176edo: Difference between revisions
+intro and prime harmonics table |
+RTT table |
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== Theory == | == Theory == | ||
176edo is [[consistent]] to the [[11-odd-limit]], tempering out 78732/78125 ([[sensipent comma]]) and | 176edo is [[consistent]] to the [[11-odd-limit]], tempering out 78732/78125 ([[sensipent comma]]) and {{monzo| 41 -20 -4 }} ([[undim comma]]) in the 5-limit; [[6144/6125]], [[10976/10935]], and 50421/50000 in the 7-limit; [[441/440]], 3388/3375, 6912/6875, and [[8019/8000]] in the 11-limit, supporting the [[bison]] temperament and the [[commatic]] temperament. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Primes in edo|176}} | {{Primes in edo|176}} | ||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" | Subgroup | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{monzo| 279 -176 }} | |||
| [{{val| 176 279 }}] | |||
| -0.100 | |||
| 0.100 | |||
| 1.47 | |||
|- | |||
| 2.3.5 | |||
| 78732/78125, {{monzo| 41 -20 -4 }} | |||
| [{{val| 176 279 409 }}] | |||
| -0.400 | |||
| 0.432 | |||
| 6.34 | |||
|- | |||
| 2.3.5.7 | |||
| 6144/6125, 10976/10935, 50421/50000 | |||
| [{{val| 176 279 409 494 }}] | |||
| -0.243 | |||
| 0.463 | |||
| 6.79 | |||
|- | |||
| 2.3.5.7.11 | |||
| 441/440, 3388/3375, 6144/6125, 8019/8000 | |||
| [{{val| 176 279 409 494 609 }}] | |||
| -0.250 | |||
| 0.414 | |||
| 6.08 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 351/350, 364/363, 441/440, 2197/2187, 3146/3125 | |||
| [{{val| 176 279 409 494 609 651 }}] | |||
| -0.123 | |||
| 0.473 | |||
| 6.93 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per octave | |||
! Generator<br>(reduced) | |||
! Cents<br>(reduced) | |||
! Associated<br>ratio | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 17\176 | |||
| 115.91 | |||
| 77/72 | |||
| [[Countermiracle]] / countermiraculous (176f) / counterbenediction (176) | |||
|- | |||
| 1 | |||
| 35\176 | |||
| 238.64 | |||
| 147/128 | |||
| [[Tokko]] | |||
|- | |||
| 1 | |||
| 65\176 | |||
| 443.18 | |||
| 162/125 | |||
| [[Sensipent]] | |||
|- | |||
| 1 | |||
| 73\176 | |||
| 497.73 | |||
| 4/3 | |||
| [[Gary]] / [[cotoneum]] | |||
|- | |||
| 1 | |||
| 83\176 | |||
| 565.91 | |||
| 13/9 | |||
| [[Tricot]] / [[trident]] | |||
|- | |||
| 2 | |||
| 23\176 | |||
| 20.45 | |||
| 81/80 | |||
| [[Commatic]] (176f) | |||
|- | |||
| 2 | |||
| 23\176 | |||
| 156.82 | |||
| 35/32 | |||
| [[Bison]] | |||
|- | |||
| 8 | |||
| 83\176<br>(5\176) | |||
| 565.91<br>(34.09) | |||
| 168/121<br>(55/54) | |||
| [[Octowerck]] (176f) | |||
|- | |||
| 11 | |||
| 73\176<br>(7\176) | |||
| 497.73<br>(47.73) | |||
| 4/3<br>(36/35) | |||
| [[Hendecatonic]] | |||
|- | |||
| 22 | |||
| 73\176<br>(1\176) | |||
| 497.73<br>(6.82) | |||
| 4/3<br>(385/384) | |||
| [[Icosidillic]] | |||
|} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||