581edo: Difference between revisions
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The ''581 equal division'' divides the octave into 581 equal steps of 2.065 cents each. It is a very strong 19- and 23-limit system, uniquely [[consistent|consistent]] to the 25-limit. It tempers out 2401/2400 in the 7-limit, 3025/2025, 19712/19683, 151263/151250 in the 11-limit, and 2080/2079, 4096/4095, 4225/4224, 6656/6655 and 10648/10647 in the 13-limit. It [[support]]s and gives a good tuning for the 41&229 microtemperament, which has a neutral thirds generator. It is the first division after 270 with a lower 19-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]], and the first past 311 with a lower 23-limit relative error, and not until [[1578edo|1578]] do we reach a lower 23-limit relative error. | The '''581 equal division''' divides the octave into 581 equal steps of 2.065 cents each. It is a very strong 19- and 23-limit system, uniquely [[consistent|consistent]] to the 25-limit. It tempers out 2401/2400 in the 7-limit, 3025/2025, 19712/19683, 151263/151250 in the 11-limit, and 2080/2079, 4096/4095, 4225/4224, 6656/6655 and 10648/10647 in the 13-limit. It [[support]]s and gives a good tuning for the 41&229 microtemperament, which has a neutral thirds generator. It is the first division after 270 with a lower 19-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]], and the first past 311 with a lower 23-limit relative error, and not until [[1578edo|1578]] do we reach a lower 23-limit relative error. | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | |||
Revision as of 01:02, 4 July 2022
The 581 equal division divides the octave into 581 equal steps of 2.065 cents each. It is a very strong 19- and 23-limit system, uniquely consistent to the 25-limit. It tempers out 2401/2400 in the 7-limit, 3025/2025, 19712/19683, 151263/151250 in the 11-limit, and 2080/2079, 4096/4095, 4225/4224, 6656/6655 and 10648/10647 in the 13-limit. It supports and gives a good tuning for the 41&229 microtemperament, which has a neutral thirds generator. It is the first division after 270 with a lower 19-limit relative error, and the first past 311 with a lower 23-limit relative error, and not until 1578 do we reach a lower 23-limit relative error.