224edo: Difference between revisions
ArrowHead294 (talk | contribs) |
Added info about Sagittal |
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 224 factors into {{factorisation|224}}, 224edo has subset edos {{EDOs| 2, 4, 8, 16, 32, 7, 14, 28, 56, and 112 }}. | Since 224 factors into {{factorisation|224}}, 224edo has subset edos {{EDOs| 2, 4, 8, 16, 32, 7, 14, 28, 56, and 112 }}. | ||
== Notation == | |||
=== 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> | |||
{| class="wikitable" | |||
|+Sagittal notation | |||
!217edosteps | |||
!-21 | |||
!-20 | |||
!-19 | |||
!-18 | |||
!-17 | |||
!-16 | |||
!-15 | |||
!-14 | |||
!-13 | |||
!-12 | |||
!-11 | |||
!-10 | |||
!-9 | |||
!-8 | |||
!-7 | |||
!-6 | |||
!-5 | |||
!-4 | |||
!-3 | |||
!-2 | |||
!-1 | |||
!0 | |||
!1 | |||
!2 | |||
!3 | |||
!4 | |||
!5 | |||
!6 | |||
!7 | |||
!8 | |||
!9 | |||
!10 | |||
!11 | |||
!12 | |||
!13 | |||
!14 | |||
!15 | |||
!16 | |||
!17 | |||
!18 | |||
!19 | |||
!20 | |||
!21 | |||
|- | |||
|Revo | |||
|{{sagittal|\!!/}} | |||
|{{sagittal|\!!)}} | |||
|{{sagittal|\\!!}} | |||
|{{sagittal|(!!(}} | |||
|{{sagittal|!!/}} | |||
|{{sagittal|!!)}} | |||
|{{sagittal|\!!}} | |||
|{{sagittal|~!!(}} | |||
|{{sagittal|)!!(}} | |||
|{{sagittal|(!/}} | |||
|{{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|/||\}} | |||
|- | |||
|Evo | |||
|{{sagittal|b}} | |||
|{{sagittal|b}}{{sagittal||(}} | |||
|{{sagittal|b}}{{sagittal|)|(}} | |||
|{{sagittal|b}}{{sagittal|~|(}} | |||
|{{sagittal|b}}{{sagittal|/|}} | |||
|{{sagittal|b}}{{sagittal||)}} | |||
|{{sagittal|b}}{{sagittal||\}} | |||
|{{sagittal|b}}{{sagittal|(|(}} | |||
|{{sagittal|b}}{{sagittal|//|}} | |||
|{{sagittal|b}}{{sagittal|/|)}} | |||
|{{sagittal|b}}{{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 === | |||
The 5-up (quup) alteration neatly maps to the pythagorean/septimal comma. | |||
{| class="wikitable" style="text-align:center;" | |||
|+Ups-and-downs notation | |||
! rowspan="3" |217edosteps | |||
!-21 | |||
!-20 | |||
!-19 | |||
!-18 | |||
!-17 | |||
!-16 | |||
!-15 | |||
!-14 | |||
!-13 | |||
!-12 | |||
!-11 | |||
!-10 | |||
!-9 | |||
!-8 | |||
!-7 | |||
!-6 | |||
!-5 | |||
!-4 | |||
!-3 | |||
!-2 | |||
!-1 | |||
!0 | |||
!1 | |||
!2 | |||
!3 | |||
!4 | |||
!5 | |||
!6 | |||
!7 | |||
!8 | |||
!9 | |||
!10 | |||
!11 | |||
!12 | |||
!13 | |||
!14 | |||
!15 | |||
!16 | |||
!17 | |||
!18 | |||
!19 | |||
!20 | |||
!21 | |||
|- | |||
| rowspan="2" |b | |||
|<<<< | |||
|^<<<< | |||
|vvv<<< | |||
|vv<<< | |||
|v<<< | |||
|<<< | |||
|^<<< | |||
|vvv<< | |||
|vv<< | |||
|v<< | |||
|<< | |||
|^<< | |||
|vvv< | |||
|vv< | |||
|v< | |||
|< | |||
|^< | |||
|vvv | |||
|vv | |||
|v | |||
| rowspan="2" |h | |||
|^ | |||
|^^ | |||
|^^^ | |||
|v> | |||
|> | |||
|^> | |||
|^^> | |||
|^^^> | |||
|v>> | |||
|>> | |||
|^>> | |||
|^^>> | |||
|^^^>> | |||
|v>>> | |||
|>>> | |||
|^>>> | |||
|^^>>> | |||
|^^^>>> | |||
|v>>>> | |||
|>>>> | |||
| rowspan="2" |# | |||
|- | |||
|^b | |||
|^^b | |||
|^^^b | |||
|v>b | |||
|>b | |||
|^>b | |||
|^^>b | |||
|^^^>b | |||
|v>>b | |||
|>>b | |||
|^>>b | |||
|^^>>b | |||
|^^^>>b | |||
|v>>>b | |||
|>>>b | |||
|^>>>b | |||
|^^>>>b | |||
|^^^>>>b | |||
|v>>>>b | |||
|>>>>b | |||
|<<<<# | |||
|^<<<<# | |||
|vvv<<<# | |||
|vv<<<# | |||
|v<<<# | |||
|<<<# | |||
|^<<<# | |||
|vvv<<# | |||
|vv<<# | |||
|v<<# | |||
|<<# | |||
|^<<# | |||
|vvv<# | |||
|vv<# | |||
|v<# | |||
|<# | |||
|^<# | |||
|vvv# | |||
|vv# | |||
|v# | |||
|} | |||
== Approximation to JI == | == Approximation to JI == | ||