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]]'''. | ||
Revision as of 22:21, 4 October 2022
| ← 12275edo | 12276edo | 12277edo → |
(semiconvergent)
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.