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 | |||
Revision as of 13:05, 29 November 2021
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
Script error: No such module "primes_in_edo". 5040 is both a superabundant and a highly composite number, meaning it's amount of symmetrical chords and subscales increases to a record, and the amount of notes which make up those scales, if stretched end-to-end, also is largest relative to the number's size.
The best subgroup in the patent val for 5040edo is 2.7.13.17.29.31.41.47.61.67.
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. 5040 (number)
- https://mathworld.wolfram.com/PlatosNumbers.html