6250/6237

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Interval information
Ratio 6250/6237
Factorization 2 × 3-4 × 55 × 7-1 × 11-1
Monzo [1 -4 5 -1 -1
Size in cents 3.604717¢
Names liganellus comma,
liganellisma,
liganelluma
FJS name [math]\text{dd}{-2}^{5,5,5,5,5}_{7,11}[/math]
Special properties reduced
Tenney height (log2 n⋅d) 25.2163
Weil height (max(n, d)) 6250
Benedetti height (n⋅d) 38981250
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.45403 bits
Comma size small
open this interval in xen-calc

6250/6237, the liganellus comma, otherwise known as the liganellisma, or – in the earliest materials where this comma is named – the liganelluma, is a small 11-limit comma with a value of roughly 3.6 cents. It is the difference between 100/99 (ptolemisma) and 126/125 (septimal semicomma), and between the symbiotic comma and the amity comma. In addition, it is the sum of 3025/3024 (lehmerisma) and 4000/3993 (wizardharry comma). The liganellus comma is also the interval that separates the keenanisma from the kleisma on one side, and from the undecimal hemifourths comma on the other. When this comma is tempered out, 80/77 – the difference between 5/4 and 77/64 – is equated with the major diesis of 648/625. Although this comma is more commonly tempered out as a byproduct of tempering out other commas, those temperaments in which this comma is tempered out in a linearly independent fashion are called "liganellus temperaments".

The term "liganellus", from which this comma's names are derived, is a portmanteau of Latin ligare (to tie, to bind[1]) and Latin anellus (refering to a little ring[2], including the sort which forms an element in a chain) that was coined in reference to the fact that 6250/6237 is tempered out in octoid, tritiklesmic, catakleismic, quadritikleismic, compton, unthirds, amity, alphaquarter, hanuman, and enlil (thus linking all of these temperaments together, hence Latin "ligare"), as well as to its aforementioned relationship with the keenanisma where it forms the "links" that make up the aforementioned chain (hence Latin "anellus").

See also

References