Nexus comma: Difference between revisions

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== 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 [[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]]).

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 [[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. Furthermore, the name has 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, and, splitting both the [[perfect fourth]] into two [[semifourth]]s, the latter in turn splitting the [[Pythagorean limma]] into two as well.

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]].

@@ Line 14: / Line 14: @@
 == 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 [[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]]).
+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 [[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.  Furthermore, the name has 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, and, splitting both the [[perfect fourth]] into two [[semifourth]]s, the latter in turn splitting the [[Pythagorean limma]] into two as well.
+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]].