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. An interesting variation upon the scale ~~would be~~ the ISOWeek[71], which contains all the years which [[Wikipedia:ISO week date|have 53 weeks]] in the current calendar system. 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.

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.

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.

=== Prime harmonics ===

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| 33

| small septendecimal semitone

| [[18/17]]

| [[18/17]], [[55/52]]

|-

| 35

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| 231

| Gregorian leap week fifth

| 85/57, 94/63

| 525/352, 3/2 / (81/80)^(5/12)

|-

| 234

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| 125/96

| [[Majvamic]]

|-

|1

|169\400

|507.00

|525/352

|[[Gregorian leap week]]

|-

| 2

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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. An interesting variation upon the scale would be the ISOWeek[71], which contains all the years which [[Wikipedia:ISO week date|have 53 weeks]] in the current calendar system. 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.
+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.
+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.
 === Prime harmonics ===
@@ Line 35: / Line 37: @@
 | 33
 | small septendecimal semitone
-| [[18/17]]
+| [[18/17]], [[55/52]]
 |-
 | 35
@@ Line 59: / Line 61: @@
 | 231
 | Gregorian leap week fifth
-| 85/57, 94/63
+| 525/352, 3/2 / (81/80)^(5/12)
 |-
 | 234
@@ Line 164: / Line 166: @@
 | 125/96
 | [[Majvamic]]
+|-
+|1
+|169\400
+|507.00
+|525/352
+|[[Gregorian leap week]]
 |-
 | 2