23ed6: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''23ED6''' is the [[ED6|equal division of the sixth harmonic]] into 23 equal parts. It is similar to [[9edo]], but has the [[6/1]] tuned just instead of the octave. Octaves are stretched by 13.8{{c}} and the step size is 134.868{{c}}. It also approximates [[Pelog]] tunings in Indonesian gamelan music very well, since Pelog is well-approximated by [[9edo]] with stretched octaves. | '''23ED6''' is the [[ED6|equal division of the sixth harmonic]] into 23 equal parts. It is similar to [[9edo]], but has the [[6/1]] tuned just instead of the octave. Octaves are stretched by 13.8{{c}} and the step size is 134.868{{c}}. It also approximates [[Pelog]] tunings in Indonesian gamelan music very well, since Pelog is well-approximated by [[9edo]] with stretched octaves. | ||
== 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 01:52, 30 November 2024
| ← 22ed6 | 23ed6 | 24ed6 → |
23ED6 is the equal division of the sixth harmonic into 23 equal parts. It is similar to 9edo, but has the 6/1 tuned just instead of the octave. Octaves are stretched by 13.8 ¢ and the step size is 134.868 ¢. It also approximates Pelog tunings in Indonesian gamelan music very well, since Pelog is well-approximated by 9edo with stretched octaves.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 134.9 | 13/12, 14/13 |
| 2 | 269.7 | 7/6 |
| 3 | 404.6 | 14/11, 19/15, 24/19 |
| 4 | 539.5 | 11/8, 15/11, 19/14 |
| 5 | 674.3 | 22/15 |
| 6 | 809.2 | 8/5, 19/12 |
| 7 | 944.1 | 12/7, 19/11 |
| 8 | 1078.9 | 13/7, 15/8 |
| 9 | 1213.8 | |
| 10 | 1348.7 | 13/6, 24/11 |
| 11 | 1483.5 | |
| 12 | 1618.4 | 23/9 |
| 13 | 1753.3 | 11/4 |
| 14 | 1888.1 | |
| 15 | 2023 | 16/5 |
| 16 | 2157.9 | 7/2 |
| 17 | 2292.7 | 15/4 |
| 18 | 2427.6 | |
| 19 | 2562.5 | 22/5 |
| 20 | 2697.4 | 19/4 |
| 21 | 2832.2 | |
| 22 | 2967.1 | |
| 23 | 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) | |