Some observations on the limits of time notation in music.

"James Ingram has sent me a portfolio of email discussions
about musical time. I have written a little piece in response "

I remember a fierce and ultimately inconclusive debate starting in July 1977 in the pages of Early Music, regarding the correct interpretation of dotted rhythms in baroque music. Frederick Neumann took issue with Quantz's advice on notes inegales, preferring the views of Hotteterre. He also berated the amiable Robert Donington and other present-day early music scholars for what he considered a too literal and unrestrictive application of overdotting inmusic in the French Overture style.

The argument turned on whether a composer's notation of time values is or ought to be literally consistent with what a performer should play, or onlysometimes consistent, or never consistent (as in the case of those dotted rhythms in jazz that are notated as equal duplets).

Twenty years on musicologists are beginning to realize that notation itself is not enough: you have to understand the intellectual or social context. The controversy over double-dotting in French Overture style can be resolved if one looks beyond the notation of time to the model of time articulation the notation is designed to emulate. A French Overture is not a dance form. Its dynamic of time is universal rather than human. (The opposite case is the prelude non mesure of d'Anglebert, where timing is intentionally to be regulated in accordance with a prevailing room acoustic and instrument.) The unequal or 'jerky' style excoriated by Neumann imitates the regular but unequal motion of a pendulum. We all know how a pendulum behaves and what it does. It measures time more accurately than any human intuition, but it does so in a motion which consists of an acceleration, a retard, and a moment of motionlessness before turning back. We may have invented the pendulum clock to keep track of time as a continuous regular flow, but the pendulum itself articulates time as a sequence of regular beats in which the motion of the pendulum is constantly changing. It follows that a music designed to follow the movement of a pendulum in representing 'scientific time' is not going to move evenly: rather it will fluctuate between moments of suspended time: indeed much like certain scores of Boulez today. The pendulum style was invented in France along with the pendulum metronome; it gave rise both to Maelzel's familiar clockwork musical timekeeping device and to the style of baton conducting familar today. The answer to Neumann is that performance of such music should seek to recapture the feel of pendulum motion: this will lead from time to time (no pun intended) to exaggerations of dotted-note values.

I think most of us agree that notated time values are not to be taken literally. If they were to be taken at face value then mechanical synthesized performances, being literal executions of notation, would be preferable to human performances. Since this is not the case, because most people notice when a musical performance is mechanical rather than real, and prefer a live performance, the question is whether notation can adapt sufficiently to the nuances of live performance, rather than the other way round. A hundred years ago composers such as Bartok and Vaughan Williams were touring country pubs recording grizzled old folksingers (male and female) on Edison cylinder phonographs, recordings which they then had to transcribe into standard notation. These were real live performances of music from unwritten oral traditions, and they proved difficult or impossible to notate, simply because the performers' sense of time was far more refined than classical notation could handle. The opposite case is represented by mechanical instruments such as the musical box, the pianola, or the computer synthesizer. These instruments express music as a completely literal translation of a notated score, and we all know how unrealistic such performances can sound. Haydn was fascinated by Maelzel's musical automata and he realized that something had to be done to make music sound more human: his answer was to insert ornaments to break up the mechanical flow of beats and inject a sense of human uncertainty. Beethoven not only composed his Op 91 Wellington's Sieg to be performed on Maelzel's Panharmonicon, he also examines the relationship of mechanical time to human time perception in his Symphony IV, where a mechanical beat structure is methodically varied in the distribution and density of musical content to produce a fluctuating sense of 'empty' and 'filled' time. (See Arthur W.H.G. Ord-Hume, Joseph Haydn and the mechanical organ, Cardiff, 1982)

As a student in the 1960s I tackled the subdivisions of Stockhausen's Piano Piece I with gusto. I do not take seriously the composer's footnote about converting subdivisions to tempo changes, which strikes me as an afterthought for two obvious reasons, one: if that is all the subdivisions amount to, why have them in the first place, and two: subdivided beats within a consistent time frame are an entirely different experience from a tempo change. I studied the Piano Piece I with Aloys Kontarsky in Cologne after having mastered the time subdivisions myself, and was surprised when he brought out a little ruler and marked up my piano score to show the changes in tempo, because it always felt to me that the various subdivisions of the beat structure should be construed as changes in tension, and not simply as shifts in speed. Years later I came across a study of speech patterning that seemed to correspond very closely to the timing of the notorious measure 6 in Stockhausen's Piano Piece I, the same measure that a number of correspondents to the musical press, including Perspectives of New Music (bless their souls) had decided were impossible to perform (they should look at measure 287 in Stravinsky's The Flood for real complication). Geoffrey Leech's English in Advertising: a linguistic study of advertising in Great Britain (London, 1966) in a section entitled 'Compound Pre-modifiers' cites an example of advertising copy that conforms extremely closely to the compound rhythms of Stockhausen's 5:4 measure further subdivided into groups of 7:8 and 11:12. The phrase '(fan-) tastic acceleration from the : 95 bhp Coventry Climax OHC (engine)' can be notated musically as a 5:4 measure subdivided into a 9:8 for the first two, and 14:12 for the last three pulses. The phrasing and timing of the phrase is governed by the target word 'engine', and is not calculated as a sequence of tempo shifts. And if an ordinary reader can reproduce rhythmic divisions of this complexity automatically through understanding its adjectival function, there is no reason why pianists cannot do the same for music.

No discussion for or against translating subdivisions into tempo changes is complete without some consideration of Elliott Carter's metrical modulation, an intellectual approach to multiple time-layers derived from Conlon Nancarrow's experiments with piano rolls and coincident with Stockhausen's impulse-shower related cadenzas in Zeitmasse. In a famous interview pianist David Tudor described how to perform graphic scores such as Cage's Music of Changes by learning to watch time rather than read it (in Music and Musicians 1972, 20.12).

Impossibility of reproducing intentional time values accurately is matched by a corresponding difficulty in reproducing truly independent tempo-layers in a multi-group live performance setting. The best example that comes to mind is Boulez's Rituel in memoriam Maderna which asks designated groups of instruments in the orchestra to play independently of one another without a principal conductor (an image corresponding to ripples in a pond). In the original version it proved impossible for the players to concentrate on individually distinct tempi first because there was no visual sign from the conductor and second because they tended in the circumstances to listen to one another and ended up playing in a sort of average tempo instead of up to seven distinct time-layers. What Boulez did was to add percussion players as sub-conductors, each with a distinct instrument: claves, wood-block, maracas etc. But the percussionists have trouble themselves in maintaining separate tempos, and their clicks and clacks add a disturbing element to what should be an image of tranquillity. This is a case better than most for electronic intervention in the form of preset winking lights or synthesised musical cues.

The nature and experience of musical time are significant philosophical issues affecting the history of musical notation and I think it is unduly restrictive to attempt to legislate one way or the other. Plainchant notation is indeterminate in timing because its timing was determined not by mechanical clocks (which did not then exist) but by the words, the need to articulate a sacred text with appropriate expression, and also the prevailing acoustic, whether of a small chapel or a vast cathedral. Then when one ponders the issue of timing in (say) Gabrieli's polychoral compositions it becomes apparent that among the consequences of distributing singers and instrumentalists to remote locations, in addition to the difficulty of achieving absolute synchronization, would be the discovery that in fact absolute synchronisation to a written score such as the 1600 Canzon Duodecimi Toni No 2 can only be achieved for a single location in space. The notion that simultaneity is a spatial as well as a temporal concept is one that Einstein would have recognized

We can no more expect total accuracy in music timing than we can expect accuracy in tuning. Without mean-tone tuning the point of (say) Froberger's keyboard toccatas is completely lost: these are pieces that explore the tonal domain as though it were the Sargasso of Columbus or Francis Drake: the further one moves away from the diatonic keys the closer one gets to alien territories: 'Here bee dragons' indeed. Standard notation cannot deal adequately with enharmonic relations, although it may hint at them eg in Chopin's Nocturnes.

Even Stockhausen's own notations can be singled out for absence of precision in various domains, often intentionally. The whole point of Zyklus's hybrid notation is examining the differences in performer interpretation that arise from a notation that ranges from more or less deterministic to more or less improvisatory. Stockhausen's scores are deeply fascinating and rewarding to study precisely because they represent an ongoing debate with the limitations of performer accuracy and notation itself.

05.02.99. Revised 06.05.99

Robin Maconie,


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