Nexus comma
| Interval information |
nexisma nexuma
The nexus comma, otherwise known as the nexisma, or – in the earliest materials where this comma is named – the nexuma, is an 11-limit (also 2.3.11 subgroup) unnoticeable comma with a ratio of 1771561/1769472 and a value of approximately 2 cents. It is the amount by which a stack of three 128/121 Alpharabian diatonic semitones falls short of a 32/27 minor third, or equivalently stated, the amount by which a stack of three 121/96's exceeds of the octave. It is also the difference between the rastma and the Alpharabian comma, or the sum of the schisma and the parimo. 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.