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Cmloegcmluin (talk | contribs) Created page with "7 steps of 10ed2 closely approximates the 13th harmonic. The 13th harmonic is close to acoustic phi. If we divide acoustic phi into 7 steps, then 10 of those steps gets us clo..." |
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7 steps of 10ed2 closely approximates the 13th harmonic. The 13th harmonic is close to acoustic phi. If we divide acoustic phi into 7 steps, then 10 of those steps gets us close to an octave. | 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. | ||
{| class="wikitable" | |||
|+ | |||
| | |||
| colspan="4" |'''10ed2''' | |||
| colspan="4" |'''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 | |||
|} | |||
Revision as of 18:39, 8 February 2020
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 | ||