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]]. | 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]] | 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 "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 [[nexus family]]. | ||
== Temperaments == | |||
In rank-2 environments, tempering it out in the full 11-limit leads to the [[nexus family #nexal family|nexal]] temperament, enabling [[nexal chords]], or, in the 2.3.11 subgroup, the [[nexus family #nexal family|tribilo]] temperament, enabling [[tribilo chords]]. | |||
[[Category:11-limit]] | [[Category:11-limit]] | ||
Revision as of 13:48, 19 April 2021
| Interval information |
nexisma nexuma
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 rastma and the Alpharabian comma, or the sum of the 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 Aura considering the temperament that tempers out this comma to be some sort "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 nexus family.
Temperaments
In rank-2 environments, tempering it out in the full 11-limit leads to the nexal temperament, enabling nexal chords, or, in the 2.3.11 subgroup, the tribilo temperament, enabling tribilo chords.