Talk:1288/1287

As to the origins of the naming of the trisphonisma (1288/1287), I suspect that I may have done this in 2002 as a result of designing what I recall Erv Wilson and John Chalmers term a triaphonismic system, the Just Octachord Tuning in 17 notes (JOT-17). That is, there were two disjunct divisions of 4:3 into "octachords" -- eight notes and seven intervals -- and a division of the 9:8 tone of disjunction (4/3-3/2. This was three divisions in all, thus triaphonismic.

I found that 1288/1287 is equal to the amount by which 168/143 (14/13 x 12/11) exceeds 27/23. That comparison, or a similar one, could have led me to this ratio, JOT-17 as I recall it looked like this:

1/1-28/27-14/13-44/39-7/6-28/23-14/11-4/3 4/3-112/81-56/39-3/2 3/2-14/9-21/13-22/13-7/4-42/23-21/11-2/1

Note that 4/3 and 3/2 are duplicated, since they occur in more than one of the three genera making up this triaphonismic tuning.

John Chalmers, _Divisions of the Tetrachord_, is a good source on this approach to tuning.

Mschulter1325 00:19, 13 June 2024 (UTC)