1920edo: Difference between revisions

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The '''1920 division''' divides the octave into 1920 equal parts of exactly 0.625 cents each. It is distinctly consistent through the 25 limit, and in terms of 23-limit [[Tenney-~~Euclidean_temperament_measures~~#TE simple badness|relative error]], only [[1578edo|1578]] and [[1889edo|1889]] are both smaller and with a lower relative error. In the 29-limit, only 1578 beats it, and in the 31, 37, 41, 43 and 47 ~~limits~~, nothing beats it. Because of this and because it is a ~~highly~~ composite number divisible by 12, it is another candidate for [[~~Interval_size_measure|~~interval size measure]].

The '''1920 division''' divides the octave into 1920 equal parts of exactly 0.625 cents each. It is distinctly [[consistent]] through the 25-odd-limit, and in terms of 23-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], only [[1578edo|1578]] and [[1889edo|1889]] are both smaller and with a lower relative error. In the 29-limit, only 1578 beats it, and in the 31-, 37-, 41-, 43- and 47-limit, nothing beats it. Because of this and because it is a very composite number divisible by 12, it is another candidate for [[interval size measure]].

1920 = 2^7 * 3 * 5; some of its divisors are [[10edo|10]], [[12edo|12]], [[15edo|15]], [[16edo|16]], [[24edo|24]], [[60edo|60]], [[80edo|80]], [[96edo|96]], [[128edo|128]], [[240edo|240]], [[320edo|320]] and [[640edo|640]].

=== Prime harmonics ===

=== Miscellany ===

1920 = 2<sup>7</sup> × 3 × 5; some of its divisors are [[10edo|10]], [[12edo|12]], [[15edo|15]], [[16edo|16]], [[24edo|24]], [[60edo|60]], [[80edo|80]], [[96edo|96]], [[128edo|128]], [[240edo|240]], [[320edo|320]] and [[640edo|640]].

[[Category:Equal divisions of the octave|####]]

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 {{Infobox ET}}
-The '''1920 division''' divides the octave into 1920 equal parts of exactly 0.625 cents each. It is distinctly consistent through the 25 limit, and in terms of 23-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]], only [[1578edo|1578]] and [[1889edo|1889]] are both smaller and with a lower relative error. In the 29-limit, only 1578 beats it, and in the 31, 37, 41, 43 and 47 limits, nothing beats it. Because of this and because it is a highly composite number divisible by 12, it is another candidate for [[Interval_size_measure|interval size measure]].
+The '''1920 division''' divides the octave into 1920 equal parts of exactly 0.625 cents each. It is distinctly [[consistent]] through the 25-odd-limit, and in terms of 23-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], only [[1578edo|1578]] and [[1889edo|1889]] are both smaller and with a lower relative error. In the 29-limit, only 1578 beats it, and in the 31-, 37-, 41-, 43- and 47-limit, nothing beats it. Because of this and because it is a very composite number divisible by 12, it is another candidate for [[interval size measure]].
-= 2^7 * 3 * 5; some of its divisors are [[10edo|10]], [[12edo|12]], [[15edo|15]], [[16edo|16]], [[24edo|24]], [[60edo|60]], [[80edo|80]], [[96edo|96]], [[128edo|128]], [[240edo|240]], [[320edo|320]] and [[640edo|640]].
+=== Prime harmonics ===
+{{Harmonics in equal|1920|columns=11}}
+=== Miscellany ===
+= 2<sup>7</sup> × 3 × 5; some of its divisors are [[10edo|10]], [[12edo|12]], [[15edo|15]], [[16edo|16]], [[24edo|24]], [[60edo|60]], [[80edo|80]], [[96edo|96]], [[128edo|128]], [[240edo|240]], [[320edo|320]] and [[640edo|640]].
 [[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->