12276edo: Difference between revisions

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12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo|6691]]. 12276 tempers out the [[Kirnberger's atom|atom]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively~~. In addition~~, ~~12276edo tempers out the [[~~septimal ~~ruthenia]], meaning that [[64/63]]~~ is ~~exactly~~ 1/44 of the octave, or 279 ~~primas~~.

12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo|6691]]. 12276 tempers out the [[Kirnberger's atom|atom]] and the [[septimal ruthenia]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas, 240 and 220 steps respectively, and septimal comma is represented by 1/44 of the octave, 279 steps.

=== Prime harmonics ===

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=== Interval size measure ===

12276edo factors as 22 × 32 × 11 × 31, and among its divisors are [[12edo|12]], [[22edo|22]], [[31edo|31]], [[99edo|99]] and [[198edo|198]]. 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 unit]]s.

12276edo factors as 22 × 32 × 11 × 31, and among its divisors are [[12edo|12]], [[22edo|22]], [[31edo|31]], [[99edo|99]] and [[198edo|198]]. This creates a unit known as the ''[[prima]]'', useful for measurement of 11-limit intervals and commas. A prima is almost exactly three [[tuning unit]]s.

[[Category:Equal divisions of the octave|#####]]

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 {{EDO intro|12276}}
-is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo|6691]]. 12276 tempers out the [[Kirnberger's atom|atom]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively. In addition, 12276edo tempers out the [[septimal ruthenia]], meaning that [[64/63]] is exactly 1/44 of the octave, or 279 primas.
+is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo|6691]]. 12276 tempers out the [[Kirnberger's atom|atom]] and the [[septimal ruthenia]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas, 240 and 220 steps respectively, and septimal comma is represented by 1/44 of the octave, 279 steps.
 === Prime harmonics ===
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 === Interval size measure ===
-edo factors as 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31, and among its divisors are [[12edo|12]], [[22edo|22]], [[31edo|31]], [[99edo|99]] and [[198edo|198]]. 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 unit]]s.
+edo factors as 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31, and among its divisors are [[12edo|12]], [[22edo|22]], [[31edo|31]], [[99edo|99]] and [[198edo|198]]. This creates a unit known as the ''[[prima]]'', useful for measurement of 11-limit intervals and commas. A prima is almost exactly three [[tuning unit]]s.
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