2964edo: Difference between revisions
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In the 13-limit, 2964edo shares the same [[patent val]] with [[494edo]] except for the [[7/1|7th harmonic]], which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is the denominator to a [[convergent]] to log<sub>2</sub>7. Bordering 2964edo's patent val 7/1 on either side are [[26edo]]'s sharp approximation and [[57edo]]'s flat approximation of 7/1, having nearly identical 0.4048{{c}} errors; 2964edo exactly divides the octave into 26 and into 57 equal steps, splitting the difference between 160\57 and 73\26, as 2964 is expressible as {{nowrap|26 × 57 × 2}}. | In the 13-limit, 2964edo shares the same [[patent val]] with [[494edo]] except for the [[7/1|7th harmonic]], which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is the denominator to a [[convergent]] to log<sub>2</sub>7. Bordering 2964edo's patent val 7/1 on either side are [[26edo]]'s sharp approximation and [[57edo]]'s flat approximation of 7/1, having nearly identical 0.4048{{c}} errors; 2964edo exactly divides the octave into 26 and into 57 equal steps, splitting the difference between 160\57 and 73\26, as 2964 is expressible as {{nowrap|26 × 57 × 2}}. | ||
A basis for the 13-limit commas consists of [[4225/4224]], [[6656/6655]], and [[43940/43923]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||