2022edo: Difference between revisions

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== Theory ==

~~{{Harmonics in equal~~|~~2022}}~~

2022edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. Nonetheless, it offers good appoximations of the 2.3.5.11.17.29.41.43.53.61 [[subgroup]]. When using smaller numbers, 2.3.5.11 is a good choice, and if rougher errors are allowed, no-sevens 29-limit is a satisfactory choice.

~~2022edo~~ offers good appoximations of the 2.5.11.17.29.41.43.53.61 subgroup. When using smaller numbers, 2.3.5.11 is a good choice, and if rougher errors are allowed, no-sevens 19-limit is a ~~reasonable~~ choice.

In the 5-limit, 2022edo supports the pirate temperament, 323 & 407, and tempers out the [-90, -15~~, 49⟩~~ comma.

In the 5-limit, 2022edo supports the [[pirate]] temperament, 323 & 407, and tempers out the {{monzo| -90 -15 49 }} comma.

In the 2.3.5.11 subgroup, 2022edo [[support]]s the rank 3 temperament that eliminates the [25,-17,-23~~,16⟩~~ comma. If the 11-limit is taken as a whole, 2022edo tempers out [[3025/3024]] and [[4375/4374]] when it's [[7/4]] is put on the 1633rd step (2022d val), and [[41503/41472]] with [[250047/250000]] when using the 1632nd step of the patent val.

In the 2.3.5.11 subgroup, 2022edo [[support]]s the rank-3 temperament that eliminates the {{monzo| 25 -17 -23 16 }} comma. If the 11-limit is taken as a whole, 2022edo tempers out [[3025/3024]] and [[4375/4374]] when it is [[7/4]] is put on the 1633rd step (2022d val), and [[41503/41472]] with [[250047/250000]] when using the 1632nd step of the patent val.

In the 2.5.11.17.29.41.43.53.61 subgroup, 2022edo tempers out 17630/17629, 18491/18490, 21200/21199, and 22528/22525.

If the 29-limit is taken as a whole even including the 7-limit inconsistency, 2022edo tempers out 2002/2001, 3451/3450, 5104/5103, and 16445/16443.

=== Prime harmonics ===

=== Subsets and supersets ===

Since 2022 factors into {{factorization|2022}}, 2022edo has subset edos 2, 3, 6, 337, 674, and 1011.

== Regular temperament properties ==

~~Assuming a no-seven 29 limit subgroup, 2.3.5.11.13.17.19.~~

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

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

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

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

~~! rowspan="2" |Optimal~~

~~8ve stretch (¢)~~

~~! colspan="2" |Tuning error~~

|-

![[TE error|Absolute]] (¢)

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

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

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

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

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

! colspan="2" | Tuning Error

|-

! [[TE error|Absolute]] (¢)

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

|-

|2.3

| 2.3

|{{~~Monzo~~|3205, -2022}}

| {{monzo| 3205 -2022 }}

|[{{~~Val~~|2022 3205}}]

| {{mapping| 2022 3205 }}

|~~<nowiki>-0~~.038534~~</nowiki>~~

| −0.038534

|0.038533

| 0.038533

|6.493

| 6.493

|-

|2.3.5

| 2.3.5

|[25, -48, ~~22⟩, [~~-90, -15~~, 49⟩~~

| {{monzo| 25 -48 22 }}, {{monzo| -90 -15 49 }}

|[{{~~Val~~|2022 3205 4695}}]

| {{mapping| 2022 3205 4695 }}

| -0.030920

| −0.030920

|0.033254

| 0.033254

|5.603

| 5.603

|-

|2.3.5.11.13.17.19.23.29

| 2.3.5.11.13.17.19.23.29

|2431/2430, 2755/2754, 3520/3519, 142025/141984,

| 2431/2430, 2755/2754, 3520/3519, 142025/141984, 2582624/2581875, 9096256/9092061, 11293425/11290976, 51054848/51046875

| {{mapping| 2022 3205 4695 6955 7482 8265 8589 9147 9283 }}

2582624/2581875, 9096256/9092061, 11293425/11290976, 51054848/51046875

| −0.010752

|~~[⟨2022~~ 3205 4695

| 0.036910

6955 7482 8265

| 6.219

|}

~~8589 9147 9283]]~~

~~| -0.010752~~

~~|0.036910~~

~~|6.219~~

|}

== Music ==

; [[Eliora]]

* [https://www.youtube.com/watch?v=IulKlMjxAM8 ''Noble Gas''] (2021)

* [~~https~~:~~//www.youtube.com/watch?v=IulKlMjxAM8 Noble Gas~~] ~~by Cinnamon Mavka~~

[[Category:Listen]]

~~== Trivia ==~~

~~It is notable that it is the equal division corresponding to the current year, and also that music was composed in it before the wiki page about it was written.~~

@@ Line 1: / Line 1: @@
-{{EDO intro|2022}}
+{{Infobox ET}}
+{{ED intro}}
 == Theory ==
-{{Harmonics in equal|2022}}
+edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. Nonetheless, it offers good appoximations of the 2.3.5.11.17.29.41.43.53.61 [[subgroup]]. When using smaller numbers, 2.3.5.11 is a good choice, and if rougher errors are allowed, no-sevens 29-limit is a satisfactory choice.
-edo offers good appoximations of the 2.5.11.17.29.41.43.53.61 subgroup. When using smaller numbers, 2.3.5.11 is a good choice, and if rougher errors are allowed, no-sevens 19-limit is a reasonable choice.
-In the 5-limit, 2022edo supports the pirate temperament, 323 & 407, and tempers out the [-90, -15, 49⟩ comma.
+In the 5-limit, 2022edo supports the [[pirate]] temperament, 323 & 407, and tempers out the {{monzo| -90 -15 49 }} comma.
-In the 2.3.5.11 subgroup, 2022edo [[support]]s the rank 3 temperament that eliminates the [25,-17,-23,16⟩ comma. If the 11-limit is taken as a whole, 2022edo tempers out [[3025/3024]] and [[4375/4374]] when it's [[7/4]] is put on the 1633rd step (2022d val), and [[41503/41472]] with [[250047/250000]] when using the 1632nd step of the patent val.
+In the 2.3.5.11 subgroup, 2022edo [[support]]s the rank-3 temperament that eliminates the {{monzo| 25 -17 -23 16 }} comma. If the 11-limit is taken as a whole, 2022edo tempers out [[3025/3024]] and [[4375/4374]] when it is [[7/4]] is put on the 1633rd step (2022d val), and [[41503/41472]] with [[250047/250000]] when using the 1632nd step of the patent val.
 In the 2.5.11.17.29.41.43.53.61 subgroup, 2022edo tempers out 17630/17629, 18491/18490, 21200/21199, and 22528/22525.
+If the 29-limit is taken as a whole even including the 7-limit inconsistency, 2022edo tempers out 2002/2001, 3451/3450, 5104/5103, and 16445/16443.
+=== Prime harmonics ===
+{{Harmonics in equal|2022|columns=11}}
+=== Subsets and supersets ===
+Since 2022 factors into {{factorization|2022}}, 2022edo has subset edos 2, 3, 6, 337, 674, and 1011.
 == Regular temperament properties ==
-Assuming a no-seven 29 limit subgroup, 2.3.5.11.13.17.19.
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" |[[Subgroup]]
-! rowspan="2" |[[Comma list]]
-! rowspan="2" |[[Mapping]]
-! rowspan="2" |Optimal
-ve stretch (¢)
-! colspan="2" |Tuning error
 |-
-![[TE error|Absolute]] (¢)
+! rowspan="2" | [[Subgroup]]
-![[TE simple badness|Relative]] (%)
+! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Mapping]]
+! rowspan="2" | Optimal<br>8ve Stretch (¢)
+! colspan="2" | Tuning Error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
 |-
-|2.3
+| 2.3
-|{{Monzo|3205, -2022}}
+| {{monzo| 3205 -2022 }}
-|[{{Val|2022 3205}}]
+| {{mapping| 2022 3205 }}
-|<nowiki>-0.038534</nowiki>
+| −0.038534
-|0.038533
+| 0.038533
-|6.493
+| 6.493
 |-
-|2.3.5
+| 2.3.5
-|[25, -48, 22⟩, [-90, -15, 49⟩
+| {{monzo| 25 -48 22 }}, {{monzo| -90 -15 49 }}
-|[{{Val|2022 3205 4695}}]
+| {{mapping| 2022 3205 4695 }}
-| -0.030920
+| −0.030920
-|0.033254
+| 0.033254
-|5.603
+| 5.603
 |-
-|2.3.5.11.13.17.19.23.29
+| 2.3.5.11.13.17.19.23.29
-|2431/2430, 2755/2754, 3520/3519, 142025/141984,
+| 2431/2430, 2755/2754, 3520/3519, 142025/141984, 2582624/2581875, 9096256/9092061, 11293425/11290976, 51054848/51046875
+| {{mapping| 2022 3205 4695 6955 7482 8265 8589 9147 9283 }}
-2582624/2581875, 9096256/9092061, 11293425/11290976, 51054848/51046875
+| −0.010752
-|[⟨2022 3205 4695
+| 0.036910
-7482 8265
+| 6.219
+|}
-9147 9283]]
-| -0.010752
-|0.036910
-|6.219
-|}
 == Music ==
+; [[Eliora]]
+* [https://www.youtube.com/watch?v=IulKlMjxAM8 ''Noble Gas''] (2021)
-* [https://www.youtube.com/watch?v=IulKlMjxAM8 Noble Gas] by Cinnamon Mavka
+[[Category:Listen]]
-== Trivia ==
-It is notable that it is the equal division corresponding to the current year, and also that music was composed in it before the wiki page about it was written.