93ed6: Difference between revisions
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== Theory == | |||
93ed6 is nearly identical to [[36edo]], but with the 6th harmonic rather than the [[2/1|octave]] being just. The octave is stretched by about 0.757 [[cent]]s. | |||
=== Harmonics === | |||
{{Harmonics in equal|93|6|1|intervals=integer|columns=11}} | |||
{{Harmonics in equal|93|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 93ed6 (continued)}} | |||
== | == See also == | ||
* [[21edf]] – relative edf | |||
* [[36edo]] – relative edo | |||
* [[57edt]] – relative edt | |||
* [[101ed7]] – relative ed7 | |||
[[ | * [[129ed12]] – relative ed12 | ||
Revision as of 10:39, 27 May 2025
| ← 92ed6 | 93ed6 | 94ed6 → |
93 equal divisions of the 6th harmonic (abbreviated 93ed6) is a nonoctave tuning system that divides the interval of 6/1 into 93 equal parts of about 33.4 ¢ each. Each step represents a frequency ratio of 61/93, or the 93rd root of 6.
Theory
93ed6 is nearly identical to 36edo, but with the 6th harmonic rather than the octave being just. The octave is stretched by about 0.757 cents.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.8 | -0.8 | +1.5 | +15.5 | +0.0 | -0.0 | +2.3 | -1.5 | +16.2 | -15.4 | +0.8 |
| Relative (%) | +2.3 | -2.3 | +4.5 | +46.3 | +0.0 | -0.1 | +6.8 | -4.5 | +48.6 | -46.1 | +2.3 | |
| Steps (reduced) |
36 (36) |
57 (57) |
72 (72) |
84 (84) |
93 (0) |
101 (8) |
108 (15) |
114 (21) |
120 (27) |
124 (31) |
129 (36) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.4 | +0.7 | +14.7 | +3.0 | -1.9 | -0.8 | +5.7 | -16.4 | -0.8 | -14.6 | +8.5 | +1.5 |
| Relative (%) | -13.2 | +2.2 | +44.1 | +9.1 | -5.6 | -2.3 | +17.1 | -49.1 | -2.4 | -43.8 | +25.4 | +4.5 | |
| Steps (reduced) |
133 (40) |
137 (44) |
141 (48) |
144 (51) |
147 (54) |
150 (57) |
153 (60) |
155 (62) |
158 (65) |
160 (67) |
163 (70) |
165 (72) | |