6250/6237: Difference between revisions
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'''6250/6237''', the '''liganelluma''' or '''liganellus comma''', a [[small comma|small]] [[11-limit]] comma with a value of roughly 3.6 [[cent]]s. It is the sum of the [[lehmerisma]] and the [[4000/3993|wizardharry comma]] and the difference between the [[symbiosma|symbiotic comma]] and the [[amity comma]]. The liganellus comma is also the interval that separates the [[385/384|keenaisma]] from the [[kleisma]] on one side, and from the undecimal hemifourths comma on the other. When this comma is tempered out, [[160/77]]- the difference between [[5/2]] and [[77/64]]- is equated with a stack of four [[6/5]] minor thirds, and a stack of five [[5/4]] major thirds is similarly equated with a stack consisting of an [[octave]] plus [[81/64]] plus 77/64. 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]]'''". | '''6250/6237''', the '''liganelluma''' or '''liganellus comma''', a [[small comma|small]] [[11-limit]] comma with a value of roughly 3.6 [[cent]]s. It is the sum of the [[lehmerisma]] and the [[4000/3993|wizardharry comma]] and the difference between the [[symbiosma|symbiotic comma]] and the [[amity comma]]. The liganellus comma is also the interval that separates the [[385/384|keenaisma]] from the [[kleisma]] on one side, and from the undecimal hemifourths comma on the other. When this comma is tempered out, [[160/77]]- the difference between [[5/2]] and [[77/64]]- is equated with a stack of four [[6/5]] minor thirds, and a stack of five [[5/4]] major thirds is similarly equated with a stack consisting of an [[octave]] plus [[81/64]] plus 77/64. 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 both of this comma's names are derived, is a | The term "liganellus", from which both of this comma's names are derived, is a portmanteau of Latin "ligans" (meaning "uniting") and Latin "anellus" (refering to a little ring, 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 [[Ragismic microtemperaments #Octoid|Octoid]], [[Kleismic family #Tritikleismic|Tritiklesmic]], [[Kleismic family #Catakleismic|Catakleismic]], [[Kleismic family #Quadritikleismic|Quadritikleismic]], [[Pythagorean family#Compton temperament|Compton]], [[Breedsmic temperaments #Unthirds|Unthirds]], [[Amity family|Amity]], [[Hemifamity temperaments #Alphaquarter|Alphaquarter]], [[Lehmerismic temperaments #Hanuman|Hanuman]], and [[Kleismic rank three family #Enlil|Enlil]] (thus linking all of these temperaments together, hence Latin "ligans"), as well as to its aforementioned relationship with the keenanisma (hence Latin "anellus", where this comma forms the "rings" that make up the aforementioned chain). | ||
[[Category:11-limit]] | [[Category:11-limit]] | ||
[[Category:Small comma]] | [[Category:Small comma]] | ||
[[Category:Liganellus]] | [[Category:Liganellus]] | ||
Revision as of 18:44, 25 December 2020
| Interval information |
liganellus comma
6250/6237, the liganelluma or liganellus comma, a small 11-limit comma with a value of roughly 3.6 cents. It is the sum of the lehmerisma and the wizardharry comma and the difference between the symbiotic comma and the amity comma. The liganellus comma is also the interval that separates the keenaisma from the kleisma on one side, and from the undecimal hemifourths comma on the other. When this comma is tempered out, 160/77- the difference between 5/2 and 77/64- is equated with a stack of four 6/5 minor thirds, and a stack of five 5/4 major thirds is similarly equated with a stack consisting of an octave plus 81/64 plus 77/64. 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 both of this comma's names are derived, is a portmanteau of Latin "ligans" (meaning "uniting") and Latin "anellus" (refering to a little ring, 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 "ligans"), as well as to its aforementioned relationship with the keenanisma (hence Latin "anellus", where this comma forms the "rings" that make up the aforementioned chain).