The Notation Game – Chris Dench

A change in my notation occurred in about 1995. Previously I had adopted a semiotically information-rich notation that I thought conveyed a considerable amount of useful information to the perceiver. However, a couple of decades of explanations and performances seemed to have had little effect in making this notation acceptable, and I acknowledged that in order to stop annoying performers I was going to have to revert to a more traditional presentation style. An announcement at the time that I was intending to “simplify my notation system” was meant quite literally: the music remained the same but the notational coding became more conformist. However, this change continues to seemingly confuse people who read the statement as meaning that I have, ever since, dumbed-down the actual musical content. It doesn’t seem to matter how many times I say that “the underlying music didn’t change a jot,” people still impute some kind of simplification in musical substance to the less sophisticated (and more pragmatic) notation I adopted for such works as ik(s)land[s] and the Fourth Symphony.

I’m a bit weary of this enduring misunderstanding, so I thought I would give a worked example to clarify the difference between my older ‘high-resolution’, and my newer ‘lower-resolution’ notational solutions. While it is true that the ‘lower-res’ is slightly less elastic than the ‘high-res’ notation, it is misleading to speak of them as somehow intrinsically different: they just have different degrees of grain. My older notation was, to a high degree, analogical–despite appearances, it was a close-to-accurate depiction of a smooth rhythmic process. The newer system, because the music is resolved at a much coarser grain, is more digital in character, more quantal.

So, to demonstrate the difference I provide the following four segments. This uses material I have generated for my new vibraphone solo, luminous—a useful choice as there are no subtleties of sonic envelope involved, no pulses, glissandi, phase transitions. Just notes that are on/off: it inhabits attack space; only the pedal (and occasionally, bow) take the vibes into envelope space. This material might find its way into the finished work …but more likely will end up on the cutting-room floor, by the time more of the work is completed; I frequently discard early material as the writing evolves. I’m leaving aside how and why the music shaped up like this, my only concern here is the look of it.

The excerpt consists of a twenty-one quaver segment at crotchet = 60. I did the example at 4 centimetres per second (larger than my standard 3cms/per sec) although it will resize in reproduction. Thus we have a segment, a ‘bar’ , that is 10.5″, or 42 cms in extension, and a beat-mark is inserted every 1″ or 4cms, leaving a hanging quaver–2cms–at the end. [It is bar 18, and uses Soft sticks only.] The material deploys itself as two different duration-types, three long notes and five medium, of which only the two longest are of exactly equal duration, in the form M–L–M–M–M–M–L—L. This basic layout (in admittedly a rather more complex form) is subjected to permutation, segmentation, and compression.

[Pitches are arrived at similarly, but that is not our concern today.]

The subdivisions are distributed thus. Upper voice:

Medium: M–L–M
Long: L[subdiv]–M–L—L–M–M–M–M
Medium: M–L–M–M
Medium: M–L
Medium: M–M–M–M–L
Long: M–M–L–M–L—L
Medium: undivided
Long: L–M–L–M–L–M–M

Lower voice:

M–L–M–L–M–M–L–M (2+3+2+3+2+2+3+2 = 19 units)

Example A

Example A is the primary material expressed entirely in time-space terms: bald proportional notation. This is how the raw material of my works look once the compositional process is done. If it were for an envelope instrument, flute or violin, say, I would add a horizontal line from each notehead to indicate that the attack is sustained for some or all of the duration, where relevant; as this is for vibraphone I am not bothering as the pedalling governs the extension of the sound. This level of detail would be sufficient for the music to be performed, but it provides no explanatory or indicative metatext that might assist the performer in ‘finding the music within’. The range of performer responses to such notation might include

assuming that there is information in the on-page distances and playing as precisely as possible but without any deeper probing;
assuming that there is some information in the on-page distances but that the vagueness encourages laissez-faire;
concluding in the absence of clues that no subtext exists and supplying their own;
assuming that the composer is short of ideas and requires the performer to elaborate the music to inject meaning;
assuming the composer is slack and/or oblivious therefore treating the music with contempt;

and so on.

My expectation would be that performances from a notation like this would exhibit considerable variation, and probably a lot of interpretative input. From my point of view none of these are particularly desirable performance outcomes.

Example B

Example B provides a minimal amount of extra dimension—it shows what the pitch allegiances are, that the music is to be considered polyphonically, and which skein in the fabric the attack events belong to. This provides a much more detailed insight into how the music is made up, and it’s ebb and flow, its flux. The range of performer responses to this notation might include

assuming that the composer expects the performer to supply a metalogic that ties all the on-score details together;
concluding that the metalogic will emerge from performing the music with attention to the available detail;
assuming that this is about as much metalogic as the composer has up their sleeve and that a superficial performance is all that is called for; etc.

Again, I would anticipate considerable variation in performance outcome, and a degree of interpretative input. I would however also expect a more sculpted performance from Example B—not necessarily more precise, but more finessed—in response to the informative extra notational detail.

Example C

Example C presents a possible notational solution that I might have adopted prior to about 1995. My primary preoccupations when notating my works then was to provide a time-space description of the rate of change of the music—you’ll see that the actual attack events are precisely as they were in Example A—but also a high-resolution coding of the relationships within and between the musical objects. This second layer of information assists with understanding how each musical object is constituted, how they relate to one another, and even, for anyone studying the score, how the abstract structure manifests at each structural level; to quote myself, “structure and rhythm are the same thing on different scales”. If you refer back to my summary above of the deployment of L/M durations it will be apparent how clear this notation is as a descriptor of the musical structure, whatever else might be said about it. I doubt that I really have to set out what performer responses to this kind of notation might be; I am writing this Blog because of them. But for sake of completeness, here are a few, all of which I have actually heard said in some form

this music is trying to be too clever;
this notation is evidence of a lack of understanding of rhythm;
this notation is a performative straitjacket;
I’m contemptuous of this notation because I can play it with as much liberty as I like;
it’s written unperformably to make players anxious and get an edgier sound;
he’s obviously not the slightest bit interested in what it sounds like;
these rhythms are unplayable nonsense;
I was never very good at mathematics…;
I’ll play it wrong and see if he notices—this game is known as catch-the-composer, and the player can’t lose: if the composer notices and picks up the performer s/he appears bad-mannered and autocratic, if s/he does but declines to speak out s/he appears incompetent.

I thought I was offering enrichment to performers by providing a deeper-than-usual insight into how the music came out the way it was, its metabolism, if you like, so that they could give a particularly informed rendition. In fact, it seemed that no matter how hard I tried to explain this I only succeeded in antagonising the majority of players. My hope was that over time resistance might erode as performers came to see that I was inviting them into the creative process, and that they might even find it stimulating—I imagined a player seeking to actively demonstrate the relationships the notation revealed through their performance. Sadly that optimism was, generally, misplaced.

Example D

So: Example D is how I notate this musical material today. Very little has changed from Example C: the attack events are in almost exactly the same relationship, except that the grain of rhythmic detail has been coarsened. Significantly, the rhythmic contour is a tad smoother, the subdivisions simpler, the ‘tuplets rationalised. What in the dress of Example C is cryptic is here unambiguous. Ironically, in some ways Example D is more imaginatively confining than Example C. If you refer back to my summary above of the deployment of L/M durations it will also be apparent that this notational solution obscures as much as it reveals about the underpinning musical ideas; nonetheless, it has the considerable benefit of being universally intelligible.

This is what I meant when I made my, by now notorious, remark that I was ‘simplifying my rhythmic notation’. As the examples show, the layout in time-space of the attacks is virtually unchanged from Example A to D, but the rhythmic meaning is parsed utterly differently, with both gains and losses. Essentially, though, it is the same music. Which notation you regard as preferable, or more ‘musical’, is a matter of personal choice.

Of course, the tension between a liberal and literal reading is quite another issue, but that merits a future discussion.

…icyw, numerology

I prefer not to dwell at any great length on the gematrical substrate to my works beyond admitting it is there and providing a few clues for those who really insist on knowing. But, given that this is a worked example, I’ll summarise below the basic numbers that operate in this bar, in an elaborated excerpt from the main text.

The excerpt consists of a twenty-one quaver–21/8–segment at crotchet = 60. I did the example at 4 centimetres per second (larger than my standard 3cms/per sec) although it will resize in reproduction. Thus we have a segment, a ‘bar’ , that is 10.5″, or 42 cms in extension, and a beat-mark is inserted every 1″ or 4cms, leaving a hanging quaver–2cms–at the end. [It is bar 18, and uses Soft sticks only.] The material deploys itself as two different duration-types, three long notes and five medium, of which only the two longest are of exactly equal duration, in the form

L/12/M—U/21a/L—M/13/M—I/11/M—N/14/M—O/15/M—U/21b/L—S/19/L

[Pitches are arrived at similarly, but that is not our concern today.]

This basic layout is subjected variously to permutation, segmentation, and compression as part of the flux of the piece.

Upper voice, permutated and compressed:

{13=11}—{21b=17}—{14=11}—{12=10}—{15=12}—{19=15}—{11=9}—{21a=17}

Segmentation:

Medium (11): 12–21–13 [3 events]
Long (17): 21[subdiv]–14–21—19–11–12–15–13 [8]
Medium (11): 13–21–14–12 [4]
Medium (10): 11–19 [2] …..{11+17+11+10 = 49:40/32 in 5/4}
Medium (12): 14–11–15–13–19 [5]
Long (15): 15–12–19–14–21–21 [6]
Medium (9): undivided [1]
Long (17): 19–13–21–15–21–11–14 [7]
…..{12+15+9+17 = 53:44/32 in 11/8}

Note that the events in the sub-subdivisions are too fast-moving for any of the smaller structural distinctions to be practicably realised. Also, for reasons of where the primary attacks fell, the top subdivision has been resolved slightly asymmetrically {49:40/32, then 53:44/32, rather than 2 x 51:42/32}. The difference is too small to discern: .816/32nd, then .830/32nd.

Lower voice, permutated and considerably more compressed:

{11=2}—{19=3}—{12=2}—{21b=3}—{13=2}—{14=2}—{21a=3}—{15=2}

…..{= 2 x 19:21/16}