tierce. Thus the number 60 in this column requires a pendulum length of 3 pieds and 8 lignes, the correct length for a second.

    27 Pajot, Description, 187f.: Tout le monde sait quune heure se divise en 60 minutes, 1 minute en 60

    secondes, et 1 seconde en 60 tierces ou 120 demi-tierces; cela nous donnera une division suffisamment

    petite pour ce que nous proposons. On sait aussi que la longueur que doit avoir un Pendule, pour que

    chaque vibration soit dune seconde ou de 60 tierces, doit tre de 3 pieds 8 lignes et demi.

    Figure 4Pajot, Table for pendulum lengths (fragment).

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    Figure 5Pajot, Mtromtre.

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    Pajot describes his machine (Figure 5, which includes a simple pendulum in between front and side views of his own device) as follows:

    The two vertical pieces A, B, and C, D are each about five feet in length . On top of these two pieces is a pendulum E, whose beats of the bob are heard distinctly; thus one hears the beginning and end [part] of each vibration. There are holes to mark 76 demi-tierces; in other words, from 30 to 68 tierces.28

    In his chart of tempo numbers for pieces from Lully, Pascal Collasse, Andr Campra, Andr-Cardinal Destouches, and Jean-Baptiste Matho (Figure 6), the third column supplies the time signature; the fourth, the number of beats per bar; the fifth, the number of tierces per bar; and the sixth, the number of tierces per beat. As with the tierce interpretation of LAffilards numbers, Pajots numbers are amazingly rapid.

    28 Pajot, Description, 184ff.: Les deux montants verticaux A,B, & C, D, ont chacun environ 5 pieds de hauteur

    . Sur ces deux montant est une Pendule E, dont les battements du rocher se sont entendre distinctement,

    ainsi on connoit par loreille le commencement & la fin de chaque vibration. lon a fait des trous pour

    marquer 76 demi-tierces, savoir depuis 30 jusqu 68 tierces.

    Figure 6Pajot, Chart of tempos.

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    According to Pajots text, his machine has an aural signal to mark both the beginning of each pendulum swing and its return (a period). A period lasting one second (60''') would therefore have audible signals spaced a half second apart (or M 120). For the fastest tempo on his machine (30'''), these signals would be at quarter-second intervals (or M 240). But it is doubtful that technology existed for attaining an audible signal at such speed. Moreover, the ear cannot distinguish individual components moving so rapidly, making the machine useless for determining tempo. Thus Pajots tierce numbers for pieces in Figure 6 do not appear to correlate with his machines description. After Loulis death in 1702, Pajot acquired his chronomtre. In 1696, Louli noted that he had consulted with musicians who had performed under Lully, after which he calculated tempo numbers for various pieces.29 These numbers may have been inserted into Loulis personal copies of scores in his extensive library, which was apparently dispersed after his death, or they may have existed in a master list. No trace of them has come to light. When obtaining Loulis chronomtre, the collector Pajot may also have acquired some of his library or a list of his tempo numbers. All of the pieces for which Pajot provided tierce numbers in Figure 6 were composed during Loulis lifetime. As has been proposed, these numbers may have derived from Loulis missing ones.30

    Just as LAffilard was not a mathematician, Pajot had no music credentials, as can be verified by certain items in his chart. For instance, the second Air des songes funestes from Lullys Atys(Act3,Scene4)hasatimesignatureof3/2.31 Yet Pajot divides the bar intotwoparts(thus6/4)insteadofthree. Even though Pajots chart specifies that Les Dmons (actually Feste Infernale; Act 4, Scene 3) from Lullys Alceste has 4 temps, he divides the C signature into two parts, instead of four. Therefore, he did not himself provide the four-beat description. This signature conveyed four beats, normally slow unless indicated otherwise. The designation 4tempslikelyderivesfromanotationinalistthatLoulicompiled,foritwouldbeunnecessary in the edition itself. Since the other pieces in this scene have different time signatures, it served to identify the one intended. An incipit for the Loure from Collasses Thetis & Pele in Pajots chart is included in Hotteterres description (1719) of the 6/4 signature. Calling its tempo grave, he recommendsfourunequalbeats(twominim/crotchetunits).32 Since Pajot implausibly assigns the Loure the same tempo as the rapid Gigue, the tempo number itself is probably incorrect. Further errors or questionable aspects of Pajots table include:

    AGiguefromLullysAmadis is misattributed to Collasse. TheMenuetfromCampraslEurope galante has an incorrect time signature of 2. LullysFtes de lamour et de Bacchus has no Chaconne des Arlequins. Its purported

    number 68 for a full bar measured in tierces would produce a tempo almost twice as fast as Feuillets chaconne.

    AlthoughPajot lists aDivinits de la terre fromLullysPerse, none exists in this opera. Scholars have inferred that it must be the Entre de divinitez infernales, but

    29 Louli, lments, 88.

    30 See Patricia M. Ranum, Mr de Lully en trio: Etienne Louli, the Foucaults, and the Transcription of the

    Works of Jean-Baptiste Lully (1673-1702), in: Jrome de La Gorce and Herbert Schneider (eds), Jean-Baptiste

    Lully: Actes du colloque = Kongressbericht: Saint-Germain-en-Laye, Heidelberg 1987, Laaber: Laaber-Verlag,

    1990, 314.

    31 For this piece, Wolff, Das Metronom, 216, and Miehling, Das Tempo, 80, select the preceding chorus, also

    in 3/2.

    32 Hotteterre, LArt de prluder, 59. Until corrected in Miehlings second edition of Das Tempo (81), writers

    have cited a different piece from this opera, which, however, is not a Loure, but carries the expression mark

    Lour.

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    this is speculative. Perhaps Pajot listed the wrong piece or opera. MultiplepossibilitiesexistforLesDmonsfromLullysPsych: the Prlude in Act 4,

    Scene 1, where the demons enter and begin to terrify Psych; the next piece (Scene 2) with the three Furies and Psych; the Air des Dmons that follows; and the Prlude to Act 4, Scene 3, which involves the three Furies, two Nymphes of Acheron, and Psych (writers today have chosen the latter).

    ForthefirstAirdesSongesfunestesfromLullysAtys, different possibilities have been presented today.33

    TheCourantenearlyalwayshadatimesignatureof3/2,sothebeatunitofMathosunidentified Courante is probably a minim.

    These discrepancies indicate that the chart was not completely Pajots own work. It is more likely that he compiled it from Loulis numbers in a list incorporating abbreviations and notations. This list may have comprised nothing more than a title for each piece and its pendulum length. Using this thesis, the last column in Pajots chart (Figure 6) contains Loulis numbers. When this column is blank, Loulis number includes an entire bar in triple metre and is found in the preceding column. The one exception Le Printemps de Phaton may have an incorrect time signature (several possibilities fit this title), for duple metre could be halved to obtain a number for the last column. Pajot then misread Loulis numbers as tierces, instead of pendulum pouces. He calculated the number of beats in each bar and the resulting number of tierces. But in some instances he may have misinterpreted the beat unit. Like us, he sometimes had to guess which piece Louli meant. Moreover, handwriting can easily be misread. Table 4 provides Pajots original number for a beat (or bar when indicated), and the metronome marks derived from both tierce and pouce measurement. Pajots chart appears to have been prepared independently of his own machine, which, if its description is accurate, would have produced audible signals too rapid to be useful in most cases. While he clearly intended to achieve tierce measurement, his machine may actually have been based on pendulum length. He presents himself as building on Loulis work, and the highest number on his machine is nearly the same as on Loulis chronomtre. In contrast to the questionable identity of some free forms in Pajots chart, that of the dance forms is more certain. When the numbers from LAffilard, Pajot, and Feuillet are all interpreted as pendulum lengths, as Feuillets must be, the metronome derivations for each dance form are remarkably similar (Table 5). Besides providing reasonable tempos, pouce measurement removes the disparity found among some of the dances when measured in tierces.Forexample,thepaceofLAffilardsSarabandein6/4 measured in pouces is not greatly faster than the other Sarabandes; with tierce measurement; on the other hand, the metronome marks are 72, 86, and 133. While early sources define the Chaconne as just somewhat faster than the Passacaille, tierce measurement produces M 157 for the former and 106 for the latter. None of the numbers in Table 5 should be regarded as a fixed tempo, but as an approximation to be adjusted up or down according to the pieces texture. Some dances existed in multiple forms: for example, Jean-Jacques Rousseau describes the Gavotte as ordinarily graceful, often gai; also sometimes tender and slow.34 Choquel makes an interesting point when observing that it would be better to write theMenuet in 6/4 instead of 3, because the Pas de Menuet comprises two bars of 3, each of which has one step. Thus the Matres Danser beat the Menuet in two one beat for each bar of 3, which

    33 See Miehling, Das Tempo, 79; and Wolff, Das Metronom, 216.

    34 J.-J. Rousseau, Dictionnaire, Gavotte.

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    184

    LuLLy

    Boure de Phaton

    La Marie des Ftes de Bacchus &

    de lAmour

    Le Printemps de Phaton

    Gavotte de Roland

    Les Dmons de Psich

    1.er Air des Songes funestes dAtis

    2.d Air des Songes funestes dAtis

    Les Dmons du 4.me acte de Proserpine

    Passacaille de Perse

    Les Dmons dAlceste 4 temps

    Les Divinits de la terre de Perse

    La Chaconne des Arlequins des Ftes de

    Bacchus & de lAmour

    COLLASSe

    Gigue dAmadis [actually Lully]

    Loure de Thtis & Pele

    LOuverture de Thtis & Pele,

    Le Commencement

    Et la Reprise

    CAMPRA

    Passepied de lEurope galante

    Rigaudon de lEurope galante

    Menuet de lEurope galante

    DeSTOuCHeS

    Sarabande dIss

    Boure dOmphale

    Menuet de Marthsie

    MATHO

    Courante

    Pajots

    number

    32

    34

    68 (full bar)

    37

    45

    63

    32

    30

    38

    48

    361/2

    68 (full bar)

    32

    32?

    56

    45

    36 (full bar)

    31

    51 (full bar)

    49

    30

    51 (full bar)

    44

    Beats/bar*

    2

    ?

    ??

    2

    ??

    ??

    3

    2

    3

    4

    ??

    ??

    2

    ?

    2

    2

    1

    2

    1

    3

    2

    1

    3

    Metronome

    mark from

    tierces

    112

    106

    106

    98

    80

    58

    112

    120

    95

    76

    100

    53

    112

    112

    64

    80

    100

    116

    71

    72

    120

    71

    79

    Metronome

    mark from

    pouces

    64

    62

    44

    59

    54

    45

    64

    66

    58

    52

    60

    44

    64

    64

    48

    54

    60

    65

    50

    51

    66

    50

    54

    Table 4Pajots numbers measured in Tierces and Pouces.

    * ? indicates a questionable beat unit, and ?? an uncertain piece.

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    185

    moves too quickly for the hand to beat it comfortably in three.35 His remarks fit with Table 5s Menuet metronome mark of 50 or 52 for one bar of 3; if the hand had to make three motions per bar at this speed, it would shortly become fatiguing. From the similar tempos for each dance form in Table 5, it can be seen that LAffilards and Pajots numbers were based not on Sauveurs system of tierce measurement, but on the same pendulum-length measurement that was required for Feuillets device. The

    35 Choquel, La Musique, 127: Je crois quil vaut mieux appliquer cette mesure 6 & 4 au Menuet que celle du

    triple simple; car le Pas de Menuet absorbant deux mesures trois temps simples, puisque les Matres

    Danser font battre le Menuet deux temps dont chacun emporte une mesure triple simple par chaque Pas,

    il seroit beaucoup mieux de se runir sur ce point avec eux. La mesure trois temps simples est dailleurs

    si presse pour le vrai mouvement du Menuet que la main na pas tout le temps ncessaire pour marquer

    chaque temps suivant le triangle que forme cette sorte de mesure.

    Bourre

    Gavotte

    Rigaudon

    Sarabande

    Passacaille

    Chaconne

    Menuet

    Gigue

    Passepied

    Courante

    Canaries

    Loure

    Time signature

    2

    2

    C-barr

    2

    3/2

    3

    6/4

    3

    3

    3

    6/8

    3/8

    6/8

    6/4

    3/8

    3/2

    6/8

    6/4

    Beats/bar

    2

    2

    2

    2

    3

    3

    2

    3

    3

    1

    2

    1

    2

    2

    1

    3

    2

    2

    LAffilard

    66

    66

    66

    51

    56

    69

    62

    75

    50

    52

    65

    60

    56

    57

    62

    Pajot

    Phaton, 64

    Omphale, 66

    Roland, 59

    LEurope, 65

    Iss, 51

    Perse, 58

    ?

    LEurope, 50

    Marthsie, 50

    Amadis, 64

    LEurope, 60

    54

    ?

    Feuillet

    66

    59

    69

    58

    60

    73

    52

    66

    57

    60

    71

    41

    Table 5A comparison of numbers for dance forms. Metronome marks derived from numbers interpreted as pouces instead of tierces.

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    186

    many discrepancies in Pajots chart indicate that he constructed it from Loulis missing pendulum numbers.

    Views from ContemporariesAccording to Rousseau, Pajots machine succeeded in neither one tempo, nor another.36 Nicolas Framerys comment on Rousseaus article reveals that none of these time-measuring devices made an impact:

    Several have built and proposed different machines, which were aimed at marking and, in particular, conserving the true tempo of each piece as conceived by the composer; but, too complicated in their means and too limited [for achieving] their object, none has been adopted.37

    According to Jean-Philippe Rameau, Loulis chronomtre was neglected because of its difficulty, although it was in other respects an ingenious invention.38 Writing from the Berlin court in 1752, the flautist Johann Joachim Quantz had never known anyone who used it.39 The one device that seems to have had practical application (for use with dancing) was Feuillets. Perhaps more scores with tempo numbers for the dances await discovery. Instead of setting tempo with a chronomtre device, the encyclopedist Denis Diderot suggested in 1748 that composers indicate the amount of time needed to play their piece in its entirety.40 This method was employed in an autograph manuscript of Lalandes Te Deum (between 1715 and 1726). At the end of most versets is an annotation with the performance length, which totals 29 minutes or une bonne demi-heure, written on the last page. The Te Deum had to fit within the time frame specified by the king. While the tempo for some movements cannot be established exactly because of different versions, cuts, optional repeats, or internal metre changes, that for eight movements with a single time signature and no complicating factors is obtainable.41 All are moderate, and in keeping with the tempos above from Louli, Sauveur, Feuillet, most of Choquels vocal pieces, and LAffilards and Pajots numbers when interpreted as pendulum pouces instead of tierces. Choquels few extreme numbers for dance forms appear to derive from assuming that LAffilards numbers were tierces. For lack of a beat unit, La Chapelles numbers are unreliable for scientific inquiry. Because their standards were not our standards, and their equipment not ours, all of their numbers must be construed as approximations with a greater or lesser degree of inaccuracy. They also are subject to the same errors of misprints, mechanical malfunction,

    36 J.-J. Rousseau, Dictionnaire, Chronomtre, 99: Il y a une trentaine dannes quon vit parotre le projet dun

    Instrument semblable, sous le nom de Mtromtre, qui battoit la Mesure tout seul; mais il na russi ni dans

    un tems, ni dans lautre.

    37 Nicolas Framery, Chronomtre, in: Dictionnaire mthodique. Musique, Nicolas Framery and Pierre Ginguen

    (eds), Paris: Panckoucke, 1791, vol. 1, 280: Plusieurs mchaniciens ont excut & propos diffrentes

    machines, qui avoient pour but de marquer & surtout de conserver le vritable mouvement de chaque

    morceau, tel quil a t conu par lauteur; mais trop compliques dans leurs moyens, & trop bornes dans

    leur objet, aucune na t adopte.

    38 Jean-Philippe Rameau, Trait de lharmonie, Paris: Jean-Baptiste-Christophe Ballard, 1722, 158.

    39 Johann Joachim Quantz, Versuch einer Anweisung die Flte traversire zu spielen, Berlin: J. F. Voss, 1752, XVII/

    vii/46, 261.

    40 Denis Diderot, Mmoires sur diffrens sujets de mathmatique, Paris: Durant et Pissot, 1748, 195f.

    41 See Lionel Sawkins, Doucement and lgrement: Tempo in French Baroque Music, Early Music 21 (1993),

    365-374. The manuscript (F-Pn H400D) is described by Genevive Thibault, Le Te Deum de Lalande:

    Minutage de lpoque, Fontes artis musicae 12 (1965), 162-165.

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    and human judgement we see today. Moreover, their lack of metronome training for musicians led to what we would term rhythmic inaccuracy, which was not entirely undesirable. As Diderot comments:

    Connoisseurs will object to the chronomtre because there are perhaps not four bars in an air that have the same duration . A musician who knows his art sings or plays more slowly or less slowly from one bar to another, and even from one beat or quarter-beat to the following.42

    Rhythmic freedom was acceptable for soloists, but created havoc in ensembles. This explains why leaders had to beat time audibly and why tempos therefore had to be very moderate in comparison to ours.43 If we had never undergone metronome training from childhood, we, too, would perform as erratically as Diderot describes. As for the numbers themselves, it is impossible to obtain an accurate tempo measurement without first acquiring the ability to maintain a perfectly steady tempo. The dancing master Feuillet probably had as sound a rhythmic sense as anyone of the period a further reason for the importance of his numbers. Together with the visual evidence of the pendulum for which they were intended, these numbers provide the key to interpreting the questionable or ambiguous numbers of others. With few exceptions, the various sources now present greater uniformity and plausibility of tempo.

    42 Diderot, Mmoires, 193f.: Ils objecteront contre tout Chronomtre en gnral, quil ny a peut-tre pas dans

    un air quatre mesures qui soient exactement de la mme dure . Un Musicien qui sait son art chante ou

    jou plus ou moins lentement dune mesure un autre & mme dun tems & dun quart de tems celui qui

    le suit. Le seul bon Chronomtre que lon puisse avoir, cest un habile Musicien qui ait du got, qui ait bien

    l la Musique quil doit faire excuter, & qui sache en battre la mesure.

    43 See, for example, J.-J. Rousseau, Dictionnaire, Battre la mesure, 51.

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  • Appendix

    The transcription of Uffenbachs handwritten text in old German script.1*

    [249] Nach dieem hergeleenen und an dem Weltmodell erluterten beyden Aufstzen, zeigte ich der Gesellschafft eine gewie zu der Music dienliche Machine, so ehedeen auf Befehl Knig Ludwig des XIV. von einem Mitglied der Kniglichen Academie, Feuillet, erfunden worden, inmaen er sowohl in der Music als insonderheit denen Opern keine Stimmen der Instrumenten hren, noch einige Ungleichheit oder Unordnung vertragen konte, weilen es nun unter denen Tntzern und dem Orchester deren Opern einen immerwhrender Streit gesezet, ob man nehmlich ein Ballet entre oder andern Gesang nicht geschwind oder langsam genug vorgespiehlet, so hat der Erfinder ein Mittel ausgesonnen, vermge eines kleinen Instrumentes den Tact Mensur oder Tempo allemahl einerley zu haben und sich so wohl in dem Orchestere als inter denen Scenen vor die Tnzer darnach zu richten. Es bestehet aber solches [250] in einem 5 Schu langen und 2 Zoll im Quadrat dicken holzernen viereckenden Stabe, welcher nach Magebung des hin und her schwenckens eines Senckels, der fornen an einer seidenen dnnen Schnur vibrirt, viele ungleiche Abtheilungen auf einem aufgeklebeten langen Papier hat, worber ein meinger viereckender Ring mit einem kleinen Arm, dadurch die Schnur gezogen, hoch oder niederig gerutschet und gestellet werden kan, da das centrum oscillationis oder die Lnge des Fadens an dem Perpendicul verndert werden knne, stellet man nun daelbe hoch oben hin und lt den Faden lang, so giebt es langsame Vibrationes die mehr Zeit wegnehmen, als wenn der Faden kurtz gelaen wird, durch dieen Unterschied hat der Erfinder einen Masstab formiren knnen, welcher die accurate Zeit eines Tacts, er seye lang oder kurtz, bestimmen kan. Die uere Gestalt von dem ganzen Werck kan man aus beygesezter Zeichnung abnehmen, wo a, b der lange viereckende Stab mit seinem Aufgeklebeten Masstabe ist, c aber stellet den meingen Schieber vor, der durch den hinter der Machine befindlichen Faden in die Hhe und hernieder gestellt werden kan, angesehen derselbe oben und unten ber kleine Rollen d, e gehet, und mit seinen beyden Enden an einander fest geknpfet ist. Damit aber besagter Schieber allezeit fest auf dem Masstabe wieder gedruckt werde, so sind 2 eiserne Federn hinten [251] her an demselben gemacht, die in einer Nuthe so lngst des holzernen Stabes eingehobelt worden, auf und ab gerutschet werden knnen. Oben her bey f ist ein anderer unbeweglicher Arm mit 2 Lcher, wodurch der seidene Faden gezogen wird, feste eingeschraubet, ber demselben aber befindet sich ein Knopf g, der in einem Loch auf der Hirnseide des viereckenden langen Stabes sich gedrange herumdrehen let, und um welchen der berflige Seidenfaden gewickelt werden kan, angesehen das Bleygewichte oder der Senckel k, nicht lnger vor dem Stabe hangen mu als da er juste in seinen Vibrationen bey dem Zirckel h, welcher unten auf dem Masstabe gezeichnet ist, vorbey streiche, ohne welches die Vibrationes nicht wichtig seyn wrden und bey deen Vorbeypassierung man jedes Mahl den Tact schlagen und also die Geschwindigkeit des Tempo erkennen mu. Damit man aber die eigendliche Einrichtung des beweglichen Schiebers desto beer sehen knne, so habe sie in nachfolgender Figur [Enlargement of K and C from Figure 2 - BJ] besonders abgezeichnet.

    Wie auch das Bleygewichte nach seiner nathrlichen Gre. Aus dem Masstabe, welcher auf dem viereckenden Stock lngst herunter stehet, siehet man brigends wie die Mensur sich immer verkrze, nachdem sie weiter herun[252]ter kommet, wie ich solche nach eigendliche Verjngung nach angeben eines besondern Maasstabes aufgetragen. In

    * Transcription courtesy of Dr. Paul Peucker, Archivist of the Moravian Church, Northern Province, Bethlehem, Pennsylvania, USA.

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  • den runden Zirckel fr welchem das Bleygewichte sonst zu vibriren pfleget, setzet man Ziehrats wegen ein klein rund Spiegel Glas, damit man die Vibrationen desto beer sehen kan. Unter demselben aber stehet nachfolgendes Register von Tntzen, deren Tempo man zu sehen verlanget, und weil der Raum in der Abzeichnung alhier zu klein geween, so will sie folgendermaen hier einrcken. Verlangt man nun dieem nach das Tempo eines Tantzes, e.g. Menuets zu sehen, so faet man die Schnur so ber beyde Rollen hinten an dem Instrumente gehet und den untersten beweglichen Schieber anziehet, an, und stellet solchen ber die Zahl wo 48 stehet, siehet zu, da das Bleygewichte nicht lnger an seinem Faden als vor dem Spiegelgen, wie auch nicht krtzer hange, giebt demselben einen Sto, oder lt es seine Vibrationes machen, und schlgt so offt der Senckel bey dem Spiegelgen vorbey fhret den Tact, so wird das rechte Tempo vor einen solchen Tantz herauskommen, welches die Operisten so wohl als Musicos in Ordnung und einer gleichen Mensur halten, auch sonsten in der Music nicht wenig Nutzen kan. Es ist brigends aus denen Gesezen der Bewegung und der Mechanic bekant, da ein Senckel in seiner Schwenckung nicht mehr Zeit erfodere, wenn er ein groes Zirckelstck fhret oder wenn er nur ein kleines anweiet, inmaen er in dem ersten Fall desto geschwinder, im lezten aber desto langsamer gehet, und wenn anderst eine lnge [253] von Faden, oder ein Centrum oscillationis behalten werden, einerley Zeit Versaumung erfordert da entwegen darff man also bey dieem Instrument, so seyn Erfinder Mons. Feuillet, cronometre betittult, nicht frchten, da der Tact ungleich werde angegeben werden, sintemahl die Schwenckung eben so viel Zeit wenn sie weit ausgreiffet, oder wenn sie nur ein kleines Zirckelstck abschneidet und einen schwachen Sto bekommen, oder auch wenn sie in der Lnge allmhlig nachlet, erfodert, und den Tact immer einerley accurat angiebt bi der Senckel sich gar nicht mehr rhret, das doch eine ziemliche Zeit whren kan. Es wird brigends die Machine selbst in Paris von dem Autore verfertigt, woran es gleichfal bekommen, und welcher zu deutlicherm Unterricht noch nachfolgende Beschreibung gemeiniglich mit bey leget:

    [French text explaining the crescents that accompany the pouce numbers in Figure 3.]

    [254 bottom] Da man nun also mit dieer Machine die Tnzer und Musicos nicht allein ber einen Kamm, auch ohne Abrede bringen kan, sondern auch bey allen Concerten die Strittigkeiten wegen des rechten Tempo vermindern werden, ein solches siehet man nicht nur gar leichtlich aus der Beschreibung, es dienet aber auch diejenige, so noch nicht gar feste und richtig im Tacte sind, zu strcken und das Geklopfe bey einer Music berhoben zu seyn.

    dutch journal of music theory

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    TvM_15_#3_nov_2010_7.indd 189 15-11-2010 12:27:57


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