2684edo: Difference between revisions
Jump to navigation
Jump to search
Cleanup and +prime error table |
A simpler comma basis |
||
| Line 1: | Line 1: | ||
The '''2684 equal divisions of the octave''' divides the octave into 2684 equal parts of 0.4471 [[cent]]s each. It is a very strong 13-limit tuning, with a lower 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any division until we reach [[5585edo]]. It is distinctly consistent though the [[17-odd-limit]], and is both a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak and zeta integral edo]]. A basis for its 13-limit commas is {9801/9800, 10648/10647, 196625/196608, 823680/823543 | The '''2684 equal divisions of the octave''' divides the octave into 2684 equal parts of 0.4471 [[cent]]s each. It is a very strong 13-limit tuning, with a lower 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any division until we reach [[5585edo]]. It is distinctly consistent though the [[17-odd-limit]], and is both a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak and zeta integral edo]]. A basis for its 13-limit commas is {9801/9800, 10648/10647, 140625/140608, 196625/196608, 823680/823543}; it also tempers out 123201/123200. It factors as 2<sup>2</sup> × 11 × 61, with divisors 2, 4, 11, 22, 44, 61, 122, 244, 615, and 1230. | ||
{{Primes in edo|2684}} | {{Primes in edo|2684}} | ||
Revision as of 12:56, 21 October 2021
The 2684 equal divisions of the octave divides the octave into 2684 equal parts of 0.4471 cents each. It is a very strong 13-limit tuning, with a lower 13-limit relative error than any division until we reach 5585edo. It is distinctly consistent though the 17-odd-limit, and is both a zeta peak and zeta integral edo. A basis for its 13-limit commas is {9801/9800, 10648/10647, 140625/140608, 196625/196608, 823680/823543}; it also tempers out 123201/123200. It factors as 22 × 11 × 61, with divisors 2, 4, 11, 22, 44, 61, 122, 244, 615, and 1230.
Script error: No such module "primes_in_edo".