Triwellisma: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = | | Name = Triwellisma | ||
| Monzo = 1 -1 -7 6 | | Monzo = 1 -1 -7 6 | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
The ''' | The '''triwellisma''' is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 6.8 [[cent]]s. It has the [[monzo]] {{monzo| 1 -1 -7 6 }} and the ratio 235298/234375. It is the amount by which a stack of six [[7/5]]'s [[octave reduction|octave reduced]] exceeds [[15/8]], or by which a stack of seven 7/5's octave reduced exceeds 21/16. Note that two 7/5's make [[49/25]], which is short of the octave by [[50/49]], so in other words, this comma is the difference between [[16/15]] and a stack of three 50/49's. | ||
== Temperaments == | |||
[[Tempering out]] this comma results in the triwellismic temperament. Some edos that temper it out are {{EDOs| 31, 99, 159, 258 and 487 }}. | |||
[[Category:Commas | == Etymology == | ||
This comma was named by [[Xenllium]] in 2021 after the [[triwell]] temperament, in which it is the second simplest comma. | |||
[[Category:Triwellismic]] | |||
[[Category:Commas named for their regular temperament properties]] | |||
Latest revision as of 12:44, 2 November 2025
| Interval information |
The triwellisma is a small 7-limit comma measuring about 6.8 cents. It has the monzo [1 -1 -7 6⟩ and the ratio 235298/234375. It is the amount by which a stack of six 7/5's octave reduced exceeds 15/8, or by which a stack of seven 7/5's octave reduced exceeds 21/16. Note that two 7/5's make 49/25, which is short of the octave by 50/49, so in other words, this comma is the difference between 16/15 and a stack of three 50/49's.
Temperaments
Tempering out this comma results in the triwellismic temperament. Some edos that temper it out are 31, 99, 159, 258 and 487.
Etymology
This comma was named by Xenllium in 2021 after the triwell temperament, in which it is the second simplest comma.