Nexus comma: Difference between revisions

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The '''nexus comma''', otherwise known as the '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – 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. In color notation, this same comma is referred to as the '''tribilo comma'''. 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 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, led to [[User:Aura|Aura]] considering the temperament that tempers out this comma to be some sort of "nexus temperament", which it turn gave rise to most 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 nexus comma, see [[the ~~nexus~~]].

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, led to [[User:Aura|Aura]] considering the temperament that tempers out this comma to be some sort of "nexus temperament", which it turn gave rise to most 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 nexus comma, see [[the Nexus]].

== Temperaments ==

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 The '''nexus comma''', otherwise known as the '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – 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.  In color notation, this same comma is referred to as the '''tribilo comma'''.  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 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, led to [[User:Aura|Aura]] considering the temperament that tempers out this comma to be some sort of "nexus temperament", which it turn gave rise to most 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 nexus comma, see [[the nexus]].
+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, led to [[User:Aura|Aura]] considering the temperament that tempers out this comma to be some sort of "nexus temperament", which it turn gave rise to most 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 nexus comma, see [[the Nexus]].
 == Temperaments ==