Edϕ
7 steps of 10ed2 closely approximates the 13th harmonic. The 13th harmonic is close to acoustic phi (1.618033989). If we divide acoustic phi into 7 steps, then 10 of those steps gets us close to an octave.
| 10ed2 | 7edφ | |||||||
| scale step | frequency multiplier (definition) | 10ed2 frequency multiplier (decimal) | pitch (¢) | Δ (¢) | frequency multiplier (definition) | frequency multiplier (decimal) | pitch (¢) | Δ (¢) |
| 1 | 2^(1/10) | 1.071773463 | 120 | 120 | 1.071162542 | 119.0128995 | 119.0128995 | |
| 2 | 1.148698355 | 240 | 120 | 1.147389191 | 238.025799 | 119.0128995 | ||
| 3 | 1.231144413 | 360 | 120 | 1.229040323 | 357.0386984 | 119.0128995 | ||
| 4 | 1.319507911 | 480 | 120 | 1.316501956 | 476.0515979 | 119.0128995 | ||
| 5 | 1.414213562 | 600 | 120 | 1.410187582 | 595.0644974 | 119.0128995 | ||
| 6 | 1.515716567 | 720 | 120 | 1.510540115 | 714.0773969 | 119.0128995 | ||
| 7 | 1.624504793 | 840 | 120 | 1.618033989 | 833.0902964 | 119.0128995 | ||
| 8 | 1.741101127 | 960 | 120 | 1.7331774 | 952.1031958 | 119.0128995 | ||
| 9 | 1.866065983 | 1080 | 120 | 1.85651471 | 1071.116095 | 119.0128995 | ||
| 10 | 2 | 1200 | 120 | 1.988629015 | 1190.128995 | 119.0128995 | ||