source file: m1469.txt Date: Wed, 8 Jul 1998 10:18:43 -0700 (PDT) Subject: Helmholtz's and Ellis's tunings From: John Chalmers 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