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.

581edo is a very strong 19- and 23-limit system, distinctly [[consistent]] to the [[25-odd-limit]]. It tempers out [[2401/2400]] in the 7-limit, [[3025/3024]], [[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 [[newt]], 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|###]]

[[Category:Newt]]

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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&amp;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.
+{{EDO intro|581}}
+edo is a very strong 19- and 23-limit system, distinctly [[consistent]] to the [[25-odd-limit]]. It tempers out [[2401/2400]] in the 7-limit, [[3025/3024]], [[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 [[newt]], the 41 &amp; 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.
+{{Harmonics in equal|581|columns=11}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+[[Category:Newt]]