28812/28561: Difference between revisions

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'''28812/28561''' (the Tesseract Comma) is a small comma in the 2.3.7.13 subgroup. It is the amount by which four [[13/7]] sevenths fall short of the [[6/1|sixth harmonic]], and the amount by which four [[14/13]] semitones fall short of the [[4/3]] perfect fourth.

It can be factored into the [[28672/28561|Voltage Comma]] and the [[1029/1024|Gamelisma]], which provides the 77 & 87 temperament '''Cubical''' (see below); it can also be factored into the [[Octaphore]] plus four [[729/728|Squbemas]] (squbemae?), which makes the Tesseract Comma a useful extension to the rank-3 Octaphore ~~temperament~~.

It can be factored into the [[28672/28561|Voltage Comma]] and the [[1029/1024|Gamelisma]], which provides the 77 & 87 temperament '''Cubical''' (see below); it can also be factored into the [[Octaphore]] plus four [[729/728|Squbemas]] (squbemae?), which makes the Tesseract Comma a useful extension to the rank-3 Octaphore and to rank-2 Unicorn temperaments.

== Temperaments ==

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=== Other temperaments ===

Temperaments discussed elsewhere that temper out the Tesseract comma include:

Tridecimal Octaphore → [[Octaphore#Tridecimal%20Octaphore|Octaphore]]

2.3.5.7.13 subgroup Unicorn (+351/350 +126/125) → [[Unicorn family#2.3.5.7.13%20subgroup|Unicorn Family]]

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 '''28812/28561''' (the Tesseract Comma) is a small comma in the 2.3.7.13 subgroup.  It is the amount by which four [[13/7]] sevenths fall short of the [[6/1|sixth harmonic]], and the amount by which four [[14/13]] semitones fall short of the [[4/3]] perfect fourth.
-It can be factored into the [[28672/28561|Voltage Comma]] and the [[1029/1024|Gamelisma]], which provides the 77 & 87 temperament '''Cubical''' (see below); it can also be factored into the [[Octaphore]] plus four [[729/728|Squbemas]] (squbemae?), which makes the Tesseract Comma a useful extension to the rank-3 Octaphore temperament.
+It can be factored into the [[28672/28561|Voltage Comma]] and the [[1029/1024|Gamelisma]], which provides the 77 & 87 temperament '''Cubical''' (see below); it can also be factored into the [[Octaphore]] plus four [[729/728|Squbemas]] (squbemae?), which makes the Tesseract Comma a useful extension to the rank-3 Octaphore and to rank-2 Unicorn temperaments.
 == Temperaments ==
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 === Other temperaments ===
 Temperaments discussed elsewhere that temper out the Tesseract comma include:
+Tridecimal Octaphore → [[Octaphore#Tridecimal%20Octaphore|Octaphore]]
 .3.5.7.13 subgroup Unicorn (+351/350 +126/125) → [[Unicorn family#2.3.5.7.13%20subgroup|Unicorn Family]]