224edo: Difference between revisions
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== Intervals == | == Intervals == | ||
{{ | {{Todo|create page|comment=Table of 224edo intervals}} | ||
{{Interval table}} | {{Interval table}} | ||
== Notation == | == Notation == | ||
=== Sagittal === | === Sagittal === | ||
224edo can be written in Sagittal using almost the entire Athenian extension (except for {{sagittal|(|}} {{sagittal|(!}} {{sagittal|)||~}} {{sagittal|)!!~}} since it tempers [[1240029/1239040]]), by virtue of its apotome being equal to 21 edosteps, which is the maximum equal division of the apotome (eda) supported by Athenian<ref name=":0">[[Ragismic microtemperaments#Brahmagupta]]</ref>. It is identical to [[217edo]]'s Sagittal notation, but it uses the 55C for the +6/-6 alteration instead of 11/7C.<ref>https://sagittal.org/sagittal.pdf p. 11</ref> | 224edo can be written in Sagittal using almost the entire Athenian extension (except for {{sagittal|(|}} {{sagittal|(!}} {{sagittal|)||~}} {{sagittal|)!!~}} since it tempers [[1240029/1239040]]), by virtue of its apotome being equal to 21 edosteps, which is the maximum equal division of the apotome (eda) supported by Athenian<ref name=":0">[[Ragismic microtemperaments#Brahmagupta]]</ref>. It is identical to [[217edo]]'s Sagittal notation, but it uses the 55C for the +6/-6 alteration instead of 11/7C.<ref>https://sagittal.org/sagittal.pdf p. 11</ref> | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Sagittal notation | |+ Sagittal notation | ||
!224edosteps | ! 224edosteps | ||
!0 | ! 0 | ||
!1 | ! 1 | ||
!2 | ! 2 | ||
!3 | ! 3 | ||
!4 | ! 4 | ||
!5 | ! 5 | ||
!6 | ! 6 | ||
!7 | ! 7 | ||
!8 | ! 8 | ||
!9 | ! 9 | ||
!10 | ! 10 | ||
!11 | ! 11 | ||
!12 | ! 12 | ||
!13 | ! 13 | ||
!14 | ! 14 | ||
!15 | ! 15 | ||
!16 | ! 16 | ||
!17 | ! 17 | ||
!18 | ! 18 | ||
!19 | ! 19 | ||
!20 | ! 20 | ||
!21 | ! 21 | ||
|- | |- | ||
|Revo | | Revo | ||
| rowspan="2" |{{sagittal||//|}} | | rowspan="2" | {{sagittal||//|}} | ||
| rowspan="2" |{{sagittal||(}} | | rowspan="2" | {{sagittal||(}} | ||
| rowspan="2" |{{sagittal|)|(}} | | rowspan="2" | {{sagittal|)|(}} | ||
| rowspan="2" |{{sagittal|~|(}} | | rowspan="2" | {{sagittal|~|(}} | ||
| rowspan="2" |{{sagittal|/|}} | | rowspan="2" | {{sagittal|/|}} | ||
| rowspan="2" |{{sagittal||)}} | | rowspan="2" | {{sagittal||)}} | ||
| rowspan="2" |{{sagittal||\}} | | rowspan="2" | {{sagittal||\}} | ||
| rowspan="2" |{{sagittal|(|(}} | | rowspan="2" | {{sagittal|(|(}} | ||
| rowspan="2" |{{sagittal|//|}} | | rowspan="2" | {{sagittal|//|}} | ||
| rowspan="2" |{{sagittal|/|)}} | | rowspan="2" | {{sagittal|/|)}} | ||
| rowspan="2" |{{sagittal|/|\}} | | rowspan="2" | {{sagittal|/|\}} | ||
|{{sagittal|(|)}} | | {{sagittal|(|)}} | ||
|{{sagittal|(|\}} | | {{sagittal|(|\}} | ||
|{{sagittal|)||(}} | | {{sagittal|)||(}} | ||
|{{sagittal|~||(}} | | {{sagittal|~||(}} | ||
|{{sagittal|/||}} | | {{sagittal|/||}} | ||
|{{sagittal|||)}} | | {{sagittal|||)}} | ||
|{{sagittal|||\}} | | {{sagittal|||\}} | ||
|{{sagittal|(||(}} | | {{sagittal|(||(}} | ||
|{{sagittal|//||}} | | {{sagittal|//||}} | ||
|{{sagittal|/||)}} | | {{sagittal|/||)}} | ||
|{{sagittal|/||\}} | | {{sagittal|/||\}} | ||
|- | |- | ||
|Evo | | Evo | ||
|{{sagittal|#}}{{sagittal|\!/}} | | {{sagittal|#}}{{sagittal|\!/}} | ||
|{{sagittal|#}}{{sagittal|\!)}} | | {{sagittal|#}}{{sagittal|\!)}} | ||
|{{sagittal|#}}{{sagittal|\\!}} | | {{sagittal|#}}{{sagittal|\\!}} | ||
|{{sagittal|#}}{{sagittal|(!(}} | | {{sagittal|#}}{{sagittal|(!(}} | ||
|{{sagittal|#}}{{sagittal|!/}} | | {{sagittal|#}}{{sagittal|!/}} | ||
|{{sagittal|#}}{{sagittal|!)}} | | {{sagittal|#}}{{sagittal|!)}} | ||
|{{sagittal|#}}{{sagittal|\!}} | | {{sagittal|#}}{{sagittal|\!}} | ||
|{{sagittal|#}}{{sagittal|~!(}} | | {{sagittal|#}}{{sagittal|~!(}} | ||
|{{sagittal|#}}{{sagittal|)!(}} | | {{sagittal|#}}{{sagittal|)!(}} | ||
|{{sagittal|#}}{{sagittal|!(}} | | {{sagittal|#}}{{sagittal|!(}} | ||
|{{sagittal|#}} | | {{sagittal|#}} | ||
|} | |} | ||
=== Ups-and-downs notation === | === Ups-and-downs notation === | ||
The 4-up (quup) alteration maps to the pythagorean/syntonic comma. | The 4-up (quup) alteration maps to the pythagorean/syntonic comma. | ||
{| class="wikitable" style="text-align:center;" | {| class="wikitable" style="text-align:center;" | ||
|+Ups-and-downs notation | |+ Ups-and-downs notation | ||
! rowspan="6" |224edosteps | ! rowspan="6" | 224edosteps | ||
!0 | ! 0 | ||
!1 | ! 1 | ||
!2 | ! 2 | ||
!3 | ! 3 | ||
!4 | ! 4 | ||
!5 | ! 5 | ||
!6 | ! 6 | ||
!7 | ! 7 | ||
!8 | ! 8 | ||
!9 | ! 9 | ||
!10 | ! 10 | ||
|- | |- | ||
| rowspan="2" |h | | rowspan="2" | h | ||
|^ | | ^ | ||
|^^ | | ^^ | ||
|^^^ | | ^^^ | ||
|v> | | v> | ||
|> | | > | ||
|^> | | ^> | ||
|^^> | | ^^> | ||
|^^^> | | ^^^> | ||
|v>> | | v>> | ||
|>> | | >> | ||
|- | |- | ||
|<<<<# | | <<<<# | ||
|^<<<<# | | ^<<<<# | ||
|vvv<<<# | | vvv<<<# | ||
|vv<<<# | | vv<<<# | ||
|v<<<# | | v<<<# | ||
|<<<# | | <<<# | ||
|^<<<# | | ^<<<# | ||
|vvv<<# | | vvv<<# | ||
|vv<<# | | vv<<# | ||
|v<<# | | v<<# | ||
|- | |- | ||
!11 | ! 11 | ||
!12 | ! 12 | ||
!13 | ! 13 | ||
!14 | ! 14 | ||
!15 | ! 15 | ||
!16 | ! 16 | ||
!17 | ! 17 | ||
!18 | ! 18 | ||
!19 | ! 19 | ||
!20 | ! 20 | ||
!21 | ! 21 | ||
|- | |- | ||
|^>> | | ^>> | ||
|^^>> | | ^^>> | ||
|^^^>> | | ^^^>> | ||
|v>>> | | v>>> | ||
|>>> | | >>> | ||
|^>>> | | ^>>> | ||
|^^>>> | | ^^>>> | ||
|^^^>>> | | ^^^>>> | ||
|v>>>> | | v>>>> | ||
|>>>> | | >>>> | ||
| rowspan="2" |# | | rowspan="2" |# | ||
|- | |- | ||
|<<# | | <<# | ||
|^<<# | | ^<<# | ||
|vvv<# | | vvv<# | ||
|vv<# | | vv<# | ||
|v<# | | v<# | ||
|<# | | <# | ||
|^<# | | ^<# | ||
|vvv# | | vvv# | ||
|vv# | | vv# | ||
|v# | | v# | ||
|} | |} | ||
| Line 181: | Line 182: | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| -355 224 }} | ||
| {{ | | {{Mapping| 224 355 }} | ||
| +0.053 | | +0.053 | ||
| 0.0534 | | 0.0534 | ||
| Line 189: | Line 190: | ||
| 2.3.5 | | 2.3.5 | ||
| 32805/32768, {{monzo| -5 -32 24 }} | | 32805/32768, {{monzo| -5 -32 24 }} | ||
| {{ | | {{Mapping| 224 355 520 }} | ||
| +0.122 | | +0.122 | ||
| 0.1059 | | 0.1059 | ||
| Line 196: | Line 197: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 4375/4374, 16875/16807, 32805/32768 | | 4375/4374, 16875/16807, 32805/32768 | ||
| {{ | | {{Mapping| 224 355 520 629 }} | ||
| +0.018 | | +0.018 | ||
| 0.2009 | | 0.2009 | ||
| Line 203: | Line 204: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 540/539, 1375/1372, 4000/3993, 32805/32768 | | 540/539, 1375/1372, 4000/3993, 32805/32768 | ||
| {{ | | {{Mapping| 224 355 520 629 775 }} | ||
| −0.012 | | −0.012 | ||
| 0.1899 | | 0.1899 | ||
| Line 210: | Line 211: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 540/539, 625/624, 729/728, 1375/1372, 2200/2197 | | 540/539, 625/624, 729/728, 1375/1372, 2200/2197 | ||
| {{ | | {{Mapping| 224 355 520 629 775 829 }} | ||
| −0.035 | | −0.035 | ||
| 0.1805 | | 0.1805 | ||
| Line 217: | Line 218: | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 375/374, 540/539, 625/624, 715/714, 729/728, 2200/2197 | | 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 | | 0.2420 | ||
| Line 379: | Line 380: | ||
| [[Barium]] | | [[Barium]] | ||
|} | |} | ||
<nowiki/>* [[Normal | <nowiki/>* [[Normal forms|Octave-reduced form]], reduced to the first half-octave, and [[normal forms|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||
; [[Gene Ward Smith]] | ; [[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] – | * ''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]] | ; [[Mercury Amalgam]] | ||
* [https://www.youtube.com/watch?v=iFi1zKsRBfY ''Kindness Is A Weakness''] (2023) – | * [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:Indra]] | ||