II

Time Signatures
in the Eighteenth Century

TIME SIGNATURES in the eighteenth century were generally recognized as signifying how many notes of what value were included in a measure, although the signature sometimes indicated this information only indirectly. Signatures became associated with genres of music; for example, music in the stile antico used mensural signs, such as and and simple proportions, such as 3/1 and 3/2. Music in the theatrical style used the new Italian or French signs that were associated with particular dances, character pieces, or even emotional affects.

Theorists in the eighteenth century were concerned with logical classifications of time signatures—simple and compound duple and triple meters. The notational systems that they attempted to classify, however, challenged the logical mind, since mensural signs and proportions (reinterpreted as they were) were mixed with new time signatures (even though they were derived from proportions). Composers as well as performers needed to tread carefully between traditional and newly fashionable interpretations of notation.

Changes in notation in the eighteenth century stimulated some theorists to suggest additional innovations, in the hope that a logical system could be found. Reforms of notation were avidly discussed in eighteenth-century France; some theorists advocated note values as the best indicator of tempo, and others (Italianate, and perhaps more forward-looking) preferred the use of tempo words. Various reforms were proposed, but none were accepted in practice.

Theorists also discussed new techniques of conducting musical meter, and the relationship of time signatures to the expressive content of the music.

French Theorists

In the late seventeenth century, a few French theorists abandoned the traditional categories under which the signs of mensural notation were discussed, and to which the new signs were appended. The traditional order began with the mensural signs and followed (in old-fashioned treatises) by O, , and perhaps ʘ. In practice, all of these signified duple metrical organization. Next were “proportions,” whether they were actually used as proportions or as fractional numbers; these were primarily signs for triple meter. A final category included “sextuplae,” or compound triples that were based on a mixture of mensural signs and proportions. The new signs 3/4, 6/4, 3/8, 6/8, 9/8, 12/8, and so on, were placed and defined in one of the two latter categories.

Etienne Loulié’s Elements is, perhaps, the first treatise to base categories for meter signs on the number and kind of beats included in the measure; this became the method by which almost all eighteenth-century theorists classified the notation of meter. Loulié defined six types of measures: duple, triple, quadruple, compound duple, compound triple, and compound quadruple. Duple measures were 2, , and 2/4 (he was the only seventeenth-century theorist to include 2/4). C was considered to be a mesure à quatre temps, as well as (which was included in two categories) and 4/8. The mesure à trois temps was signified by 3/1, 3/2, 3/4, 3/8, 3/16, and 3 (triple simple, which he stated was the same as 3/4). Compound duple meters included 6/4, 6/8, and 6/16, and compound triple meters 9/4, 9/8, and 9/16. Compound quadruple meters were 12/4, 12/8, and 12/16.

Loulié further explained meter signs in a section of his treatise written for those “capable of reasoning on the principles of music.” before a numerical sign or fraction identified the beat as slow quadruple time, and before a numerical sign identified the beat as fast quadruple time. However, Loulié did not favor the use of and in conjunction with fractional numbers; he remarked that “foreigners have retained some of them in their works, but their practice is not very certain; some use them in one manner, some in another.”

Loulié criticized the use of mensural signs and other outmoded forms of notation, such as coloration (triple noire) and void notation (triple blanc, or white ternary), “where there is more caprice than reason.” According to him, reason groups meter signs only by the number of beats in a measure.¹

Michel Pignolet de Montéclair reduced the number of categories to two, stating that “essentially there are only two kinds of measures to which all others are related—the duple and the triple.”² With the simple duple and triple, the hand beats every note in the measure. When the beat is very fast, the hand compensates by omitting every other stroke or, in the case of the triple beat, omitting two strokes. If it is not possible to beat every note in a bar, measures are classified as compound (composée). Even though 6/4 is fundamentally related to the triple beat, it is called compound because it equals two 3/4 measures, a downbeat for one and an upbeat for the other. ³

French classifications of meter signs make almost no reference to the tactus, choosing instead to recognize the number of beats (temps) in a measure. Since temps can be translated “beat,” “pulse,” or “time,” English equivalents must be chosen with caution. The system of classification for meter signatures most favored by French theorists was by duple, triple, and compound measures (with two, three, or four beats). C came to be considered a compound of two measures of 2/4, and it was sometimes replaced by 4/4. The number 2 was used as well as . Saint Lambert classified signatures as duple (, , 2, 4/8), triple (3/2, 3, 3/4, 3/8), and compound (6/4, 6/8, 12/4, 12/8, 9/4, 9/8). Dupont⁴ and David⁵ followed this classification, as did Rousseau.⁶ An Italian, Manfredini, also used this duple-triple-compound classification.⁷

Borin and J. F. Démotz de la Salle advocated another system that classified signatures as simple or complex. The signes simples were 2, 3, C, and and the signes composées indicated measures with two, three, or four beats:

De deux tems 2/4, 4/8, 4/16, 6/4, 6/8, 6/16

De trois tems 3/2, 3/4, 3/8, 3/16, 9/4, 9/8, 9/16

De quatre tems 12/4, 12/8, 12/16.⁸

This system therefore retained something of the seventeenth-century groupings of mensural signs (duple) and proportions (triple). Borin⁹ and Corrette¹⁰ adhered to this classification, and Rousseau offered it as an alternative in his Dictionnaire article “Mesure.”

The tempo significance of meter signs and note values was still recognized. In general, quarter notes in measures of 6/4 and 9/4 (but not 2/4 and 3/4) were to be taken graves (slowly); eighths in measures of 6/8, 9/8, and 12/8 (but not 4/8 or 3/8) were légers (vivace), the slowest of quick tempos; and sixteenths in 6/16, 9/16,12/16 (but not 3/16) were vîtes (fast). 2/4 and 3/4 were to be taken léger; 3/8 and 4/8 vîte; 3/16 and 4/16, très vîte.¹¹

Borin classified all measures as having two, three, or four beats. He based five categories of tempo on “airs de characteres,” listing three tempos for four-beat measures, four tempos for two-beat measures, and five tempos for three- beat measures:¹²

Saint Lambert’s Principes du Clavecin described several different conducting patterns. For the triple measure, instead of down (two beats) and up (one beat), he gave one beat down, one beat to the right, and one beat up. For common time of four beats, instead of two down then two up, Saint Lambert gave one beat down, one beat to the right, one beat across to the left, and then one beat up. Other theorists advocated different patterns; Dupont gave a tactus inaequalis figure of one down, then two up instead of the more usual two down, one up. French writers continued to discuss different ways of beating the measure throughout the eighteenth century.

New ways of beating time give additional evidence of the changed status of the measure. The tactus- beat was an anachronism when musicians no longer thought of the measure as a beat, even a very slow beat. The French theorists describe conducting techniques that are similar to modern ones.

English Theorists

According to Alexander Malcolm, an English theorist:

Things that are designed to affect our Senses must bear a due Proportion with them; and so where the Parts of any Object are numerous, and their Relations per-plext, and not easily perceived, they can raise no agreeable Ideas; nor can we easily judge of the Difference of Parts where it is great; therefore that the Proportion of the Time of Notes may afford us Pleasure, they must be such as are not difficultly perceived: For this Reason the only Ratios fit for Musick, besides those of Equality, are the double and triple, or the Ratios of 2:1 and 3:1; of greater Differences we could not judge, without a painful Attention. ¹³

Further on he returned to this topic:

The Measures are only subdivided into 2 or 3 equal Parts; and if there are more, they must be Multiples of these Numbers as 4 to 6 is composed of 2 and 3; again observe, the measures of several Songs may agree in the total Quantity, yet differ in the Subdivision and combination of the lesser Notes that fill up the measure. . . .

Of Common and Triple Time

1. Common Time is of Two Species: the first where every measure is equal to a semibreve . . . The second where every measure is equal to a Minim. The movements are very various, but there are three common Distinctions, slow signified by , brisk—, very quick—, but what that slow, brisk and quick is, is very uncertain, and must be learned by Practice. . . .

Triple time

1. Simple triple measure: 3♩, 3♩, 3♩, or 3♪ (two notes are beat down and one up)

2. Mixt triple measure: 6♩,6♩ or 6♪

3. Compound Triple: 9♪

4. Compound mixt triple: 12♪¹⁴

Malcolm distinguished between measures with the same total number of notes but with a different structure. His method of recognizing this distinction was akin to Butler’s (1636). The word “accented” was used to describe the aural perception of measure organization:

Of the several Species of Triple, there are some that are of the same relative measure, as 3/2, 6/4, 12/8, and 3/4, 6/8. These are so far of the same mode as the Measure of each contains the same total quantity . . . but the different constitutions of the Measure with respect to the Subdivisions and connections of the Notes, make a most remarkable Difference in the Air: For example, the Time of 3/2 consists generally of Minims, and these sometimes mixt with Semibreves or with Crotchets, and some Bars will be all Crotchets: but 3/2 is contrived so that the Air requires the Measure to be divided and is beat by three times, and will not do another Way without manifestly changing and spoiling the Humour of the Song: Suppose we would beat it by two Times, the first Half will always (except when the Measure is actually divided into 6 Crotchets, which is very seldom) end in the Middle, or within the Time of some note; and tho’ this is admitted sometimes for Variety ... yet it is rare compared with the general Rule, which is to contrive the Division of the Measure so that every Down and Up of the Beating shall end with a particular Note; for upon this depends very much the Distinctness and, as it were, the Sense of the Melody; and therefore the Beginning of every Time or Beating in the Measure is reckoned the accented Part thereof. ¹⁵

Malcolm placed a greater reliance for tempo on Italian tempo words than on time signatures. He wrote:

Because the Italian Compositions are the Standard and Model of the better Kind of Musick, I shall explain the Words by which they mark their Movements, and which are generally used by all others in Imitation of them: They have 6 common Distinctions of Time, expressed by these Words, grave, adagio, largo, vivace, allegro, presto, and sometimes prestissimo,¹⁶

The first was the slowest, the rest were gradually faster, but Malcolm warned that only practice would allow a musician to know precisely how much faster or slower one was from another.

The same tempo word used with a triple meter sign indicated a faster speed than when used with common time. Common time could be accompanied by any of the tempo words, but some triple signs were associated with certain tempos. 3/2 was ordinarily adagio but could be taken vivace, 3/4 could have any tempo, 3/8 was allegro or vivace. 6/4, 6/8, and 9/8 were usually allegro. 12/8 was usually allegro, but could sometimes be adagio.

Malcolm suggested that meter signs had lost their precise tempo significance, but complained that tempo words were much too variable. Meter signs such as 3/2, 3/4, and 3/8 indicated the same basic meter, and if the tempo were left entirely to “the arbitrary Direction of these words, adagio, allegro, &c .,” the difference between such meter signs was “more Caprice than Reason.” His discussion leaves the reader aware of the problems but not of solutions. ¹⁷

William Turner offered an equally detailed discussion of time signatures; he was less concerned with fundamental principles but carefully weighed each signature for its meaning. The signs for common time, according to Turner, indicated tempo, with being “somewhat faster” than . For triple time, however,

The only Rule that is to be given for the Length of Notes in this Case, is that where the Movement is Slow; they will always write the word Slow at the Beginning of each Lesson: or at least ought always to do so, the Moods in Triple-Time not at all denoting now, (though formerly they did) what is to be sung Slow or Fast, as they do in Common-Time.¹⁸

Turner’s logical conclusion from the lack of tempo significance of triple signs is that 6/4 and 6/8, 9/4 and 9/8 are unnecessary. However, he does not object to the duplications of simple triples such as 3/1, 3/2, 3/4, and 3/8.

In a later remark about 12/8, Turner made it clear that he considered that tempo was indicated by note values in conjunction with time signatures, not by the signatures alone:

I will not be so Ill-natur’d as to dispute the Reasonableness of this Mood, where it is aptly applied; which is in very swift Movements, as Jiggs, etc. but why it should be made use of in slow (sometimes very slow) Movements, I cannot conceive; since the Mood of 3/8 (which takes in but one of these four Measures) may do much better, especially for the convenience of Scholars, or rather, the Mood of 3/4 or that of 3/2; which barrs in three Minims, they seeming to me, to be much more Proper than Quavers, to denote slow Movements: For if such a Method were put in Practice, there would be no manner of Occasion to write (at the beginning of Lessons) the Italian words, Adagio, Grave, Largo & . (which are put before slow Movements) or Allegro, Presto, Vivace, & . (which are applied to swift Movements; and which they do in all the Moods hitherto spoken of, without Exception) there being Variety sufficient in the different Species of the Notes themselves, to shew what movement is slow, and what brisk; without putting our Pupils or our selves, to the trouble of learning Foreign Languages. ¹⁹

This statement verifies a dependence on tempo words even though Turner regrets their necessity. Using large notes for slow tempos and small notes for quick tempos was a conservative practice that was advocated by a number of theorists.

Turner’s classification of triple measures stated how many beats were included in each measure and indicated that these individual beats were of triple subdivision:

3 × 1 (one beat of triple subdivision)-3/2, 3/4, 3/8;

3 × 2 (two beats of triple subdivision)—6/4, 6/8;

3 × 3—9/4, 9/8;

3 × 4—12/8.²⁰

William Tans’ur was very old-fashioned in wanting the sign or placed before the fractional number of triple signatures. Tans’ur preserved an ideal tactus beat as the norm, indicated by the old mensural signs and varied by “proportions.” Most other theorists of the eighteenth century paid no attention to this vestige of mensural notation.

Or better would it be, if our Tripla-Time-Moods had the Common-Time- Moods always assigned just before them thus: 3/2 & ., or at least, the terms Adagio, Largo, or Allegro, set over the Cliff, at the Beginning of a Piece of Music, or when the Time differs; for them you might at one view know what sort of Binary Movement your Ternary is compared unto; and how quick or slow the Movement was intended by the Author. This, I say, would make Time very easy to every Practitioner, and take away many obscurities that have heretofore Confounded the Ignorant: for when things are falsely compared together, the absurdity thereof greatly darkeneth the Understanding.²¹

Tans’ur’s idea that tempo words convey equivalent information to the mensural signs ʘO, and echoes Printz’s statement of 1689. He seems badly out of date.

The Dictionnaire of Brossard, translated into English and expanded by James Grassineau, gave a thorough exposition of early eighteenth-century meter signatures. Five duple time signatures were described in the article on “time,” in which Alexander Malcolm’s words quoted above are repeated, and tempo is considered as follows:

But then what that slow, brisk, and quick is, is very uncertain, and only to be learned by practice; the nearest measure we know of it, is to make a quaver the length of a pulse of a good watch; then a crotchet will be equal to two pulses, a minim four, and the whole bar or measure eight; this may be reputed the measure of brisk Time, for slow ‘tis as long again, and for the quick only half as long.²²

The subject was not complete until the reader was informed of how to keep time:

Now to keep time equally, we make use of a motion of the hand or foot; knowing the time of the crotchet, we shall suppose the measure actually divided into four crotchets, for the first species of common time; then half the measure will be two crotchets; therefore the hand or foot being up, if we put it down with the very beginning of the first note or crotchet, and then raise it with a third, and then down again to begin with the next measure; this is what we call beating of Time.²³

The implication of his discussion is that time signatures were gauged in reference to a standard tempo.

Concerning Measure, Grassineau said:

Ternary or triple measure is that wherin the fall is double the rise, or è contra; or where two minims are played during a rise and but one in a fall; and vice versa; to this purpose the number three, or 3/8 &c. are placed at the beginning of the lines when the measure is intended to be triple, and a semicircle when it is to be common.²⁴

Under Triple, Grassineau’s translation refers to “the Italians,” although Brossard specifically mentioned Bononcini and Penna. “The common name of Triple time is taken hence, that the whole or half of the bar is divisible into three parts, and beat accordingly, the first time down, the second time with the return of the hand, and at last with the hand quite up, and it is this motion that makes what the Italians mean by the phrase Ondeggiare la mano.”²⁵

Grassineau discussed some twenty different triple meter signs, including some identified as obsolete or obsolescent. He mentioned four species of triple signs, the first being simple triple: 3/1, 3/2, 3/4, 3/8, and 3/16. “The ancients had, and the Italians at present have four different signs for triple major [the first sign, 3/1, is ‘triple major’]: 3/1, 3/1, 3/2, 3/2.”²⁶ These were not of practical importance to Grassineau, however, since he considered them obsolete. The second species of triple was compound triple: 9/1, 9/2, 9/4, 9/8, and 9/16. The third species of triple was mixed triple or binary triple: 6/4, 6/8, or 6/16. The fourth species was called dodecupla: 12/1, 12/2, 12/4, 12/8, and 12/16.

Finally Grassineau mentioned the 5/2 and 7/2 meters discussed by Penna, but commented, “These raising some difficulty and confusion were rejected, and not admitted into the number of mixed triples.”

The classification of meter signs according to duple and triple was used by Prelleur,²⁷ Tans’ur, Holden,²⁸ Steele,²⁹ and, in New England, by John Stickney.³⁰

More complicated classifications are found in increasing number in the second half of the century. The English translation of Rameau’s Traité omitted the radical proposals of the French version (to be discussed with Rameau’s proposed reforms of notation) and established four categories: common time (,, 2, and 2/4); triple time (3/2, 3/4, 3/8); composed triple time (9/4, 9/8); and common time composed of triple time (6/4,12/8).³¹ This categorization, in essence, was used by Antoniotto³² and Callcott³³ as well.

Kollmann³⁴ and Elias Mann³⁵ relied on a simple-compound classification, as follows:

Note that 4/4 has replaced .

German Theorists

Early in the eighteenth century, Johann Peter Sperling used the word Zeichung (signatures), rather than “proportions,” for meter signs. This change in terminology recognized a new function of the fractional numbers that were inherited from mensural notation. By not coupling fractional number signatures with C, he marked them as independent signs rather than proportions:

Zu wissen ist nur/ dass wann eine unbekannte/ und in diesem dritten Capitel nicht vorgestellte Zeichung des Tacts vorkommet/ man zu betrachten habe solche aus zweyen über einander gesetzten numeris bestehende Zeichung; und zwar erstlich den obern Numerum, welcher anzeiget die Quantität, wieviel nemlich noten aufm Tact gehen: Und hernacher den untern Numerum, welcher anzeiget die Qualität! was nemlich für noten es seyn/ deren so viel auffm Tact gehen; Ist nun solcher unterer Numerus/ 1. so gehen so viel eintheilige Noten/ das ist gantze/ auffm Tact: Ist dieser Numerus 2. so gehen so viel zweytheilige Noten, das ist halbe/ auffm tact.³⁶

When an unknown figure, one not explained in this third chapter, is encountered, consider the two numbers written one above the other. First, the upper number shows the quantity or how many notes are in the measure. Next, the bottom number shows the quality or what kind of note makes up the number counted in the measure. If this bottom number is 1, so many single-part notes or whole notes go to a tact. If the number is 2, so many two-part notes or half notes go to a tact.

Sperling’s names for notes correspond to the fraction of the tactus- beat that the note occupies. Ein halbschlagig Note, “a half-beat note,” is half of a semibreve, as one semibreve is equal to a tactus beat. The terms “half note,” “whole note,” etc., appear in Sperling’s Principia because of the identification of the tactus with the semibreve, or whole note.

Sperling’s third chapter explains a total of fifty-nine time signatures. These are systematically considered: all possible combinations of 1, 2, 4, 8, and 16 are used as numerators and 1, 2, 4, 8, and 16 as denominators for “four-part measures”; and 3, 6, 9, 12, and 24 are used as numerators and 1, 2, 4, 8, and 16 as denominators for “three-part measures.” Sperling included 12/8 and 6/8 as three-part measures or trippel-Tacts, as he was following a classification system established in the seventeenth century, even though it is clear that these are four-part and two-part measures of triple subdivision.

Sperling included five other signs that he said could be found in the works of Schmelzer (d. 1680) and Walther (possibly Johann Jacob Walther, a late seventeenth-century violinist-composer, or perhaps the sixteenth-century Lutheran composer Johann Walther; both were composers who probably would use an older style of notation). These five signs, said to occur in “artistic sonatas of other authors,” were 24/32, 10/8, 12/6, 4/3, and 9/6. “Betreffend die erst Species, ist zwar gewiss/ dass es/ wie aus obigen numero 24 zu sehen/ ein Tripel sey/ worinnen Vierund Zwanzig dreymahl gestrichene/ oder Chromata Triplicata aufm Tact gehen” (Concerning the first kind, it is certain from the upper number, 24, that it is a triple in which twenty-four three-flagged notes or chromata triplicata go to one tact).³⁷ The other four signs were inverted “proportions.”

Die übrigen 5. Species aber referir en sich allzeit auf etwas vorhergehendes/ das ist entweder auf einen vorhergehenden Ordinar-Tact, oder auf einen vorhergehenden Tripel/ oder ja auf den Ordinar-Tact absolute, obschon solcher nicht vorangangen ist.. . . Setze allhier pro Exemplo wiederum den drey viertel- Tripel. Dieser drey viertel-Tripel wird in dem Ordinar-Tact versetzet durch 4/3, oder 8/6, oder 16/12, &c. Dann weil dieser Tripel bestehet aus drey viertel oder Sechs-Actel/ oder Zwölf Semifusen &c . Als wird der fünfftige Tact [4/3] bestehen aus vier drey- Theille/ das ist viertel/ oder aus acht Sechs-theile/ das ist Achtel/ oder aus Sechszehen zwölf-Theile/ das ist Semifusen, zweymahl gestrichen & . welches nichts anders ist/ als der formale Ordinar-Tact. Mehrers Nachdencken hierüber/ überlasse den erfahrnen Musicis. ³⁸

The aforementioned five kinds refer always to something that has preceded them, either common time, or a triple measure, or even the “absolute common time”; whether or not it has actually been put down before. . . . Let us take the three-quarter triple for an example again. This three-quarter is put back in common time through 4/3, or 8/6, or 16/12, etc., for because this triple consists of three quarters or six eighths or twelve sixteenths, through [4/3] it would consist of four third-parts or quarters, or of eight sixth-parts or eighths, or of sixteen twelfth- parts or sixteenths, which is nothing but the usual common time. As experienced musicians think more about this, it is given up.

Inverted signatures intended to restore common time, as well as explanations of them, disappear in the later eighteenth century. Sperling continues:

Zwischen den ersten und andern machen etliche einen Unterscheid/ sagend: Das Erste bedeutet einen langsamen/ das andere aber einen geschwinden Tact;Solcher Unterscheid aber wird von vielen componist en nicht observiret sondern des Tactus geschwind- und Langsamkeit mit absonderlichen terminis bemercket/ als da sind: tardo, presto, alia breve &c. Das dritte bedeutet zwar einen Ordinar-Tact, welcher 4. Viertel in sich hat: Es wird aber solcher Tact sehr geschwind tractir et/ also/ dass zwey dergleichen Tacte fast nur so lange dauren als sonsten einer: Diese 3te Manier oder Species des Tacts ist von denen Frantzosen zu uns kommen/ als welche sich derselben gebrauchen in denen Ouverture.n, Bourée n, &c.³⁹

Between the first () and second, many make this difference, the first means a slow measure and the second a fast measure. Such a difference is not observed by many composers, but the quickness or slowness of the measure is indicated by particular terms such as tardo, presto, alia breve, etc. The third (2) indicates common time with four quarters to a measure, but it is beaten so quickly that two of such measures are nearly of the same length as one. This third kind of measure comes to us from the French and is used by them in overtures and bourées, etc.

The classification of time signatures to distinguish between duple and triple was used by most early eighteenth-century German writers, including Fuhrmann⁴⁰ and Johann Gottfried Walter.⁴¹ Both explained the signatures according to the definitions of Penna and Bononcini.

Brossard’s Dictionaire, already discussed in its English translation by James Grassineau, influenced Walther’s Lexicon of 1732. The same terms were used—”tempo” for the duple meters and “triple” for the three-part meters, each under its separate heading. Walther also cited Fuhrmann, Bononcini, Carissimi (from his German translation), and Praetorius as his sources of information for the various articles on triple.⁴² Walther included 6/4, 6/8, and 12/8 under triples but called them “spondaic triples” and equated them with the triple binaire of Brossard and the sextupla of Praetorius.

Walther cited Johann Mattheson in amplifying his discussion of the difference between the “spondaic triples” (6/8 and 6/4) and those that were completely triple:

Die Mensur ist ja nicht ungerade, eben so wenig als die Theilung; dann ob sich 6 gleich sonst in drey Theile schneiden lassen, so geschiehet doch solches nimmer in obigen Tact-Arten, da partes aequales vorhanden sind, und der NiederSchlag so wohl als der Auffschlag drey membra haben muss. Wer in proportione sesquialtera 3/2, sechs Viertel betrachtet, und mercket, was die 4 im Niederschlage, und die 2 im Auffschlage für ein mouvement enthalten, der wird den Unterscheid zwischen Tripel und aequal Täcten mit Händen greiffen konnen.⁴³

The measure is not triple and its subdivision is just as little triple, for should six equal notes be divided into three parts, the measure could never be written in the meter signature above (6/4), which is for equal parts, in which the downstroke as well as the upstroke must have three pulses. Whoever sees six quarters in proportione sesquialtera 3/2, and knows that four are contained in the downbeat and two in the upbeat of one complete conducting gesture, understands the difference between triple and equal beating of the hand.

Although there was general agreement in classifying time signatures, it was not total. Johann Mattheson’s system of classification was derived from even and uneven tactus beats and it divided all meters into duple and triple.⁴⁴

The duple meters included 2, 2/4, , 6/4, 6/8, 12/4, 12/8, 12/16, and “12/24.” This last meter sign may have been a slip of Mattheson’s pen, but it was retained by later theorists until it was finally denounced by Leopold Mozart in 1756. The triples included three subdivisions: simple, composed, and mixed. The simples were 3/1, 3/2,3/4, and 3/8, and the composed were 9/8 and 9/16. Several duple meters, 12/4,12/8,12/16, and 24/16, were assigned to the category of mixed triples.

Mattheson emphasized the distinction between tempo (which he usually called le mouvement) and meter (Mensuram) . He considered tempo “spiritual,” as more expressive of feeling and emotion, and meter “physical.”⁴⁵ His interpretation of the sign 12/8 offers a particular example of the separation of tempo and meter that points to the changing function of time signatures in the early eighteenth century:

12/8 Ist nur/ als Zwölfachtheil/ kleinerer proportion, sonst in numero und membris wie in Theilen/ eben als der vorige Tact [12/4], das ist/ sie differiren nur in qualitate nicht aber in quantitate. Dieser ist sehr geschickt vor die Sachen à la moderne, weil darinnen/ obgleich die Glieder mit dem 6/8 in gleicher Geltung sind das verlangte Mouvement und die doppelte Anzahl eine gewisse Ernsthafftigkeit/ mit der/ den achteln sonst abhängenden/ hurtigkeit/ dermassen verbindet/ dass man die sonst hüpffende Mensur zu den aller tendres ten und beweglichsten Sachen gar wol/ es sey in Kirchen/ oder Theatral-vocal-Music wie auch in Cantaten & . zu gebrauchen weitz. Vorzeiten hat man nach dieser Mensur nichts anders/ als gar geschwinde Sachen/ wie es denn noch gewisser massen geschieht/ gesetzet/ als nemlich in Giquen und dergleichen; heutiges Tages aber dienet dieselbe vielmehr traurige und touchante Affecten denn lustige zu exprimiren.⁴⁶

12/8 is in a smaller proportion than 12/4, but in number and parts as well as beats it is the same. That is, it differs only in quality, not in quantity. It is much used for pieces à la moderne because in it, although the notes are of the same value as in 6/8, the slower tempo and doubled number add a certain gravity to the quickness attached to the note value. The otherwise hopping meter is widened in use to include all tender and changeable pieces, whether in church or theater vocal music and also in cantatas. Formerly this was used only for fast pieces such as gigues and the like. Nowadays it is used to express sad and touching passions as well as merry ones.

In a later chapter on note values, Mattheson mentions the tempo of 12/8 again, as an example of a general notational trend.

Es ist zwar oben bey Gelegenheit des zwölfachtel Tactes erinnert worden/ dass die langsame Music es bey itziger Zeit der geschwinden abgewinne; dem ungeachtet aber hat man nicht vor nöthig gehalten/ auch die langen grossen und choquanten Noten wieder hervor zu suchen/ sondern man hat die kleinem Proportiones behalten/ und ihnen nur ein langsahmeres Mouvement gegeben. Wobey der wichtige/ aber wenigen recht bekandte unterschied zwischen Tact und Mouvement, welches die meisten vor einerley nehmen/ oder doch nicht recht kennen/ beyläuffig angemercket und in praxi untersuchet werden mag.⁴⁷

In discussing the 12/8 measure above, we observed that nowadays slow music is prevailing over fast, despite the fact that long, big, and disagreeable notes are no longer used; but quick proportions are used, although they are given a slower tempo. In connection with this, the important but little-understood difference between measure and tempo which is taken to be the same by many, or not correctly understood, can be recognized and examined in practice.

12/8 may have an “affective” tempo or a fast tempo, yet the measure is the same. This is possible with other measures, and the performer needs to gauge the important, yet delicate, distinction according to his judgment and taste.

Despite such important variations, Mattheson suggests a standard tempo for each of the fifteen time signatures in general use, based on the genre of composition or its affekt, and on the size of the notes in each measure. Time signatures with 16 as denominator (12/16,24/16, and 9/16) are all faster versions of time signatures with 8 as denominator (12/8, 6/8, 9/8). Likewise 8 as the denominator suggests a faster tempo than 4. Signatures are neither proportions nor tempo indications: note values indicate an absolute speed, which, however, can be modified by the genre of the piece or by a tempo word.

Joseph F. B. L. Maier classified many time signatures according to whether they were even (duple) or uneven (triple). The duple meters were 2, 2/4, , 6/4, 6/8, 12/4, and 12/8, and the triple meters were 3/1, 3/2, 3/4, 3/8, and 9/8.⁴⁸ Maichelbeck,⁴⁹ Eisel,⁵⁰ Münster,⁵¹ and Adlung⁵² followed this classification system. Adlung paraphrased Mattheson and faithfully copied out the errant time signature 12/24 but added a footnote to the effect that he did not really understand it, and included it only because Mattheson had.

Quantz⁵³ and Leopold Mozart⁵⁴ retained duple-triple categories for meter signs. C is called vierviertheiltact rather than schlechter or ordinarii (common) time. Leopold Mozart exhorted:

Let not our friends the critics be startled if I omit the times 4/8, 12/8, 9/8, 9/16, 12/16, 12/24, and 12/4. In my eyes they are worthless stuff. One finds them seldom or not at all in the newer pieces; and there really are enough variations of times for expressing everything, to be able to do without these last. He who likes them, let him grasp them with might and main. Yea I would even generously present him with the 3/1 time, were it not that it still gazes defiantly at me out of a few old church pieces.⁵⁵

In the same year, Marpurg subdivided the classification of duple-triple into simple and compound duple and triple.⁵⁶ Hiller⁵⁷ and Kalkbrenner⁵⁸ classified measures as: “Duple two-part, thus 2/2, 4/2, 2/4, 4/4; duple three-part, thus 6/4, 6/8, 12/8; triple two-part, thus 3/2, 3/4, 3/8, [two-part in the sense of two pulses of the tactus inaequalis ], and triple three-part, thus 9/4, 9/8.”

Kirnberger’s classification was more complicated because he distinguished two-part from four-part even meters, as well as separated triple from duple:

Kirnberger summarizes the significance of meters in German compositions of the eighteenth century, particularly for the music of J. S. Bach, his idol and teacher. For Kirnberger, note values had a definite tempo significance, just as described by Mattheson in 1713, and they also implied articulation or a style of performance. Large note values were described as “weighty and emphatic” (schwere und nachdrückliche) in 2/1, 6/2, 4/2, 3/1, and 9/2. Small note values were “light and quick”(leicht und lebhaft) and allowed no stress on the first notes of beats in 6/16, 24/16, 12/16, 9/16, and 3/16. Violinists were to play these quick notes of light meters with the point of the bow, but weightier meters required a longer stroke and more bow pressure.

One of the most important points made by Kirnberger is that there is a tempo giusto, or “natural tempo,” for every meter. He stated that these would best be learned by studying all kinds of dance pieces, their meter signatures, and the note values used. Tempo words such as “largo, adagio, andante, allegro, presto, and their modifications larghetto, andantino, allegretto, and prestissimo, modify this natural tempo, rather than set absolute tempos determined by the words alone.”⁶⁰ The kind of dance or the genre of the piece also determines the tempo; for example, a sarabande in 3/4 is slower than a minuet in 3/4.

Kirnberger implies that individual time signatures can be grouped into categories of tempos, although he does not give any absolute indications of their speed. He states that those in the slowest category (2/1, 6/2, 4/2, 12/4, 3/1, and 9/2) are seldom used, and that their tempos are designated by signs in the next faster category, to which the word Grave is added. All imply “weighty tempos and emphatic performance.”

The signs in the next faster category are , 2, 6/4, 3/2, and 9/4. In these the shortest note values commonly used are eighth notes, is “twice as fast as the note values indicate,” apparently a reflection of the ancient proportional significance of this sign. Generally these are “serious and emphatic,” with 3/2 being “ponderous,” and 6/4 “more moderate.”

, 12/8, 3/4, and 9/8 are in the middle category of tempos. and 12/8 indicate a more lively tempo and execution than and may include sixteenth notes. 3/4 is lighter than 3/2; it includes mainly eighths but allows occasional sixteenths. The tempo giusto of 3/4 is that of the minuet, and therefore it is rather fast, but it can be modified by allegro, adagio, etc. 9/8 has the same tempo as 3/4.

The next faster signatures are 2/4 (which has the same tempo as alia breve but is lighter and more playful) and 3/8 (having the tempo giusto of the passepied). Quicker yet are 2/8 and 4/8, with “fast tempos and light execution.”

The fastest tempos of all are indicated by 6/16, 24/16, 12/16, 9/16, and 2/16. All of these are “extremely light and quick” and are not frequently used, to Kirnberger’s regret. He says that they are usually replaced by their next slower equivalents, with the addition of the word presto, which adequately indicates the tempo but not the required lightness of articulation.

Some additional fine distinctions are made clear by Kirnberger, such as the difference between 3/4 with eighth-note triplets and 9/8, which have the same tempo. In 3/4, the triplets are to be performed very lightly without the slightest pressure on the last of the three, but in 9/8 the eighths are heavier with some weight on the last eighth note. This allows a change of harmony on the last eighth note in 9/8, but not on the third triplet in 3/4. Triplets in 3/4 cannot be subdivided into arpeggiated sixteenth notes, but eighths in 9/8 can be. If these special qualities are not observed, 6/8 gigues might as well be written in 2/4, and 12/8 written in .⁶¹

Kirnberger’s classification of meters, although logical and suited to the use of eighteenth-century composers, did not serve as a model for other theorists, even Heinrich Christoph Koch, who was otherwise strongly influenced by Kirnberger’s discussion of meter. Koch and other writers divided meter into simple: 2, 2/4, ; simple triple: 3/2, 3/4, 3/8; mixed measures, such as a duple 2/4 that made use of triplets; and compound measures, divided in turn into compound duple and compound triple.⁶² This is almost the classification adopted by Scheibe, which is frequently accepted as the norm today: (1) simple even meters (duple or quadruple), (2) simple triple meters, (3) compound even meters, and (4) compound triple meters.⁶³

Notational Reforms

Many theorists suggested reforms of metrical notation in the eighteenth century. According to Jean-Philippe Rameau, the impulse for reform arose from the desire for simplicity:

Il faut supposer d’abord, que puisque la mesure ne se distingue qu’en 2, 3, ou 4, tems, nous n’avons pas besoin d’autres chiffres pour la marquer, & rien ne seroit plus propre à nous faire distinguer sa lenteur & sa vitesse, que la valeur des Nottes dont chaque mesure peut être remplie; car sçachant que le mouvement de la Ronde est plus lent que celui de la Blanche, & ainsi de la Blanche à la Noire, de la Noire à la Croche, & de la Croche à la double-Croche; qui est-ce qui ne comprendra pas sur le champ, qu’une mesure où la Ronde ne vaudra qu’un tems, sera plus lente que celle où la Blanche vaudra un temps.⁶⁴

We must first say that since the measure has only 2, 3, or 4 beats, we have no need of other signs to indicate this, and nothing will be more appropriate to distinguish slowness or quickness than the value of the notes which make up each measure. As we know that the speed of the whole note is slower than that of the half note, and the half note slower than the quarter, and the quarter slower than the eighth, who would not understand immediately that a measure in which the whole note is worth one beat will be slower than one in which the half note is worth one beat.

Rameau demonstrated how the various kinds of measures would be equal to different Italian tempo terms, presumably by definition first and later by practice. Expressive terms would still be needed, such as tendrement, détaché, and louré, but the note values themselves would replace the terms allegro and andante.

Le chiffre mis à la tête d’une Piece nous marquant la quantité des temps de chaque mesure; & ne s’agissant plus que de sçavoir distinguer la valeur de la Notte qui doit remplir chaque temps, l’Auteur pourra (pour l’intelligence des Concertans) mettre immédiatement avant la Clef, la Notte qui conviendra pour lors, pour épargner la peine de calculer une certaine quantité de Nottes, dont chaque temps peut être composé, & dont la valeur doit égaler celle des Nottes qui valent pour lors un temps; l’on peut mettre de plus cette Notte sur la lig;ne du Ton dans lequel la Pièce est composé comme pour l’observons dans les Examples suivans.

Il sera inutile de mettre ces mots lentment, vif, &c. parce que cela est désigné par la lenteur ou par la vitesse naturelle aux Nottes placées à la tête de chaque Pièce; mais le triste & le lugubre étant naturels aux movemens lents, le tendre & le lugubre aux mouvemens lents & gais; le furieux aux mouvemens très-vifs & c. l’on peut y ajoûter ces mots, quand l’expression le demande.⁶⁵

The signature marked at the beginning of the piece would indicate the number of beats in each measure; it is not intended to do more than to indicate the note value that is equal to one beat. The composer could put the appropriate note just before the clef. This would be for the information of the performers, to save them the trouble of calculating the beat-note, that is, the quantity of notes that make up each beat. Further, the note could be placed on the line of the key note of the piece, as can be seen in the following examples [Ex. 2.1].

It would be needless to add the words lentement, vif, etc. because this is indicated by the natural speed of the note at the beginning of each piece, but sadness and lugubriousness are suitable in slow tempos, tenderness and graciousness in moderate and gay ones, and fury in very fast tempos; these words may be added when needed in order to indicate the proper affect.

EX 2.1

Rameau, therefore, confirms Mattheson’s and Kirnberger’s use of note values as the primary indication of tempo, although he retains descriptive terms to convey the emotional quality of a piece of music.

Rameau provided a separate signature for temps inégaux (the tactus inaequalis) by placing two note values before the clef, such as a half note and a quarter note; the first of these was the value of the downbeat, the second the value of the upbeat. Mouvements à temps inégaux are distinguished from measures of three equal notes.

L’habitude où l’on est de marquer des mêmes chiffres ces mouvements à temps inégaux; & ceux où l’on fait passer trois Nottes d’égale valeur pour chaque temps, nous ôte la facilité de les distinguer, & fait qu’on les confond souvent; d’où il arrive que l’on ne donne pas toûjours à un Air le mouvement qui luy convient; car les temps inégaux obligent d’appuyer un peu sur le second, le quatrième, & le sixième temps, en introduisant je ne sçai quoi de gracieux dans les premier, troisième, & cinquième temps, dont l’effet est bien different de celui que pro- duiroient ces mêmes mouvemens battus à temps égaux.⁶⁶

The custom we have of marking measures with unequal beats the same as those with three equal notes on each beat robs us of the faculty of distinguishing them and causes them to be often confused. From this it happens that an air is not always given the animation that suits it. Unequal beats cause [the performer] to lean a little on the second, fourth, and sixth notes, while giving a certain gracious je-ne-sçai-quoi to the first, third and fifth notes. This is entirely different from the effect produced by the same tempo given with equal beats.

Rameau provides examples of the notation of equal and unequal beats (Ex. 2.2).

The examples of beats à deux temps inégaux with the signature 2 are equivalent to the tactus inaequxilis, but those with the signatures 4 and 6 are more complicated.

EX 2.2

La mesure à six temps inégaux n’est pas fort en usage, par la difficulté qu’il y a à la battre: Ceux qui voudront cependent s’en servir (car il est certain qu’elle convient à des expressions particulières) pourront frapper le premier temps, baisser la main au deuxième par un mouvement du poignet, & la baisser encore plus au troisième par un mouvement du bras, en le levant ensuite pour les autres temps, comme dans la mesure à quatre temps.⁶⁷

The measure of six unequal beats is not much used because it is difficult to beat. For those who nevertheless want to use it (as it certainly is suitable to some affects), give a downbeat on the first beat, lower the hand by a movement of the wrist on the second, lower it again by a movement of the arm on the third, and then raise it after that for the other beats as in the four-beat measure.

This method of beating suggests a slow tempo. The assignment of a je-ne- sçai-quoi de gracieux to the unequal beats, while charming, is not precise enough to help the performer. It is not easy to describe the subtleties of measure organization.

In an expanded version of his Nouvelle Méthode, Montéclair described another reform of notation: “Tous les musiciens conviennent que toutes les mesures se raportent à deux et à trois temps. Pourquoi donc employent-t-ils jusqu’à 19 signes pour marquer ces deux mesures? La mesure à quatre tems n’est autre chose que la mesure de deux temps doubles” (All musicians agree that all measures are of two or three beats. Why then do we use up to 19 signatures to indicate these two measures? The measure of four beats is nothing but a two-beat measure doubled).⁶⁸

Montéclair did not wish to rely exclusively on note values as tempo indications. Although in general, larger note values indicated a slower tempo than smaller ones, the genre of the piece of music also conveyed a sense of tempo. For instance, the passepied and passacaille were both marked 3, but the first was fast and the second was slow. Montéclair advocated replacing the tempo significance of time signatures with the terms grave, lent, aisement, modéré, gay, leger, and vîte. This is intended to prevent any confusion about the speed of the piece.

In Montéclair’s system, meter signs became a simple 2 for duple, or 3 for triple measures when there was a duple subdivision of the principal beat, and 2 or 3 when there was a triple subdivision of the principal beat. The measure of four beats was abandoned, and with it the whole note or semibreve. Example 2.3 is a diagram of the system. No provision was made for the subdivision of eighth notes, either duple or triple. Montéclair supports his system by a quasihistorical account of seventeenth-century changes in mensural notation.

EX. 2.3

Another reform of notation was offered by Jean-Jacques Rousseau, who made this his first endeavor on arriving in Paris from the provinces in 1742. Rousseau began by describing the needless difficulties of musical notation and then proposed to substitute seven arabic numerals for the notes of the scale and to change time signatures to just 2 for duple and 3 for triple.

Rousseau flatly contradicted Rameau on the subject of note values as desirable tempo indicators:

Un défaut considérable dans la musique est de représenter, comme valeurs absolues, des notes qui n’en ont que de relatives, ou du moins d’en mal appliquer les relations: car il est sûr que la durée des rondes, des blanches, noires, croches, etc., est déterminée, non par la qualité de la note, mais par celle de la mesure où elle se trouve: de là vient qu’une noire, dans une certaine mesure, passera beaucoup plus vite qu’une croche dans une autre; laquelle croche ne vaut cependant que la moitié de cette noire, et de là vient encore que les musiciens de province, trompés par ces faux rapports, donneront aux airs des mouvements tout différents de ce qu’ils doivent être, en s’attachant scrupuleusement à la valeur absolue des notes, tandis qu’il faudra quelquefois passer une mesure à trois temps simples beaucoup plus vite qu’une autre à trois huit, ce qui dépend du caprice du compositeur, et de quoi les opéra présentent des exemples à chaque instant.⁶⁹

It is a considerable fault in music to represent notes as having an absolute value when their value is only relative, and to make wrong applications of their relations; as it is certain that the duration of whole notes, half notes, quarters, and eighths is determined not by the quality of the notes but by the measures in which they are found. It follows from this that a quarter note in one measure may be made faster than an eighth in another; that eighth note, nevertheless, is worth only half of the quarter. Misled by these false relationships, provincial musicians give some airs quite different tempos than they should by adhering closely to the absolute duration of the notes, whereas it is sometimes necessary to play a measure of trois temps simples (3/4) much faster than another of 3/8, as this depends on the caprice of the composer. Many examples of this can be found in operas.

Rousseau objected to the insufficiency of notation to indicate the subdivisions of triple in duple meters without extra signs, and also to the lack of a sign to divide each beat from every other. His system proposed that a straight line be drawn over or under the number of notes—whether two, three, or four—that combine to form one beat. Each beat would be set off by a comma.⁷⁰

Rousseau also provided rests (indicated by a zero) and prolonged notes or tied notes (indicated by a dot to signify undetermined duration). Rousseau’s system was best suited to single-line melodic notation and posed significant problems to anyone reading music for harmonic relationships. By abandoning conventional notes and the staff, Rousseau made it much more difficult for musicians to adopt his system than it would be to adopt the comparatively mild reforms of Rameau and Montéclair. Rousseau repeated his proposed reform and gave more examples in his Dissertation sur la musique moderne (Paris, 1743), but the Dictionnaire de musique, which included his music essays for the Encyclopédie, restricted itself to conventional notation and added only a paragraph of criticism of the many signs of meter.

Rousseau was probably aware of Montéclair’s Principes, published six years earlier, and their systems were similar in some respects. The idea of reforming musical notation was evidently in the air in eighteenth-century France; still another reform was proposed by the Abbé Joseph de Lacassagne in 1776.

Lacassagne gave a thorough explanation of conventional meter signs, and divided them into mesures simples and mesures composées. The mesures simples were 2 or 2/4, or 4/8 (à deux temps); or (à quatre temps); 3/2, 3/4 or 3,3/8 (à trois temps). Mesures composées were 6/4,6/8 (à deux temps; 12/4,12/8(à quatre temps); 9/4, 9/8 (à trois temps) (Ex. 2.4).⁷¹

He continued:

Les chiffres qu’on place au commencement d’un Air pour indiquer l’espèce de Mesure qui en fait le caractère, pouroient se réduire à un 2. un 3. et 2/3. Cette réduction suffiroit pour exprimer tous les Movements possibles. Le 2. Signifieroient la Mesure partagée en Deux Temps égaux. Le 3., en Trois-Temps aussi égaux. Le 2/3 signifieroient la Mesure à Deux-Temps inégaux, et on l’écriroit comme s’il n’y avoit qu’un 3. La différence qu’on trouveroit dans cette inégalité, seroit la même que celle de 2 à 1, c’est-à-dire que si trois Notes de la même espèce composaient la valeur d’une mesure, on en mettroit deux pour le premier Temps; et une pour le second.⁷²

The signatures put at the beginning of an air to indicate the kind of measure and determine its character can be reduced to 2, 3, and 2/3. This reduction will suffice to express all possible tempos. The 2 will signify the measure divided into two equal beats, the 3, the measure of three equal beats. The 2/3 will signify the measure of two unequal beats, which will be written as if it had the signature 3. The difference found in this inequality is that of 2:1, that is to say that if three notes of the same kind make up the value of a measure, two would be on the first beat and one on the second.

Lacassagne agreed with Rousseau that note values should have no tempo significance, so he advocated the use of the conventional Italian and French tempo words.

Si je n’ai pas le mérite d’être le premier à proposer cette Réforme utile, j’ai du moins celui de démontrer par des principes et des Exemples sensibles, celle que je crois la plus practicable; et d’adopter sans restriction les vues des grands maîtres (Mrs. Rameau, Rousseau et Montéclair) qui ont traité le même sujet.⁷³

Although I do not have the merit of being the first to propose this useful reform, at least I am the first to show by principles and understandable examples that part which is, I believe, the most practical, and to adopt without restriction the views of the great masters (Messrs. Rameau, Rousseau and Montéclair) who have considered this subject.

Lacassagne entirely rejected compound measures, so that only the simple duple, simple triple, and his equivalent of the tactus inaequalis remained. It is difficult to understand why the distinction between a simple triple and an uneven two-beat measure was necessary, unless it was for clarification in beating the measure.

EX. 2.4

Lacassagne proposed a different system later in the same book. This second proposal reduced the measures to two formulas that were not fully explained but seem to have been invented in order to include compound measures. He stated that it would not matter which system was adopted—either would be a boon to students—and he suggested an “Académie de Musique” to consider reforms and decide on one that would be adopted all over France as the “indispensable rule for all musicians who write new music.” Lacassagne’s proposals and those of other reformers were ridiculed in Boyer’s letter to Diderot.⁷⁴

Jean-Benjamin de Laborde, a violinist-composer who was court chamberlain to Louis XV, accused Lacassagne of not perceiving “the essential constituent differences between certain measures.” This criticism is found in his four-volume Essai sur la musique ancienne et moderne,⁷⁵ which in turn was severely criticized by Fétis as “a masterpiece of ignorance, disorder, and carelessness.”⁷⁶ However, the raillery to which Laborde subjected the proposed “Académie de Musique” was not wholly undeserved. Laborde had the misfortune to be guillotined in 1794, the result of a more serious controversy than the one with Lacassagne.

However, the spirit of musical reform remained alive, for in 1801 another attempt was made, this time by Frédéric Thiémé, who reduced all time signatures to either 2, 3, or 6/8.⁷⁷ The quarter note was to be used as the common denominator of music. He thought that Italian tempo indications, which were imprecise, should be replaced by a system of numbers, beginning with 1 for largo and continuing to 5 for presto. Intermediate speeds could be indicated by adding the word vif to the numbers, as in 1 vif, 2 vif, etc.

Reformers’ projects are more likely to be taken seriously when there are only a few of them. The very number of these systems of reform in eighteenth- century France was an indication of their lack of practical success.

The proposed reforms of notation differ on the subject of whether or not note values in themselves indicate tempo. The view that they do follows a practice of notation established in the mensural system that was continued in the eighteenth century. Mattheson and Kirnberger agree with this view, as does the practice of J. S. Bach. However, there were enough uncertainties about the tempos indicated by notation that the necessity for tempo words remained. The more forward-looking reforms emphasized notation that showed metrical order divorced from tempo significance.

Additional Meanings of Time Signatures

The following summary shows some of the special associations of the most frequently used time signatures of the eighteenth century, as gleaned from the comments of theorists.

DUPLE METER SIGNS

The first signature mentioned in many theory books was C; it was derived from the mensuration sign “imperfect of the less” and indicated a duple meter. In the seventeenth century, diminution signs often indicated a change in the speed of the tactus instead of a change in the speed of notes in relation to the tactus. Consequently the precise meaning of , , and varied depending on the signs’ relations to one another. In come cases in contrast to , meant a 2:1 change of tempo, in others, merely a faster tempo not necessarily in the ratio of 2:1.

In the eighteenth century most theorists agreed that indicated a speed “somewhat faster” than C. Among those who advocated “somewhat faster” were Malcolm,⁷⁸ Turner,⁷⁹ Prelleur,⁸⁰ Maier,⁸¹ David,⁸² and Rameau in his English translation.⁸³ Grassineau quoted Malcolm on this subject, but did not acknowledge the quotation.⁸⁴ Kirnberger said that “allabreve” (, 2, or 2/2) was suitable for “church pieces, fugues, and elaborate choruses.” It was considered “serious and emphatic, yet performed twice as fast as its note values indicate, unless grave, or adagio is added.”⁸⁵

Another interpretation of the difference between these signs—an interpretation that did not specify a time relationship—was that indicated a two-beat measure and a four-beat measure. French writers made this distinction, among them Borin,⁸⁶ Démotz de la Salle,⁸⁷ and Corrette.⁸⁸

Some writers maintained the 2:1 diminution ratio, among them Tans’ur,⁸⁹John Stickney,⁹⁰ Brossard,⁹¹ and Quantz.⁹² The retorted () was considered to double the tempo of .

2

The meter sign 2 was regarded as an alternate to by the French and by Quantz.⁹³ David⁹⁴ considered 2, and 2/2 to be identical. Corrette said 2 was used in rigaudons, bransles, bourées, gaillardes, villageoises, cotillions, and gavottes, etc.;⁹⁵ Mattheson⁹⁶ and Maier⁹⁷ said that it was commonly used in the first part of overtures, gavottes, rigaudons, and entrées.

2/4

2/4 was sometimes considered to be the equivalent of and sometimes of retorted it was regarded as quicker than the other signs of duple meter. Mattheson wrote that “it produces singing pieces almost by itself.”⁹⁸ Corrette said that it was often used for the “reprise of overtures and it is much used by Italians in pieces marked Vivace, Allegro, Presto, and in ariettes. Composers presently use it for Andante and Adagio.”⁹⁹ Lacassagne said that it was used in the rigaudon, bourée, gavotte, and tambourin, with a tempo range from modéré to très vif. ¹⁰⁰ Quantz, who related his tempos to the pulse, said that in Allegro 2/4 or quick 6/8 time, there was one pulsation for every bar.¹⁰¹ Kirnberger said that 2/4 has the same tempo as but is more playful and is performed much more lightly.¹⁰²

TRIPLE METER SIGNS

Triple meter signs indicated definite tempos to some and vague ones to others. Tans’ur interpreted 3/2 as a proportion sign, which meant that three half notes should be equivalent to two of common time.¹⁰³ Triple meter signs that included the mensural C with the numerical fraction were sometimes still interpreted as proportion signs. On the other hand, Turner described “the moods in Tripletime [as] not at all denoting now, (though formerly they did) what is to be sung slow or Fast, as they do in Common Time.”¹⁰⁴

3/2

Mattheson wrote, “It is found in many pieces, particularly sad arias, in sonatas, adagios, sarabandes, and pieces which depend on the composer’s fantasy, but it is not frequently used today.”¹⁰⁵ Corrette said that this signature was seldom used by the French but frequently used by Italian composers for Sarabands and Adagios.¹⁰⁶ Tans’ur said that it was used mostly in church music and performed slower than the rule.¹⁰⁷ Kirnberger agreed that it was suitable for church pieces because of its ponderous and slow quality when the fastest notes are eighth notes. In the chamber style, sixteenth notes may be used in 3/2.¹⁰⁸

3

Turner¹⁰⁹ objected to the use of this signature, but Grassineau¹¹⁰ called it the same as C3/4 or 3/4. Démotz said it indicated “a measure of three beats (Tems) more or less fast. . . . each beat is a quarter note or its value.”¹¹¹ Corrette said that it was used in “menuets, sarabandes, courantes, passacailles, chaconnes, and in the folies d’Espagne.”¹¹² Grassineau said it was usually played affectuoso or allegro.¹¹³

3/4

Mattheson writes, “It is the most frequently used of all the triples and is applied to many pieces, mostly merry ones, of which menuets are the greater part.”¹¹⁴ Maier states: “The three quarter measure is the most used and it consists of three quarter notes which make up a whole measure. It is used especially in happy pieces.”¹¹⁵ Corrette said that it was used in the courantes of sonatas,¹¹⁶ and Tans’ur said it was used mostly in anthems, menuets, etc.¹¹⁷ Grassineau wrote: “When the character 3/4 is used, the air is to be played in a tender affecting manner, of a moderate movement, neither quick nor slow.”¹¹⁸ Kirnberger says that the tempo giusto of 3/4 is that of the menuet, and that its execution is much lighter than 3/2. It is therefore not much used in the church style but very often used in the chamber and theatrical styles. It can assume all degrees of tempo, from indications of allegro to that of adagio. It is “gentle and noble, particularly when containing mostly quarter notes.”¹¹⁹

3/8

Mattheson wrote, “Par affectation (played more slowly and emotionally) this often takes the place of the preceding (3/4), and has become so favored that it is used in arias, with the addition of adagio or the like, even though it is properly used in the passepied, canarie and other hopping dances.”¹²⁰ This statement is echoed by Maier.¹²¹ Grassineau said, “This kind of triple is usually gay or animating,”¹²² but Tans’ur said, “This sort is mostly used for Minuets but is Gently slow”¹²³ Corrette wrote that it is “used in French music in passepieds and sometimes in the reprise of overtures. Italians use it in allegros, adagios, affectuosos, vivaces and ariettes. Look in the Italian operas of Handel, Bononcini, Pepusch, Scarlatti, Porpora and all the sonatas composed by our illustrious Frenchmen, where this meter is found. It is song-like and tasteful in sentimental pieces (les Affetuoso).”¹²⁴ Kirnberger wrote that it indicates the lively tempo of a passepied, performed in a light but not entirely playful manner. It is widely used in the chamber and theatrical styles.¹²⁵

6/4

Mattheson said, “this is used for serious pieces, in particular the slow gigue that is called the loure,”¹²⁶ a statement echoed by Maier.¹²⁷ According to Corrette, “French music uses this for loures, forlanes, and sometimes in the reprise of overtures; it is found very little in Italian music.”¹²⁸ Lacassagne amplified this: “The loure is an air grave marked 6/4. It begins usually with a short eighth note that is the middle of the second beat. . . . The forlane is an air modéré marked with 6/4.”¹²⁹ Grassineau said, “This movement is very proper for moving, tender expressions, though some use it in very hasty motions.”¹³⁰ Tans’ur wrote, “The 6/4 has no meaning for Jiggs, unless for very slow ones.”¹³¹

6/8

“6/8 is proper for gay, lively, animating strains,” said Grassineau.¹³² Mattheson wrote, “it is used most beautifully by composers today and is suitable for flowing melodic pieces as well as fresh and quick pieces.”¹³³ Corrette adds: “French music uses this for canaries, gigues and sometimes for the reprises of overtures. It is often found in sonatas and concertos.”¹³⁴ According to Lacassagne, “The Gigue is an air more or less long, marked by 6/8, its tempo is very quick.”¹³⁵ The 6/8 was “for moderate lively menuets or Dancing casts, of equal down and up, being both lively gentle Sicilian movements,” according to Tans’ur.¹³⁶

9/8

According to Corrette: “This is found very little in French music, but often enough in Italian music, such as gigues, allegros, prestos, and sometimes in adagios; see Vivaldi, etc.”¹³⁷ Grassineau commented, “This is proper for brisk and gay pieces.”¹³⁸ Tans’ur said that “9/8 and 12/8 are only for very brisk jiggs.”¹³⁹ Kirnberger wrote that 9/8 meter is derived from and has the same tempo as 3/4, but the eighth notes are performed more lightly than in 3/4.¹⁴⁰

12/8

“This is fit for gay and brisk movements. Sometimes the words affetuoso and adagio are placed to direct what the movement is to be; for itself ‘tis naturally quick,” said Grassineau.¹⁴¹ Turner said this was appropriate in “very swift Movements, as jiggs, etc., but why it should be made use of in slow (sometimes very slow) movements I cannot conceive.”¹⁴² Mattheson commented at length on the use of this fast meter for slow pieces, in that it gave a feeling of gravity despite the usual quickness of eighth notes. He felt that using 12/8 for slow music, marked grave or adagio, was a sign of the general preference for slow music.¹⁴³

By the end of the eighteenth century, time signatures in the form of numerical fractions replaced almost all mensural signs, even though C still held its place against the 4/4 sign that rationally should have replaced it. The more conservative notation of the eighteenth century retained the concept that notes had tempo significance in themselves. Tempo words were regarded as subsidiary indications of the speed of the music, and as modifiers of a “natural” tempo. Tempo words also suggested a composition’s proper expressive quality. In more modern notation, tempo words gained an almost absolute significance. As this trend continued, time signatures indicated only metrical structure.

Some writers discussed conducting or time-beating patterns that depicted the measure as a single beat or a group of beats. As tempo influenced a musician’s perception of the beat and indicated whether beats were simple or compound, it was essential to know the tempo in order to determine the metrical structure. The time signature alone, therefore, was often inadequate, and the additional information provided by a conducting pattern became critically important.

The fact that there were various classifications of time signatures does not indicate fundamental differences in notation. By the end of the eighteenth century, time signatures were defined in very nearly their present-day significance. In the nineteenth century, note values seem to have lost even more of their power to indicate tempos, and tempo words seem to have gained more importance. Until the creation of notation devised for partially improvised styles in the twentieth century, the time signatures and tempo words of the late eighteenth century continued to serve as the standard for musical notation.