Triwellisma: Difference between revisions
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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. | 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. | ||
It factors into simpler commas as ([[2401/2400]])⋅([[3136/3125]]). | |||
== Temperaments == | == Temperaments == | ||
[[Tempering out]] this comma results in the triwellismic temperament. Some edos that temper it out are {{EDOs| 31, 99, 159, 258 and 487 }}. | [[Tempering out]] this comma results in the [[triwellismic]] temperament. Some edos that temper it out are {{EDOs| 31, 99, 159, 258 and 487 }}. | ||
== Etymology == | == Etymology == | ||
Latest revision as of 15:09, 13 July 2026
| 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.
It factors into simpler commas as (2401/2400)⋅(3136/3125).
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.