561/560: Difference between revisions
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'''561/560''', the '''monardisma''' or '''tsaharuk comma''' is a [[17-limit]] [[superparticular]] [[comma]] of about 3.1 [[cent]]s. It is the difference between [[33/32]] and [[35/34]]. Tempering | '''561/560''', the '''monardisma''' or '''tsaharuk comma''' is a [[17-limit]] [[superparticular]] [[comma]] of about 3.1 [[cent]]s. It is the difference between [[33/32]] and [[35/34]]. | ||
== Temperaments == | |||
[[Tempering out]] this comma in the 2.3.5.7.11.17 [[subgroup]] results in the '''monardic temperament''', or in the full 17-limit, the '''monardismic temperament''', enabling [[monardismic chords]]. | |||
=== Monardismic === | |||
[[Subgroup]]: 2.3.5.7.11.13.17 | |||
[[Mapping]]: <br> | |||
{| class="right-all" | |||
|- | |||
| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 4 || ], | |||
|- | |||
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || -1 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 1 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 1 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || -1 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | |||
|} | |||
: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1200.0000, ~3/2 = 701.7805, ~5/4 = 386.6883, ~7/4 = 969.3735, ~11/8 = 550.4865, ~13/8 = 840.5277 | |||
* [[CWE]]: ~2 = 1200.0000, ~3/2 = 701.6204, ~5/4 = 386.3575, ~7/4 = 968.9591, ~11/8 = 550.2059, ~13/8 = 840.0917 | |||
{{Optimal ET sequence|legend=1| 12f, 14cf, 15, 17cg, 19g, 22, 26, 29g, 31, 38df, 41g, 43, 46, 58, 72, 103, 111, 130, 140, 183, 243e, 301, 373g, 886eefgg, 1362bdeeefgggg }}* | |||
<nowiki/>* [[optimal patent val]]: [[484edo|484]] | |||
== See also == | == See also == | ||