Re: Octony

I used the term OCTONY in my book to describe an 8-tone homolog of the
hexany. Octonies have the melodic pattern dcbabcde (and its circular or
modal permutations) and are not CPS.

Ervin showed that they are instead 8-tone Euler Genera, a 7-limit of
which is 3.5.7 ( 1/1 3/2 5/4 7/4 15/8 21/16 35/32 and 105/64) where 1/1
is the tonic and 105/64 (3x5x7) is the guiding tone.

I had originally called there structures octanies, but Erv wanted to
retain the -any suffix for the CPS, so I changed it to -ony.

Octonies are partitionable in to sets of inversionally related tetrads
analogously to the partition of the hexany into inversionally related triads.
In general, octony tetrads are not as simple as those of the hexany nor
as consonant.

Melodic octonies are definable in ETs (e.g., the 8-tone MOS in 13, 22122121).

--John