137ed6: Difference between revisions
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== | == Theory == | ||
137ed6 is practically identical to [[53edo]], but with the 6/1 rather than the [[2/1]] being just. The octave is about 0.0264 cents stretched. Like 53edo, 137ed6 is [[consistent]] to the [[integer limit|10-integer-limit]]. | |||
=== Harmonics === | |||
{{Harmonics in equal|137|6|1|intervals=integer}} | |||
{{Harmonics in equal|137|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 137ed6 (continued)}} | |||
=== Subsets and supersets === | |||
[[ | 137ed6 is the 33rd [[prime equal division|prime ed6]], following [[131ed6]] and before [[139ed6]]. It does not contain any nontrivial subset ed6's. | ||
[[ | |||
== Scales == | |||
* [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic|Gutierrez-Lambeth quasi-subharmonic pentatonic]] | |||
== See also == | |||
* [[9ed9/8]] – relative ed9/8 | |||
* [[31edf]] – relative edf | |||
* [[53edo]] – relative edo | |||
* [[84edt]] – relative edt | |||
Latest revision as of 09:01, 27 September 2025
| ← 136ed6 | 137ed6 | 138ed6 → |
(convergent)
(convergent)
137 equal divisions of the 6th harmonic (abbreviated 137ed6) is a nonoctave tuning system that divides the interval of 6/1 into 137 equal parts of about 22.6 ¢ each. Each step represents a frequency ratio of 61/137, or the 137th root of 6.
Theory
137ed6 is practically identical to 53edo, but with the 6/1 rather than the 2/1 being just. The octave is about 0.0264 cents stretched. Like 53edo, 137ed6 is consistent to the 10-integer-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.03 | -0.03 | +0.05 | -1.35 | +0.00 | +4.83 | +0.08 | -0.05 | -1.32 | -7.83 | +0.03 |
| Relative (%) | +0.1 | -0.1 | +0.2 | -5.9 | +0.0 | +21.3 | +0.3 | -0.2 | -5.8 | -34.6 | +0.1 | |
| Steps (reduced) |
53 (53) |
84 (84) |
106 (106) |
123 (123) |
137 (0) |
149 (12) |
159 (22) |
168 (31) |
176 (39) |
183 (46) |
190 (53) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.69 | +4.86 | -1.37 | +0.11 | +8.36 | -0.03 | -3.06 | -1.29 | +4.81 | -7.80 | +5.81 | +0.05 |
| Relative (%) | -11.9 | +21.5 | -6.1 | +0.5 | +36.9 | -0.1 | -13.5 | -5.7 | +21.2 | -34.5 | +25.6 | +0.2 | |
| Steps (reduced) |
196 (59) |
202 (65) |
207 (70) |
212 (75) |
217 (80) |
221 (84) |
225 (88) |
229 (92) |
233 (96) |
236 (99) |
240 (103) |
243 (106) | |
Subsets and supersets
137ed6 is the 33rd prime ed6, following 131ed6 and before 139ed6. It does not contain any nontrivial subset ed6's.