31edo solfege

Andrew Heathwaite system

Andrew Heathwaite proposes the following solfege system for singing the intervals of 31edo. Note that this is a subset of the syllables used for singing 41edo.

	interval	syllable
0	P1	do
1	^1	di
2	vm2	ro
3	m2	ra
4	~2	ru
5	M2	re
6	^M2	ri
7	vm3	ma
8	m3	me
9	~3	mu
10	M3	mi
11	^M3	mo
12	v4	fe
13	P4	fa
14	^4 / ~4	fu
15	A4 / vd5	fi
16	^A4 / d5	se
17	v5 / ~5	su
18	P5	so or sol
19	^5	si
20	vm6	lo
21	m6	le
22	~6	lu
23	M6	la
24	^M6	li
25	vm7	ta
26	m7	te
27	~7	tu
28	M7	ti
29	^M7	to
30	v8	da
31	P8	do

For intervals that appear in the diatonic scale, the traditional solfege names are grandfathered in. While this makes it easier to learn the new syllables as extensions of the old ones — if you are trained with the old ones to begin with — it also makes for many irregularities.

The syllables do, re, mi, fa, so[l], la, ti have the same meaning as traditional major and perfect intervals. The names for minor intervals are also retained: ra, me, le, te, as well as the augmented fourth, fi, and diminished fifth, se. Some traditional names for chromatically-altered intervals appear here, but altered by a semisharp or semiflat, rather than a full sharp or flat: di for a semiaugmented unison, da for a semidiminished unison, ri for a semiaugmented second, fe for a semidiminished fourth, si for a semiaugmented fifth, and li for a semiaugmented sixth. The remaining syllables flesh out the septimal and undecimal intervals which are not represented in 12edo.

Note that there is little pattern to the traditional names.

Between do and fa, there is a somewhat consistent pattern in the syllables associated with each interval and the interval a perfect fifth above it. This is especially helpful for learning to sing tetrachordal scales and seventh chords. The irregularities between do and fa are grandfathered in from the traditional system and are easy to learn.

do => so[l]

di => si

ro => lo (lo is a "low" sixth)

ra => le (an irregularity from the traditional names)

ru => lu (the "u" vowel for undecimal intervals)

re => la (another irregularity grandfathered in; but notice the symmetry of the two irregularities)

ri => li

ma => ta

me => te (grandfathered in, but fits the pattern)

mu => tu (undecimal)

mi => ti (grandfather and fits)

mo => to

fe => da (breaks the pattern of vowels, but we do see the consonants change together)

fa => do (The pattern mostly breaks down here, and we are no longer within a tetrachord. However, there are a few fits, which are indicated below.)

fu => di

fi => ro

se => ra

su => ru (fits)

so[l] => re

si => ri (fits)

lo => ma

le => me (fits, and grandfathered)

lu => mu (fits)

la => mi (grandfathered)

li => mo

ta => fe

te => fa (grandfathered)

tu => fu (fits)

ti => fi (fits, and grandfathered)

to => se

da => su

Kite Giedraitis system

Kite's system is similar to Andrew's system, but uses a uniform vowel sequence for each degree. It runs front to back (or bright to dim) -i -e -a -o -u for upmajor-major-mid-minor-downminor. It can be adapted to 24edo: 1\24 = da/ru, 5\24 = ri/mu, etc. 12\24 would be fe/so.

	interval	syllable
0	P1	do
1	^1	da
2	vm2	ru
3	m2	ro
4	~2	ra
5	M2	re
6	^M2	ri
7	vm3	mu
8	m3	mo
9	~3	ma
10	M3	me
11	^M3	mi
12	v4	fu
13	P4	fo
14	^4 / ~4	fa
15	A4 / vd5	fe/su
16	^A4 / d5	fi/so
17	v5 / ~5	sa
18	P5	se
19	^5	si
20	vm6	lu
21	m6	lo
22	~6	la
23	M6	le
24	^M6	li
25	vm7	tu
26	m7	to
27	~7	ta
28	M7	te
29	^M7	ti
30	v8	du
31	P8	do

Many scales use only 2 or 3 vowels:


major scale	Do	Re	Me	Fo	Se	Le	Te	Do
minor scale	Do	Re	Mo	Fo	Se	Lo	To	Do
downminor scale	Do	Re	Mu	Fo	Se	Lu	Tu	Do