Nexus comma: Difference between revisions

Line 10:

== 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. 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".

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]]).

@@ Line 10: / Line 10: @@
 == 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.  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".
+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]]).