Nexus comma: Difference between revisions

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The '''~~nexuma~~''', or '''nexus comma''', is an [[11-limit]] [[unnoticeable comma]] with a ratio of '''1771561/1769472''' ~~= {{Monzo|-16 -3 0 0 6}}~~ and a value of approximately 2.~~04265 cents~~. It is the ~~sum~~ of ~~the~~ [[~~32805~~/~~32768|schisma~~]] ~~and the~~ [[~~parimo~~]], ~~as well as~~ the amount by which a stack of three [[~~128~~/~~121~~]] ~~undecimal diatonic semitones~~ fall 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 both the ~~important~~ functions of the ~~3-limit~~ and the ~~fact~~ that the 11-limit is [[~~User:Aura/Aura%27s_Ideas_on_Tonality#Navigational_Primes_and_the_Parachromatic~~-~~Paradiatonic_Contrast|demonstrably~~]] the ~~best p~~-limit for ~~representing~~ quartertones, ~~lends itself~~ to ~~this temperament being dubbed '''nexus temperament'''-~~ the ~~source~~ of the comma~~'s names~~.

{{Infobox Interval

| Ratio = 1771561/1769472

| Name = diatonic-paradiatonic nexus comma, nexus comma, nexisma, nexuma

| Color name = Tribilo comma

| Comma = yes

}}

The '''diatonic-paradiatonic nexus comma''', otherwise known as the '''nexus comma''', 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]] Axirabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96 intervals exceeds the octave. It is also the amount by which a stack of six [[12/11]] neutral seconds fall short of a [[27/16]] major sixth, the interval that separates [[243/242|rastma]] and the [[Alpharabian comma]], and the result of stacking the [[32805/32768|schisma]] and the [[parimo]].

== Temperaments and Name ==

Tempering out this comma in the full 11-limit leads to the rank-4 [[nexus family #Nexus|nexus]] temperament, or, in the 2.3.11 subgroup, the rank-2 [[tribilo family #Tribilo|tribilo]] temperament. Either way, it 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 [[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. Furthermore, the names have since turned out to be justified in light of the comma's additional functions, such as splitting the [[Pythagorean comma]] into three instances of the rastma, splitting the [[perfect fourth]] into two [[semifourth]]s, and in turn splitting the [[Pythagorean limma]] into two as well – all functions that contribute to both diatonic and paradiatonic significance, hence the longer descriptive name "diatonic-paradiatonic nexus comma".

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 of various ranks that temper out the nexus comma, see [[the Nexus]].

== See also ==

* [[Unnoticeable comma]]

[[Category:Alpharabian]]

[[Category:Nexus]]

[[Category:Commas named for their regular temperament properties]]

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-The '''nexuma''', or '''nexus comma''', is an [[11-limit]] [[unnoticeable comma]] with a ratio of '''1771561/1769472''' = {{Monzo|-16 -3 0 0 6}} and a value of approximately 2.04265 cents.  It is the sum of the [[32805/32768|schisma]] and the [[parimo]], as well as the amount by which a stack of three [[128/121]] undecimal diatonic semitones fall 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 both the important functions of the 3-limit and the fact that the 11-limit is [[User:Aura/Aura%27s_Ideas_on_Tonality#Navigational_Primes_and_the_Parachromatic-Paradiatonic_Contrast|demonstrably]] the best p-limit for representing quartertones, lends itself to this temperament being dubbed '''nexus temperament'''- the source of the comma's names.
+{{Infobox Interval
+| Ratio = 1771561/1769472
+| Name = diatonic-paradiatonic nexus comma, nexus comma, nexisma, nexuma
+| Color name = Tribilo comma
+| Comma = yes
+}}
+The '''diatonic-paradiatonic nexus comma''', otherwise known as the '''nexus comma''', 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]] Axirabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96 intervals exceeds the octave. It is also the amount by which a stack of six [[12/11]] neutral seconds fall short of a [[27/16]] major sixth, the interval that separates [[243/242|rastma]] and the [[Alpharabian comma]], and the result of stacking the [[32805/32768|schisma]] and the [[parimo]].
+== Temperaments and Name ==
+Tempering out this comma in the full 11-limit leads to the rank-4 [[nexus family #Nexus|nexus]] temperament, or, in the 2.3.11 subgroup, the rank-2 [[tribilo family #Tribilo|tribilo]] temperament.  Either way, it 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 [[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.  Furthermore, the names have since turned out to be justified in light of the comma's additional functions, such as splitting the [[Pythagorean comma]] into three instances of the rastma, splitting the [[perfect fourth]] into two [[semifourth]]s, and in turn splitting the [[Pythagorean limma]] into two as well – all functions that contribute to both diatonic and paradiatonic significance, hence the longer descriptive name "diatonic-paradiatonic nexus comma".
+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 of various ranks that temper out the nexus comma, see [[the Nexus]].
+== See also ==
+* [[Unnoticeable comma]]
+[[Category:Alpharabian]]
+[[Category:Nexus]]
+[[Category:Commas named for their regular temperament properties]]