with max. error < 5.35 ct
on isomorphic hexagonal keyboard rotated by ≈ 10.89°
(whole tone steps in right direction and semitone steps in down-right direction)
Published: 2026-09-19 (last rev. 2026-09-27)
The document below describes a tuning for isomorphic keyboards based on a 5-tone scale (4 whole tones and 1 semitone per octave) with whole tones tuned to ≈ 271.6 ct and semitones tuned to ≈ 113.6 ct. Compared to just intonation, the tuning achieves interval errors smaller than 5.35 ct for many desired frequency ratios. On a two-dimensional isomorphic keyboard, relevant intervals do not lie close to a line but rather cover a two-dimensional area.