# 206edo

 ← 205edo 206edo 207edo →
Prime factorization 2 × 103
Step size 5.82524¢
Fifth 121\206 (704.854¢)
Semitones (A1:m2) 23:13 (134¢ : 75.73¢)
Dual sharp fifth 121\206 (704.854¢)
Dual flat fifth 120\206 (699.029¢) (→60\103)
Dual major 2nd 35\206 (203.883¢)
(semiconvergent)
Consistency limit 3
Distinct consistency limit 3

206 equal divisions of the octave (abbreviated 206edo or 206ed2), also called 206-tone equal temperament (206tet) or 206 equal temperament (206et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 206 equal parts of about 5.83 ¢ each. Each step represents a frequency ratio of 21/206, or the 206th root of 2.

## Theory

206edo is closely related to 103edo, but the patent vals differ on the mapping for 3, 11, and 19.

It is inconsistent to the 5-odd-limit and higher limits, with four mappings possible for the 19-limit:

• 206 327 478 578 713 762 842 875] (patent val)
• 206 326 478 578 713 762 842 875] (206b)
• 206 326 478 578 712 762 842 875] (206be)
• 206 327 479 579 713 763 842 875] (206cdf)

Using the patent val, it tempers out 48828125/47775744 (sycamore comma) and 32768000000/31381059609 in the 5-limit; 4000/3969, 84035/82944, and 458752/455625 in the 7-limit; 385/384, 2401/2376, 6875/6804, and 9375/9317 in the 11-limit; 352/351, 1575/1573, 1625/1617, 2197/2178, and 4096/4095 in the 13-limit; 289/288, 375/374, 442/441, 715/714, and 2000/1989 in the 17-limit; 190/189, 361/360, 665/663, 969/968, 1235/1232, and 1375/1368 in the 19-limit.

Using the 206b val, it tempers out 78732/78125 (sensipent comma) and 34171875/33554432 (ampersand) in the 5-limit; 225/224, 1029/1024, and 177147/175000 in the 7-limit; 4375/4356, 9801/9800, 15309/15125, and 73728/73205 in the 11-limit; 351/350, 364/363, 625/624, 1701/1690, and 31213/30976 in the 13-limit; 273/272, 833/832, 850/847, 1089/1088, 1225/1224, and 1458/1445 in the 17-limit; 210/209, 495/494, 729/722, 1235/1232, and 1445/1444 in the 19-limit.

Using the 206be val, it tempers out 243/242, 385/384, 441/440, and 43923/43750 in the 11-limit; 351/350, 625/624, 847/845, 1001/1000, and 1573/1568 in the 13-limit; 273/272, 375/374, 561/560, 715/714, and 833/832 in the 17-limit; 363/361 and 729/722 in the 19-limit.

Using the 206cdf val, it tempers out 2048/2025 (diaschisma), and [4 -45 29 in the 5-limit; 4375/4374, 110592/109375, and 235298/234375 in the 7-limit; 176/175, 896/891, and 1331/1323 in the 11-limit; 640/637, 847/845, 1001/1000, and 2197/2187 in the 13-limit; 136/135, 256/255, 561/560, and 1275/1274 in the 17-limit; 190/189, 476/475, 608/605, 836/833, and 969/968 in the 19-limit.

### Odd harmonics

Approximation of odd harmonics in 206edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +2.90 -1.85 -1.84 -0.03 +2.08 -1.69 +1.05 -0.10 -0.43 +1.06 +0.85
Relative (%) +49.8 -31.7 -31.5 -0.5 +35.7 -29.1 +18.1 -1.7 -7.3 +18.3 +14.6
Steps
(reduced)
327
(121)
478
(66)
578
(166)
653
(35)
713
(95)
762
(144)
805
(187)
842
(18)
875
(51)
905
(81)
932
(108)

### Subsets and supersets

206edo contains 2edo and 103edo as subsets. 412edo, which doubles it, provides an excellent correction to the approximation of harmonic 3.