# 201edo

 ← 200edo 201edo 202edo →
Prime factorization 3 × 67
Step size 5.97015¢
Fifth 118\201 (704.478¢)
Semitones (A1:m2) 22:13 (131.3¢ : 77.61¢)
Dual sharp fifth 118\201 (704.478¢)
Dual flat fifth 117\201 (698.507¢) (→39\67)
Dual major 2nd 34\201 (202.985¢)
Consistency limit 5
Distinct consistency limit 5

210 equal divisions of the octave (abbreviated 210edo or 210ed2), also called 210-tone equal temperament (210tet) or 210 equal temperament (210et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 210 equal parts of about 5.71 ¢ each. Each step represents a frequency ratio of 21/210, or the 210th 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

Approximation of odd harmonics in 201edo
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.