My sincere apologies - the title of this post should read Synergetic Geometry, not Synthetic Geometry. For some reason I am experiencing very buggy problems in my comment box - spell check does not function often, words are changed in my text, long strings of repeated letters when using italics, bold, underline commands - sorry about the mistake. I'm not even sure there is such a thing as Synthetic Geometry!

My question follows - could the more asymmetrical synergetic geometry be usual or applicable for generating less symmetrical patterns? I am working on approaches to this myself with geodesic models and various angle frequencies substituted for Mod 12, say Mod 9, Mod 10, or maybe even non divisible angle sums like a Mod 11. I wouldn't expect it to facilitate conventional Mod 12 functions.

## Comments

3 Commentssorted by Votes Date Added0Vote UpVote DownOur brain does not treat music as "mod 12". We interpret the enharmonic difference between intervals even if they are tuned to 12tet.

The geometry of music is very simple, it is a chain of fifths and octaves. You can display this in 2d in various ways including (most naturally) isomorphic ways. For instance: http://musicnotation.org/wp-content/uploads/2013/03/Wicki-Hayden.png

0Vote UpVote DownMy sincere apologies - the title of this post should read

Synergetic Geometry, notSynthetic Geometry. For some reason I am experiencing very buggy problems in my comment box - spell check does not function often, words are changed in my text, long strings of repeated letters when using italics, bold, underline commands - sorry about the mistake. I'm not even sure there is such a thing as Synthetic Geometry!0Vote UpVote DownThanks Marcel. This looks similar to Tonnetz examples I've seen:

https://www.bing.com/images/search?q=tonnetz+music&qs=AS&form=QBIR&sp=2&pq=tonnetz&sk=AS1&sc=6-7&cvid=0710EA3BD594458DA972E06F6C35F857

My question follows - could the more asymmetrical synergetic geometry be usual or applicable for generating less symmetrical patterns? I am working on approaches to this myself with geodesic models and various angle frequencies substituted for Mod 12, say Mod 9, Mod 10, or maybe even non divisible angle sums like a Mod 11. I wouldn't expect it to facilitate conventional Mod 12 functions.

Carson