201edo
| ← 200edo | 201edo | 202edo → |
201 equal divisions of the octave (abbreviated 201edo or 201ed2), also called 201-tone equal temperament (201tet) or 201 equal temperament (201et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 201 equal parts of about 5.97 ¢ each. Each step represents a frequency ratio of 21/201, or the 201st root of 2.
201edo is only consistent to the 5-odd-limit, and harmonic 3 is about halfway between its steps.
Using the patent val, it tempers out 393216/390625 (würschmidt comma) and [25 -26 7⟩ in the 5-limit; 245/243, 50421/50000, and 2100875/2097152 in the 7-limit; 385/384, 896/891, 1331/1323, and 47432/46875 in the 11-limit; 196/195, 325/324, 2080/2079, 2200/2197, and 3146/3125 in the 13-limit.
Using the 201e val, it tempers out 441/440, 2200/2187, 3388/3375, and 65536/65219 in the 11-limit; 196/195, 325/324, 352/351, 1001/1000, and 106496/105875 in the 13-limit.
Using the 201de val, it tempers out 4000/3969, 10976/10935, and 4194304/4134375 in the 7-limit; 540/539, 896/891, 1375/1372, and 234375/234256 in the 11-limit; 325/324, 352/351, 364/363, 640/637, and 4394/4375 in the 13-limit (supporting the pluto temperament).
Using the 201b val, it tempers out 1990656/1953125 (valentine comma) and [-31 24 -3⟩ in the 5-limit; 126/125, 1029/1024, and [-2 19 0 -10⟩ in the 7-limit; 540/539, 1944/1925, 2835/2816, and 483153/480200 in the 11-limit; 1287/1280, 1575/1573, 1716/1715, 2200/2197, and 3146/3125 in the 13-limit.
Using the 201bcf val, it tempers out 15625/15552 (kleisma) and [-56 31 3⟩ in the 5-limit; 1029/1024, 250047/250000, and 273375/268912 in the 7-limit; 385/384, 441/440, 4000/3993, and 295245/290521 in the 11-limit; 351/350, 975/968, 1287/1280, 1573/1568, and 10935/10816 in the 13-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.52 | +1.75 | -1.66 | -0.92 | -2.06 | +1.26 | -1.70 | +2.51 | +0.99 | +0.86 | -1.41 |
| Relative (%) | +42.3 | +29.2 | -27.8 | -15.5 | -34.6 | +21.2 | -28.5 | +42.0 | +16.7 | +14.4 | -23.6 | |
| Steps (reduced) |
319 (118) |
467 (65) |
564 (162) |
637 (34) |
695 (92) |
744 (141) |
785 (182) |
822 (18) |
854 (50) |
883 (79) |
909 (105) | |
Subsets and supersets
Since 201 factors into 3 × 67, 201edo contains 3edo and 67edo as its subsets. 402edo, which doubles it, provides a good correction to the approximation of harmonic 3.