1729/1728: Difference between revisions
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Added FJS name, edited color name, misc. edits |
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 1729/1728 | | Ratio = 1729/1728 | ||
| Monzo = -6 -3 0 1 0 1 0 1 | | Monzo = -6 -3 0 1 0 1 0 1 | ||
| Cents = 1.00158 | | Cents = 1.00158 | ||
| Name = ramanujanisma | | Name = ramanujanisma | ||
| Color name = nothozo | | Color name = Nothozo, 19o3oz2, nothozo 2nd | ||
| FJS name = | | FJS name = d2<sup>7,13,19</sup> | ||
| Sound = | | Sound = | ||
}} | }} | ||
'''1729/1728''', known as the '''ramanujanisma''', is a [[19-limit]] (more accurately, 2.3.7.13.19 subgroup) [[superparticular]] interval and an [[unnoticeable comma]] that is remarkably close to one cent in size. It forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]], and less likely, the difference between [[19/18]] and [[96/91]]. | '''1729/1728''', known as the '''ramanujanisma''', is a [[19-limit]] (more accurately, 2.3.7.13.19 subgroup) [[superparticular]] interval and an [[unnoticeable comma]] that is remarkably close to one cent in size. It forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]], and less likely, the difference between [[19/18]] and [[96/91]]. | ||
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>). | ||
Tempering out this comma enables the '''ramanujanismic chords''', the [[essentially tempered chord]]s in the 19-odd-limit, a basic form of which comprises the steps of 7/6-13/12-19/12 closing at the octave. | Tempering out this comma enables the '''ramanujanismic chords''', the [[essentially tempered chord]]s in the 19-odd-limit, a basic form of which comprises the steps of 7/6-13/12-19/12 closing at the octave. | ||
== Terminology == | == Terminology == | ||