12276edo: Difference between revisions
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{{EDO intro|12276}} | |||
==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 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. | |||
[[Category:Equal divisions of the octave|#####]] <!-- 5-digit number --> | [[Category:Equal divisions of the octave|#####]] <!-- 5-digit number --> | ||
Revision as of 15:36, 21 December 2022
| ← 12275edo | 12276edo | 12277edo → |
(semiconvergent)
Theory
12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from 6691. 12276 tempers out the 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 12, 22, 31, 99 and 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 units.
In addition, 12276edo tempers out the septimal ruthenia, meaning that 64/63 is exactly 1/44th of the octave, or 279 primas.