Klarinet Archive - Posting 000002.txt from 2004/07

From: Joseph Wakeling <joseph.wakeling@-----.net>
Subj: Re: [kl] "Tunes create context like language"
Date: Thu, 1 Jul 2004 06:25:42 -0400

Ormondtoby Montoya wrote:

> In addition to instruments such as bagpipes and sitars, which have
> 'drone hardware', there are compositions for non-droning instruments
> wherein a certain note is repeated on a rhythmic basis and effectively
> serves a drone. If each repetition of the 'drone' was included in the
> tabulation of 'rank', what would happen to the math? I presume it
> would corrupt the 'straight line' aspect.

Remember that all Zanette's analysis gives is a statistical picture of
the occurrences of notes. It doesn't tell you anything about *what*
those notes are. In fact the idea of a "drone" fits pretty well with
the notion that the next note to appear will probably be one that has
already appeared numerous times before. So, I suspect you would get the
same fundamental statistical relationships appearing, although exponents
might differ (the latter being an interesting possibility to examine).

>If a drone is considered as an individual note, it may corrupt the
>straight line aspect of Zipf's law; but if the drone is paired with each
>note of the melody, there will be many different intervals, and Zipf's
>law may still produce a straight line or perhaps even an unusually
>strong 'context'.
>

I don't think it will "corrupt" the statistics at all. For a melody
with drone accompaniment there is a one-to-one correspondence between
the intervals and the notes of the melody, so the statistics will be the
same as for the melody alone.

Of course, it should be relatively simple, given (say) a clever computer
programme, to generate patterns of notes which violate the statistics
observed. Various modern composers, such as Gordon Downie, already make
use of computer-generated material with the deliberate intention of
making different patterns to those found in earlier music. In a sense I
think that may be a lot of what Zanette was getting at in trying to draw
a distinction between tonal and atonal music.

Incidentally, Zipf's law doesn't "produce" anything. It's the name for
a particular mathematical relationship---not for a type of dynamics.

-- Joe

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