Monteverdi fans will recognise this snippet as part of the tenor solo, Nigra sum, from the 1610 Vespers. The text is usually given in English as ‘the time of the singing of birds is come’, translating direct from the original Hebrew of the Song of Solomon. Monteverdi’s setting creates a musical picture of the word tempus (time) with a succession of semibreves.
Around the year 1600, the semibreve is the note-value where Time as musical notation and Time in the real world meet. That meeting is governed by the Tactus, the physical movement of the hand, down-and-up. Down and up again corresponds to a semibreve, and lasts about 2 seconds. [Read more about how 17th-century notation was calibrated against real time in Quality Time, here]. So Monteverdi’s semibreves for tempus putationis are a musical picture of Time itself.
However, the Latin word putatio actually means ‘pruning’, so Monteverdi’s text actually refers to the early spring pruning of the vines [the Song of Solomon has more to say about the ‘vine with the tender grape’]. That might encourage some pruning of any bird-song ornaments from this phrase! And it inspires me to cut away all the excess foliage to show what I believe to be the essential structure of Time, in Monteverdi’s period.
For this ‘pruned down’ post, instead of arguing from original sources towards my personal conclusions, I’m going to begin by setting out (my take on) the starting assumptions of Monteverdi’s generation. Starting from these period assumptions (very different to those of today’s musicians), we’ll see what kind of music-making might grow, as buds from these particular shoots.
This post is also inspired by Bill Hunt’s comments and challenges to my article on Proportions in Monteverdi’s Ballo, here. Thank you, Bill for your thought-provoking remarks: my replies and ripostes are below!
So let’s start at the very beginning, with the ut re mi of seicento Time. But keep in mind: this is not simply a matter of practical music-making. We are dealing here with renaissance ‘Science’, that is to say the Philosophy of splendid, cosmic, divinely-ordained things, the knowledge of what really counts.
MONTEVERDI’S TIME: PHILOSOPHY
- Monteverdi understood Time (as a philosophical concept) in Aristotelian terms, as defined by motus (movement, or change). This is very different from Newton’s concept of Absolute Time (1687) that still today underpins our intuitive grasp of Time.
- Time in the real world was defined by the heavenly clock of the cosmos. Each day, the sun reaches its zenith and defines noon.
- The best clocks of Monteverdi’s period could indicate the passing seconds, but could not measure seconds accurately. They were only accurate to about 15 minutes a day.
- Smaller intervals of time could be measured by the human pulse, the heartbeat. Although the heart-beat varies from person to person, and according to the physical state of the individual, it offered higher precision than the best clocks. But there was no means of calibrating this accurately to clock-time, since clock-time itself was insufficiently precise.
- Even smaller intervals of time could be measured by musical rhythm, subdividing to, say, 1/8th of a second. This was the highest precision timing known in this period (renaissance swordfighters wished to emulate singers’ sense of precision timing). Again, there was no means of calibrating this accurately to clock-time, since clocks themselves were inadequate.
- There was a strong belief in the existence of a single, divinely ordained, correct Time, defined by the cosmos, e.g. by the noon-day sun.
MONTEVERDI’S TIME: MUSIC
- Music itself was cosmic [musica mondana, the Music of the Spheres], and human [musica humana, the harmonious nature of the human body], as well as sound [musica instrumentalis, music sung and played here on earth].
- Musical Time was measured by the Aristotelean motus of the perfect movement of the cosmos, of the steady beat of the human heart, by the down-and-up movement of the Tactus hand.
- Just as citizens tried to regulate their clocks to run steadily (for practical convenience, and as faithful microcosms of solar time), so musicians tried to keep Time as steadily as humanly possible. This regulation was at the level of about one second of clock-time; in music, it was at the level of the Tactus beat.
- Smaller intervals of Musical Time were measured by sub-dividing the Tactus beat.
- Just as citizens tried to calibrate their clocks to agree with each other, and with Solar Time, so musicians tried to agree with each other about Musical Time. The various members of a musical ensemble needed to agree on Time, in order to play together, just as citizens had to agree on a time of day, in order to meet each other. From one day to another, from one place to another, citizens and musicians alike tried to keep a consistent sense of Time. However, they had no means of precise calibration: they could only make their best human estimate. Consistent Time was what felt consistent.
- There was a strong assumption of a single, heavenly-inspired, correct Musical Time. A musician’s job was to get it right, not to have a personal clock that ran unsteadily, or differently from everyone else’s.
MONTEVERDI’S TIME: TACTUS
- All this philosophy was put into practice using the Tactus, the down-up movement of the hand, which calibrated musical notation to real-world Time. The Tactus could be physically enacted, or just kept in mind as an organising concept: either way, it was compared to the heartbeat.
- Under mensuration symbol C, the complete Tactus cycle (down-up) corresponds to a semibreve. Down for a minim; up for a minim.
- In Tripla Proportion, down corresponds to three minims, up to another three minims. The Tactus-beat is maintained without change.
- In Sestupla Proportion, down corresponds to six semi-minims (these look like crotchets in 6/4); up to another six semi-minims. The Tactus-beat is maintained without change.
- In Sesquialtera Proportion, down corresponds to two semibreves; up to one semibreve. The duration of the complete Tactus-cycle does not change, but now the down is longer than the up, the beat is ‘unequal’.
MONTEVERDI’S TIME: QUALITY
- Like the Cosmos, like a clock (but better!), like the heartbeat (but slower), the Tactus beats steadily and slowly.
- A musician’s job is to get it right, to keep it steady, to make it consistent from day to day and with everyone else’s.
- Like the stars in heaven, like a clock at the back of the room, the Tactus (as a concept) existed before the music started, will persist after the music stops, and continues across silences within the music. This Tactus-as-concept directs the music. The Tactus itself is the director, not the human who waves the Tactus-hand.
MONTEVERDI’S TIMES: CALIBRATION
- Music was calibrated to the Tactus at the level of semibreve (complete cycle) and minim (down alone, or up alone).
- The Tactus shared many vital qualities with the heartbeat, but was not calibrated to it (the heartbeat was generally faster).
- The Tactus felt slow and steady, as perceived in the human arm. This sets some limits (a finger could wag faster, the entire body might sway slower), but does not offer precise calibration.
- There was no means to calibrate the Tactus accurately to clock-time. The best approximation was about 1 beat (down, or up) per second for minims, i.e. about 2 seconds for the complete down-up cycle, for the semibreve. Tactus was calibrated not by clocks, but by a feeling of consistency.
- The Tactus felt the same, whatever the circumstances. We can imagine that in a large resonant building, the Tactus might actually proceed a little slower, in order to get the same feeling as in a small rehearsal room. We can imagine that, at moments of great excitement, or deep, genuine emotion, musicians might feel their Tactus to be consistent with the rehearsal, but this subjective impression would be altered by their human emotions.
MONTEVERDI’S TIME: HUMAN INTERVENTION
- Like the Cosmos, like the heartbeat, the Tactus has a conceptual existence and an authority that mere humans should not try to mess with. It is better than any clock, not in the sense of being ‘less mechanical’, but in the quality of being more accurate, more steady.
- A musician’s job is to maintain the Tactus steadily, consistently and in agreement with all colleagues.
- Within these assumptions, as a daring challenge to the stability of the Cosmos, and at the risk of upsetting one’s own heartbeat, performers began to flirt with the notion that the authority of the Tactus might not be wholly Absolute. In certain, strictly limited, situations, a human musician might intervene to alter (momentarily, minutely, infrequently) the way in which Tactus directs music.
- Caccini describes (and Monteverdi notates) a senza misura (out of measure) in which the singer temporarily ignores the Tactus. The Tactus continues as a concept, and in the continuo accompaniment. This is like a jazz singer floating elegantly around a steady beat in the rhythm section. This is a special effect, not to be over-used.
- Caccini and Frescobaldi describe (and Frescobaldi links to Monteverdi-type madrigals) ways to guidare il tempo (drive Time), in which the Tactus beats sometimes faster, sometimes slower, and even hesitates (momentarily) on the up-stroke. These changes are between sections (passi, movements), at the boundary of contrasting rhythmic structures and emotional content, not within one section. The alteration is a ‘step-change’, rather than a smooth acceleration/deceleration; it’s like changing gears, rather than using the accelerator/brake; it’s like the way a horse changes pace by changing gait (from walk to trot, canter and gallop), not the smooth acceleration of jet-plane. This is a special effect, not to be over-used.
- When ‘driving the Time’ any change to the Tactus itself is small. The purpose is that the listener should perceive a change of emotion, not simply to turn the speed-dial up or down. When a noticeable change in the speed of the notes is wanted, the composer can notate this with changes in note-values, or changes in Proportion.
Source references for these period assumptions can be found in many of my previous postings on Tactus, Time and Rhythm (use the Search button and Tags elsewhere on this page) and in Citations and Sources, below. There’ll be more in future posts, too. Tactus and the Philosophy of Time are discussed in great detail in Roger Matthew Grant Beating Time and Measuring Music in the Early Modern Era, hot off the Oxford University Press, and highly recommended, here.
But since this posting is pruned back to the essentials, I’m now going to apply these starting assumptions to Bill Hunt’s excellent list of questions.
In the discussion that follows, the challenges come from the eminent English viola-player, William Hunt, profile here. Three articles about the Ballo in Monteverdi’s Orfeo are under discussion: Roger Bowers on proportions here, Virginia Lamothe on dance here, ALK on tactus, proportions and dance here.
WH: I’d like to propose a contrary view. Part of the problem with Andrew’s fascinating discussion is that he sets up a number of straw men in order to arrive at his conclusions. Principal amongst these, in referring to the articles by Lamothe and Bowers on L’Orfeo, is the assertion “Their suggested metronome mark of approximately 50/60 as the Tactus Aequalis is certainly highly plausible. And Bowers agrees that the notation implies the same Tactus for the whole opera”. Bowers makes no such claim.
ALK: (See ‘Citations and Sources’ below). I should first state clearly that I have great respect for Prof Bowers, and I agree with his points of principle. Indeed, I wish to go even further in the same direction of consistency that he recommends. I set up the assumption of single Tactus for the whole opera, not as a ‘straw man’ to be cast away, but as a strong principle that I thoroughly agree with. Indeed, I believe that a particular notation implies the same Tactus wherever it is encountered in this entire repertoire (to the limits of subjective, human ability to maintain a single Tactus without any clock to confirm it).
For Orfeo, Bowers argues that the original notation conveys precise information that should be respected in performance. I agree. He argues that proportions are mathematically precise, and I agree. I disagree only on the detail of which mathematical ratio applies in certain instances.
In the Ballo, Bowers argues that there is no change in the meaning of note-values between the two triple-metre sections [3/2 and 6/4]. I agree. I go further to argue for equivalence of note-values between all triple-metre sections within the work [3/2 and 6/4 are the only triple-metre ‘time-signatures’ that occur in the whole of Orfeo]. I go further again, and argue for equivalence of note-values between sections in duple-metre too. Therefore, note-values only change, when the Proportion changes between duple and triple.
Bowers notes that all ‘time-signatures’ are governed by C throughout the whole work. He argues for a consistent Tactus from Sinfonia at the end of Act I to the entrance of the Messagiera. I agree, and I go further: I argue for a consistent Tactus throughout the whole work. I see no indication for a great increase of speed at the end of Act I, as the Sinfonia starts (Bowers’ argument requires a three-fold increase in speed at this moment). I see no evidence for doubling the speed (or more) between a “recitative” in C and the ballo also in C.
Bowers seems to be inconsistent about when he applies the principle of constant tactus, and when he does not. He wishes to apply it during the Ballo and through the Act I-Act II sequence, through many changes of ‘time-signature’, coloration etc. I agree. I go futher, I wish to apply it consistently throughout the work. But Bowers rejects the argument for constant tactus in general (see Bowers ‘footnote 33), without careful argument. Does he mean to say “Tactus is constant when I want it to be, and otherwise not”?
I say that Tactus is always constant, with only small and infrequent exceptions. I note Frescobaldi’s and Caccini’s discussions of when and how to change the tactus. They describe very restricted circumstances when tactus may be changed. And those changes should be small – if a composer wants double speed, he writes shorter note-values or switches to C-slash. [Some sources indicate that even C-slash is less than twice as fast as C]. If a composer wants a gear-shift of 3:2 or 3:1, proportional notation is available.
So I conclude that a performer’s personal choice of tempo-change would be within a small speed-range. And this personal choice would be exercised very infrequently. In his example madrigal, Caccini changes the Tactus only once (in response to an obvious cue from the words). Frescobaldi similarly sets specific conditions for change of Tactus: break between sections, change of rhythmic structure, change of affetto. Since they follow the affetto, these changes in tactus exaggerate what the composer has already notated: long note-values (for a sad affetto, say) are played in slower Tactus, short note-values (for a happy affetto) in faster Tactus. The affetto is determined on the short-scale, “line by line, even word by word” [Il Corago, Monteverdi and many other sources], but the Tactus only changes between sections, if at all.
Finally, when one considers the audience – it is after all their ‘affetti‘ we want to ‘muovere‘ – one realises that doubling or halving the speed has no effect. The listener perceives the same pulse, with different levels of activity. But a small increase in speed, in the context of precisely regular Tactus, has a strong emotional effect. It may even entrain the listener’s heartbeat, which was previously aligned with the regular, slow tactus, and increase it. As Renaissance theory of emotions describes, a performer might move the listener’s ‘affetto‘ and even create physiological changes in the body and blood (the doctrine of the Four Humours).
A fine example of this is Led Zeppelin’s “Stairway to Heaven” which accelerates between sections (within the general context, throughout pop music of that period, of steady tactus). There is some fascinating interview material with the performers, where they discuss the general context (“getting faster was absolutely prohibited”) and the emotional effect of a few small, but perceptible changes, in this song. I hear echoes of Caccini and Frescobaldi….
WH: I do firmly believe, as Andrew clearly does, that tactus was an essential structural constant that could unite consecutive and contrasting passages in logically proportionate tempi. On the face of it, the section which Bowers identifies, running from the Sinfonia to Act 2 up to the entrance of Messaggiera, is exactly such an instance, because of the succession of mensural signatures and the absence of intervening double barlines or fermata (the same is not true of the passage from “Lasciate i monti” up to the end of Act 1). Here, if one follows through Bowers’ notational logic, one ends up with a pretty fast tempo for “Vi ricordi boschi ombrosi”, as he says. Personally, I find that persuasive both musically and dramatically, but I have yet to experience it in performance, due to directorial intervention.
ALK: The entire opera (indeed this whole repertoire) offers ‘a succession of mensural signatures’. And I know of no period evidence that a fermata or a double-bar implies a change of Tactus. In Orfeo, Monteverdi sometimes places a fermata in one voice, when simultaneously another voice has no fermata: the fermata sign simply indicates ‘the end of something’, and cannot imply any alteration in the motus of the Tactus. Double-bars are often used to seperate consecutive strains of a single dance-movement, where a change of Tactus would be most implausible.
I don’t accept the argument that the passage from Lasciate i monti up to the end of Act I is somehow ‘different’.. It too has a ‘succession of mensural signatures’. Sure, it has some fermatas and double bar-lines, but so what? If Tactus is ‘an essential structural constant that could unite consecutive and contrasting passages in logically proportionate tempi’ [and it surely is!], then why not for the passage after the Ballo, as well as for the Ballo itself? Why not for the end of Act I, as well as for the bridge from Act I into Act II?
Does WH wish to say that “Tactus is constant when I want it to be, and can be changed when I want”? Or does he know of evidence of a fermata or double-bar as an instruction to change Tactus?
I believe that Tactus is constant, with only small and infrequent changes. Frescobaldi and Caccini list the circumstances in which the Tactus might be changed: neither of them mention fermata or double-bar.
WH: Bowers … analysis of the notation is that … semibreve of the C equates to dotted semibreve of the 3/2. I suggest a tempo of something like semibreve = 52 for the opening (not a minim tactus, for reasons which I am coming to) becoming dotted semibreve = 52 for the 3/2, and finally bar = 52 (i.e. the ‘new’ semibreve = 52) for the 6/4: in other words a constant tactus.
ALK: I agree with the principle of a pulse that is maintained, and I have no objection to approximately MM52 for that pulse. And this interpretation of the proportions works too, in this place, starting from semibreve = 52 at the beginning of the ballo. But how do we find this tempo at the beginning of the ballo? Semibreve = 52 cannot apply to the whole opera – just try it for the beginning of the opera, for the Toccata or the Ritornello to La Musica or for any recitative: it is about twice as fast as possible. Why pick this fast tempo for this place notated in C, and not for another, also notated in C?
According to modern assumptions, directors can choose their own tempo, whenever there is a reasonable excuse (a fermata, a double-bar, personal inspiration, whatever). But according to period assumptions, the Tactus itself directs the tempo, and that Tactus is as constant as we humans can make it. (Caccini and Frescobaldi list limited circumstances where small and infrequent changes of Tactus might occur). My approach is to take that Tactus (somewhere around minim = 60), apply it at the beginning of the work, and maintain it, as best I can, until the end. And I’ll try to establish and maintain the same Tactus tomorrow, to the limits of my subjective perceptions of musical tempo.
The movement of the hand in beating Tactus is specified in period sources: in C, down for a minim, up for a minim. I find semibreve = MM52, i.e. minim = MM104 inconveniently fast for this mode of time-beating. I also find the resultant motus incompatible with the qualities of slow, steadiness that are associated with Tactus. I’m more convinced by the motus of minim around 60.
My approach starts from a broad principle, of a constant tactus. I apply this general principle first, before I look for solutions to particular problems of Proportions. I then apply the same solution to parallel situations. Following the Ballo under discussion, the next Proportional change in Orfeo is between the recitative (C) Ma se il nostro goir and the Ritornello (3/2), which moves in dotted semibreves and minims. My solution to the Ballo is C: minim = 60 leads to 3/2: dotted semibreve = 60. My solution to the following, parallel situation is the same.
Bill’s solution to the Ballo [C: semibreve = 52 leads to 3/2: dotted semibreve = 52] does work there. But it does not work for the parallel situation of Recitative & Ritornello. Either the 52 pulse or the proportional relationship (or both) have to be abandoned. Is it Bill’s argument that although the notation is parallel, the second situation allows a personal choice, whereas the first situation indicates the composer’s tempo intentions? Why?
My belief is that the entire concept of personal choice of tempo is foreign to this period and its repertoire. Mensural notation indicates the composer’s intentions.
WH. … treating the central section of the first “Lasciate” as not being repeated. (No repeat is marked, of course, but a second verse of text is underlayed. I subscribe to Andrew Parrott’s view that this is a printer’s error, and that the second text should have been printed in the second “Lasciate”, instead of the repeated underlay of “Qui miri il sole”. This would result in an ABC form for each chorus, though, as Andrew (LK rather than P) points out, the uninformed listener would hear it as AABCC, because of the written-out repeats in the outer sections. This has a perfectly satisfactory symmetry. What is hard to believe is the format as it is printed).
ALK: I agree that the sequence of movements in the Orfeo Ballo is ambiguous – Lamothe has much to say on this. Andrew Parrot’s suggestion of a printing error in the 1609 edition is plausible, though one might have expected the editor of the 1615 edition to have fixed the problem, since much smaller errors were corrected (albeit at the cost of introducing some new errors too!). Lamothe makes a good point that the opening section (with the associated choreography of reverences and passi gravi, slow steps on the ground) would not be repeated in a court social dance. My point is that a similar opening section (which is not danced) is repeated in Cavalieri’s theatrical ballo for Anima & Corpo. We do not know which sections of the Orfeo ballo were danced, though it is sure that the singers themselves could not have danced a galliard, with all its jumps, whilst singing. Consideration of the repeat scheme for the Orfeo ballo has include all these points, together with scholarship on the total number of singers (between 7 and 9), the possibility that dancing masters might have participated (as is specified by Cavalieri), and the prohibition against women acting on stage, still in force in Mantua in 1607.
Good arguments can be made to support several possible solutions.
WH: Having read many of the linked sites here with great interest, particularly the one on “Text, Rhythm, Action / Rhythm: what really counts?”, I am curious to know what Andrew thinks about the semibreve, which so many theorists describe as the fundamental unit of time. There is so much emphasis throughout all his articles on the minim and the fixing to it of a constant tempo, viz “Around 1600, typically the Tactus will be on minims (half-notes), somewhere around MM60. Down for one second, Up for the next second”
Leaving aside the massive nature of this generalisation (is this really supposed to be typical of all music around 1600?), what about the concepts of Thesis and Arsis? It seems to me that these are essential to an understanding of musical structure in this period, especially the setting of text. Unless the semibreve is the unit on which one is principally focussed, not the minim, a whole vocabulary of subtlety is missed, to my mind. But that is a huge subject for another occasion!
ALK: Bill is absolutely right to draw attention to the fundamental significance of the semibreve. The complete Tactus-cycle (down-up) corresponds to a semibreve. I could equally well, perhaps better, express my view as “The Tactus-cycle will last for a semibreve, approximately two seconds, i.e. somewhere around MM30 for the complete down-up.” In duple time, this results in the same “Down for one second, Up for the next second”.
But an advantage of the focus on the semibreve is that it allows you to negotiate the tricky change into Sesquialtera more easily. The complete Tactus-cycle (down-up) still lasts two seconds, but the Down lasts longer than the Up. This is why triple time is described as ‘unequal’ in this period. I agree with Bill that there are interesting and beautiful subtleties to be found in a heightened focus on the semibreve.
However, period sources specify that the mode of beating time for Tactus is that the semibreve corresponds to the complete down-up cycle. There is no suggestion of beating Down for one semibreve, Up for the next: the Down and Up are on successive minims. Thus a heightened focus on the semibreve implies a heightened focus on the complete cycle, as opposed to the individual down/up movements: it does not imply a different mode of beating time. The concept of Thesis and Arsis (Down and Up) is therefore located in the alternation of minims (under mensural sign C). See my discussion of ‘The Hobbit problem’ in Quality Time, here.
Of course, there are duple (or other) symmetries at semibreve and longer durations too. It’s very good to be aware of these.
THE MASSIVE GENERALISATION
Returning to the fundamental assumptions with which I began, I agree that it is a massive generalisation to state that musical tempo was consistent throughout the whole repertoire in circa-1600 Italy, to the limits of human perception. It is a generalisation that is hard for us post-Romantics to comprehend. But it fits well with the evidence, not only of musical treatises, but of period philosophy in general. And we can observe the gradual change through the later 17th and 18th centuries; the persistence of notions of tempo giusto or tempo ordinario as late as Beethoven; the developing presumption of personal choice that comes to characterise the 19th-century; the glorification of Rubato circa 1910 that is taken by some today as a musical absolute. Those changes in musical practice follow changes in the scientific and philosophical understanding of Time itself, from Aristotle and Plato via Galileo and then Newton to Einstein and then Hawking.
It helps to keep in mind the 17th-century identification of musical tempo with Time itself, alluded to in Monteverdi’s setting of the word tempus at the beginning of this post. The ideal is to keep Time. A musician does not seek to develop a personal opinion about tempo, just as he does not seek to acquire a clock that runs differently from everyone else’s.
The difficulty is that we tend to read historical treatises on Music in the light of our modern assumptions of Science and Philosophy. If we start by assuming period philosophy, musical treatises reveal new, quite surprising details. To do this, we must be ready to abandon some modern assumptions so familiar that we hardly even notice them.
Most modern directors assume they have the right to choose their own tempo, movement by movement, through a baroque opera: most of those directors fail even to notice the anachronism of conducting, as a means of imposing those choices. But period sources tell us that music is directed by Tactus itself: not by the whim of a Tactus-beater!. And Il Corago tells us that operas are not conducted.
CITATIONS & SOURCES
At the opening of my article on the Orfeo Ballo, I tacitly linked up citations of Bowers and Lamothe with my own assumptions. So here are the individual elements:
Lamothe quotes Bowers on MM 50/60 (but identifies this with the semibreve, which would not work for the whole opera. I identify this sort of pulse with the minim). Bowers states that the notation implies the same Tactus for the lengthy excerpt from the end of Act I until the entrance of the Messaggiera halfway through Act II. Bowers remarks that the notation is the same throughout the rest of the opera too. I take the logical step that the same Tactus is implied for the whole opera.
George Houle’s (brief) discussion of constant tactus throughout the repertoire is on pages 3-5 of ‘Metre in Music’, citing Heyden, Mersenne and secondary sources. On page 2, Houle mentions (all too briefly) ‘degrees of change intermediate to those determined by diminution or proportion.’
Constant Tactus for the whole repertoire is supported by Il Corago, page 47 (see future postings on this blog).
Houle cites Dowland’s explanation of Tactus and Semi-Tactus on page 4. This is the ‘Hobbit Question’, aka ‘there and back again': the semibreve corresponds to the complete down-up cycle. See Quality Time here.
Bowers cites Banchieri’s ‘Conclusioni’ chapter 14 “when there is no numerical sign”, in support of his Sesquialtera interpretation of proportional change. Of course, in Orfeo, there are numerical signs [3/2 and 6/4]. Banchieri addresses this situation in chapter 15, at the end of which he describes the Tripla interpretation that I propose.
I admit that Banchieri describes two interpretations, and does not discuss how to decide between them. But my general point is that we can approach such decisions by requiring consistency, not only of interpretations of Proportional relationships, but also in constancy of the underlying Tactus. If we consistently interpret the same notation the same way, if we apply a consistent tactus (perhaps allowing SMALL changes, but not doubling/halving the speed), we can rule out certain interpretations as impossible. [I try to distinguish carefully between ‘unfamiliar’ and ‘impossible’]. When – as in Orfeo and the Vespers – we have many proportions at work, the accumulated constraints of ‘impossibilities’ gradually reduce the number of possible solutions – ideally to a single answer.
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Opera, orchestra, vocal & ensemble director and early harpist, Andrew Lawrence-King is director of The Harp Consort and of Il Corago, and Senior Visiting Research Fellow at the Australian Research Council Centre for the History of Emotions.