Nexus comma

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 a stack of what are effectively 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.