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 [[12/1|twelfth harmonic]], and the amount by which four [[14/13]] semitones | '''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 [[12/1|twelfth harmonic]], and the amount by which four [[14/13]] semitones exceed 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]], which makes the tesseract comma a useful extension to the rank-3 octaphore and to rank-2 unicorn temperaments. | 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]], which makes the tesseract comma a useful extension to the rank-3 octaphore and to rank-2 unicorn temperaments. | ||
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{{Optimal ET sequence|legend=1| 9, 10, 19, 29, 37b, 48, 49f, 58, 67, 68, 77, 87 }} | {{Optimal ET sequence|legend=1| 9, 10, 19, 29, 37b, 48, 49f, 58, 67, 68, 77, 87 }} | ||
[[Badness]] ( | [[Badness]] (Sintel): 2.528 | ||
==== 2.3.5.7.13 subgroup ==== | ==== 2.3.5.7.13 subgroup ==== | ||