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{{Infobox Interval | {{Infobox Interval | ||
| Name = monardisma | | Name = monardisma | ||
| Color name = 17o1org1, <br>solorugu unison, <br>Solorugu comma | | Color name = 17o1org1, <br>solorugu unison, <br>Solorugu comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''561/560''', the '''monardisma''' | '''561/560''', the '''monardisma''' is an [[unnoticeable comma|unnoticeable]] [[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]]. This temperament has a number of notable properties: | |||
* [[14/11]] and [[20/17]] become [[fifth complement]]s; | |||
* [[11/10]] and [[17/14]] become [[fourth complement]]s. | |||
=== 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]] | |||
== Etymology == | |||
This comma was named by [[Scott Dakota]] in 2023 after the [[Monarda]] scale, a 12-tone scale of [[tannic]], where this is one of the commas being tempered out. | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Monardismic]] | [[Category:Monardismic]] | ||
[[Category:Commas with unknown etymology]] | |||
Latest revision as of 23:37, 11 April 2025
| Interval information |
solorugu unison,
Solorugu comma
reduced
561/560, the monardisma is an unnoticeable 17-limit superparticular comma of about 3.1 cents. 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. This temperament has a number of notable properties:
- 14/11 and 20/17 become fifth complements;
- 11/10 and 17/14 become fourth complements.
Monardismic
Subgroup: 2.3.5.7.11.13.17
| [⟨ | 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
- 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: 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*
Etymology
This comma was named by Scott Dakota in 2023 after the Monarda scale, a 12-tone scale of tannic, where this is one of the commas being tempered out.