Nexus comma: Difference between revisions

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== Temperaments ==

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 [[~~nexus~~ family #Tribilo|tribilo]] temperament.

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.

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]]).

@@ Line 14: / Line 14: @@
 == Temperaments ==
-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 [[nexus family #Tribilo|tribilo]] temperament.
+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.
 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]]).