Tymoczko is at it again

http://www.sciencemag.org/cgi/content/abstract/320/5874/346

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> http://www.sciencemag.org/cgi/content/abstract/320/5874/346
>
> -Carl
>

For those of us without subscriptions to Science, this

http://www.music.princeton.edu/~dmitri/geometry.pdf

is apparently an earlier version of the paper.

-Carl

I wrote...
> > http://www.sciencemag.org/cgi/content/abstract/320/5874/346
//
> For those of us without subscriptions to Science, this
>
> http://www.music.princeton.edu/~dmitri/geometry.pdf
>
> is apparently an earlier version of the paper.

How this stuff gets into Science where ordinary "music
set theory" does not is a bit of a puzzle. If the abstract
is to be believed it is just as flawed...

"Western musicians traditionally classify pitch sequences by
disregarding the effects of five musical transformations:
octave shift, permutation, transposition, inversion, and
cardinality change."

It's hard to imagine being more wrong in the first sentence
of a paper on music theory. Permutation and inversion were
very rarely used until the appearance of serialism, and
when they were (in a few Bach canons for example) it was not
as symmetries of equivalence. Octave shift is one of the
strongest symmetries in music, and just randomly shifting
each pitch in a famous melody by -1, 0, +1 octaves will
quickly demonstrate its limitations. Alongside transposition
is modal transposition (in the diatonic scale, for example),
which is a much more common and arguably much more fundamental
symmetry in Western music.

On page 3 it is suggested that chords can be explained in
terms of octave, permutation, and cardinality invariance.
No mention of psychoacoustic consonance, as is typical of
the kinds of academic music theory papers that normally do
not appear in Science.

-Carl

Tymoczko is really quite a brilliant guy and I think his work is important (some of his small items on the SMT list are really interesting, particularly in voice leading) but I agree here with Carl that it's very strange for this to appear in Science instead of a music theory platform.

"Western musicians traditionally classify pitch sequences by
disregarding the effects of five musical transformations:
octave shift, permutation, transposition, inversion, and
cardinality change."

Some of these are true if we step back to the most trivial cases: musicians (and most lay listeners) will recognize a melody as the same if it is played in different octaves, but dropping or lifting isolated tones out of the melody will likely render a melody unrecognizeable; permutation of the tones in an arpeggiated chord usually preserves chordal identity; transposition, like octave shift, will preserve the identity if the transposition is applied to the entire sequence. But inversion? You'd have to fight with a lot of solid psychoacoustics to make that one fly. The sentence definitely deserves some qualifications and corrections; in a music theory platform there presemably would have been a music theorist to catch this before publication.

djw

Daniel Wolf wrote:
> Tymoczko is really quite a brilliant guy and I think his work is important > (some of his small items on the SMT list are really interesting, > particularly in voice leading) but I agree here with Carl that it's very > strange for this to appear in Science instead of a music theory platform.

It is strange. I could understand him getting one paper published on the geometry, because it's a fairly simple concept that's original and may be of interest to scientists. I'm not sure what this new paper adds that isn't obvious. They barely talk about music. I don't think anything's of mathematical interest. And it isn't science. All they do is, as they say, define the language. It's a good work-horse type paper that should be published somewhere, but not as the second ever piece of music theory in a prestigious science journal.

> "Western musicians traditionally classify pitch sequences by
> disregarding the effects of five musical transformations:
> octave shift, permutation, transposition, inversion, and
> cardinality change."
> > Some of these are true if we step back to the most trivial cases: > musicians (and most lay listeners) will recognize a melody as the same if > it is played in different octaves, but dropping or lifting isolated tones > out of the melody will likely render a melody unrecognizeable; > permutation of the tones in an arpeggiated chord usually preserves chordal > identity; transposition, like octave shift, will preserve the identity if > the transposition is applied to the entire sequence. But inversion? > You'd have to fight with a lot of solid psychoacoustics to make that one > fly. The sentence definitely deserves some qualifications and > corrections; in a music theory platform there presemably would have been a > music theorist to catch this before publication.

Inversions are equivalent when you write chord symbols. There's a table on page 57 of the free PDF that says what means what. They don't say all the transformations have to be equivalent all the time. The trouble is they don't say very much at all...

Graham

He is a music theorist though.
I sense he is attempting to lay the groundwork of some type of unified field theory of harmony and melody. The problems are what academia has created which he can not be blamed.
Politicians who must excel at logical watertight obscurities.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Daniel Wolf wrote:
> Tymoczko is really quite a brilliant guy and I think his work is important > (some of his small items on the SMT list are really interesting, > > The sentence definitely deserves some qualifications and > corrections; in a music theory platform there presemably would have been a > music theorist to catch this before publication.
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> djw
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