11859211/11859210: Difference between revisions
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'''11859211/11859210''', the '''tredekisma''', is the smallest [[superparticular ratio]] in the [[19-limit]] and [[23-limit]]. | '''11859211/11859210''', the '''tredekisma''', is the smallest [[superparticular ratio]] in the [[19-limit]] and [[23-limit]]. | ||
It can be seen as the difference between a stack of | It can be seen as the difference between a stack of four [[38/33]]'s and a stack consisting of [[10/7]] and [[16/13]]: (38/33)<sup>4</sup>/((10/7)⋅(16/13)). | ||
A possible S-expression of it is (S76⋅S441)/(S77⋅S324). | |||
== Temperaments == | == Temperaments == | ||
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[[Optimal tuning]]s: TBA | [[Optimal tuning]]s: TBA | ||
{{Optimal ET sequence||legend=1 TBA }} | {{Optimal ET sequence||legend=1|TBA }} | ||
[[Badness]] (Sintel): TBA | [[Badness]] (Sintel): TBA | ||
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== Etymology == | == Etymology == | ||
The name ''tredekisma'' comes from ''tredek'', which is one step of [[270edo]], | This comma was named by [[Eufalesio]] in 2026. The name ''tredekisma'' comes from ''tredek'', which is the name of one step of [[270edo]] by [[Joseph Monzo]], and 270edo is an excellent 2.3.5.7.11.13.19-subgroup system that tempers it out. | ||
[[Category:Commas named for their regular temperament properties]] | [[Category:Commas named for their regular temperament properties]] | ||
Latest revision as of 13:27, 12 April 2026
| Interval information |
19o^43o1u^4zg4,
Quadno-athoquadlu-azogu comma
reduced
11859211/11859210, the tredekisma, is the smallest superparticular ratio in the 19-limit and 23-limit.
It can be seen as the difference between a stack of four 38/33's and a stack consisting of 10/7 and 16/13: (38/33)4/((10/7)⋅(16/13)).
A possible S-expression of it is (S76⋅S441)/(S77⋅S324).
Temperaments
Only being 0.00014 cents, it is an insanely, unfathomably narrow comma; hundreds of times narrower than well known atomic commas like the chalmersia and Kirnberger's atom. As such, tempering out or fudging this alone either way is aurally identical to JI to human ears. It is tempered out in notable edos like 24, 84, 94, 118, 152, 176, 364, 388, 624, 742, 3125, 8269, 8539, … among others. It is also tempered out in any union between these edos, such as vishnu and gariwizmic.
Tredekic
Subgroup: 2.3.5.7.11.13.19
| [⟨ | 1 | 0 | 0 | 0 | 0 | 1 | 0 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 1 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 3 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | -4 | 1 | ]] |
- mapping generators: ~2, ~3, ~5, ~7, ~11, ~133/33
Optimal tunings: TBA
Badness (Sintel): TBA
Tredekismic
Subgroup: 2.3.5.7.11.13.17.19
| [⟨ | 1 | 0 | 0 | 0 | 0 | 1 | 0 | ], | |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 3 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | -4 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ]] |
- mapping generators: ~2, ~3, ~5, ~7, ~11, ~17, ~133/33
Optimal tunings: TBA
Optimal ET sequence: TBA
Badness (Sintel): TBA
Etymology
This comma was named by Eufalesio in 2026. The name tredekisma comes from tredek, which is the name of one step of 270edo by Joseph Monzo, and 270edo is an excellent 2.3.5.7.11.13.19-subgroup system that tempers it out.