Nexus comma: Difference between revisions

The nexus comma, otherwise known as the nexisma, or- in the earliest materials where this comma is named- the nexuma, is an 11-limit unnoticeable comma with a ratio of 1771561/1769472 and a value of approximately 2 cents. It is the sum of the schisma and the parimo, the difference between the rastma and the Alpharabian comma, and the amount by which a stack of three 128/121 Alpharabian diatonic semitones falls short of a 32/27 minor third. 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 this temperament being dubbed the "nexus temperament"- the source 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 nexuma, see nexus family.

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-The '''nexus comma''', otherwise known as the '''nexisma''', or- in the earliest sources where this comma is named- the '''nexuma''', is an [[11-limit]] [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents.  It is the sum of the [[32805/32768|schisma]] and the [[parimo]], the difference between the [[243/242|rastma]] and the [[Alpharabian comma]], and the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third.  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 this temperament being dubbed the "'''nexus temperament'''"- the source 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 nexuma, see [[nexus family]].
+The '''nexus comma''', otherwise known as the '''nexisma''', or- in the earliest materials where this comma is named- the '''nexuma''', is an [[11-limit]] [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents.  It is the sum of the [[32805/32768|schisma]] and the [[parimo]], the difference between the [[243/242|rastma]] and the [[Alpharabian comma]], and the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third.  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 this temperament being dubbed the "'''nexus temperament'''"- the source 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 nexuma, see [[nexus family]].
 [[Category:11-limit]]

Nexus comma: Difference between revisions

Revision as of 16:40, 17 January 2021

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