Semicanousma: Difference between revisions
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The '''semicanousma''', 14641/14580 = {{monzo| -2 -6 -1 0 4 }}, is an [[11-limit]] [[comma]] measuring about 7.2 [[cent]]s, named for the fact that it is one of the commas tempered out in the [[semicanou]] temperament. | The '''semicanousma''', 14641/14580 = {{monzo| -2 -6 -1 0 4 }}, is an [[11-limit]] [[comma]] measuring about 7.2 [[cent]]s, named for the fact that it is one of the commas tempered out in the [[semicanou]] temperament. It is the amount by which a stack of four [[11/9|Alpharabian artoneutral thirds (11/9)]] exceeds the [[20/9|ptolemaic ninth (20/9)]]. It is also the difference between [[121/120]] (biyatisma) and [[243/242]] (rastma). | ||
== Temperaments == | == Temperaments == | ||
Tempering it out leads to the rank-4 '''semicanousmic temperament''', which splits the [[81/80|syntonic comma]] into two equal parts, each representing 121/120~243/242, so | Tempering it out leads to the rank-4 '''semicanousmic temperament''', which splits the [[81/80|syntonic comma]] into two equal parts, each representing 121/120~243/242, so the comma can be said to be the undecimal counterpart of both [[3136/3125|hemimean]] and [[canousma]]. It also identifies [[20/11]] by three [[11/9]]'s stacked, so an octave is divided into 11/9-11/9-11/9-[[11/10]]. | ||
== See also == | == See also == | ||
Revision as of 09:24, 12 February 2024
| Interval information |
The semicanousma, 14641/14580 = [-2 -6 -1 0 4⟩, is an 11-limit comma measuring about 7.2 cents, named for the fact that it is one of the commas tempered out in the semicanou temperament. It is the amount by which a stack of four Alpharabian artoneutral thirds (11/9) exceeds the ptolemaic ninth (20/9). It is also the difference between 121/120 (biyatisma) and 243/242 (rastma).
Temperaments
Tempering it out leads to the rank-4 semicanousmic temperament, which splits the syntonic comma into two equal parts, each representing 121/120~243/242, so the comma can be said to be the undecimal counterpart of both hemimean and canousma. It also identifies 20/11 by three 11/9's stacked, so an octave is divided into 11/9-11/9-11/9-11/10.
See also
- Rank-4 temperament #Semicanousmic (14641/14580)
- Semicanousmic clan, the clan of rank-3 temperaments where it is tempered out
- Small comma