A term used by Fokker to describe a musical interval which is small enough that it can be disregarded (possibly due to tempering), thereby setting up an equivalence relationship in the tonespace.
The unison-vector most frequently invoked by Fokker was the variety of the septimal kleisma with ratio 225/224, allowing 7/4 and 225/128 to be perceived as being interchangeable with each other. This particular unison-vector is also an example of a xenharmonic-bridge.
In Fokker's lattice theory, the unison vectors divide the lattice into regions called periodicity blocks.
In the case of temperaments, where a certain unison-vector and all of its multiples are tempered-out ("vanish"), the set of monzos that vanish are vapros.
Tanaka, Shohé. 1890.
A unison-vector in the "pure" sense is an interval which is not an actual unison. It is an interval with a real pitch difference by however small or large an amount. at least as often as not, it is a rational interval.
The essential concepts embodied in the term "unison-vector", are these:
Now, venturing into my own terminology ...
There is also a specific type of unison-vector called a "xenharmonic-bridge", which links a note within the periodicity-block of a certain prime-space, to one which lies not only in another "tiling" of the periodicity-block, but also in a different prime-space.
I coined this term, but Fokker often invoked the septimal-kleisma in precisely the way i describe here -- to make singers become familiar with the 5-limit just intonation "augmented-6th", then have them use it as a "target pitch" when he notates a harmonic-7th in his compositions. This was at least as early as his 1949 English book on singing JI.
The unison-vector has, within the past couple of years, also been referred to as a "comma", a usage which i personally do not encourage, because "comma" has already had a millennia-long established meaning, as an interval of about 12 to 35 cents.
A unison-vector certainly may be a "real" comma ... for example, the syntonic-comma (ratio 81:80 = 2,3,5-monzo [-4 4, -1> = ~ 21.5 cents) definitely does exist in theory in 5-limit just intonation.
In theory and in practice, a unison-vector may be tempered-out ("vanish"), ignored, or deliberately used as a valid scale degree (or "step"), either to play around with a listener's expectations, or to secure exact just intonation with commatic drift.
A unison-vector's multiples, both positive and negative, are all equivalent to it. thus they may be modeled geometrically as a line cutting across the lattice.
The monzo describing the one, of the pair of unison-vectors closest to the origin-point of the lattice, which has a positive pitch-height (the other will always be negative), is chosen to represent the whole line, and is a "promo" (projective monzo).
If a promo vanishes in a temperament, i propose to call that a "vapro".
The tonalsoft.com website is almost entirely the work of one person: me, Joe Monzo. Please reward me for my knowledge and effort by choosing your preferred level of financial support. Thank you.