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 ==

[[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 ==

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 | Comma = yes
 }}
-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 ==
-[[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 ==