Nexus comma: Difference between revisions
Expansion, in the order of intervals > commas, and 2.3.11 > full 11-limit; some styling |
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The '''nexus comma''', otherwise known as the '''nexisma''', or – in the earliest materials where this comma is named – 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. 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 '''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''', and this is the name that gives source to the names of a number of rank-2 temperaments that temper out this comma, though not all of them. 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, lends itself to rank-3 and higher temperaments formed by this comma being dubbed '''nexus temperaments''' – the source of 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]]. | ||
[[Category:11-limit]] | [[Category:11-limit]] | ||
Revision as of 03:04, 18 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, and this is the name that gives source to the names of a number of rank-2 temperaments that temper out this comma, though not all of them. 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, lends itself to rank-3 and higher temperaments formed by this comma being dubbed nexus temperaments – the source of 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.