400edo

The 400 equal divisions of the octave (400edo) is the equal division of the octave into 400 parts of exact 3 cents each.

Theory

400edo is consistent in the 21-odd-limit. It tempers out the unidecma, [-7 22 -12⟩, and the qintosec comma, [47 -15 -10⟩, in the 5-limit; 2401/2400, 1959552/1953125, and 14348907/14336000 in the 7-limit; 5632/5625, 9801/9800, 117649/117612, and 131072/130977 in the 11-limit; 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095, 4225/4224 and 39366/39325 in the 13-limit, supporting the decoid temperament and the quinmite temperament. In the 17-limit, it tempers out 4914/4913.

400edo doubles 200edo, which holds a record for the best 3/2 fifth approximation. 400 is also the number of years in the Gregorian calendar's leap cycle. 400edo supports the Sym454 calendar scale with 231\400 as the generator, which can be treated as 5/12 syntonic comma meantone, which is the first meantone in the continued fraction that offers good precision. Other items like 1/3 and 2/5 eventually become inconsistent with the edo.

Table of intervals

Step	Name	Associated ratio	Notes
0	unison	1/1 exact
28	5/12-meantone semitone	6561/6250
35	septendecimal semitone	17/16
231	Gregorian leap week fifth	118/79, twelfth root of 800000/6561
234	perfect fifth	3/2
372	5/12-meantone seventh	12500/6561
400	octave	1/1 exact

Scales

• Huntington7
• Huntington10
• Huntington17
• LeapWeek[71]
• LeapDay[97]