300edo

Revision as of 07:12, 24 June 2023 by BudjarnLambeth (talk | contribs) (Added "harmonics in equal" table)

300edo is the equal division of the octave into 300 parts of exactly 4 cents each. It is the largest number EDO which tempers out the pythagorean comma, 531441/524288.

← 299edo 300edo 301edo →
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

It is inconsistent to the 5-limit and higher limit, 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.


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)