Thanks for the reminder on these articles and algorithms, Michael.
It is an interesting approach to algorithmic composition.
Oeyvind

2007/11/12, Michael Gogins <gogins@pipeline.com>:
> Tim Mortimer asked:
> > Particularly in the case of silence. For example (that pops immediately to
> > mind), Are your voice leading algorithms operating along similar lines to
> > the Athena ones Mike?
>
> Not at all. My voice-leading algorithms are based upon the work of Dmitri
> Tymoczko, see for example
> http://music.princeton.edu/~dmitri/sciencearticle.html. I believe that some
> theorists, including Tymoczko, Clifton Callender, Ian Quinn and others, are
> initiating a revolution in music theory comparable to that of Riemann, who
> created what we now call "functional harmony."
>
> The new theory views chords as points in a space with one dimension per
> voice, and chord progressions and voice-leadings and motions within that
> space, which actually is an orbifold. An orbifold is a space in which an
> equivalence relation exists or, in other words, distances along one or
> another dimension are not infinite, but reflect from or wrap around a
> specific distance, a modulus. In pitch-class space, the obvious equivalence
> relation is the octave, and its modulus (in MIDI note numbers) is 12. There
> are several important equivalence classes in music theory....
>
> I presented a paper about this at the New Orleans ICMC, and you can find a
> PDF of my paper online at http://ruccas.org/pub/Gogins/icmc2006-mkg.pdf, as
> as a more recent paper that describes the specific operations implemented in
> CsoundAC at http://ruccas.org/pub/Gogins/music_atoms.pdf.
>
> This approach has several advantages, not the least of which is that
> voice-leadings can be computed efficiently. That is because almost always,
> the musically best voice-leading between two chords is the shortest path
> between them in this orbifold.
>
> Regards,
> Mike
>
>
>
>
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