Nexus comma: Difference between revisions
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The '''nexuma''', or '''nexus comma''', is an [[11-limit]] [[unnoticeable comma]] with a ratio of '''1771561/1769472''' = {{Monzo|-16 -3 0 0 6}} and a value of approximately 2.04265 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. Furthermore, the 11-limit can be shown to host a clear sequence of intervals in which every other member is the octave complement of a stack of | The '''nexuma''', or '''nexus comma''', is an [[11-limit]] [[unnoticeable comma]] with a ratio of '''1771561/1769472''' = {{Monzo|-16 -3 0 0 6}} and a value of approximately 2.04265 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. Furthermore, 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]]. That's why 3 and 11 can be considered "navigational primes" as elaborated starting in: [[User:Aura/Aura's Ideas on Tonality #Navigational Primes and the Parachromatic-Paradiatonic Contrast]]. For a list of temperaments that temper out the Nexuma, see [[Nexus family]]. | ||
[[Category:11-limit]] | [[Category:11-limit]] | ||
[[Category:Unnoticeable comma]] | [[Category:Unnoticeable comma]] | ||
Revision as of 03:45, 26 October 2020
The nexuma, or nexus comma, is an 11-limit unnoticeable comma with a ratio of 1771561/1769472 = [-16 -3 0 0 6⟩ and a value of approximately 2.04265 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. Furthermore, 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 diatonic semitones. That's why 3 and 11 can be considered "navigational primes" as elaborated starting in: User:Aura/Aura's Ideas on Tonality #Navigational Primes and the Parachromatic-Paradiatonic Contrast. For a list of temperaments that temper out the Nexuma, see Nexus family.