1193edo: Difference between revisions
m →Theory: nullity-1 temps are best given by commas |
m changed EDO intro to ED intro |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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== 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 25: | Line 26: | ||
| {{monzo| 1891 -1193 }} | | {{monzo| 1891 -1193 }} | ||
| {{mapping| 1193 1891 }} | | {{mapping| 1193 1891 }} | ||
| | | −0.0443 | ||
| 0.0443 | | 0.0443 | ||
| 4.41 | | 4.41 | ||
| Line 32: | Line 33: | ||
| {{monzo| 10 -40 -23 }}, {{monzo| 77 -31 -12 }} | | {{monzo| 10 -40 -23 }}, {{monzo| 77 -31 -12 }} | ||
| {{mapping| 1193 1891 2770 }} | | {{mapping| 1193 1891 2770 }} | ||
| | | −0.0209 | ||
| 0.0491 | | 0.0491 | ||
| 4.88 | | 4.88 | ||
| Line 39: | Line 40: | ||
| 2401/2400, {{monzo| -13 -12 15 -1 }}, {{monzo| 41 -15 -5 -2 }} | | 2401/2400, {{monzo| -13 -12 15 -1 }}, {{monzo| 41 -15 -5 -2 }} | ||
| {{mapping| 1193 1891 2770 3349 }} | | {{mapping| 1193 1891 2770 3349 }} | ||
| | | −0.000028 | ||
| 0.0558 | | 0.0558 | ||
| 5.55 | | 5.55 | ||
| Line 53: | Line 54: | ||
| 2401/2400, 3025/3024, 4096/4095, 78125/78078, 114345/114244 | | 2401/2400, 3025/3024, 4096/4095, 78125/78078, 114345/114244 | ||
| {{mapping| 1193 1891 2770 3349 4127 4415 }} | | {{mapping| 1193 1891 2770 3349 4127 4415 }} | ||
| | | −0.0121 | ||
| 0.0617 | | 0.0617 | ||
| 6.14 | | 6.14 | ||
| Line 67: | Line 68: | ||
=== 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 92: | Line 94: | ||
| [[Dodifo]] | | [[Dodifo]] | ||
|} | |} | ||
<nowiki>* | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||