12276edo: Difference between revisions
Jump to navigation
Jump to search
m Removing from Category:Theory using Cat-a-lot |
m Sort key |
||
| Line 3: | Line 3: | ||
12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo|6691]]. It factors as 12276 = 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]]. 12276 tempers out the [[Kirnberger's atom|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]]. It factors as 12276 = 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]]. 12276 tempers out the [[Kirnberger's atom|atom]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively. | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave|#####]] <!-- 5-digit number --> | ||
Revision as of 01:41, 4 July 2022
12276EDO is the equal division of the octave into 12276 parts of exactly 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 lower division aside from 6691. It factors as 12276 = 22 × 32 × 11 × 31, and among its divisors are 12, 22, 31, 99 and 198. 12276 tempers out the atom, so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively.