Nexus comma: Difference between revisions

Line 10:

}}

The '''nexus comma''', otherwise known as the '''nexisma''', or- in the earliest materials where this comma is named- the '''nexuma''', is an [[11-limit]] [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. It is the ~~sum~~ of ~~the~~ [[~~32805~~/~~32768|schisma~~]] ~~and the~~ [[~~parimo~~]], the difference between the [[243/242|rastma]] and the [[Alpharabian comma]], ~~and~~ the ~~amount by which a stack~~ of ~~three~~ [[~~128~~/~~121~~]] ~~Alpharabian diatonic semitones falls short of a~~ [[~~32/27~~]] ~~minor third~~. Tempering it out leads to the joining of the [[11-limit]] and the [[3-limit]], a fact which, in light of the importance of both p-limits, lends itself to this temperament being dubbed the "'''nexus temperament'''"- the source of this comma's names. While the importance of the 3-limit is generally accepted (see [[Pythagorean tuning]], [[circle of fifths]], [[FJS]], [[Helmholtz-Ellis notation]]), it can be derived mathematically that the 11-limit is an excellent basis for quartertones in terms of ratio simplicity, and the 11-limit can be shown to host a clear sequence of intervals in which every other member is the octave complement of what is effectively a stack of 128/121 diatonic semitones (see [[Alpharabian tuning]]). For a list of temperaments that temper out the nexuma, see [[nexus family]].

The '''nexus comma''', otherwise known as the '''nexisma''', or – in the earliest materials where this comma is named – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. It is the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96's exceeds of the octave. It is also the difference between the [[243/242|rastma]] and the [[Alpharabian comma]], or the sum of the [[32805/32768|schisma]] and the [[parimo]]. Tempering it out leads to the joining of the [[11-limit]] and the [[3-limit]], a fact which, in light of the importance of both p-limits, lends itself to this temperament being dubbed the '''nexus temperament''' – the source of this comma's names. While the importance of the 3-limit is generally accepted (see [[Pythagorean tuning]], [[circle of fifths]], [[FJS]], [[Helmholtz-Ellis notation]]), it can be derived mathematically that the 11-limit is an excellent basis for quartertones in terms of ratio simplicity, and the 11-limit can be shown to host a clear sequence of intervals in which every other member is the octave complement of what is effectively a stack of 128/121 diatonic semitones (see [[Alpharabian tuning]]). For a list of temperaments that temper out the nexuma, see [[nexus family]].

[[Category:11-limit]]

@@ Line 10: / Line 10: @@
 }}
-The '''nexus comma''', otherwise known as the '''nexisma''', or- in the earliest materials where this comma is named- the '''nexuma''', is an [[11-limit]] [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents.  It is the sum of the [[32805/32768|schisma]] and the [[parimo]], the difference between the [[243/242|rastma]] and the [[Alpharabian comma]], and the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third.  Tempering it out leads to the joining of the [[11-limit]] and the [[3-limit]], a fact which, in light of the importance of both p-limits, lends itself to this temperament being dubbed the "'''nexus temperament'''"- the source of this comma's names.  While the importance of the 3-limit is generally accepted (see [[Pythagorean tuning]], [[circle of fifths]], [[FJS]], [[Helmholtz-Ellis notation]]), it can be derived mathematically that the 11-limit is an excellent basis for quartertones in terms of ratio simplicity, and the 11-limit can be shown to host a clear sequence of intervals in which every other member is the octave complement of what is effectively a stack of 128/121 diatonic semitones (see [[Alpharabian tuning]]).  For a list of temperaments that temper out the nexuma, see [[nexus family]].
+The '''nexus comma''', otherwise known as the '''nexisma''', or – in the earliest materials where this comma is named – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. It is the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96's exceeds of the octave. It is also the difference between the [[243/242|rastma]] and the [[Alpharabian comma]], or the sum of the [[32805/32768|schisma]] and the [[parimo]]. Tempering it out leads to the joining of the [[11-limit]] and the [[3-limit]], a fact which, in light of the importance of both p-limits, lends itself to this temperament being dubbed the '''nexus temperament''' – the source of this comma's names. While the importance of the 3-limit is generally accepted (see [[Pythagorean tuning]], [[circle of fifths]], [[FJS]], [[Helmholtz-Ellis notation]]), it can be derived mathematically that the 11-limit is an excellent basis for quartertones in terms of ratio simplicity, and the 11-limit can be shown to host a clear sequence of intervals in which every other member is the octave complement of what is effectively a stack of 128/121 diatonic semitones (see [[Alpharabian tuning]]). For a list of temperaments that temper out the nexuma, see [[nexus family]].
 [[Category:11-limit]]