1600edo: Difference between revisions
Adopt template: Factorization; misc. cleanup |
m →Regular temperament properties: crazy update |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
| Line 17: | Line 17: | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
| Line 27: | Line 28: | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| -53 10 16 }}, {{monzo| 26 -75 40 }} | ||
| {{ | | {{Mapping| 1600 2536 3715 }} | ||
| | | −0.0003 | ||
| 0.0228 | | 0.0228 | ||
| 3.04 | | 3.04 | ||
| Line 35: | Line 36: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 4375/4374, {{monzo| 36 -5 0 -10 }}, {{monzo| -17 5 16 -10 }} | | 4375/4374, {{monzo| 36 -5 0 -10 }}, {{monzo| -17 5 16 -10 }} | ||
| {{ | | {{Mapping| 1600 2536 3715 4492 }} | ||
| | | −0.0157 | ||
| 0.0332 | | 0.0332 | ||
| 4.43 | | 4.43 | ||
| Line 42: | Line 43: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 3025/3024, 4375/4374, {{monzo| 24 -1 -5 0 1 }}, {{monzo| 15 1 7 -8 -3 }} | | 3025/3024, 4375/4374, {{monzo| 24 -1 -5 0 1 }}, {{monzo| 15 1 7 -8 -3 }} | ||
| {{ | | {{Mapping| 1600 2536 3715 4492 5535 }} | ||
| | | −0.0172 | ||
| 0.0329 | | 0.0329 | ||
| 4.39 | | 4.39 | ||
| Line 49: | Line 50: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 823875/823543 | | 3025/3024, 4096/4095, 4375/4374, 78125/78078, 823875/823543 | ||
| {{ | | {{Mapping| 1600 2536 3715 4492 5535 5921 }} | ||
| | | −0.0087 | ||
| 0.0356 | | 0.0356 | ||
| 4.75 | | 4.75 | ||
| Line 56: | Line 57: | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 14875/14872, 63888/63869 | | 2500/2499, 3025/3024, 4096/4095, 4375/4374, 14875/14872, 63888/63869 | ||
| {{ | | {{Mapping| 1600 2536 3715 4492 5535 5921 6540 }} | ||
| | | −0.0163 | ||
| 0.0331 | | 0.0331 | ||
| 4.41 | | 4.41 | ||
| Line 64: | Line 65: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 76: | Line 77: | ||
| 162.75 | | 162.75 | ||
| 1125/1024 | | 1125/1024 | ||
| [[ | | [[Crazy]] | ||
|- | |- | ||
| 32 | | 32 | ||
| Line 102: | Line 103: | ||
| [[Tetraicosic]] | | [[Tetraicosic]] | ||
|} | |} | ||
<nowiki>* | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[normal lists|minimal form]] in parentheses if distinct | ||