• Pablo Ziffer

Costa: enharmony-study in 31-EDO on a chromatic 1/5-tone line (VERSION 1)



0:00 -- 31-EDO: Historic Winds

2:55 -- 31-EDO: Organ

5:52 -- 31-EDO J.I.: Historic Winds

8:48 -- 31-EDO J.I.: Organ

11:43 -- 31-EDO: Historic Winds + Organ

14:38 -- 31-EDO J.I.: Historic Winds + Organ

17:33 -- 31-EDO J.I.: Modern Winds


The division of the octave in 31 equal parts makes it possible to approximate all intervals of the overtone series up to 25 with a maximum error of only 10 cents, with the possibility of enharmony, since intervals are equal. This 3-min. study is a harmonization of an chromatic line, ascending in fifth-tones (or diesis, the smaller interval of 31-EDO) in the rhythm of half-notes. The 6- to 9-part harmony changes every half-note (twice in each 4/4-bar) with 1 to 4 common, enharmonic intervals. Harmonic limit is 19 (or minor third), of course including 7, 11 and 13. There is (1) a (equal) 31-tone version and (2) an adaptive Just-Intonation version of each of 3 virtual orchestrations: Historic Winds, Organ and both combined, plus a J.I version with modern winds. Just intonation is achieved at any given moment/harmony by keeping the fundamental note of the harmony in 31-EDO and adjusting all other intervals to the harmonic series (as said, at most 10 cents) by: 3(fifth): + 5c // 5(third): is just // 7(seventh): is just // 9 (major ninth): + 10c // 11(eleventh): +10c // 13(thirteenth): -10c // 15(major seventh):+5c // 17 (minor ninth): -10c // 19(minor third): -10c I find that the different timbre and sound of each version gives a slightly different and complementary perspective, or feel, on the harmony or the perception of the harmonic information.