132edo: Difference between revisions
Created page with "'''132edo''' is the equal division of the octave into 132 parts of 9.0909 cents each. Using the patent val, it tempers out 531441/524288 (pythagorean comma) and 488281..." Tags: Mobile edit Mobile web edit |
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{{Infobox ET}} | |||
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[[ | 132edo is only [[consistent]] to the [[5-odd-limit]]. It [[tempering out|tempers out]] 531441/524288 ([[Pythagorean comma]]) and 48828125/47775744 ([[sycamore comma]]) in the 5-limit. | ||
Using the [[patent val]], it tempers out [[1728/1715]], [[4000/3969]], and 234375/229376 in the 7-limit; 625/616, 1350/1331, 2187/2156, and 2420/2401 in the 11-limit; [[169/168]], [[325/324]], [[364/363]], [[640/637]], and 1875/1859 in the 13-limit. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|132}} | |||
=== Subsets and supersets === | |||
Since 132 factors into {{factorization|132}}, 132edo has subset edos {{EDOs| 2, 3, 6, 11, 12, 22, 44, and 66 }}. | |||
Latest revision as of 19:23, 20 February 2025
| ← 131edo | 132edo | 133edo → |
132 equal divisions of the octave (abbreviated 132edo or 132ed2), also called 132-tone equal temperament (132tet) or 132 equal temperament (132et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 132 equal parts of about 9.09 ¢ each. Each step represents a frequency ratio of 21/132, or the 132nd root of 2.
132edo is only consistent to the 5-odd-limit. It tempers out 531441/524288 (Pythagorean comma) and 48828125/47775744 (sycamore comma) in the 5-limit.
Using the patent val, it tempers out 1728/1715, 4000/3969, and 234375/229376 in the 7-limit; 625/616, 1350/1331, 2187/2156, and 2420/2401 in the 11-limit; 169/168, 325/324, 364/363, 640/637, and 1875/1859 in the 13-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.96 | -4.50 | +3.90 | -3.91 | +3.23 | -4.16 | +2.64 | +4.14 | +2.49 | +1.95 | -1.00 |
| Relative (%) | -21.5 | -49.5 | +42.9 | -43.0 | +35.5 | -45.8 | +29.0 | +45.5 | +27.4 | +21.4 | -11.0 | |
| Steps (reduced) |
209 (77) |
306 (42) |
371 (107) |
418 (22) |
457 (61) |
488 (92) |
516 (120) |
540 (12) |
561 (33) |
580 (52) |
597 (69) | |
Subsets and supersets
Since 132 factors into 22 × 3 × 11, 132edo has subset edos 2, 3, 6, 11, 12, 22, 44, and 66.