305edo

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← 304edo305edo306edo →
Prime factorization 5 × 61
Step size 3.93443¢ 
Fifth 178\305 (700.328¢)
Semitones (A1:m2) 26:25 (102.3¢ : 98.36¢)
Dual sharp fifth 179\305 (704.262¢)
Dual flat fifth 178\305 (700.328¢)
Dual major 2nd 52\305 (204.59¢)
Consistency limit 7
Distinct consistency limit 7

305 equal divisions of the octave (abbreviated 305edo or 305ed2), also called 305-tone equal temperament (305tet) or 305 equal temperament (305et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 305 equal parts of about 3.93 ¢ each. Each step represents a frequency ratio of 21/305, or the 305th root of 2.

305edo has a flat tendency, with the 3, 5, 7 and 11 of the patent val all flat, and the equal temperament tempers out 2109375/2097152, the semicomma (orson comma) in the 5-limit, 2401/2400 in the 7-limit, and 243/242, 441/440, and 540/539 in the 11-limit. It provides the optimal patent val for 7- and 11-limit neominor temperament.

Odd harmonics

Approximation of odd harmonics in 305edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.63 -0.74 -0.96 +0.68 -0.50 +1.44 +1.57 +1.27 +1.50 +1.35 +1.23
Relative (%) -41.4 -18.8 -24.3 +17.3 -12.7 +36.6 +39.8 +32.4 +38.2 +34.3 +31.4
Steps
(reduced)
483
(178)
708
(98)
856
(246)
967
(52)
1055
(140)
1129
(214)
1192
(277)
1247
(27)
1296
(76)
1340
(120)
1380
(160)

Subsets and supersets

Since 305 factors into 5 × 61, 305edo has 5edo and 61edo as its subsets.