5040edo: Difference between revisions
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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. | 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. | ||
== Theory == | == Theory == | ||
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5040 is both a superabundant and a highly composite number, meaning its 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 abundance index of 5040 is about 2.84, or exactly 298/105. | 5040 is both a superabundant and a highly composite number, meaning its 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 abundance index of 5040 is about 2.84, or exactly 298/105. | ||
The best subgroup in the patent val for 5040edo is 2.7.13.17.29.31.41.47.61.67. | The best subgroup in the patent val for 5040edo is 2.7.13.17.29.31.41.47.61.67. In this subgroup, it makes a rank two temperament with 1111edo (1111 & 5040), which is from a numerical standpoint quite amusing - a repunit and a highly composite number. | ||
It tempers out [[9801/9800]] in the 11-limit. | It tempers out [[9801/9800]] in the 11-limit. | ||
5040 is a sum of 43 consecutive primes, running from 23 to 229 inclusive. | |||
== Scales == | == Scales == | ||