Klarinet Archive - Posting 000488.txt from 2004/06

From: Joseph Wakeling <joseph.wakeling@-----.net>
Subj: Re: [kl] "Tunes create context like language"
Date: Tue, 29 Jun 2004 11:10:47 -0400

Ormondtoby Montoya wrote:

>The following is an observation, I don't know if it proves anything:
>
>The "add a random item" example that you cited may tend toward a
>different level of skewed-ness with music than with language --- simply
>because there are fewer items in music's vocabulary of pitches than in
>language's vocabulary of words.
>
>

It's certainly true that the data set is much larger for language than
for music. The data set Zanette quotes for literary text, Dickens'
"David Copperfield", has some 13,884 different words in it. By contrast
the four pieces of music he quotes have about 100 (Bach, Mozart) to 200
(Debussy, Schoenberg) individual pitches (as I said before, this is
because he considers not just note name but octave). However, it's
worth remembering that the 12-tone even tempered system is only a
keyboard approximation to the much wider range of pitches employed by
musicians on more "flexible" instruments---cf. the articles cited in one
of Tony Pay's posts:
http://test.woodwind.org/Databases/Klarinet/2004/03/001191.txt

Were one to really look at music from the point of view of the pitches
*performed* by musicians, I suspect the number of "words" might well be
larger (with the exception, obviously, of solo keyboard works). But of
course to do this data analysis (from recordings...?) could be
prohibitively difficult.... ;-)

That said I don't think it introduces any particular "bias" in the data
sample to have this reduced number of available words. The exponents of
the equations are certainly different from those for text, but the
fundamental character remains the same.

>However, if you were to analyze *intervals* between notes, this bias in
>the case of music would be weaker because the possible permutations
>would increase so quickly. 12 tones = 12^12 permutations, and perhaps
>we can add octaves, etc.
>
>

Funnily enough I was thinking of a similar idea myself last night,
though in a slightly different manner to what you propose. If we simply
think of *intervals* then the data set is actually the same size as for
pitches, consisting of any number of the form

z = x +12y

where x is a number in the range 0-11 (i.e. the note name) and y is the
octave. However, if as you say we think of the number of possible note
combinations, we do indeed get far more words. The question is then,
how should one define notes as being "linked"?

For example, if we have a low C quarter-note and, an octave above,
triplet-eighths C'-D'-E', what do we link? Do we simply link C to each
C', D', E' (i.e. linking any pair of notes that occupies the same
horizontal space) or do we also respect the melodic patterns, e.g. also
linking C'-D', D'-E'?

Probably the former is the best way to start, but the latter might also
generate interesting patterns. Interesting problem, no... ?

Then one comes to the question: what is the musical (i.e. harmonic)
place of the highest-ranked notes, intervals and/or note combinations
... ?

As you can see I'm really quite intrigued by the possibilities of
extending this analysis, and connecting it to existing knowledge in
music theory. I found some colleagues of mine independently discussing
Zanette's paper last week and I'm very tempted to try and do some work
on this. The problem is going to be fitting it into an already pretty
busy schedule, including (supposedly) the intention to try and finish a
PhD thesis by the end of this year.... ;-)

-- Joe

---------------------------------------------------------------------
Klarinet is a service of Woodwind.Org, Inc. http://www.woodwind.org