41ed6: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''41ED6''' is the [[ED6|equal division of the sixth harmonic]] into 41 equal parts. It is similar to [[16edo]], but has the [[6/1]] tuned just instead of the octave. Octaves are stretched by 10.5{{c}} and the step size is 75.66{{c}}. It can be used as a tuning for [[Mavila]] and also approximates [[Pelog]] tunings in Indonesian gamelan music. | '''41ED6''' is the [[ED6|equal division of the sixth harmonic]] into 41 equal parts. It is similar to [[16edo]], but has the [[6/1]] tuned just instead of the octave. Octaves are stretched by 10.5{{c}} and the step size is 75.66{{c}}. It can be used as a tuning for [[Mavila]] and also approximates [[Pelog]] tunings in Indonesian gamelan music. | ||
== Intervals == | |||
{{Interval table}} | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 99 | |||
| num = 6 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 99 | |||
| num = 6 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Revision as of 01:53, 30 November 2024
| ← 40ed6 | 41ed6 | 42ed6 → |
41ED6 is the equal division of the sixth harmonic into 41 equal parts. It is similar to 16edo, but has the 6/1 tuned just instead of the octave. Octaves are stretched by 10.5 ¢ and the step size is 75.66 ¢. It can be used as a tuning for Mavila and also approximates Pelog tunings in Indonesian gamelan music.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 75.7 | 22/21, 23/22, 24/23, 25/24 |
| 2 | 151.3 | 12/11, 23/21, 25/23 |
| 3 | 227 | 8/7, 25/22 |
| 4 | 302.6 | 25/21 |
| 5 | 378.3 | |
| 6 | 453.9 | 13/10, 30/23 |
| 7 | 529.6 | 23/17 |
| 8 | 605.3 | 17/12, 27/19 |
| 9 | 680.9 | |
| 10 | 756.6 | 17/11 |
| 11 | 832.2 | 21/13, 29/18 |
| 12 | 907.9 | 22/13 |
| 13 | 983.5 | 23/13, 30/17 |
| 14 | 1059.2 | 24/13 |
| 15 | 1134.9 | 25/13, 29/15 |
| 16 | 1210.5 | |
| 17 | 1286.2 | 21/10 |
| 18 | 1361.8 | 11/5 |
| 19 | 1437.5 | 16/7, 23/10 |
| 20 | 1513.1 | 12/5 |
| 21 | 1588.8 | 5/2 |
| 22 | 1664.5 | 21/8 |
| 23 | 1740.1 | 30/11 |
| 24 | 1815.8 | 20/7 |
| 25 | 1891.4 | |
| 26 | 1967.1 | 25/8 |
| 27 | 2042.8 | 13/4 |
| 28 | 2118.4 | 17/5 |
| 29 | 2194.1 | |
| 30 | 2269.7 | 26/7 |
| 31 | 2345.4 | |
| 32 | 2421 | |
| 33 | 2496.7 | |
| 34 | 2572.4 | |
| 35 | 2648 | 23/5 |
| 36 | 2723.7 | 29/6 |
| 37 | 2799.3 | |
| 38 | 2875 | 21/4 |
| 39 | 2950.6 | 11/2 |
| 40 | 3026.3 | 23/4 |
| 41 | 3102 | 6/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -9.4 | +9.4 | +12.6 | +2.3 | +0.0 | +15.1 | +3.3 | -12.6 | -7.0 | -15.4 | -9.4 |
| Relative (%) | -29.8 | +29.8 | +40.3 | +7.4 | +0.0 | +48.3 | +10.5 | -40.3 | -22.5 | -49.1 | -29.8 | |
| Steps (reduced) |
38 (38) |
61 (61) |
77 (77) |
89 (89) |
99 (0) |
108 (9) |
115 (16) |
121 (22) |
127 (28) |
132 (33) |
137 (38) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +8.7 | +5.8 | +11.7 | -6.1 | +14.3 | +9.4 | +9.7 | +14.9 | -6.9 | +6.6 | -7.7 |
| Relative (%) | +27.9 | +18.4 | +37.2 | -19.4 | +45.7 | +29.8 | +31.1 | +47.7 | -21.9 | +21.1 | -24.5 | |
| Steps (reduced) |
142 (43) |
146 (47) |
150 (51) |
153 (54) |
157 (58) |
160 (61) |
163 (64) |
166 (67) |
168 (69) |
171 (72) |
173 (74) | |