12276edo: Difference between revisions

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~~==Theory==~~

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.

~~===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|tuning units]].

In addition, 12276edo tempers out the [[septimal ruthenia]], meaning that [[64/63]] is exactly 1/~~44th~~ 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]], 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.

=== Prime harmonics ===

=== 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.

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

[[Category:12276edo| ]]

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 {{Infobox ET}}
 {{EDO intro|12276}}
-==Theory==
-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.
-===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|tuning units]].
-In addition, 12276edo tempers out the [[septimal ruthenia]], meaning that [[64/63]] is exactly 1/44th 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]], 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.
+=== Prime harmonics ===
+{{Harmonics in equal|12276|columns=11}}
+=== 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.
 [[Category:Equal divisions of the octave|#####]] <!-- 5-digit number -->
+[[Category:12276edo| ]] <!-- main article -->