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A re-examination of the evidence on absolute tempo before 1700.

Part 2 of Ephraim Segerman's discussion of tempo is scheduled to appear in the November issue.

We readily accept new research findings if they make sense in terms of our previous knowledge and perceptions. The evidence being re-examined here has not made sense to generations of musicologists because it implies tempos which have been felt to be much too slow. In this re-examination the evidence is shown to be much less ambiguous than has previously been assumed; it is also shown to make a sense of its own in terms of how tempo could have evolved through the centuries.

Vetulus, c.1350

Major proration minim = MM 72

Johannes Vetulus (or Verulus) de Anagnia (c.1350) wrote that the breve in tempus perfectum medium lasted for the time of an uncia, which he made clear was 1/480th of an hora, which was 1/24th of a day. In our units the uncia is 1/8th of a minute or 7 1/2 seconds. In addition, the uncia was made up of 54 athomi, which were the smallest possible (indivisible) units of time. This breve, then, had a tempo of MM 8.

Vetulus identified tempus perfectum medium with the novenaria divisione, which had perfect time and major proration, the same proration for which the French used the sign ??. This mensuration had nine minims in a breve, so the tempo of a minim would be MM 72. Since the normal rate of the pulse of the blood is about MM 60-80, I shall call this a minim-pulse tempo. We know from the writings of Marchetto de Padua, Vetulus and Prosdocimus that there was a characteristic tempo for minims in mensurations with major proration, and one in those with minor proration, which was 4/3 as fast. Minims in minor proration would then have a tempo of MM 96.

Sachs's (1953) analysis of Vetulus's information assumed that the minim length was the same in both prorations. So Sachs's reported breve MM values (in minor proration) should be 4/3 faster. This would not have affected his conclusion, which was that such a tempo was too slow, and a speed of three times faster is necessary to make a `satisfactory enunciation of the text' possible: `Verulus must have been mistaken.'

Gullo (1964) manipulated what Vetulus wrote to get a more acceptable tempo of MM 216 for the minim. He assumed that Vetulus's `tempus rectum and perfectum, not the maius [major] or the minus [minor] tempus, but the mediocritir [mean], which consists of a quadrangular shape in the image of the four parts of the world' was a long (in spite of the quadrangular shape describing the symbol for a breve), and it was different from tempus perfectum medium, which, at 1/3 the length, was supposed to be the true breve.

Vetulus defined tempus perfectum medium by writing that the `universal time unit contains in itself 54 athomi, 27 particulariter vocis [which he elsewhere defined as the vocal analogue to the athomus, i.e. the indivisible unit of vocal time], 9 minims of major proration and the tempus [breve] of the novenaria divisione'. Gullo twisted this to mean that the universal time unit was a general one, that particulariter vocis represented minims, and that the following items referred to that new particular unit, and not to the 54 athomi at the beginning of the sentence. Gullo also had to assume that there was no difference between minims in major and minor proration, in spite of Vetulus's obviously being careful about it. His interpretation of what Vetulus wrote cannot be considered an objective reading.

Savanarola, c.1440

Minims in major and minor proration

bracket the pulse range

Kummel (1970) has discussed the writings (1498) of the Italian physician Michaele Savanarola (13841468) that bear on tempo. Sherr (1992) made this more widely known. In essence, Savanarola said that he found that the normal pulse is somewhat slower than the divisione he knew as quaternaria, yet faster than the divisione he knew as senaria imperfecta. He suggested that doctors could tell what the normal pulse was by knowing the tempos of these two divisiones, which could be learned from a good musician in eight hours. The French mensuration signs for these divisiones are C and ?? respectively.

Savanarola did not specify the note values he was referring to in these divisiones. Kummel assumed that they were breves. The breves or semibreves of quaternaria were twice as fast as those of senaria imperfecta. This makes them very unlikely as the appropriate note values for two reasons. One is that the factor of two would be too wide a range for diagnosis of pulse normality. The other is that if they were the intended note values, the way to check the normality of the pulse would be to determine whether the length of the pulse beat was between that of one or two beats of quaternaria. But for this, one would need to learn just one divisione, not the two that Savanarola mentions.

Only the minim works, and it works perfectly since the limits of the pulse rate (MM 60 and 80) happen to be in the identical ratio of 3:4 as that of the minim speeds of senaria imperfecta and quaternaria. This makes all the tempos 5/s times those of Vetulus.

Gaffurius, 1496

Breathing time (4 x the pulse) =

the `regular' semibreve

Howard Mayer Brown (1980) states that Gaffurius (1496) wrote that `one tactus equalled the pulse of a man breathing normally, suggesting that there was an invariable tempo then of MM = c.60-70 for a semibreve in integer valor'. This most probably is in error. Bonge (1982) has pointed out that Gaffurius was ambiguous in relating the pulse and tempo. In one passage Gaffurius discussed how physicians considered the pulse as the basic unit of time measurement in medicine, and that it was composed of two components of equal time each-dilatation and contraction. In a second passage, he mentioned that modern musicians considered the regular semibreve in a similar way, as the basic unit of time measurement in music, also composed of two components of equal time each (minims). In a third passage he stated that a dissonance in counterpoint cannot last as long as a regular semibreve, a full measure of time, namely tin modem scilicet pulsus aeque respirantis'. Bonge translated the phrase left here in Latin as `in the manner of the pulse of [someone] breathing evenly'. This is the most obvious and direct interpretation of the Latin, and essentially agrees with the readings of Brown, Sachs and others.

Bonge's point is that the grammar of these passages strongly implies analogy between the regular semibreve and the pulse, rather than equality. He strengthened this point by noting that the comparison was between the semibreve and the full pulse by Gaffurius, and between the semibreve and half the pulse by Ramos (1482) in a similar passage. If equality were implied rather than analogy, then there would have been a disagreement, and this passage was not commented on in the margin of Gaffurius's copy of Ramos's book, as other disagreements were.

The problem with this translation of Gaffurius's third passage is why he mentioned breathing at all. How could `the pulse of someone breathing evenly' provide any different information from `the pulse'? Medicine then and now has recognized a close correlation between the pulse and breathing, both going up and down in roughly the same proportion (of about 1:4 in rates) as a result of emotion, exertion or illness. When for medical reasons the pulse is even or uneven, so is the breathing. In this translation it is the pulse that counts in relation to `the full measure of time' of the regular semibreve, and nothing that could be said about breathing qualifies or clarifies the statement. This makes the exploration of other translations worthwhile, to see if they can make more sense.

Young (1969) realized this and suggested that the use of the word `breathing' in this passage was as an analogous description of the dilatation and contraction (or `breathing') of the pulse. In Segerman (1992), following a comment by Fallows (1980), I suggested the opposite, interpreting the use of the word `pulse' as an analogous description of the dilatation and contraction (or pulse) of breathing. `Pulse' would mean both the process of pulsation and that a complete cycle is involved, as it is with the pulse. The motivation according to my interpretation is that in this passage Gaffurius was interested in a practical situation rather than in the theory of the other passages, so he had rather more reason to be specific about the real tempo involved, and he switched to the breathing cycle because it actually did correspond with the regular semibreve tactus.

Gaffurius had every reason to want to clarify what kind of semibreve he was referring to. In another part of the book he defined a `regular' semibreve as a semibreve not reduced in length by a canon or proportion, or by a stroke (cut time) in the time signature. This semibreve was particular because it had the same tempo for C, O, C and ??. At the time he wrote, the `regular' semibreve was a rarity since time signatures with a stroke were much more widely used than those without. He would not have been interested in saying that `tine pulse was the tempo of the crotchet in minor proration without a stroke' (as my interpretation implies) because that was a special and uncommon kind of crotchet, and he was concerned with more general things such as the tactus of the regular semibreve, which in my interpretation, corresponded with the breathing rate.

Of course, this evidence is much weaker than that of Vetulus and Savanarola. But the conclusion (that crotchet = pulse in C and 0, and minim = pulse in C and [Phi] at the end of the 15th century) gains greatly in strength when we discover the difficulty in postulating any alternative that reasonably fits in with the evidence from before and after.

Fastest playing speeds

10.7, 13 and 16 notes per second

in different circumstances

We have information about how fast musicians could play before high speed became an essential component of good technique. This is useful in interpreting some of the evidence below. Marin Mersenne (1636), in his Third Book, Prop. XIV, wrote that the fastest speed was 16 notes per second in divisions or graces ('aux passages & aux fredons') played by `those who are esteemed to have a very fast and light hand, when they use all the speed possible for them'. Instruments specifically mentioned were the viol and the spinet. The voice could not go so fast.

In the Sixth Book, Prop. XLI, Mersenne discussed a diminution that `the cleverest and quickest hands are able to execute'. There were 64 notes per measure, and he gave the measure as the time of a complete vibration of a pendulum 2 feet long. This calculates to 1.8 seconds, leading to a playing speed of 35 notes per second, a rapidity that any modern keyboard player would be proud of.

This passage is not in contradiction with the one from the Third Book. Very exceptional musicians in various ways are liable to appear at any time. The Third Book passage was concerned with what would normally be encountered, and that is our interest here.

Quantz (1752) indicated that the fastest speed was 10.7 notes per second (eight notes per pulse beat, which he defined as 80 beats per minute) in articulated notes (`with double tonguing or with bowing') played by competent musicians. The difference between the two figures includes the difference between speed specialists and other competent musicians, and between playing with one set of muscles (keyboards and unarticulated music on strings and winds) and having to co-ordinate two sets of muscles (articulated music on strings and winds). An intermediate fastest speed, say 13 notes per second, would apply to competent keyboard players not especially esteemed for speed, as well as graced or otherwise unarticulated notes played on strings and winds.

Attaingnant, 1531

Keyboard demisemiquavers

imply crotchet = pulse

As discussed above, only exceptional instrumentalists could play as fast as 16 notes per second. Thus the appearance of demisemiquavers in a published source would imply that the tempo for a minim was significantly less than MM 60. We would expect some note value to fall in the range of the pulse. The largest note value that fits this criterion is the crotchet. Thus when Pierre Attaingnant (January 1530/31) published keyboard music including demisemiquavers under the time signature, the tempo most likely had crotchet = pulse.

Neusidler, 1536

Counting money and bell stroke period

implies crotchet = pulse

Hans Neusidler (1536), in a section entitled `don der Mensur', wrote that the tablature semibreve (a vertical stroke, |), `should be played so that it sounds neither longer nor shorter than the striking of the hour or bells on a tower, or when one adds up money nice and gently while saying "Bins, zwey, drey, vier", [each] one as long as another. The striking of the bell or this adding up of money corresponds to the long stroke |, and is called one schlag.' Concerning the tablature minim rest written with one flag on the stroke and called a suspiri, he wrote that `one can neither pronounce nor count this--instead one must draw breath in, just as if drinking soup out of a spoon.'

The first quote is most readily understood to mean that the saying of all four numbers represented one schlag, with each number corresponding to a quarter of a schlag. This is how Sachs (1953) read it. If one is tempted to interpret it as saying that each number represented a schlag, this is argued against by the second quote. It is much more likely that the drawing in of breath (as in drinking soup out of a spoon) took the time of counting two numbers rather than half the time of counting one number. The word schlag is usually translated as `beat', but this is misleading nowadays because we think of the beat in music as a subdivision of the bar (or measure), while in Neusidler's time it was like the tactus vocalists used, similar to our bar. When discussing how the schlag was subdivided into various note values, Neusidler included four crotchets notated by four strokes with two flags beamed, called a long ladder (leitterlein) or complete run (ganz laiflein). He did not associate the crotchets with the money counting, probably because they were not necessarily played evenly (the way the numbers were counted), as explained by Santa Maria (1565).

Neusidler did not use a time signature, but we can assume that it would be ??, which was ubiquitous at that time. The question is whether his crotchets were in the tempo region of twice the pulse rate (as implied by ?? c.1500), or of the pulse rate (as with Gaffurius's integer valor C earlier, and with common time in the 17th century).

There was much counting instruction in late 17th-century English sources, all counting four crotchets to a semibreve, just like Neusidler's. For the slow duple time (with the time signatures of C and ?? then) Simpson (1665) mentioned the counting of `One, Two, Three, Four' pronounced `as you would (leisurely) read them'. Mace (1676) instructed the counting to be `with Deliberation'. Playford (1694 edition, `Corrected and Amended by Mr. Henry Purcell') used the term `telling distinctly'. For the fast duple time (with the time signature ??), the last reference just used the term `tell'. Purcell (1696) first described all speeds of duple time and then prescribed the counting using the term `moderately tell', apparently neglecting to take care to distinguish between the different duple-time speeds.

The tempos in this period were specified (see below). Except for the final piece of evidence here which is ambiguous, the crotchet corresponded with the pulse whenever the word for counting was modified to indicate that it was somewhat relaxed, and half a pulse when there was no such indication. According to this criterion, Neusidler's counting instruction indicates that the crotchet corresponded with the pulse.

An independent test of the above conclusion about the tempo standard Neusidler was writing about is the period or repeat time of tower bell strokes in Nuremberg at that time. Since that was the time of a semibreve, that time would be 1 1/2-2 seconds, 3-4 seconds or 6-8 seconds if the pulse corresponded with the minim, crotchet or quaver respectively. Dr J. J. L. Haspels, director-curator of the Nationaal Museum van Speelklok tot Pierement, a leading authority on historical bells and their striking mechanisms, was asked for an estimate. He writes: `The combination and interaction of transmission ratios, weight, air brake, blade position and hammer weight and hammer resistance may, in my opinion, well result in a stroke-period between two and six seconds.' In spite of its wide range, the only possibility that is consistent with this estimate is that the crotchet corresponded with the pulse.

Gerle, 1546

If the music is too fast, one augments

the note values

Parts 1 and 2 of Hans Gerle's book Musica und Tablatur . . . (1546) concern grosser Geigen or viols. In the section `Ein Prob wie du die Mensur solst lernen' of Part 1, Gerle wrote, as Neusidler did, that the tablature semibreve (or schlag) I corresponded with `the striking of a bell which indicates the hour'. Part 2 of the book concerns reading mensural notation and transcribing it into tablature. The mensurations he discussed were ??, [Phi], ??3 and 3. The last two of these were called proportz or tripel. If we assume that they were truly in proportion, this resolves an ambiguity in his explanations and the duration of the schlag was constant in all mensurations. It included one semibreve in ?? and C, three semibreves in ??3 and three minims in 3 (see Segerman (1994)).

Gerle wrote that the schlag recognized by singers corresponded with the breve, and it was `worth two schlags in the tablature'. This is ambiguous as to whether singers performed twice as fast as instrumentalists (if the schlag was of constant length), or they performed at the same speed (with different schlag lengths). It is possible that this ambiguity was real then (rather than just in our understanding of Gerle) since he wrote that if a song went too fast, both singers and instrumentalists augmented the note values. He called this diminution, as Gaffurius (translation in Schroeder (1982)) wrote many musicians erroneously did. The way to slow down music that was too fast was to perform it half as fast. This is just what one expects when tempo standards are observed.

English dances, 1610-15

Fastest demisemiquavers in lute almains

and virginals galliards

Occasionally one encounters a source that is similar to others in origin, notation, compositional style and repertory, but which includes faster embellished notes in its notation. Embellishment tends to be fractal in nature, i.e. similar patterns appear on different scales, so the ornamental shapes cannot give us information about how close to the fastest speeds playable these notes are. Consequently, calculating a tempo on the assumption that the fastest notes that appear are at maximum playing speed can only be an upper limit. If the source includes a repertory with a variety of tempos of known tempo progression, then we can have a much closer approximation of one of these by this method, that one being the fastest that still uses the unusual faster notes.

These special criteria happen to be satisfied by the demisemiquavers in Robert Dowland's Varietie of Lute Lessons (1610) and the Fitzwilliam Virginal Book (c.1614). The few pieces with hemidemisemiquavers that appear in the latter source are assumed here to be vehicles for a truly exceptionally dexterous player such as John Bull or the one that Mersenne encountered, and are ignored. The variety of tempos in both these sources is provided by the Pavin, Almain, Galliard and Coranto. That they are in this order of increasing tempos can be inferred from Thomas Morley's discussion of them (1597).

The method used here is simply to count the numbers of pavins, almains, galliards and corantos that have demisemiquavers. In the virginal book the numbers are 35, 8, 4 and 0pieces respectively. From this we conclude that the tempo of a coranto was too fast for demisemiquavers. From the information given in `Fastest playing speeds' above, we can estimate that demisemiquavers in galliards are played at approximately 13 notes per second, or crotchet = MM 96. In the lute book the numbers are 5, 3, 1 and 1 pieces respectively. The demisemiquavers in the galliard and the coranto, being on the final cadence, can be ignored because of the expected rallentando there. From this it seems that at the almain tempo demisemiquavers were played about as fast as they could be, or at 10.7 notes per second, so crotchet = MM 80. We would expect a sesquialtera (3:2) relationship between pavin and galliard tempos, so an estimate of the pavin tempo is crotchet = MM 64. If the same was the case for almain and coranto tempos, crotchet = MM 120 in the coranto.

Charles Butler (1636) wrote `The triple is oft called Galliard-time, and the duple Pavin-time.' He was apparently referring to standard tempos, so the dance tempos estimated here should fit into the general picture of tempo standards. The tempo of the almain is high in the range of the normal pulse and the pavin low. We shall see below that the same split of the normal range of tempos for duple time into a higher portion and a lower portion was reported by Praetorius and Purcell.

Praetorius, 1619

160 breves in 15 minutes at a moderate speed:

crotchet = MM 85

Praetorius (1619) wrote that at a normal moderate speed (`wenn man einem rechten mittelmassigen Tact helt'), there were 160 tempora (breves) in a quarter of an hour. The context was in planning church services. Sachs (1953) calculated the average tempo to be crotchet = MM 85. What remains is to determine of what tempos this is the average.

Praetorius also wrote that in Orlande de Lassus's time (the second half of the 16th century), C had a semibreve tactus (called alla semibreve in Italian) and ?? had a very slow breve tactus (called alla breve). He later referred to the tactus of C in his own time as `very slow', and the example given for the early time (the first few bars of a piece by Lassus notated in alla breve above and alla semibreve below, with the bar lines continuous between the two) implies the same tactus for C and ??. Thus in Praetorius's early experience (probably as a choir boy), a minim-pulse tempo was still considered `correct' for ??.

In Praetorius's discussion of contemporary tempo, common time ?? was mainly used for motets and similar music, and the tactus was faster than for c, which was mainly used for madrigals and similar music. His discussion of performance of works of Monteverdi and Lassus indicates that there was a choice between performing ?? in this faster standard way, or with an alla breve tactus if the music had more white than black notes. This indicates that his standard ?? was different from alla breve ?? in both tempo and tactus. It had a semibreve tactus that was in between C and alla breve ?? in tempo.

With the difference between English pavin and almain tempos in mind, we may consider that Praetorius's C was at the slow end of the pulse range, and ?? at the high end (we would perceive this ?? tempo as almost half way between the C tempo and twice the C tempo). With this assumption, Praetorius's average tempo can be explained in a satisfactory way. Since it was given for music in church, we would expect music at motet tempo (crotchet = MM c.80) to dominate. He would mix in some music in C for special effects (he mentioned this), which would tend to lower the average. He certainly would have had passages in ternary time and diminished time signatures which would tend to raise the average. We would expect more of the latter, so an overall raising of the average to crotchet = MM 85 is very reasonable.

Tomkins, c.1620

Alla breve minim = MM 77

The only early publication of sacred music by Thomas Tomkins (1570-1656) was undertaken by his son Nathaniel, apparently as a memorial. The Tenbury copy of the organ part of Musica Deo sacra (1668) includes comments printed in Latin defining the pitch and tempo associated with the music's composition. The tempo information is that the semibreve corresponds with two beats of the body's pulse or the centro motus of a two-foot pendulum, with two semibreves in a bar. To be consistent with the pulse information, half a period of the pendulum is what was meant, implying minim = MM 77. The two semibreves in a bar indicates that this tactus was in alla breve.

Mersenne, 1636

Musicians take whatever tactus they wish,

including 2, 3 and 4 seconds

At several places in his book, Mersenne (1636) mentioned mesure (tactus). He wrote that musicians `make a tactus last more or less as they wish', but he felt it necessary to establish arbitrarily a definite time for the tactus to calculate other things from, like how fast one can play. Since astronomers had provided the second as a time unit, and as a second is associated with the pulse, he postulated/hat the tactus lasts for one second. This simplifies calculations, and the mathematician in Mersenne assumed that his readers would be able to adapt what he said to whatever tactus they wanted, which he wrote was generally more than a second. He mentioned 2 and 4 seconds when calculating the maximum number of notes playable in a tactus, and 2 and 3 seconds when calculating the number of string vibrations in a tactus. A tactus of 2, 3 and 4 seconds corresponds respectively with Praetorius's alla breve ??, normal ?? and C. The particularly fast tempos in 18th-century France only reached the notated speed of one second for a semibreve in dances.

Simpson, 1665

Common time crotchet = lively pulse,

plus four triple-time tempos

When discussing how to keep common time (notated with either C or ??), Christopher Simpson (1665) wrote: `Some speak of having recourse to the motion of a lively pulse for the measure of crotchets, or to the little minutes of a steady going watch for quavers, by which to compute the length of other notes ...' There is no ambiguity about a lively pulse, it being something like MM 70-80, but it is not at all clear what the `little minuses' of a watch might be.

It could mean ticks, but not ticks as we might know them. Watches and clocks then had verge escapements, and of the two sounds associated with the balance wheel, one was an escapement and the other a recoil. The sounds were different. It really was `tick, tock, tick, sock', not tick, tick, tick, tick, as with more modern timepieces. So even-without realizing that the watch had a balance wheel, one had a choice between balance wheel oscillations and saunas undifferentiated as to whether they were ticks or tocks. It would be easier-to express the latter in their language using a word such as `stroke', and a more complicated expression like `little minutes' might be necessary for the former. This expectation is fulfilled when we resolve the ambiguity-by comparison with the pulse. The most popular watches of this period sounded about 18,000 times an hour, or 300 times a minute. To match the crotchet = lively pulse, we must have quaver = MM 150, which corresponds with balance wheel oscillations.

Simpson mentioned various `Tripla' (triple-time) tempos. The first consisted of three semibreves to a bar (a common-time semibreve). This was the standard triple that went in sesquialtera with minimpulse ?? (which Simpson mentioned as a diminution without further discussion). By proportions, semibreves in this tempo would be 2/3 as long as minims in common time. Simpson, for some reason, did not think of this tempo in proportional terms and just wrote that the semibreve was shorter than the common-time minim. (In much later editions semibreves were changed to minims and there was no difference between this Tripla and 3 over 2.)

Next to be discussed was the `more common Tripla' with three minims to a bar, each minim about the length of a crotchet in common time. This bar was three-quarters as long as the common-time bar. (In much later editions minims were changed to crotchets.) After that he wrote that there were `divers Triplas of shorter measure' where the minims `were sung or played as fast as crotchets in common time, and crotchets as fast as quavers'. He then wrote that one can sometimes meet with figures such as 3 over and 6 over 4, and explained their proportional significance. In 3 over 2 there were three minims in a common-time bar, and in 6 over 4 six crotchets.

The above defines four Tripla tempos. The slowest was the first one discussed, at 3/4 the speed of common-time crotchets for semibreves (later minims). At double that speed (3/2 times the speed of common-time crotchets) were crotchets in 6 over 4. In between these two was the `more common Tripla', where minims (later crotchets) were at the speed of common-time crotchets. At double-that speed were crotchets in `divers Triplas'. The first of these pairs of tempos was what had traditionally been available by proportion for triple tempos during the 16th and earlier in the 17th centuries. The second pair was new as standard tempos, reflecting the need for finer gradations and more variety in such tempos then.

Earlier John Playford (1654) had not distinguished between the two pairs of tempos, writing that the swifter of the two types of triple time was twice as fast as the other. Here the slower one ('for Airy Songs and Galiards') already had three minims to the bar, while the fast one (`for Corants, Sarabands, Jigs, and the like') had three crotches to the bar (see illus. 2).


Later Henry Purcell (1696) mentioned all four: `to be known by this 3 over 2, this 3/1, this 3 or this 6 over 4 marke, to the first there is three Minims in the barr, and is commonly play'd very slow,the second has three Crotchets in a barr, and they are play'd slow, the third has ye same as ye former but is play'd faster, ye last has six Crotchets in a barr & is Commonly to brisk tunes as Jiggs and Paspys.'

Purcell's 6 over 4 was the fourth, while for Simpson it was the third. By this time the proportional relevance to the common-time bar was Iosing importance, and proportional symbols were beginnings take on their modern meaning of the upper number meaning how many lower-number note values (defined as the number in a semibreve) there were in whatever type of bar it was. The symbol 6 over 4 applied to the fastest triple time in the old proportional system, and this may be why it was used for the fastest one here. The symbol 3 over 2 is here correctly used proportionally. The symbol 3/1 was used by Playford (1654) for the fast tempo with three crotchets in a bar. There he called it `three to one', but in the 1674 edition (possibly influenced by Simpson's first Tripla, or a mistake) the name applied to the slow one (but the symbol was still used for the fast one, C3 being used for the slow one). It had previously been used (e.g. Byrd's My Ladye Nevills Booke) for three crotchets in black notation in the time of a white minim. The symbol 3 had been used generically for any -triple tempo earlier in the century, and this was Simpson's usage.

The 1694 edition of Playford (corrected and amended by Purcell) mentioned only three of these four triple-time tempos, the middle one marked by either 3 or 3/1. Also mentioned are bars with three quavers (twice as fast as crotchets), 6 quavers (in 6 over 4), 9 quavers or crotchets (9 over 6) and 12 quavers (12 over 8).

Much of what was happening in the music of late 17th-century England had happened much earlier in Italy. Frescobaldi also mentioned four tempos in triple time. In the preface to his Capricci ... (1694) he wrote: `Sections in ternary rhythm must be taken adagio when the values are great, but faster when the values are smaller, still more so in 3/4, and allegro in 6/4.'

Mace, 1676

Pendulum from ceiling to floor:

crotchet pulse

Thomas Mace (1676) suggested that an aid for keeping time would be to attach a string to the ceiling and tie a weight to it, almost touching the floor. To start this pendulum off, one lifts the weight to one side as high as one can reach and lets go. He made it very clear that a full oscillation of this pendulum corresponded to a semibreve in common time. Unfortunately he gave no indication of how high above the floor he expected the ceiling to be, but reasonable estimates can give useful limits on what the tempo might be.

The frequency of a pendulum equals 0.50 divided by the square root of the length expressed in metres. With four crotchets per full oscillation, their tempo equals MM 120 divided by the square root of the length. The length of the pendulum is slightly less than the height of the ceiling above the floor. That height needs to be more than the highest reach of a short man, which is at least 2 metres. This makes the tempo slower than crotchet = MM 85. If this height was more than 4 metres the tempo would be slower than crotchet = MM 60. This is possible because Mace suggested that the maximum length of the pendulum should be used for practice, implying that the weight might be raised for a performance tempo. It would be unlikely that the latter tempo was slower than crotchet = MM 60.

Mace described his own music room. It had an arched ceiling and was shaped in a square-with sides 6 yards long, having galleries 3 yards deep along each side of the square, and small balconies extending beyond the galleries. With a room of this size the ceiling would be much closer to 4 than to 2 metres high. A height of only 2 1/4 metres leads to crotchet = MM 80, SO we can say with considerable certainty that Mace's pendulum implies crotchet = pulse.

Playford/Purcell, 1694

Large chamber clock pendulum:

crotchet = MM 60 in C

In the 1694 edition of John Playford's Introduction to the Skill of Musick, `corrected and amended by Mr. Henry Purcell', three sorts of common time are described. The slowest was marked C, and for the tempo one can `Stand by a large Chamber-Clock and beat your Hand or Foot (as I have before observed [i.e. moving at each minim, alternating down and up]) to the slow Motions of the Pendulum ...' Such clocks then had a pendulum 1 metre long (39 3/8 inches), so that each oscillation took 2 seconds (each swing taking one second). Each movement of the hand or foot could be synchronized with either each oscillation or each swing. The former would imply crotchet = MM 60, and the latter minim = MM 60. The term `slow motions' implies that there are fast motions as well, so associating `slow' with the full oscillation and `fast' with a single swing would make sense. This expectation is borne out when we compare this tempo with the third type of common time discussed below.

The second sort of common time was `a little faster' than the first, and was marked ??. I estimate this to be about 25 per cent faster since the term `faster' meant 50 per cent faster when Purcell (1696) compared the tempo of 3 with 3/1.

The third sort of common time was quickest of all, and marked with ??. Of this one Playford wrote `you may tell one, two, three, four in a Barr, almost as fast as the regular Motions of a Watch.' I estimate `almost as fast' to be 10 per cent slower since this provides a small margin above what Quantz (1752) wrote was an `imperceptible' difference in tempo (five notes per minute out of 80, or 6 1/4 per cent). There should be no difficulty with associating `regular motions' of a watch with Simpson's `little minutes', so the estimate for ?? is crotchet = MM 135. Earlier editions of Playford's book only mention two common time tempos: ?? for `Songs, Anthems, Fantasies, Pavans arid Almans' and ??, which was twice as fast. In this edition the slower one of these was split into two tempos, so we would expect a tempo at half that of ?? would fall in between these two. This resolves the earlier ambiguity between full oscillations and single swings of the clock pendulum in favour of the former. The tempos then are crotchet = MM 60 in C, about MM 75 in ?? and about MM 135 in ??.

In Purcell's own book (1696) the same three common time tempos with the same marks were given. He wrote `ye first is a very slow movement, ye next a little faster, and-ye last a brisk & airry time'.

A model for the changes

The above interpretations of what the various pieces of evidence on absolute tempo imply fit into a pattern of changes that readily extrapolates to the beginning of music notation. The following model for the pattern of tempo changes includes a tempo shift related to the shift in popularity from major to minor proration, plus four augmentations in the notation of the most popular tempo type at differ-ent times.

In Vetulus's time, major proration was the most popular type of tempo and had a note value in the pulse tempo. From Gaffurius's time onwards, minor proration was the most popular tempo type, and had a note value in the pulse tempo. The Savanarola evidence is appropriately intermediate. This change dropped the tempos in all mensurations to 3/4 of what they were before. This association between the pulse and the most popular type of tempo could be general. It could be associated with Simpson's report that the minim in the most popular ternary tempo was as long as the crotchet in common time.

The other major changes implied by the evidence are augmentations in the notation. In the 15th century this affected minor proration, creating the integer valor, where the `regular' semibreve had the same tempo for C, [whole note], ?? and ??. In addition, there was augmentation of major proration when it occurred in a single voice. In the 16th century augmentation often occurred with minor proration again, converting alla breve ?? into alla semibreve ??. There seems to have been much augmentation ambiguity, which could be what made C redundant early in the century. Initially the augmentation was most stable in instrumental music (so that Gerle's schlag was the same as Gaffurius's `regular' semibreve), but later it spread to most secular and some sacred music. There were no further augmentations. In the middle of that century crotchet-pulse C was reintroduced. In the 17th century the ambiguity in tempo between C and alla semibreve ?? was sometimes resolved with the crotchet in C placed at the bottom of the pulse range, and the crotchet in alla semibreve ?? at the top.

Extrapolation of this model to the beginning of mensural music is particularly unambiguous. In Vetulus's time the minim was the fastest written note value. Previously it must have been the semibreve, and before that, the breve. If we assume that some note value of the most popular type of tempo corresponded with the pulse, and that the tempo of the fastest written note would not subsequently be abandoned, then the tempo of the pulse corresponded with the regular breve initially, and with the perfect semibreve when this note value was introduced. Thus two augmentations by a factor of three would have occurred to get to the tempos of Vetulus. The tempos of the major and minor semibreves in Vetulus's time are properly generated if we assume that the second of these augmentations affected perfect time but not the less popular imperfect time.

If anyone started with the (particularly clear) 14th- and 17th-century evidence and decided to explore possible sequences of how tempo standards could have transformed to generate the latter from the former, it is unlikely that any other sequence than the one given here would result.

It was Michael Morrow who first made me aware that there was a slowness problem about the early evidence on tempo that needed sorting out. I would like to express my regrets to musicological friends for not being able to resolve the problem in a way that they would have liked. Thanks must go to David Fallows for helping me in this investigation by inviting my contribution to the Companion to medieval and Renaissance music (1992), thus focusing my attention on pre-17th century tempo evidence, and by pointing me in the direction of some of the relevant references. Steve Heavens must also be thanked for his generously providing me with translations of all of the German references that I have used. My wife Yvonne deserves particular gratitude for helping to make my work on this project possible and enjoyable.



1318-26 Marchettus de Padua, Pomerium, ed. G. Vecci, Corpus Scriptorum de Musica, vi (Rome, 1961)

c.1350 Johannes Vetulus de Anagnia, Liber de musica, ed. E. Coussemaker (1869), iii, pp. 129-77; also ed. F. Hammond, Corpus Scriptorum de Musica, xxvii (Rome, 1977); Eng. trans. of passage in Sachs (1953), p. 187, and Busse Berger (1993), pp. 47-8

1412 Prosdocimus de Beldemandis, Tractatus ... ad modem italicorum, ed. Coussemaker (1869), iii, p. 235

1482 Bartolomeo Ramos de Pareja, Musica practica, 3.1.2, Bologna; ed. Johoannes Wolf, Publikationen der Internationalen Musikgesellschaft, Beihefte 2 (Leipzig, 1901), p.83

1496 Franchinus Gaffurius, Practica musice, Milan;Eng. trans. passage in Bonge (1982)

1498 Michaelies Savanarola, De febribus, de pulsibus, de urinus, discussed in Kummel (1970)

1530 Pierre Attaingnant, Quatorze gaillardes, Paris; illus. as facs. 2 in Apel (1953)

1536 Hans Neusidler, Ein newgeordent kunstlich Lautenbuch, Nurnberg; quoted in Sachs (1953), p.203

1546 Hans Gerle, Musica und Tablatur, Nuremberg; see Segerman (1994)

1565 Tomas de Santa Maria, Libro llamado Arte de saner fantasia, Valladolid; quoted D. Poulton, Lute Society journal, xii (1970), pp. 23-30

1597 Thomas Morley, A Plaine and Easie Introduction to Practical Musicke, London; ed. R. A. Harman (London, 1952), pp.40, 296-7

1610 Robert Dowland, A Varietie of Lute Lessons, London; facs. edn E. Hunt (London, 1958)

c.1614 The Fitzwilliam Virginal Book, ed. J. A. F. Maitland and W. B. Squire (New York, 1963)

1619 Michael Praetorius, Syntagma musicum, iii, Wolfenbuttel; facs. edn W. Gurlitt (Kassel, 1967), pp. 48-56, 87-8

1624 Girolamo Frescobaldi, Capricci fatti sopra divers) sogetti, Rome, preface; quoted Sachs (1953), p. 278

1636 Charles Butler, The principles of Musick, London

1636 Marin Mersenne, Harmonie universelle, Paris; Eng. trans. R. E. Chapman (The Hague, 1957), Third book of string instruments, Proposition XIV and XVIII (Cor,. II and IV), and Fourth book of Composition, Proposition XX and Fifth book of Composition, Proposition XI

1654 John Playford, Introduction to the Skill of Musick, London, pp. 15-16; quoted in Donington (1963), pp. 344, 348-9

1665 Christopher Simpson, A Compendium of Practical Musick, London; 1667, 2nd edn ed. P. J. Lord (Oxford, 1970), pp. 8, 10, 15-17; quoted in Donington (1963)

1668 Thomas Tomkins, Musica Deo sacra, London; quoted in E. H. Fellowes, The English madrigal composers (Oxford, 1921), p. 89f.

1676 Thomas Mace, Musick's Monument, London, pp. 80-81

1694 John Playford, Introduction to the Skill of Musick, London; edition revised by H. Purcell, pp. 25-6; quoted in Donington (1963), p. 344, 349

1696 Henry Purcell, A choice collection of lessons, London, preface; quoted in Donington (1963), pp. 344, 350-51

1752 Johann Joachim Quantz, Versuch einer Anweisung, Berlin; Eng. trans. E. R. Reilly (New York, 1966), chap. XVII, [sections] VII, pare. 51, 55

1869 E. de Coussemaker, Scriptorem de musica medii eavi, iii, iv, Paris

1953 Willi Apel, The notation of polyphonic music, Cambridge, MA

1953 Curt Sachs, Rhythm and tempo, New York, pp. 187-8, 201, 203

1963 Robert Donington, The interpretation of early music, London

1964 Salvatore Gullo, Das Tempo in der Musik des XIII. und XIV. Jahrhunderts, Berne, pp. 69-76

1969 Irwin Young, The `Practica musicae' of Francinus Gafurius, p. 137; cited in Bonge (1982)

1970 W. F. Kummel, `Zur Tempo in der italienischen Mensuralmusik des 15 Jahrhunderts', Acta musicoligal, pp. 150-63

1980 Howard Mayer Brown, `Tactus', New Grove

1980 David Fallows, `Tempo and expression marks', New Grove

1982 Dale Bonge, `Gaffurius on pulse and tempo', Musica disciplina, xxxvi, pp. 167-74

1982 Eunice Schroeder, `The stroke comes full circle', Musica disciplina, xxxvi, pp. 119-66

1992 Richard Sherr, `Tempo to 1500', Companion to medieval and Renaissance music, ed. T. Knighton and D. Fallows, London, pp. 327-36

1992 Ephraim Segerman, `Tempo and tactus after 1500', Companion to medieval and Renaissance music, ed. T. Knighton and D. Fallows, London, pp. 337-44

1993 Anna Maria Busse Berger, Mensuration and proportion signs, Oxford

1994 Ephraim Segerman, `Gerle on tempo', Comm. 1251, FoMHRI quarterly, lxxv (April), pp. 32-4

Ephraim Segerman is a historian, technologist and maker of pre-modern musical strings. He edits and contributes to FoMRHI [Fellowship of Makers and Researchers of Historical Instruments] Quarterly. His training as a physicist has led him to make judgement subservient to evidence whenever they conflict. His results are thus sometimes contrary to popular assumptions of the early music movement.
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Title Annotation:part 1
Author:Segerman, Ephraim
Publication:Early Music
Date:May 1, 1996
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