5040edo

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

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