Helmholtz's and Ellis's tunings

Helmholtz (p.421) proposed 24 tones of JI, then expanded the series to 28
or 30 notes (p.422). His translator, Ellis, suggested 27 tones of meantone
or Pythagorean (p.433-434) and it was he who named the 1/8th skhisma tuning
after Helmholtz (p.435). On page 437, Ellis says it is audibly equivalent
to
Sauveur's theoretical cycle of 301 tones/octave (heptamerides).

Ellis also constructed a 53 tone irregular tuning, which he called somewhat
oxymoronically "unequally just," from the central 56 tones of the
Duodenarium by ignoring the skhisma and using fifths of 700 and 702 cents
(pp.435 and 465).

Ellis is still a good source for extended JI tunings and instruments to
play them.

The 1/9th Skhisma tuning was discovered as far as I know by Eduardo
Sabat-Garibaldi in the 1960's. He also uses 53 tones of the tuning.


--John