133edo
| ← 132edo | 133edo | 134edo → |
133 equal divisions of the octave (abbreviated 133edo or 133ed2), also called 133-tone equal temperament (133tet) or 133 equal temperament (133et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 133 equal parts of about 9.02 ¢ each. Each step represents a frequency ratio of 21/133, or the 133rd root of 2.
133edo is only consistent to the 5-odd-limit. The equal temperament tempers out 393216/390625 (würschmidt comma) and 131072000/129140163 (rodan comma) in the 5-limit.
Using the patent val, it tempers out 245/243, 1029/1024 and 395136/390625 in the 7-limit; 385/384, 441/440, 896/891 and 43923/43750 in the 11-limit; 196/195, 325/324, 352/351, 364/363 and 3146/3125 in the 13-limit. It supports rodan and superenneadecal.
Using the 133d val, it tempers out 1728/1715, 4000/3969 and 4375/4374. It supports enneadecal.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +1.80 | +1.66 | -3.41 | -0.94 | -1.43 | +3.32 | +0.23 | +3.30 | -1.01 | +0.83 |
| Relative (%) | +0.0 | +20.0 | +18.4 | -37.8 | -10.4 | -15.8 | +36.7 | +2.6 | +36.6 | -11.1 | +9.2 | |
| Steps (reduced) |
133 (0) |
211 (78) |
309 (43) |
373 (107) |
460 (61) |
492 (93) |
544 (12) |
565 (33) |
602 (70) |
646 (114) |
659 (127) | |
Subsets and supersets
Since 133 factors into 7 × 19, 133edo contains 7edo and 19edo as its subsets.