Vector's just notation

Vector's just notation is a way of writing intervals based on the pyth-spine and combining syllables for commatic alterations, somewhat similarly to color notation.

It uses Vector's ordinal anchors, which are equal to neutral Pythagorean intervals.

3-limit alterations

The 3-limit follows standard diatonic notation. This table is for seconds, thirds, sixths, and sevenths. Note that the nominals are the C major scale, so C-E is a major third, not a neutral third, and C-Et is a semiaugmented third, not a major third.

Term	Alteration	Accidental
major	+sqrt(A1)	t
minor	-sqrt(A1)	d
semiaugmented	+A1	#
semidiminished	-A1	b
augmented	+A1*sqrt(A1)	#t
diminished	-A1*sqrt(A1)	db
etc.

Higher-limit alterations

Higher-limit alterations are single syllables, similar to and inspired by color notation, and are listed in order of increasing prime limit. The commas used are the same as in Neutral FJS. All syllables are pronounced like their IPA values, although r may be pronounced as a flap or approximant.

If a comma is tempered negative by a temperament, the meanings of the accidentals do not flip. This means that an augmented unison is an e-minor second even in meantone, where it is smaller than a minor second, and in mavila, major intervals are flatter than minor ones.

23 and 29 are written with the letters F and J instead of B and D in order to distinguish them from the flat and semiflat symbols.

Prime	Sharp 2	Sharp 1	Flat 1	Flat 2	Alteration
3	i (++)	e (+)	o (-)	u (--)	531441/524288
5	ti (^^)	te (^)	to (v)	tu (vv)	81/80
7	ki (KK)	ke (K)	ko (k)	ku (kk)	64/63
11	ri (RR)	re (R)	ro (r)	ru (rr)	sqrt(243/242)
13	si (SS)	se (S)	so (s)	su (ss)	sqrt(512/507)
17	pi (PP)	pe (P)	po (p)	pu (pp)	4131/4096
19	zi (ZZ)	ze (Z)	zo (z)	zu (zz)	513/512
23	bi (FF)	be (F)	bo (f)	bu (ff)	736/729
29	di (JJ)	de (J)	do (j)	du (jj)	261/256
31	gi (GG)	ge (G)	go (g)	gu (gg)	sqrt(2101707/2097152)

The Pythagorean comma accidental is present in order to allow any interval to be respelled with an enharmonic equivalent.

Thus, 17/16 may be either a pe-minor (P-m) second or an ope-augmented (-P-m) unison, and 14/11 may be notated as a kore-semidiminished (kR-sd) fourth or an okore-semiaugmented (-kR-sA) third.

To avoid unnecessary reduplication, to notate more than 2 repetitions of a comma, a syllable with the vowel a is used. These follow the same order as the consonants used for the primes. Additionally, for the accidentals, the corresponding letter is simply repeated the correct number of times.

Repetitions	Up	Down
1	e	o
2	i	u
3	eta	ota
4	ita	uta
5	eka	oka
6	ika	uka
7	era	ora
8	ira	ura
9	esa	osa
10	isa	usa
etc.

To derive higher primes, [TBD but involves the nasals somehow, which are conspicuously absent from the rest of the system]