224edo: Difference between revisions

Line 11:

=== Subsets and supersets ===

Since 224 = 32 × 7, 224edo has subset edos {{EDOs| 2, 4, 8, 16, 32, 7, 14, 28, 56, and 112 }}.

Since {{nowrap|224 {{=}} 32 × 7}}, 224edo has subset edos {{EDOs| 2, 4, 8, 16, 32, 7, 14, 28, 56, and 112 }}.

== Regular temperament properties ==

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

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

~~! 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

Line 48:

Line 40:

| 540/539, 1375/1372, 4000/3993, 32805/32768

| {{mapping| 224 355 520 629 775 }}

| -0.012

| −0.012

| 0.1899

| 3.54

Line 55:

Line 47:

| 540/539, 625/624, 729/728, 1375/1372, 2200/2197

| {{mapping| 224 355 520 629 775 829 }}

| -0.035

| −0.035

| 0.1805

| 3.37

Line 62:

Line 54:

| 375/374, 540/539, 625/624, 715/714, 729/728, 2200/2197

| {{mapping| 224 355 520 629 775 829 916 }}

| -0.106

| −0.106

| 0.2420

| 4.52

|}

* 224et has a lower relative error than any previous equal temperaments in the 13-limit, being the first to beat [[72edo|72]]. The next equal temperament that does better in terms of either absolute or relative error is [[270edo|270]].

* It is also notable in the 11- and 17-limit, with lower absolute errors than any previous equal temperaments. In the 11-limit it is the first to beat [[152edo|152]] and is superseded by [[239edo|239]]. In the 17-limit it is the first to beat [[217edo|217]] and is superseded by 270.

=== Rank-2 temperaments ===

{~~| class="wikitable center-all left-5"~~

~~|+Table of~~ rank-2 ~~temperaments by generator~~

~~! Periods<br>per 8ve~~

! Generator*

! Cents*

! Associated<br>Ratio*

~~! Temperaments~~

|-

| 1

Line 221:

Line 207:

| 4/3<br>(126/125)

| [[Barium]]

|}

~~<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct~~

== Music ==

; [[Gene Ward Smith]]

* ''Dreyfus'' (archived 2010) – [https://soundcloud.com/genewardsmith/genewardsmith-dreyfus SoundCloud] | [https://www.archive.org/details/Dreyfus details] | [https://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3 play] – octoid[72] in 224edo tuning

; [[Mercury Amalgam]]

* [https://www.youtube.com/watch?v=iFi1zKsRBfY ''Kindness Is A Weakness''] (2023) – octant[24], hemigamera[26], oquatonic[56], bezique[64] in 224edo tuning

[[Category:Indra]]

[[Category:Listen]]

[[Category:Mirkwai]]

[[Category:Octoid]]

[[Category:Quartismic]]

[[Category:Shibi]]

~~[[Category:Listen]]~~

@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
-Since 224 = 32 × 7, 224edo has subset edos {{EDOs| 2, 4, 8, 16, 32, 7, 14, 28, 56, and 112 }}.
+Since {{nowrap|224 {{=}} 32 &times; 7}}, 224edo has subset edos {{EDOs| 2, 4, 8, 16, 32, 7, 14, 28, 56, and 112 }}.
 == Regular temperament properties ==
-{| class="wikitable center-4 center-5 center-6"
+{{comma basis begin}}
-! rowspan="2" | [[Subgroup]]
-! 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
@@ Line 48: / Line 40: @@
 | 540/539, 1375/1372, 4000/3993, 32805/32768
 | {{mapping| 224 355 520 629 775 }}
-| -0.012
+| &minus;0.012
 | 0.1899
 | 3.54
@@ Line 55: / Line 47: @@
 | 540/539, 625/624, 729/728, 1375/1372, 2200/2197
 | {{mapping| 224 355 520 629 775 829 }}
-| -0.035
+| &minus;0.035
 | 0.1805
 | 3.37
@@ Line 62: / Line 54: @@
 | 375/374, 540/539, 625/624, 715/714, 729/728, 2200/2197
 | {{mapping| 224 355 520 629 775 829 916 }}
-| -0.106
+| &minus;0.106
 | 0.2420
 | 4.52
-|}
+{{comma basis end}}
 * 224et has a lower relative error than any previous equal temperaments in the 13-limit, being the first to beat [[72edo|72]]. The next equal temperament that does better in terms of either absolute or relative error is [[270edo|270]].
 * It is also notable in the 11- and 17-limit, with lower absolute errors than any previous equal temperaments. In the 11-limit it is the first to beat [[152edo|152]] and is superseded by [[239edo|239]]. In the 17-limit it is the first to beat [[217edo|217]] and is superseded by 270.
 === Rank-2 temperaments ===
-{| class="wikitable center-all left-5"
+{{rank-2 begin}}
-|+Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
-! Generator*
-! Cents*
-! Associated<br>Ratio*
-! Temperaments
 |-
 | 1
@@ Line 221: / Line 207: @@
 | 4/3<br>(126/125)
 | [[Barium]]
-|}
+{{rank-2 end}}
-<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+{{orf}}
 == Music ==
 ; [[Gene Ward Smith]]
-* ''Dreyfus'' (archived 2010) – [https://soundcloud.com/genewardsmith/genewardsmith-dreyfus SoundCloud] | [https://www.archive.org/details/Dreyfus details] | [https://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3 play] – octoid[72] in 224edo tuning
+* ''Dreyfus'' (archived 2010) &ndash; [https://soundcloud.com/genewardsmith/genewardsmith-dreyfus SoundCloud] | [https://www.archive.org/details/Dreyfus details] | [https://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3 play] &ndash; octoid[72] in 224edo tuning
 ; [[Mercury Amalgam]]
-* [https://www.youtube.com/watch?v=iFi1zKsRBfY ''Kindness Is A Weakness''] (2023) – octant[24], hemigamera[26], oquatonic[56], bezique[64] in 224edo tuning
+* [https://www.youtube.com/watch?v=iFi1zKsRBfY ''Kindness Is A Weakness''] (2023) &ndash; octant[24], hemigamera[26], oquatonic[56], bezique[64] in 224edo tuning
 [[Category:Indra]]
+[[Category:Listen]]
 [[Category:Mirkwai]]
 [[Category:Octoid]]
 [[Category:Quartismic]]
 [[Category:Shibi]]
-[[Category:Listen]]