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 what are effectively [[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]].

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 what are effectively [[128/121|diatonic semitones]] simpler than those of the 3-limit. 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:Unnoticeable comma]]

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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 what are effectively [[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]].
+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 what are effectively [[128/121|diatonic semitones]] simpler than those of the 3-limit.  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:Unnoticeable comma]]