Solfege

Solfege refers to any way of labelling notes with syllables to be sung, and conventionally one that utilizes syllables similar to the conventional do-re-mi-fa-so-la-ti system for labeling the notes of a heptatonic scale.

Solfege is notoriously hard to generalize. A number of different approaches to solfege for microtonal tunings exist. The core conflict at the heart of generalizing solfege is the lack of uniformity in standard solfege. While solfege uses alternative vowels for qualities, these alternate vowels are not fully uniform (due to historical conflicts with the original diatonic solfege, which took its syllables from a Latin hymn), and so generalizing them becomes rather complicated and idiosyncratic. It becomes especially so if you want to be cross-linguistically compatible, with five vowels and ~13 widespread consonants constituting a total of 60-70 combinations, if codas are ignored, which is enough to notate most commonly-used edos if equivalent notes that are spelled differently are treated as the same thing, but completely fails for more complex rank-2 or JI systems.

Standard solfege (heptatonic)

Degree (1-indexed)	Solfege
1	do
2	re
3	mi
4	fa
5	so / sol
6	la
7	ti
(8/1)	do

This solfege generally represents the major diatonic scale. However, it may be applied to other 7-form scales as well.

Solfege for accidentals

Degree (1-indexed)	Solfege
P1	do
A1	di
d2	-
m2	ra
M2	re
A2	ri
d3	-
m3	me
M3	mi
A3	-
d4	fe
P4	fa
A4	fi
d5	se
P5	so / sol
A5	si
d6	-
m6	le
M6	la
A6	li
d7	-
m7	te
M7	ti
A7	-
d8	de
P8/P1	do

This is the standard solfege for accidentals. Note that is it is designed with 12edo in mind, it cannot represent d2, d3, A3, d6, d7, or A7 (in fact, it can at maximum extend itself to 19edo).

Extended solfeges for accidentals

Neutral intervals are generally indicated by the vowel u, which goes unused in standard solfege and is prominently found in the word "neutral" and most of its cognates in other European languages.

A 31edo solfege present on [1] that makes use of this is as follows, taken directly from the website (s = subminor, S = supermajor); "uh" is pronounced as in English "strut".

	Solfege	Interval Names
1sns	Do Du	P1 S1
2nds	Ruh Re Ru Ra Ri	s2 m2 n2 M2 S2
3rds	Muh Me Mu Ma Mi	s3 m3 n3 M3 S3
4ths	Fuh Fo Fu	s4 P4 S4
Tritones	Fa/Suh Fi/Se	A4/sd5 SA4/d5
5ths	Su So Si	s5 P5 S5
6ths	Luh Le Lu La Li	s6 m6 n6 M6 S6
7ths	Tuh Te Tu Ta Ti	s7 m7 n7 M7 S7
8ves	Duh Do (Du)	s8 P8 (S8)

Solfege for scaleforms

An alternative way to extend solfege by Vector is to ignore accidentals entirely, and let, for instance, fa stand for any note mapped to 3\7, regardless of quality and exact scale used.

Instead alternative sets of syllables are provided to extend solfege to all forms up to and including the 15-form.

To start with, the basic sequence do-re-na-mi-fa-zi-so-la-be-ti-do is constructed for the 10-form.

Every other entry, that is do-na-fa-so-be-do, is used for the 5-form, and the complementary do-re-mi-zi-la-ti-do for the 6-form. The standard solfege do-re-mi-fa-so-la-ti-do is used for the 7-form, and zi is added for the 8-form. The 9-form is equivalent to the 10-form but without zi. Then, the 2- and 4-form are trivially constructible as subsets of the 8-form and similarly for the 3-form from the 6-form.

Beyond the 10-form, re, mi, la, and ti bifurcate, and so does zi in odd forms:

	7-form (1-indexed)			12-form (0-indexed)
re	2	ke	re	1, 2
mi	3	vi	mi	3, 4
la	6	pa	la	8, 9
ti	7	gi (hard "g")	ti	10, 11
zi	-	je ("ye")	wi	6

The original syllables are assigned to the major versions, as that's what they represent in standard major-scale solfege.

Therefore, the 11-form contains do-ke-re-vi-mi-je-wi-pa-la-gi-ti-do, the 12-form do-ke-re-vi-mi-fa-zi-so-pa-la-gi-ti-do, the 13-form do-ke-re-vi-mi-fa-je-wi-so-pa-la-gi-ti-do, and the 14-form do-ke-re-na-vi-mi-fa-zi-so-pa-la-be-gi-ti-do which functions as a (bifurcated) superset of 7-form.

The largest form which can be represented here is the 15-form, which functions as a superset of 5-form and is do-ke-re-na-vi-mi-fa-je-wi-so-pa-la-be-gi-ti-do. Extending solfege beyond 15 would not only be out of the range of most things considered a "form" for a tuning system (note that the Roklotian scale follows the given 15-form rather well) but it would also run into the issue that it runs out of consonants; remaining available sounds are rare (such as th).

Additionally, these may also be used as fixed solfege syllables to name the notes of a scale.