176edo: Difference between revisions
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 176 factors into {{ | Since 176 factors into primes as {{nowrap| 2<sup>4</sup> × 11 }}, 176edo has subset edos {{EDOs| 2, 4, 8, 11, 16, 22, 44, and 88 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
| Line 26: | Line 26: | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| 279 -176 }} | ||
| {{ | | {{Mapping| 176 279 }} | ||
| −0.100 | | −0.100 | ||
| 0.100 | | 0.100 | ||
| Line 34: | Line 34: | ||
| 2.3.5 | | 2.3.5 | ||
| 78732/78125, {{monzo| 41 -20 -4 }} | | 78732/78125, {{monzo| 41 -20 -4 }} | ||
| {{ | | {{Mapping| 176 279 409 }} | ||
| −0.400 | | −0.400 | ||
| 0.432 | | 0.432 | ||
| Line 41: | Line 41: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 6144/6125, 10976/10935, 50421/50000 | | 6144/6125, 10976/10935, 50421/50000 | ||
| {{ | | {{Mapping| 176 279 409 494 }} | ||
| −0.243 | | −0.243 | ||
| 0.463 | | 0.463 | ||
| Line 48: | Line 48: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 441/440, 3388/3375, 6144/6125, 8019/8000 | | 441/440, 3388/3375, 6144/6125, 8019/8000 | ||
| {{ | | {{Mapping| 176 279 409 494 609 }} | ||
| −0.250 | | −0.250 | ||
| 0.414 | | 0.414 | ||
| Line 55: | Line 55: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 351/350, 364/363, 441/440, 2197/2187, 3146/3125 | | 351/350, 364/363, 441/440, 2197/2187, 3146/3125 | ||
| {{ | | {{Mapping| 176 279 409 494 609 651 }} | ||
| −0.123 | | −0.123 | ||
| 0.473 | | 0.473 | ||
| Line 65: | Line 65: | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 99: | Line 99: | ||
| 565.91 | | 565.91 | ||
| 13/9 | | 13/9 | ||
| [[ | | [[Alphatrident]] | ||
|- | |- | ||
| 2 | | 2 | ||
| Line 114: | Line 114: | ||
|- | |- | ||
| 4 | | 4 | ||
| 73\176<br | | 73\176<br>(15\176) | ||
| 497.73<br | | 497.73<br>(102.27) | ||
| 4/3<br | | 4/3<br>(35/33) | ||
| [[ | | [[Unlit]] | ||
|- | |- | ||
| 8 | | 8 | ||
| 73\176<br | | 73\176<br>(7\176) | ||
| 497.73<br | | 497.73<br>(47.73) | ||
| 4/3<br | | 4/3<br>(36/35) | ||
| [[Twilight]] | | [[Twilight]] | ||
|- | |- | ||
| 8 | | 8 | ||
| 83\176<br | | 83\176<br>(5\176) | ||
| 565.91<br | | 565.91<br>(34.09) | ||
| 168/121<br | | 168/121<br>(55/54) | ||
| [[Octowerck]] (176f) / octowerckis (176) | | [[Octowerck]] (176f) / octowerckis (176) | ||
|- | |- | ||
| 11 | | 11 | ||
| 73\176<br | | 73\176<br>(7\176) | ||
| 497.73<br | | 497.73<br>(47.73) | ||
| 4/3<br | | 4/3<br>(36/35) | ||
| [[Hendecatonic]] | | [[Hendecatonic]] | ||
|- | |- | ||
| 22 | | 22 | ||
| 73\176<br | | 73\176<br>(1\176) | ||
| 497.73<br | | 497.73<br>(6.82) | ||
| 4/3<br | | 4/3<br>(385/384) | ||
| [[Icosidillic]] / [[major arcana]] | | [[Icosidillic]] / [[major arcana]] | ||
|} | |} | ||