186ed6: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | |||
186ED6 is related to [[72edo|72 edo]], but with the 6/1 rather than the 2/1 being just, which results in the octaves being stretched by about 1.2347{{c}}. It is consistent to the 18-[[integer-limit]], and significantly improves on 72edo's approximation to 13. | |||
Lookalikes: [[72edo]], [[114edt]] | Lookalikes: [[72edo]], [[114edt]] | ||
==Harmonics== | == Harmonics == | ||
{{Harmonics in equal|186|6|1|intervals=prime}} | {{Harmonics in equal|186|6|1|intervals=prime}} | ||
{{Harmonics in equal|186|6|1|intervals=prime|collapsed=1|start=12}} | {{Harmonics in equal|186|6|1|intervals=prime|collapsed=1|start=12}} | ||
Revision as of 19:08, 7 February 2025
| ← 185ed6 | 186ed6 | 187ed6 → |
186 equal divisions of the 6th harmonic (abbreviated 186ed6) is a nonoctave tuning system that divides the interval of 6/1 into 186 equal parts of about 16.7 ¢ each. Each step represents a frequency ratio of 61/186, or the 186th root of 6.
186ED6 is related to 72 edo, but with the 6/1 rather than the 2/1 being just, which results in the octaves being stretched by about 1.2347 ¢. It is consistent to the 18-integer-limit, and significantly improves on 72edo's approximation to 13.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.76 | -0.76 | -1.23 | -0.04 | +1.30 | -4.40 | -1.87 | +5.70 | -8.19 | +7.43 | -7.96 |
| Relative (%) | +4.5 | -4.5 | -7.3 | -0.2 | +7.8 | -26.4 | -11.2 | +34.2 | -49.1 | +44.6 | -47.7 | |
| Steps (reduced) |
72 (72) |
114 (114) |
167 (167) |
202 (16) |
249 (63) |
266 (80) |
294 (108) |
306 (120) |
325 (139) |
350 (164) |
356 (170) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.60 | +8.33 | -7.42 | +5.36 | -2.51 | -4.73 | +4.27 | -8.06 | +8.29 | -6.45 | +6.90 |
| Relative (%) | +15.6 | +49.9 | -44.5 | +32.2 | -15.0 | -28.3 | +25.6 | -48.3 | +49.7 | -38.6 | +41.4 | |
| Steps (reduced) |
375 (3) |
386 (14) |
390 (18) |
400 (28) |
412 (40) |
423 (51) |
427 (55) |
436 (64) |
443 (71) |
445 (73) |
454 (82) | |
|
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