93ed6: Difference between revisions
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{{Harmonics in equal|93|6|1|intervals=integer|columns=11}} | {{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)}} | {{Harmonics in equal|93|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 93ed6 (continued)}} | ||
=== Subsets and supersets === | |||
Since 93 factors into primes as {{nowrap| 3 × 31 }}, 93ed6 contains subset ed6's [[3ed6]] and [[31ed6]]. | |||
== See also == | == See also == | ||
Revision as of 10:40, 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) | |
Subsets and supersets
Since 93 factors into primes as 3 × 31, 93ed6 contains subset ed6's 3ed6 and 31ed6.