400edo: Difference between revisions

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400 factors into 2<sup>4</sup> × 5<sup>2</sup>, with subset edos {{EDOs| 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, and 200 }}. Notably, 200edo 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 GregorianLeapWeek[71] scale with 231\400 as the generator, which is close to 5/12 syntonic comma meantone. In the 19-limit, the generator corresponds to 525/352 and the comma basis is 969/968, 1001/1000, 2128/2125, 3328/3325, 4225/4224, and 444528/444125. An interesting variation upon the scale is the ISOWeek[71], which contains all the years which [[Wikipedia:ISO week date|have 53 weeks]] in the current calendar system.

400 is also the number of years in the Gregorian calendar's leap cycle. 400edo supports the GregorianLeapWeek[71] scale with 231\400 as the generator, which is close to 5/12 syntonic comma meantone. In the 19-limit, the generator corresponds to 525/352 and the comma basis is 969/968, 1001/1000, 2128/2125, 3328/3325, 4225/4224, and 444528/444125.

An interesting variation upon the scale is the ISOWeek[71], which contains all the years which [[Wikipedia:ISO week date|have 53 weeks]] in the current calendar system. It is a maximum variety 3 scale, with step sizes of mostly 5, 6, and once 7. Unlike the smoothly spread scale which has 231\400 in the Irvian mode, the ISOWeek[71] has 232\400 fifth, which corresponds to the 696-cent fifth of [[50edo]].

Likewise, 400edo contains GregorianLeapDay[97] scale, which is a [[maximal evenness]] version of the leap rule currently in use in the world today. The scale has a 33\400 generator which is associated to [[18/17]] and [[55/52]], and the corresponding temperament is 97 & 400, with comma list 2432/2431, 2601/2600, 2926/2925, 6175/6174, 17689/17680, and 22477/22440.

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 factors into  2<sup>4</sup> × 5<sup>2</sup>, with subset edos {{EDOs| 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, and 200 }}. Notably, 200edo holds a record for the best 3/2 fifth approximation.
-is also the number of years in the Gregorian calendar's leap cycle. 400edo supports the GregorianLeapWeek[71] scale with 231\400 as the generator, which is close to 5/12 syntonic comma meantone. In the 19-limit, the generator corresponds to 525/352 and the comma basis is 969/968, 1001/1000, 2128/2125, 3328/3325, 4225/4224, and 444528/444125. An interesting variation upon the scale is the ISOWeek[71], which contains all the years which [[Wikipedia:ISO week date|have 53 weeks]] in the current calendar system.
+is also the number of years in the Gregorian calendar's leap cycle. 400edo supports the GregorianLeapWeek[71] scale with 231\400 as the generator, which is close to 5/12 syntonic comma meantone. In the 19-limit, the generator corresponds to 525/352 and the comma basis is 969/968, 1001/1000, 2128/2125, 3328/3325, 4225/4224, and 444528/444125.
+An interesting variation upon the scale is the ISOWeek[71], which contains all the years which [[Wikipedia:ISO week date|have 53 weeks]] in the current calendar system. It is a maximum variety 3 scale, with step sizes of mostly 5, 6, and once 7. Unlike the smoothly spread scale which has 231\400 in the Irvian mode, the ISOWeek[71] has 232\400 fifth, which corresponds to the 696-cent fifth of [[50edo]].
 Likewise, 400edo contains GregorianLeapDay[97] scale, which is a [[maximal evenness]] version of the leap rule currently in use in the world today. The scale has a 33\400 generator which is associated to [[18/17]] and [[55/52]], and the corresponding temperament is 97 & 400, with comma list 2432/2431, 2601/2600, 2926/2925, 6175/6174, 17689/17680, and 22477/22440.