5040edo: Difference between revisions
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{{Primes in edo|5040|columns=20}} | {{Primes in edo|5040|columns=20}} | ||
{| class="wikitable" | {| class="wikitable" | ||
!Prime ''p'' | |||
|2 | |||
|3 | |||
|5 | |||
|7 | |||
|11 | |||
|13 | |||
|17 | |||
|19 | |||
|23 | |||
|- | |||
!Contorsion | !Contorsion | ||
order for 2.p | order for 2.''p'' | ||
subgroup | subgroup | ||
|5040 | |5040 | ||
|4 | |4 | ||
|3 | |3 | ||
|1 | |1 | ||
|12 | |12 | ||
|10 | |10 | ||
|63 | |63 | ||
|10 | |10 | ||
|7 | |7 | ||
|} | |} | ||
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. | 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. | ||
Revision as of 12:04, 5 January 2022
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
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| Prime p | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 |
|---|---|---|---|---|---|---|---|---|---|
| Contorsion
order for 2.p subgroup |
5040 | 4 | 3 | 1 | 12 | 10 | 63 | 10 | 7 |
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, ⟨5040 7988 11072 14148], it is contorted order 2 in the 7-limit and tempers out 2401/2400 and 4375/4374. Under such a val, the 5th harmonic comes from 315edo, and the 7th ultimately derives from 140edo.
It tempers out 9801/9800 in the 11-limit.
Scales
- Consecutive[43]
References
- Wikipedia Contributors. 5040 (number)
- https://mathworld.wolfram.com/PlatosNumbers.html