93ed30: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
== Theory == | |||
93ed30 is a variant of [[19edo]] with a stretched [[2/1|octave]] of about 1203 cents. Like 19edo, 93ed30 is [[consistent]] to the [[integer limit|10-integer-limit]]. It optimizes the accuracy of the 1:5:6 triad, since the 5 is as flat as the 6 is sharp. | |||
=== Harmonics === | |||
{{Harmonics in equal|93|30|1|intervals=integer|columns=11}} | |||
{{Harmonics in equal|93|30|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 93ed30 (continued)}} | |||
=== Subsets and supersets === | |||
Since 93 factors into primes as {{nowrap| 3 × 31 }}, 93ed30 contains [[3ed30]] and [[31ed30]] as subset ed30's. | |||
== See also == | |||
* [[11edf]] – relative edf | |||
* [[19edo]] – relative edo | |||
* [[30edt]] – relative edt | |||
* [[49ed6]] – relative ed6 | |||
* [[53ed7]] – relative ed7 | |||
* [[68ed12]] – relative ed12 | |||
[[Category:19edo]] | [[Category:19edo]] | ||
Latest revision as of 13:13, 30 March 2025
| ← 92ed30 | 93ed30 | 94ed30 → |
93 equal divisions of the 30th harmonic (abbreviated 93ed30) is a nonoctave tuning system that divides the interval of 30/1 into 93 equal parts of about 63.3 ¢ each. Each step represents a frequency ratio of 301/93, or the 93rd root of 30.
Theory
93ed30 is a variant of 19edo with a stretched octave of about 1203 cents. Like 19edo, 93ed30 is consistent to the 10-integer-limit. It optimizes the accuracy of the 1:5:6 triad, since the 5 is as flat as the 6 is sharp.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.0 | -2.5 | +6.0 | -0.5 | +0.5 | -13.1 | +8.9 | -5.0 | +2.5 | +27.5 | +3.4 |
| Relative (%) | +4.7 | -4.0 | +9.4 | -0.7 | +0.7 | -20.8 | +14.1 | -7.9 | +4.0 | +43.4 | +5.4 | |
| Steps (reduced) |
19 (19) |
30 (30) |
38 (38) |
44 (44) |
49 (49) |
53 (53) |
57 (57) |
60 (60) |
63 (63) |
66 (66) |
68 (68) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -8.5 | -10.2 | -3.0 | +11.9 | -29.7 | -2.0 | +31.0 | +5.5 | -15.7 | +30.4 | +16.8 | +6.4 |
| Relative (%) | -13.4 | -16.1 | -4.7 | +18.8 | -46.9 | -3.2 | +48.9 | +8.7 | -24.7 | +48.1 | +26.5 | +10.1 | |
| Steps (reduced) |
70 (70) |
72 (72) |
74 (74) |
76 (76) |
77 (77) |
79 (79) |
81 (81) |
82 (82) |
83 (83) |
85 (85) |
86 (86) |
87 (87) | |
Subsets and supersets
Since 93 factors into primes as 3 × 31, 93ed30 contains 3ed30 and 31ed30 as subset ed30's.