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]] undecimal diatonic semitones fall 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 both the important functions of the 3-limit and the fact that the 11-limit can be mathematically demonstrated to be the best p-limit for representing quartertones in terms of ratio simplicity, lends itself to this temperament being dubbed the "'''nexus temperament'''"- the source of this comma's names.

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]] undecimal diatonic semitones fall 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 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 quarter tones in terms of ratio simplicity. That's why 3 and 11 can be considered "navigational primes" as elaborated in: [[User:Aura/Aura's Ideas on Tonality #Navigational Primes and the Parachromatic-Paradiatonic Contrast]].

[[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]] undecimal diatonic semitones fall 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 both the important functions of the 3-limit and the fact that the 11-limit can be mathematically demonstrated to be the best p-limit for representing quartertones in terms of ratio simplicity, lends itself to this temperament being dubbed the "'''nexus temperament'''"- the source of this comma's names.
+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]] undecimal diatonic semitones fall 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 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 quarter tones in terms of ratio simplicity. That's why 3 and 11 can be considered "navigational primes" as elaborated in: [[User:Aura/Aura's Ideas on Tonality #Navigational Primes and the Parachromatic-Paradiatonic Contrast]].
+[[Category:11-limit]]
+[[Category:Unnoticeable comma]]