Nexus comma

Interval information

Ratio	1771561/1769472
Factorization	2-16 × 3-3 × 116
Monzo	[-16 -3 0 0 6⟩
Size in cents	2.042652¢
Names	nexus comma, nexisma nexuma
Color name	Tribilo
FJS name	[math]\displaystyle{ \text{A}{-2}^{11,11,11,11,11,11} }[/math]
Special properties	reduced
Tenney height (log2 nd)	41.5115
Weil height (log2 max(n, d))	41.5132
Wilson height (sopfr(nd))	107
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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.