The n-Category Café

Alissa and I don’t have anything specific music theory planned yet. To be honest I haven’t read her paper, and only skimmed your associated TWF. I haven’t had correspondence with her since my going to Trieste.

There is a nice quandle that covers the dihedral quandle, though, and it might be interesting to relate that to dihedral actions in chord space.

So far Dmitri’s book has been very interesting. For the hard core theorists, there is an article on his home page. The book is much more gentle both to the mathematician with an interest in music and the musician who is trying to learn the math beyond the theory.

Dmitri describes 5 items that he thinks are necessary for good music. (1) Conjunct melodic motion: melodies take small steps within the associated scales, (2) Acoustic Consonance: Consonant harmonies are preferred to dissonant ones and form stable points, (3) Harmonic Consistency: harmonies within a passage tend to be similar, (4) Limited Macroharmony: Over moderate time spans a relatively small number of tones are used, (5) Centricity: Over moderate spans of music one or more notes is more prominent than others.

A corollary is, I think, that there will be repeated patterns, motifs, or phrases, but that repetition without change leads to tedium.

His central thesis, however, seems to be that one can analyze and compose using the quotient of the n-torus by symmetries. The n-torus is the space of all ordered n-chords, and the quotient considers inversions as equivalent. Chords are connected by one step paths, where (using Dmitri’s example) CEG (C major) is one step away from BEG (e minor).