5040edo: Difference between revisions
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'''5040 equal divisions of the octave''' divides the octave into steps of 0.238 cents each. | '''5040 equal divisions of the octave''' divides the octave into steps of 0.238 cents each. | ||
== Number history == | |||
5040 is a factorial (7! = 1 2 3 4 5 6 7), superabundant, and a highly composite number. | |||
Ancient Greek philosopher Plato suggested that 5040 is the ideal number of people in a city, owing to it's large divisibility and a bunch of other traits. | |||
5040 is a sum of 43 consecutive primes, running from 23 to 229 inclusive. | |||
== Theory == | == Theory == | ||
{{Primes in edo|5040|columns=20}} | {{Primes in edo|5040|columns=20}} | ||
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5040 is [[contorted]] order-4 in the 3-limit and contorted order-2 in the 5-limit in the 5040c val. In the 5040cdd val, it is contorted order 2 in the 7-limit and tempers out [[2401/2400]] and [[4375/4374]]. It tempers out [[9801/9800]] in the 11-limit. | 5040 is [[contorted]] order-4 in the 3-limit and contorted order-2 in the 5-limit in the 5040c val. In the 5040cdd val, it is contorted order 2 in the 7-limit and tempers out [[2401/2400]] and [[4375/4374]]. It tempers out [[9801/9800]] in the 11-limit. | ||
== Scales == | |||
* Consecutive[43] | |||
== References == | |||
* Wikipedia Contributors. [[Wikipedia:5040 (number)|5040 (number)]] | |||
* https://mathworld.wolfram.com/PlatosNumbers.html | |||