12276edo: Difference between revisions

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~~The 12276~~ division ~~divides~~ the octave into ~~equal steps~~ of ~~size~~ 0.~~097752~~ cents. This creates a unit known as the '''prima,''' useful for measurement of 11-limit intervals and commas. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220. A prima is almost exactly three '''tuning units'''.

'''12276EDO''' is the [[EDO|equal division of the octave]] into 12276 parts of exact 0.09775171 cents each. This creates a unit known as the '''prima,''' useful for measurement of 11-limit intervals and commas. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220. A prima is almost exactly three '''tuning units'''.

12276 is a strong 11-limit system, with a lower 11-limit relative error than any division aside from [[6691edo|6691]]. It factors as 12276 = 2^2 * 3^2 * 11 * 31, and among its divisors are [[12edo|12]], [[22edo|22]], [[31edo|31]], [[99edo|99]] and [[198edo|198]]. 12276 tempers out the atom, so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively.

[[Category:Edo]]

[[Category:Theory]]

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-The 12276 division divides the octave into equal steps of size 0.097752 cents. This creates a unit known as the '''prima,''' useful for measurement of 11-limit intervals and commas. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220. A prima is almost exactly three '''tuning units'''.
+'''12276EDO''' is the [[EDO|equal division of the octave]] into 12276 parts of exact 0.09775171 cents each. This creates a unit known as the '''prima,''' useful for measurement of 11-limit intervals and commas. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220. A prima is almost exactly three '''tuning units'''.
 is a strong 11-limit system, with a lower 11-limit relative error than any division aside from [[6691edo|6691]]. It factors as 12276 = 2^2 * 3^2 * 11 * 31, and among its divisors are [[12edo|12]], [[22edo|22]], [[31edo|31]], [[99edo|99]] and [[198edo|198]]. 12276 tempers out the atom, so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively.
+[[Category:Edo]]
+[[Category:Theory]]