Klarinet Archive - Posting 000254.txt from 2004/07

From: Tony Pay <tony.p@-----.org>
Subj: Re: [kl] Re: Music Theory
Date: Thu, 8 Jul 2004 09:54:30 -0400

On 7 Jul, Elgenubi@-----.com wrote:

> I asked yesterday:
>
> If we consider a major scale as 8 notes in two groups with one step between
> them, then it is
> step, step, half-step, and ....
> step, step, half-step.
> Or in another way:
> C, D, E, F, and......
> G, A, B, C.
> Does this repeated pattern have anything to do with the 'natural' sound??
>
> Tony said, "Well, good try, but I don't think that's the reason." and
> further suggested that consonant notes have harmonics in common and that
> the whole subject of what sounds 'good' is complex and very interesting.

I didn't mean to suggest that what you wrote wasn't interesting. It was just
that I had assumed the question was essentially, why do we have the basic
'white note' scale, with just those intervals in them?

That question does indeed have a 'natural' (ie, biological) answer as opposed
to a 'historical' (ie, cultural) answer, as Umar had hoped; but the
explanation of that answer can't assume knowledge of semitones and tones, or
of their patterns.

Those rather arise later, as a result of wanting every 'white note' scale to
be available starting on an arbitrary white note. That generates the twelve
note chromatic scale in various temperaments, and then equal temperament.

And then.....:-)

> Well, it is interesting and I'll definately keep reading and thinking. For
> now here is another simple observation: of course the pattern I described
> above is noteworthy.... It is the start of the circle of fifths! Continue
> grouping notes in sets of four, with intervals of 'step, step, half-step',
> and you get:
>
> C, D, E, F
> G, A, B, C
> D, E, F#, G
> A, B, C#, D
> E, F#, G#, A et cetera.
>
> Play any two groups in order, and you have a major scale.
>
> This is probably pretty elementary to most of you. But neat!

Indeed it is.

What follows is a completely different topic, of course, to do with a
composer's choice of compositional constraints; but you might be interested
to look up Messiaen's 'modes of limited transposition', which is a
taxonomy of a special class of patterns of intervals that give rise to
different divisions of the octave.

Your labelling system doesn't quite do that, because you have to put in the
'extra' step between your two groups of four. So from Messiaen's point of
view, the major mode would be, 'step, step, half-step, step, step, step,
half-step', an undecomposable seven interval division of the octave.

This scale doesn't interest Messiaen much, for another reason: which is that
its transposition *isn't* limited; you can transpose it all twelve times,
obtaining a different major scale each time.

A chromatic scale, built out of repetitions of the simple 'half-step', isn't
interesting to him either, because it can't be transposed *at all*; if you
do, you get the same scale. A whole tone scale, built out of repetitions of
'step' is only a bit more interesting; it can be transposed once; there are
two whole tone scales.

But the next one, sometimes called the 'octatonic scale', is much richer.
It's built out of repetitions of 'step, half-step', and goes, starting on C:

C, D, D# 'step, half-step'
D#, F, F# 'step, half-step'
F#, G#, A 'step, half-step'
A, B, C 'step, half-step'

...or written out, C, D, D#, F, F#, G#, A, B, C.

(You can also see it as two interlocking diminished 7th chords:

C D# F# A
D F G# B)

This 'mode of limited transposition' (three possible transpositions) is much
used by Stravinsky, for example, as well as by Rimsky-Korsakov. But Messiaen
exploits it in a more thoroughgoing way.

The next one is built out of 'step, half-step, half-step' (four possible
transpositions).

The rest are: 'half-step, half-step, minor third, half-step'; 'half-step,
major third, half-step' (a subset of the previous); and finally 'step, step,
half-step, half-step'. All these have six possible transpositions.

Clearly the sequences of intervals need to add up to a number of half-steps
that divides 12.

I should say just a little of why this is interesting to Messiaen. It is
because he wants material which, when transformed, remains in some way
recognisable. (He is similarly interested in what he calls,
'non-retrogradable rhythms'. These are rhythms that, when retrograded,
remain the same -- rhythmic palindromes, like 'minim, quaver, crotchet,
quaver, minim'.)

Here is what he writes in 'The Technique of my Musical Language':

"Let us think of the hearer of our modal and rhythmic music; he will not have
time at the concert to inspect the non-transpositions and the
non-retrogradations, and, at that moment, these questions will not interest
him further; to be charmed will be his only desire. And that is precisely
what will happen; in spite of himself he will submit to the strange charm of
impossibilities: a certain effect of tonal ubiquity in the nontranspositions,
a certain unity of movement (where beginning and end are confused because
identical) in the nonretrogradation, all things which will lead him
progressively to that sort of *theological rainbow* which the musical
language, of which we seek edification and theory, attempts to be."

Tony
--
_________ Tony Pay
|ony:-) 79 Southmoor Rd tony.p@-----.org
| |ay Oxford OX2 6RE http://classicalplus.gmn.com/artists
tel/fax 01865 553339

... Quantum Mechanics: The dreams that stuff is made of

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