1729/1728: Difference between revisions
"Ramanujanismic chords" is to be created |
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Both the numerator and denominator of this interval are famous in mathematics. [[Wikipedia: 1728 (number)|1728]], being 12 to the 3rd power, is also known as mass. [[Wikipedia:1729 (number)|1729]] is known for being Ramanujan's number and the first number that can be expressed as the sum of two cubes in two different ways (1729 = 1<sup>3</sup> + 12<sup>3</sup> = 9<sup>3</sup> + 10<sup>3</sup>). | Both the numerator and denominator of this interval are famous in mathematics. [[Wikipedia: 1728 (number)|1728]], being 12 to the 3rd power, is also known as mass. [[Wikipedia:1729 (number)|1729]] is known for being Ramanujan's number and the first number that can be expressed as the sum of two cubes in two different ways (1729 = 1<sup>3</sup> + 12<sup>3</sup> = 9<sup>3</sup> + 10<sup>3</sup>). | ||
== Commatic relations == | |||
This comma is the difference between the following superparticular pairs: | |||
* [[91/90]] and [[96/95]] | |||
* [[133/132]] and [[144/143]] | |||
* [[273/272]] and [[324/323]] | |||
* [[325/324]] and [[400/399]] | |||
* [[361/360]] and [[456/455]] | |||
* [[385/384]] and [[495/494]] | |||
* [[513/512]] and [[729/728]] | |||
* [[1001/1000]] and [[2376/2375]] | |||
* [[1216/1215]] and [[4096/4095]] | |||
* [[1225/1224]] and [[4200/4199]] | |||
* [[1521/1520]] and [[12636/12635]] | |||
* [[1540/1539]] and [[14080/14079]] | |||
* [[1701/1700]] and [[104976/104975]] | |||
* [[1716/1715]] and [[228096/228095]] | |||
It factors into the following superparticular pairs: | |||
* [[2926/2925]] and [[4225/4224]] | |||
* [[2431/2430]] and [[5985/5984]] | |||
* [[2401/2400]] and [[6175/6174]] | |||
* [[2080/2079]] and [[10241/10240]] | |||
== Temperaments == | == Temperaments == | ||