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Re: Cowell/Ferneyhough Unconventional Meters

From: Trevor Bača
Subject: Re: Cowell/Ferneyhough Unconventional Meters
Date: Tue, 19 Jul 2011 13:57:39 -0400

I use this combination of semantic 'nonbinary' time signature (here 2/10) with \scaleDurations in my own scores rather a lot. It works great.

(Also the best solution if you're using proportional notation because all notes, rests, chords continue to consume the amount of horizontal space that they should.)

It might also be worth pointing out that two competing interpretations of these 'nonbinary' time signatures have developed in the literature over the past couple of decades: what we might call the 'Ferneyhough' and the 'Sciarrino' interpretations, respectively.

Ferneyhough's usage is as Joey describes and basically works by allowing the 10 in 2/10 to effect a 4/5 diminution of the notes, rests, chords governed by the time signature. (How does one extract 4/5 from 10? By dividing out all integer powers of 2 from the prime factors of 10 and then inserting this value -- call it n -- in a multiplier of the form m/n, with m defined equal to the greatest integer power of 2 *less than* n. Here, for example, we see that 10 = 2 * 5; we remove the 2 and find n = 5; the greatest integer power of 2 less than 5 is 4; so m/n = 4/5 which is exactly the prolational scaling value of the 10 in 2/10. A second example could be the time signature 5/18, the denominator of which is 18 = 2 * 3 * 3, which gives n = 3 * 3 = 9 and m/n = 8/9, which is the value by which notes, rests, chords in a measure of 5/18 will be time-scaled under this first interpretation of such meters.)

Sciarrino's (and many others') usage essentially interprets meters like 2/10 and 5/18 as indicating the amount of musical time a bar is to consume *without* attributing any time-scaling power to the time signatures in question. (Partial or 'broken') tuplets then need to be added explicitly to make the time values of notes, rests and chords calculate correctly. This is the interpretation of such meters under which Joseph originally proposed to answer Joey's question.

The two ways of interpreting these time signatures are incompatible. AFAICT the 'Sciarrino' interpretation is used by many more composers now than is the 'Ferneyhough' interpretation. But Ferneyhough is certainly the best known exemplar of the technique.



On Tue, Jul 5, 2011 at 6:26 AM, Urs Liska <address@hidden> wrote:
Probably Joey doesn't want to use \time 4/5 but to scale durations.
I adjusted your example a little bit so one sees better what happens:

    \time 2/10
    \times 4/5 { c'8 c'8 } \bar "||"

    % \scaleDurations scales without tuplet numbers or brackets
    \scaleDurations #'(4 . 5) { c'8 c'8 c'8 c'8 } \bar "||" 

    % I put a few bars of "straight" eighths to show what happens
    c'8 c' c' c' c' c' c' c'


Am 05.07.2011 11:45, schrieb Joseph Wakeling:
On 07/05/2011 08:57 AM, address@hidden wrote:
On Jul 5, 2011, at 8:29 AM, Joey wrote:

In Ferneyhough's etudes transcendentales,
he employs meters such as 2/12 or 2/10,
acting as literal subdivisions of the semi-breve.
The easiest way would be to create an override for the time signature stencil:
No, you don't need to be so complicated. :-)

Just put

  \time 2/10

Lilypond will give you a _warning_ that this is a non-standard time
signature, but it can handle the time signature and will produce a
corresponding bar of two quintuplet-eighths in length.

N.B. you _will_ need to put in place

  \times 4/5 {}

around the content of any such bar in order to ensure that quintuplets
are your base content type.

Try giving Lilypond the following:

    \time 2/10
    \times 4/5 { c'8 c'8 }
    c'8 c'8

... and compare what happens in the first and second bar.

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