126edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
126edo has a distinctly sharp tendency, with the [[3/1|3]], [[5/1|5]], [[7/1|7]] and [[11/1|11]] all sharp. The equal temperament [[tempering out|tempers out]] [[2048/2025]] in the 5-limit, [[2401/2400]] and [[4375/4374]] in the 7-limit, and [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. It provides the [[optimal patent val]] for 7- and 11-limit [[srutal]] temperament. It also creates an excellent [[Porcupine]][8] scale, mapping the generators to 17 steps, and the smaller interval to 7, which is the precise amount of tempering needed to make the thirds and fourths equally consonant within a few fractions of a cent. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|126}} | |||
=== Subsets and supersets === | |||
Since 126 factors into {{factorization|126}}, 126edo has subset edos {{EDOs| 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63 }}. | |||
[[Category:Srutal]] | |||
Latest revision as of 20:08, 17 April 2025
| ← 125edo | 126edo | 127edo → |
126 equal divisions of the octave (abbreviated 126edo or 126ed2), also called 126-tone equal temperament (126tet) or 126 equal temperament (126et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 126 equal parts of about 9.52 ¢ each. Each step represents a frequency ratio of 21/126, or the 126th root of 2.
126edo has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. The equal temperament tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 896/891, and 1331/1323 in the 11-limit. It provides the optimal patent val for 7- and 11-limit srutal temperament. It also creates an excellent Porcupine[8] scale, mapping the generators to 17 steps, and the smaller interval to 7, which is the precise amount of tempering needed to make the thirds and fourths equally consonant within a few fractions of a cent.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.81 | +4.16 | +2.60 | -3.91 | +1.06 | -2.43 | -2.55 | -0.19 | -2.27 | -4.11 | +0.30 |
| Relative (%) | +29.5 | +43.7 | +27.3 | -41.1 | +11.2 | -25.5 | -26.8 | -2.0 | -23.9 | -43.2 | +3.1 | |
| Steps (reduced) |
200 (74) |
293 (41) |
354 (102) |
399 (21) |
436 (58) |
466 (88) |
492 (114) |
515 (11) |
535 (31) |
553 (49) |
570 (66) | |
Subsets and supersets
Since 126 factors into 2 × 32 × 7, 126edo has subset edos 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.