877edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|877}} == Theory == 877edo is consistent to the 15-odd-limit. It tempers out 3025/3024, 496125/495616, 420175/419904 and 4096000..." |
Cleanup. It's best to present nullity-1 temps in terms of commas |
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== Theory == | == Theory == | ||
877edo is [[consistent]] to the [[15-odd-limit]]. | 877edo is [[consistent]] to the [[15-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[3025/3024]], 496125/495616, [[420175/419904]], 40960000/40920957, as well as the [[quartisma]] in the 11-limit; [[2080/2079]], [[123201/123200]], 91125/91091 and [[65625/65536]] in the 13-limit. Using the 2.3.7.11.23.43 [[subgroup]]<!-- explain why this subgroup is good to consider -->, it tempers out [[3312/3311]]. It [[support]]s the [[quarterframe]] temperament. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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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]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo|-1390 877}} | | {{monzo| -1390 877 }} | ||
| {{mapping|877 1390}} | | {{mapping| 877 1390 }} | ||
| 0.0052 | | 0.0052 | ||
| 0.0052 | | 0.0052 | ||
| Line 30: | Line 30: | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo|-20 -24 25}}, {{monzo|54 -37 2}} | | {{monzo| -20 -24 25 }}, {{monzo| 54 -37 2 }} | ||
| {{mapping|877 1390 2036}} | | {{mapping| 877 1390 2036 }} | ||
| 0.0685 | | 0.0685 | ||
| 0.0896 | | 0.0896 | ||
| Line 37: | Line 37: | ||
|- | |- | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 65625/65536, 420175/419904, {{monzo|18 -18 13 -7}} | | 65625/65536, 420175/419904, {{monzo| 18 -18 13 -7 }} | ||
| {{mapping|877 1390 2036 2462}} | | {{mapping| 877 1390 2036 2462 }} | ||
| 0.0575 | | 0.0575 | ||
| 0.0799 | | 0.0799 | ||
| Line 45: | Line 45: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 3025/3024, 496125/495616, 420175/419904, 40960000/40920957 | | 3025/3024, 496125/495616, 420175/419904, 40960000/40920957 | ||
| {{mapping|877 1390 2036 2462 3034}} | | {{mapping| 877 1390 2036 2462 3034 }} | ||
| 0.0398 | | 0.0398 | ||
| 0.0797 | | 0.0797 | ||
| Line 52: | Line 52: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 2080/2079, 3025/3024, 123201/123200, 91125/91091, 65625/65536 | | 2080/2079, 3025/3024, 123201/123200, 91125/91091, 65625/65536 | ||
| {{mapping|877 1390 2036 2462 3034 3245}} | | {{mapping| 877 1390 2036 2462 3034 3245 }} | ||
| 0.0508 | | 0.0508 | ||
| 0.0768 | | 0.0768 | ||
| Line 64: | Line 64: | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 70: | Line 70: | ||
| 182\877 | | 182\877 | ||
| 249.031 | | 249.031 | ||
| {{monzo|-26 18 -1}} | | {{monzo| -26 18 -1 }} | ||
| [[Monzismic]] | | [[Monzismic]] | ||
|- | |- | ||
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| [[Sesesix]] | | [[Sesesix]] | ||
|} | |} | ||
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | |||