12276edo: Difference between revisions
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'''12276EDO''' is the [[EDO|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 unit|tuning units]]'''. | '''12276EDO''' is the [[EDO|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 unit|tuning units]]'''. | ||
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 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]] | ||
[[Category:Theory]] | [[Category:Theory]] | ||