6250/6237: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Name = liganellus comma, liganellisma, liganelluma
| Name = liganellus comma, liganellisma
| Color name = 1ury<sup>5</sup>-2, luruquinyo negative 2nd
| Color name = 1ury<sup>5</sup>-2, luruquinyo negative 2nd
| Comma = yes
| Comma = yes
}}
}}
'''6250/6237''', the '''liganellus comma''' or the '''liganellisma''', is a [[small comma|small]] [[11-limit]] [[comma]] with a value of roughly 3.6 [[cent]]s.


'''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 comma|small]] [[11-limit]] comma with a value of roughly 3.6 [[cent]]s. It is the difference between [[100/99|100/99 (ptolemisma)]] and [[126/125|126/125 (septimal semicomma)]], and between the [[symbiotic comma]] and the [[amity comma]]. In addition, it is the sum of [[3025/3024|3025/3024 (lehmerisma)]] and [[4000/3993|4000/3993 (wizardharry comma)]].  The liganellus comma is also the interval that separates the [[385/384|keenanisma]] from the [[kleisma]] on one side, and from the [[seascape 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]]".
It is the difference between [[100/99|100/99 (ptolemisma)]] and [[126/125|126/125 (starling comma)]], and between the [[symbiotic comma]] and the [[amity comma]]. It is also the interval that separates the [[385/384|keenanisma]] from the [[15625/15552|kleisma]] on one side, and from the [[seascape comma]] on the other. It factors into simpler commas as ([[3025/3024]])⋅([[4000/3993]]).  


The term "liganellus", from which this comma's names are derived, is a portmanteau of Latin ''ligare'' (to ''tie'', to ''bind''<ref>[[Wiktionary: ligo #Latin]]</ref>) and Latin ''anellus'' (refering to a little ring<ref>[[Wiktionary: anellus #Latin]]</ref>, 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]], [[tritikleismic]], [[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").
== Temperaments ==
[[Tempering out]] this comma leads to the rank-4 '''liganellus''' temperament, in which [[80/77]] the difference between [[5/4]] and [[77/64]] – is equated with the major diesis of [[648/625]]. It is commonly tempered out as a byproduct of tempering out other commas.  


== See also ==
== Etymology ==
* [[Small comma]]
This comma was named by [[Aura]] in 2020. In the earliest materials where this comma is named, it was known as the ''liganelluma''. The term ''liganellus'', from which this comma's names are derived, is a portmanteau of Latin ''ligare'' ("to tie", "to bind"<ref>[[Wiktionary: ligo #Latin]]</ref>) and Latin ''anellus'' (referring to a little ring<ref>[[Wiktionary: anellus #Latin]]</ref>, 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]], [[tritikleismic]], [[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'').


== References ==
== References ==

Latest revision as of 13:08, 12 July 2026

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
Color name 1ury5-2, luruquinyo negative 2nd
FJS name [math]\displaystyle{ \text{dd}{-2}^{5,5,5,5,5}_{7,11} }[/math]
Special properties reduced
Tenney norm (log2 nd) 25.2163
Weil norm (log2 max(n, d)) 25.2193
Wilson norm (sopfr(nd)) 57
Comma size small
Open this interval in xen-calc

6250/6237, the liganellus comma or the liganellisma, 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 (starling comma), and between the symbiotic comma and the amity comma. It is also the interval that separates the keenanisma from the kleisma on one side, and from the seascape comma on the other. It factors into simpler commas as (3025/3024)⋅(4000/3993).

Temperaments

Tempering out this comma leads to the rank-4 liganellus temperament, in which 80/77 – the difference between 5/4 and 77/64 – is equated with the major diesis of 648/625. It is commonly tempered out as a byproduct of tempering out other commas.

Etymology

This comma was named by Aura in 2020. In the earliest materials where this comma is named, it was known as the liganelluma. 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 (referring 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, tritikleismic, 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).

References