437edo: Difference between revisions

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==Theory==

~~437et tempers out 4096000/4084101 and~~ [[~~2401/2400~~]] in the 7-limit~~; 25165824/25109315~~, ~~1835008~~/~~1830125, 2621440/2614689,~~ [[~~16384~~/~~16335~~]], ~~151263/151250~~, ~~107495424/107421875~~, [[~~1953125~~/~~1948617~~]], [[3025/3024]], [[41503/41472]], ~~766656~~/~~765625~~, ~~391314/390625, 20614528/20588575~~ and ~~644204~~/~~643125~~ in the 11-limit.

== Theory ==

===Odd harmonics===

437edo is [[consistent]] to the [[7-odd-limit]], but the errors of [[harmonic]]s [[3/1|3]] and [[5/1|5]] are quite large, giving us the option of treating it as either a full 11-limit temperament, or a 2.9.15.21.13.17 [[subgroup]] temperament.

Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[2401/2400]] and 4096000/4084101 in the 7-limit; [[3025/3024]], [[41503/41472]], [[16384/16335]], and 151263/151250 in the 11-limit.

=== Odd harmonics ===

===Subsets and supersets===

437 factors into ~~19 × 23 with its subset edos~~ {{~~EDOs~~|19, and ~~23}}~~. [[874edo]], which doubles it, gives a good correction to the harmonic 3.

=== Subsets and supersets ===

==Regular temperament properties==

Since 437 factors into {{factorization|437}}, 437edo contains [[19edo]] and [[23edo]] as subsets. [[874edo]], which doubles it, gives a good correction to the harmonic 3.

== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

! rowspan="2" |[[Subgroup]]

! rowspan="2" | [[Subgroup]]

! rowspan="2" |[[Comma list|Comma List]]

! rowspan="2" | [[Comma list|Comma List]]

! rowspan="2" |[[Mapping]]

! rowspan="2" | [[Mapping]]

! rowspan="2" |Optimal<br>8ve Stretch (¢)

! rowspan="2" | Optimal<br>8ve Stretch (¢)

! colspan="2" |Tuning Error

! colspan="2" | Tuning Error

|-

![[TE error|Absolute]] (¢)

! [[TE error|Absolute]] (¢)

![[TE simple badness|Relative]] (%)

! [[TE simple badness|Relative]] (%)

|-

|2.9

| 2.9

|{{monzo|-1385 437}}

| {{monzo| -1385 437 }}

|{{~~val~~|437 1385}}

| {{mapping| 437 1385 }}

| 0.1114

| 4.06

|}

==Scales==

== Scales ==

* [[Namo7]]

* [[Namo10]]

* [[Namo17]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{EDO intro|437}}
-==Theory==
-et tempers out 4096000/4084101 and [[2401/2400]] in the 7-limit; 25165824/25109315, 1835008/1830125, 2621440/2614689, [[16384/16335]], 151263/151250, 107495424/107421875, [[1953125/1948617]], [[3025/3024]], [[41503/41472]], 766656/765625, 391314/390625, 20614528/20588575 and 644204/643125 in the 11-limit.
+== Theory ==
-===Odd harmonics===
+edo is [[consistent]] to the [[7-odd-limit]], but the errors of [[harmonic]]s [[3/1|3]] and [[5/1|5]] are quite large, giving us the option of treating it as either a full 11-limit temperament, or a 2.9.15.21.13.17 [[subgroup]] temperament.
+Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[2401/2400]] and 4096000/4084101 in the 7-limit; [[3025/3024]], [[41503/41472]], [[16384/16335]], and 151263/151250 in the 11-limit.
+=== Odd harmonics ===
 {{Harmonics in equal|437}}
-===Subsets and supersets===
-factors into 19 × 23 with its subset edos {{EDOs|19, and 23}}. [[874edo]], which doubles it, gives a good correction to the harmonic 3.
+=== Subsets and supersets ===
-==Regular temperament properties==
+Since 437 factors into {{factorization|437}}, 437edo contains [[19edo]] and [[23edo]] as subsets. [[874edo]], which doubles it, gives a good correction to the harmonic 3.
+== Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" |[[Subgroup]]
+! rowspan="2" | [[Subgroup]]
-! rowspan="2" |[[Comma list|Comma List]]
+! rowspan="2" | [[Comma list|Comma List]]
-! rowspan="2" |[[Mapping]]
+! rowspan="2" | [[Mapping]]
-! rowspan="2" |Optimal<br>8ve Stretch (¢)
+! rowspan="2" | Optimal<br>8ve Stretch (¢)
-! colspan="2" |Tuning Error
+! colspan="2" | Tuning Error
 |-
-![[TE error|Absolute]] (¢)
+! [[TE error|Absolute]] (¢)
-![[TE simple badness|Relative]] (%)
+! [[TE simple badness|Relative]] (%)
 |-
-|2.9
+| 2.9
-|{{monzo|-1385 437}}
+| {{monzo| -1385 437 }}
-|{{val|437 1385}}
+| {{mapping| 437 1385 }}
 | 0.1114
 | 0.1114
 | 4.06
 |}
-==Scales==
+== Scales ==
 * [[Namo7]]
 * [[Namo10]]
 * [[Namo17]]