During a workshop on 18th-century music that I taught in Moscow recently, there was what diplomats call ‘a frank exchange of views’ [i.e. a heated argument]. I stated that mid-18th century musicians did not use mechanical clocks to measure musical time. A historian there objected strongly: suitably high-precision clocks had been invented in the 17th century already. I managed to restore peace, on the basis that we were both correct.

TIME AS A NUMBER OF MOTION

According to the Galileo Project [directed by Prof Albert Van Helden at Rice University] here, Galileo observed this chandelier in Pisa cathedral in 1582, and made notes on the pendulum effect in 1588. His serious experiments on the subject were begun in 1602. Around 1641, he designed a pendulum clock, but it was not built. The best clocks during the first half of the 17th-century marked the seconds, but did not measure them accurately: their best accuracy was plus/minus 15 minutes per day.

Around 1636, Mersenne and Descartes further investigated the pendulum effect. Mersenne defined the Tactus as one beat per second, and in 1644 he  measured the length of a 1-second pendulum as a little less than 1 metre. Christian Huygens was the first actually to build a pendulum clock, in 1656. The accuracy of the best clocks was greatly improved, to within about 15 seconds per day.

In 1696, Etienne Loulié published Élements in which he described his chronomètre, which was essentially a variable-length pendulum combined with a ruler for measuring the pendulum-length, gradated in inches. The machine was 72 inches (almost 2 metres) tall, giving a slowest possible beat around 44 beats per minute. The middle of its range (i.e.  a pendulum length a little less than 1m) was about 60 beats per minute (corresponding to Mersenne’s one-second Tactus).

18th-century devices were also very large, measuring slow beats in the range 40-60 beats per minute. The more compact, double-weighted metronome was invented by Winkel and first manufactured by Maezel in 1816.

So during the 18th century, mechanical devices for measuring musical time did exist, and were reasonably precise – good enough for all practical purposes, one would think. Their inconveniently large size is evidence of the importance of a slow count (Tactus) throughout this period. The one-second pendulum, i.e. 60 beats per minute, had a particular significance, in scientific studies.

Nevertheless, in spite of the availability of precision machines for measuring time, 18th-century musicians did not make much use of this technology. They continued to describe Tactus in the old ways. For example, Quantz  Versuch einer Anweisung die Flöte traversiere zu spielen (1752) here mentions Loulié and his chronomètre, but says (XVII -vii – 46) that nobody uses it, in spite of its reliability and precision. Instead (47), he describes musical Tempi in terms of the human Pulse, and for each different type of movement (Allegro, Adagio etc) relates this Pulse to a particular note-value.

So it seems that increasing precision about Time itself did not tell baroque musicians what they needed to know about musical Time. Musicians were not so interested in the absolute Quantitative measurement of Time, they were concerned with the subjective Qualitative nature of musical Time. Their question was not, “how fast does it go?”, but rather:

What is the Quality of Time? How does it feel?

This question places the investigation of Time within the study of the History of Emotions. [Read more about the Australian Research Council’s Centre for the History of Emotions, here.]

The Galileo Project characterises the slow change in concepts of Time from Aristotle via Galileo and Newton to the modern era as the shift from the ‘qualitative and verbal’ to the ‘quantitative and mathematical’. You can read more about Philosophies of Time, ancient, baroque, our own everyday assumptions, Einstein’s 20th-century revolution and Hawking’s 21st-century paradoxes, in A Baroque History of Time here, where I too emphasise the continuing importance circa 1600 of Aristotle’s idea of Time as ‘a number of motion’ [some translations have ‘a number of change’] circa 1600.

You can also watch a video discussion of What is Time? here 

For the Metaphysics of Quality, be sure to read Robert M Pirsig Zen and the Art of Motorcycle Maintenance (1974).

QUALITY TIME

In this post, I’d like to consider how historical philosophy affects practical music-making, in terms of Quality. What was the Quality of baroque Time? How did it feel?

In Ars Cantandi (1696), Carissimi makes it clear that 17th-century musicians appreciated the difference between Quantity and Quality of Time.

The triple-metres all agree with regard to quantity, division and proportion, as is easily understood, but in the slow or fast quality, known by the Italians as tempo and by the French as mouvement, they are utterly different.

So in the various triple-metres, the relationships between note-values agree: a semi-breve in 3/1 has the same duration as a semi-breve in 3/2.  Whatever the proportion sign, a semibreve can be divided into two minims, a minim can be divided into two semi-minims. As Carissimi says, the Quantities all agree.

But the Quality, how it feels, is very different, depending on whether the music proceeds as Sesquialtera (feeling groups of three semibreves); as Tripla 3/2 (feeling groups of three minims); or as Sestupla 6/4 (feeling groups of two dotted minims). Sesquialtera feels slow, Tripla feels medium-fast, Sestupla feels fast, even though the Quantities agree, each note-value has its true, consistent worth, the same value in all three triple-metres.

We can acquire a feeling for the Quality of early 17th-century musical Time by reminding ourselves what Music itself is, in this period. As we read in many sources, for example Dowland’s Micrologus (1609) here [translating probably the 1535 edition of Ornithoparcus: the almost-indentical 1519 edition is here], what we think of today as “music”, music as sound, practical music-making, was the least important meaning. [Read more about What is Music? here]

1. Music is firstly Mondana, Dowland’s ‘musicke of the world’, the heavenly Music of the Spheres created by ‘the very wheeling of the Orbes.. the motion of the starres and the violence of the Spheares’.
2. Next, music is Humana, Dowland’s ‘humane musicke’, the harmonious nature of the human body, ‘by which the spirituall nature is ioyned with the body…that Musicke which euery man that descends into himselfe finds in himselfe’
3. In third place, music is Instrumentalis, Dowland;s ‘instrumentall musicke’, the actual music that we play and sing here on earth.

Music was also divided into Practical (what Dowland calls Active or Pracktick) and Theoretical or Inspective:

Inspectiue Musicke, is a knowledge censuring and pondering the Sounds formed with naturall instruments, not by the eares, whose iudgement is dull, but by wit and reason.

Tact is a successiue motion in singing, directing the equalitie of the measure: Or it is a certaine motion, made by the hand of the chiefe singer, according to the nature of the marks, which directs a Song according to Measure.

Above all things, keep the equality of measure!

TACTUS

The greater [Tactus] is a Measure made by a slow, and as it were reciprocall motion. The writers call this Tact the whole, or totall Tact. And, because it is the true Tact of all Songs, it comprehends in his motion a Semibreefe.

The lesser Tact, is the halfe of the greater, which they call a Semitact. Because it measures by it motion a Semibreefe, diminished in a duple [i.e. a minim]: this is allowed of onely by the vnlearned.

TACTUS AS QUANTITY

TACTUS AS QUALITY

Since performers’ emotional state can alter their perception of an ‘equal measure’, a singing-actor representing a character’s strong passions might act out the affetto in dramatic music (in genere rappresentativo) by letting that passion alter the speed slightly. Of course, this only works, if the audience don’t notice the trick: if they become aware that you are just going faster, the illusion is gone.

 In the early seventeenth century, tarde, velociter, adagio and presto distinguished between fast and slow, that is degrees of change intermediate to those determined by diminution (2:1) or proportion (usually 2:1, 3:1 or 3:2).

THE QUALITIES OF DANCES

In the second half of the 17th century, in France, the quality of Time was linked to how it felt to perform the movements of a particular dance. Each dance had its own vrai mouvement (as Muffat calls it, in Florilegium 1698) – ‘true movement’. This deceptively simple phrase has many meanings: the particular steps of each dance, a speed-range within which those steps ‘feel right’, a particular metre (duple or triple), and also what a modern musician might call a particular ‘groove’, a regular pattern of Good and Bad beats, a tendency towards certain characteristic rhythms. Time itself ‘moves’ truly, but differently, for each dance. And of course, each dance-type is associated with a certain range of emotions. In short, each dance-type has its own feeling, its own Quality.

Modern musicologists and dance historians have worked hard to understand the precise Quantity, the actual speed for each dance-type. Commonly encountered speeds around 84 beats per minute for some dances look rather like a proportion of the earlier Italian Tactus =  a bit less than 60. But perhaps too much focus on Quantity is again the wrong approach to the whole question. We might better seek to understand the Quality of each mouvement, learn how it feels. We can find a typical range of feelings, in the sense of emotions, affetti, by examining texts sung to each dance-type. We can try to discover the right groove within the Tactus, the appropriate swing of inégalité in the shorter notes,  and – most importantly – we can learn how it feels, physically, to dance its characteristic steps.

When I first started playing the harp, I studied renaissance and baroque dance and spent a lot of time playing for dancers. I count this a most valuable part of my Early Music education. I quickly discovered that dancers are very sensitive to the precise speed of each dance, so as a dutiful young professional musician, I would measure their ideal speed in rehearsal with a metronome, and then use a silent metronome to reproduce this speed in performance. This was Quantitatively accurate, but it didn’t work at all.  Dancers’ appreciation of speed is highly subjective – it depends on the nature of the floor surface, on the size and shape of the available floor area, on their physical condition and mood at the moment of performance. It’s not a question to be answered with a metronome; it’s a matter of How does it feel?

My solution, as an instrumentalist playing for dancers, was to learn the dance-steps so that I could watch whilst playing and allow the dancer to set the tempo in the opening bars. Of course, the ‘ball-park’ tempo was known from rehearsal, but the ‘fine-tuning’ of speed was left to the performer, in the moment. Once set, this speed, the rhythmic ‘groove’, the inégal swing, the complete vrai mouvement  is maintained until the very end of the dance, just as Muffat says.

Because each dance has its own vrai mouvement, its own Time, the Quality of musical time in late 17th-century France is complex and multifarious. Time is still cosmic and divine. Indeed, dance itself is a metaphor for the perfect movement of the heavens, as well as for a perfectly organised society with Louis XIV himself as the divinely appointed principal dancer around whom everyone else must orbit. Melody, harmony and vrai mouvement (in all its meanings) work together as the head, heart and soul  of the human body. Tactus is still shown by an up and down movement of the hand, or of the big stick that led to Lully’s death. Muffat recommends that dance-musicians should tap their feet in Tactus (on the downbeat of each bar). Meanwhile, the dancers’ feet strike out faster-moving beats within the Tactus, moving with the groove of the music as they step, rise and sink, turn and balance.

French dance-Time still has the Quality of being ‘true’, rather than arbitrarily chosen according to the whim of performers. But now there are many truths, as many different types of vrai mouvement as their are types of dance. The significance of individual dance-steps within the slow count of the Tactus encouraged French musicians to think more about the ‘equalitie of measure’ beat-by-beat in crotchets. The actual speed was determined according to the Quality of each dance, rather than by the Quantity of mathematical proportions. As Houle observed in 1987, these different ways of thinking were essentially incompatible, and the attempts to reconcile them make for confusing reading in late 17th-century sources.

Logical extensions of mensural principles were sometimes in conflict.

Just as the 17th century saw opposed national styles of Music (French and Italian), so each national style had its own approach to questions of musical Time. When the musical tastes were re-united, gradually and not always completely, during the 18th century, so attitudes to Time were also gradually brought closer into alignment.

THE QUALITY OF A PENDULUM

Today, when we think about beating time, we may be reminded of the Qualities of a metronome, or of a modern conductor. Experiments we carried out at Scoil na gCláirseach (2013) and at the Royal Danish Academy of Music (2014) demonstrated that a long, slow-beating pendulum (about one metre long, at a Tactus speed of around one beat per second in each direction) has quite different Qualities.

A metronome gives a sharp click, and conductors are taught to make the precise moment of the beat as sharply defined as possible. But a pendulum slows down and stops momentarily as it turns, so that the actual moment is not sharply defined. This allows a musician to ‘place’ the beat subtly, communicating the particular feeling of this note, this harmony, the quality of this moment of time, letting the audience enjoy the moment of ‘smelling the roses’ as they walk steadily along the path of the music.

Valentini’s Trattato della battuta musicale (1643) allows the downward movement of the Tactus hand to last one quaver (approximately 1/4 sec) after which the hand remains down for three quavers (3/4 sec); similarly for the upward movement. Try this for yourself: it looks very different from modern conducting, and (like a pendulum) leaves the subtle ‘placing’ to the musician, within limits of the order of magnitude of a 1/4 sec.

Within the steady Tactus, shorter note-values need not be precisely equal. Descriptions of the ‘intrinsic’ hierarchy of Good and Bad notes (buone & cattive) remind us that the concept of a ‘half’ in this period does not necessarily imply precisely 50%.  Muffat (Florilegium 1698) explains that

Good notes are those that seem naturally to give the ear a little repose. Such notes are longer, those that come on the beat or essential subdivisions of measures.

It is not easy to put this difference in Quality between Good and Bad notes into words. Rameau in his Traité de l’harmonie (1722) asks for a certain je ne sais quoi on the Good beats, which he contrasts with a ‘slight leaning’ (appuyer un peu) on the Bad beats.

To get a feeling for the Quality of Good and Bad sub-divisions of the Tactus, first establish steady one-second Tactus. Then try saying simple words like piano, forte, dolce, arpa, pasta, pizza in your best Italian accent, one syllable on the down-position, the next on the up-position of your steady Tactus. [Don’t ‘bang’ the initial consonants, savour the vowels]. Can you reconcile the result of this tactus-beating with Valentini’s instructions above?

This subtle difference between Good and Bad (not loud and soft, but something of Long and Short) on the principal divisions of the Tactus (the ‘groove’ of a dance-movement)  is not to be confused with the stylised inégalité on shorter note-values (the ‘swing’ of short notes in French music).  Read more about The Good, The Bad, & the Early Music Phrase here. Watch a video about Good & Bad notes here.

Whereas a modern conductor might struggle to control a wayward soloist, or a modern accompanist might struggle to follow, a pendulum just swings to and fro, maintaining the ‘equalitie of measure’ calmly and gently. This quality of calm steadiness is a vital skill for a baroque accompanist to acquire. As Agazzari writes in Del Sonare (1607), the continuo’s role is to ‘guide and support the entire ensemble’: the continuo maintain the Tactus, even if a soloist chooses to place a certain note before or after the beat. But this is not an aggressive power-struggle, the continuo can remain as calm as a perfect slow-swinging pendulum.

A jazz-band provides a good model for baroque continuo, with the rhythm section keeping a steady groove, whilst the soloists syncopate or drift elegantly around the beat, depending on the affetto. 

Like a pendulum or the classic swinging pocket-watch, the calm, slow, steady beat of Tactus can be powerfully hypnotic, taking musicians and audiences into a shared trance, a dream-world where the cosmic and the human are mysteriously connected, a magical space where emotions are felt more intensely, where music unites performers and audience in a shared spiritual experience.

Did Dowland perhaps refer to the inner focus of trance in his description of musica humana as ‘that Musicke which euery man that descends into himselfe finds in himselfe’? This spiritual quality of time is enhanced by calm steadiness – any random alteration would jar. One strand of my research investigates how ‘early opera’ made deliberate use of these hypnotic qualities in the first decades of the 17th century. Read more here.

THE QUALITY OF BAROQUE TIME

The essential Quality of baroque Time emerges from the fact that 18th-century musicians did not use machines to determine time accurately, even when such machines became available. No matter how closely we investigate period sources, we cannot know the precise Quantity of baroque Time. And actually, we don’t want to, because to ask the question of Quantity doesn’t give us a useful answer. The objectively “right” metronome speed will still “feel wrong” if the subjective situation changes.

So we want Quality Time. Time that is calm, steady and deeply significant, like the movement of the heavens or the beating of our hearts. And we must work hard to maintain it. Here is my personal take on baroque Quality time:

If the Tactus breaks, the heavens will fall. If your pulse stops, the music also dies.

As we begin to appreciate the subtle Quality of baroque time, we can appreciate how period writers struggled to explain its mysteries, to define the ineffable. Here is my anonymous hero, Il Corago circa 1630:

Per lo che in quanto alla tardita e velocita de’ movimenti, o vogliamo dire brevita o lunghezza di tempo nel quale si pronunziano i suoni o voci musicali, i moderni reducono e et essaminano il tutto ad una certa misura, come a suo proprio paragone, la quale essi chiamano battuta et e quel tempo che si mette nell’ abbassare et elevato la mano o piede o altra cosa che sia in una determinata velocita che d’alcuni et in alcuni casi piu prestamente di altri et in particolari occasioni meno velocimente si muove, ma pero dentro una certa latitudine o determinazione di tempo, come piu l’esperienza s’impara che chiaramente si possa esporre con lo scrivere.

Concerning the slowness and speed of movements, or we might say brevity or length of time in which musical sounds, notes or words are pronounced, modern [i.e. early 17th-century] musicians examine the whole question and reduce it all to a certain measure, as if to its own bench-mark, which is called battuta [Tactus, or ‘beat’] and which is that time which is put into the lowering and raising of the hand, or foot, or other object, which should be at a specific speed which for some people and in some situations goes faster than others, and in certain circumstances less rapidly, but however within a certain latitude or precision of time, which experience teaches more clearly than can be explained in writing.

Tactus is the seicento musician’s paragone, defined in Florio’s 1611 dictionary as ‘paragon (i.e. model/example of excellence), a touch-stone to try gold, or to distinguish good from bad.’ Tactus is the Champion of Time. Tactus is the ideal or bench-mark of Time, the gold standard.

Tactus is Quality Time.

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