300edo

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← 299edo300edo301edo →
Prime factorization 22 × 3 × 52
Step size 4¢ 
Fifth 175\300 (700¢) (→7\12)
Semitones (A1:m2) 25:25 (100¢ : 100¢)
Dual sharp fifth 176\300 (704¢) (→44\75)
Dual flat fifth 175\300 (700¢) (→7\12)
Dual major 2nd 51\300 (204¢) (→17\100)
Consistency limit 3
Distinct consistency limit 3

300 equal divisions of the octave (abbreviated 300edo or 300ed2), also called 300-tone equal temperament (300tet) or 300 equal temperament (300et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 300 equal parts of exactly 4 ¢ each. Each step represents a frequency ratio of 21/300, or the 300th root of 2.

300edo's step size is called a savart when used as an interval size unit.

Theory

300edo is the largest-number edo which tempers out the Pythagorean comma, 531441/524288, in the patent val.

It is inconsistent to the 5-odd-limit and higher, with three mappings possible for the 5-limit: 300 475 697] (patent val), 300 476 697] (300b), and 300 475 696] (300c).

Using the patent val, it tempers out 531441/524288 and [47 7 -25 in the 5-limit; 6144/6125, 50421/50000, and 1594323/1568000 in the 7-limit.

Using the 300b val, it tempers out 393216/390625 and [51 -38 4 in the 5-limit; 153664/151875, 179200/177147, and 823543/819200 in the 7-limit. Using the 300bd val, it tempers out 10976/10935, 65536/64827, and 390625/388962 in the 7-limit.

Using the 300c val, it tempers out 531441/524288 and [-58 0 25 in the 5-limit; 225/224, 250047/250000, and 69206436005/68719476736 in the 7-limit.

Odd harmonics

Approximation of odd harmonics in 300edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.96 +1.69 -0.83 +0.09 +0.68 -0.53 -0.27 -0.96 -1.51 +1.22 -0.27
Relative (%) -48.9 +42.2 -20.6 +2.2 +17.1 -13.2 -6.7 -23.9 -37.8 +30.5 -6.9
Steps
(reduced)
475
(175)
697
(97)
842
(242)
951
(51)
1038
(138)
1110
(210)
1172
(272)
1226
(26)
1274
(74)
1318
(118)
1357
(157)

Subsets and supersets

Since 300 factors into 22 × 3 × 52, 300edo has subset edos 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, and 150. 600edo, which doubles it, gives a good correction to its approximation of the 5-limit.

External links