Out of the infinite set of “ways to tune”
- take “scale” (a finite set of definite pitches)
- take “octave repeating” (at every octave, copy the structure exactly)
- take “equal divisions” (like a meter stick)
- take “macrotonal”
& you get “macrotonal edos”. “Edo” stands for “equal divisions of the octave” – as opposed to, say “edonoi” – “equal divisions of a non-octave interval”. As microtonal means (by a literal definition) “incorporating steps smaller than a semitone” (but is often used more broadly to mean “incorporating pitches unavailable in standard 12-tone tuning”), “macrotonal” can mean “incorporating steps larger than a semitone”.
“Macrotonal edos” refers to a finite set of scales which includes 1edo, 2edo, 3edo, 4edo, 5edo, 6edo, 7edo, 8edo, 9edo, 10edo, & 11edo, & nothing else. 1edo-4edo & 6edo are available in 12edo (the common practice monoscale that most of us don’t recognize as chosen), so that leaves us with 6 macrotonal edos that demand new thoughts by new composers.
I mention this so that you might know something about the talks talked at the Microtonal Composition Study Group that continues to meet on Thursdays from 5:30 to 7 at th Oddmusic Instrumentorium at th UC-IMC (room 21A). (You continue to be not excluded!) At least one participant has taken up th invitation to try these tunings out for composing (Snow Leopard has begun some work in 7 equal divisions of the octave) & at least everyone present can now say that these scales are possible.
A wee dandy chart that I made for comparative consideration: