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'''.

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~~.

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 ===

=== Subsets and supersets ===

12276edo factors into primes as {{nowrap| 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.

[[Category:3-limit record edos|#####]]

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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'''.
+{{Infobox ET}}
+{{ED intro}}
-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.
+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 ===
+{{Harmonics in equal|12276|columns=11}}
+=== Subsets and supersets ===
+edo factors into primes as {{nowrap| 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.
+[[Category:3-limit record edos|#####]] <!-- 5-digit number -->