31edo solfege

Uniform Solfege

See Uniform solfege for a full explanation.

31edo	edosteps	solfege names		ups and downs names
unisons	0-1	Da Du		P1 ^1		C ^C
2nds	2-6	Fro Fra	Ro Ra Ru	vm2 m2	~2 M2 ^M2	vDb Db	vD D ^D
3rds	7-11	No Na	Mo Ma Mu	vm3 m3	~3 M3 ^M3	vEb Eb	vE E ^E
4ths	12-14	Fo Fa Fu/Po		v4 P4 ^4		vF F ^F/vF#
tritones	15-16	Pa/Sho Pu/Sha		A4/vd5 ^A4/d5		F#/vGb ^F#/Gb
5ths	17-19	So Sa Su		v5 P5 ^5		vG G ^G
6ths	20-24	Flo Fla	Lo La Lu	vm6 m6	~6 M6 ^M6	vAb Ab	vA A ^A
7ths	25-29	Tho Tha	To Ta Tu	vm7 m7	~7 M7 ^M7	vBb Bb	vB B ^B
8ves	30-31	Do Da		v8 P8		vC C

Extra names: Fru=Ro, Nu=Mo, Shu=So, Flu=Lo, Thu=To

circle of 5ths: Da Sa Ra La Ma Ta Pa/Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po/Fu Du Su Ru Lu Mu Tu Pu/Sha Fra Fla Na Tha Fa Da

Consistent Solfege

31edo	solfege names	ups and downs names	edosteps
1sns	Do Du	P1 ^1	0-1
2nds	Ruh Re Ru Ra Ri	vm2 m2 ~2 M2 ^M2	2-6
3rds	Muh Me Mu Ma Mi	vm3 m3 ~3 M3 ^M3	7-11
4ths	Fuh Fo/Fe Fu	v4 P4 ^4	12-14
tritones	Fa/Suh Fi/Se	A4/vd5 ^A4/d5	15-16
5ths	Su So/Sa Si	v5 P5 ^5	17-19
6ths	Luh Le Lu La Li	vm6 m6 ~6 M6 ^M6	20-24
7ths	Tuh Te Tu Ta Ti	vm7 m7 ~7 M7 ^M7	25-29
8ves	Duh Do (Du)	v8 P8 (^8)	30-31 (32)

Example scales

Major scale	Do	Ra	Ma	Fo	So	La	Ta	Do
Minor scale	Do	Ra	Me	Fo	So	Le	Te	Do
Upmajor scale	Do	Ra	Mi	Fo	So	Li	Ti	Do
Downminor scale	Do	Ra	Muh	Fo	So	Luh	Tuh	Do
Mid scale	Do	Ra	Mu	Fo	So	Lu	Tu	Do

The system shown preserved vowels in perfect fifths in any scale that only uses notes from meantone[7] modes, mohajira[7] modes, and substitutions of meantone intervals with corresponding septimal subminor or supermajor intervals, allowing for any diatonic type scale to be simple as easy to learn, as the inconsistencies of So-Ra and Te-Fo can be smoothed out by the fact that Ra can also be called Ro, for perfect second, or 9/8, and Fo is also Fe, as it's the "minor fourth", as 4/3 is tempered together with 27/20. These commas being tempered allows the system to preserve a surprising amount of consistency, being extremely easy to learn. Du is used for the up unison because it helps consistency, is generally used as a quartertone in scales like Centaurus, and because it allows the also common augmented and upaugmented unisons to be named, with Da and Di.

The system is built on this consistency, and preserves the standard minor intervals names, as well as -a as the standard major from La, and Ti as the strongest leading tone, here being the upmajor seventh. The remaining vowels of -uh for sub and -u for neutral are used because they correspond to the vowel sounds from their respective words.

Expanding the System

To expand into intervals that surpass these, such as the A1 or the ^A5, we will extend to Augmented, Diminished, Upaugmented, and Downdiminished intervals. The vowels for these are -ah (short a sound), -ih (for the short i in diminished), oy, and ow (for down) respectively. They work similarly to the others, and are first used in the second set of unisons, allowing the M7-A4 and d5-m2 perfect fifths and others of the sort to still use consistent vowels, as they show up in diatonic scales.

If intervals are used solely for their 3-limit role, such as the M2 or in some cases the M6, the names Ro and Lo may be used, for perfect second or perfect sixth, as Ra can be thought of to imply 10/9, while Ro would imply 9/8, similarly to Lo and 27/16. In other cases, Mo would be 32/27 and To would be 16/9. A situation where this naming scheme may be used would be in Harrison Major, P1 M2 ^M3 P4 P5 M6 ^M7 P8, where the M6 is used so that the ii chord has a perfect fifth, while the vi chord has a wolf fifth in order to be used as a "wolf tonic" to prevent tonicization.

Kite Giedraitis's solfege

Kite's solfege uses the conventional consonants D, R, M, F, S, L and T. It uses unconventional vowels. For each degree, the sequence runs front to back (i.e. bright to dim) -i -e -a -o -u for upmajor-major-mid-minor-downminor. Kite's 24edo solfege is a subset of this solfege.

31edo	solfege names	ups and downs names	edosteps
unisons	Do Da	P1 ^1	0-1
2nds	Ru Ro Ra Re Ri	vm2 m2 ~2 M2 ^M2	2-6
3rds	Mu Mo Ma Me Mi	vm3 m3 ~3 M3 ^M3	7-11
4ths	Fu Fo Fa	v4 P4 ^4	12-14
tritones	Fe/Su Fi/So	A4/vd5 ^A4/d5	15-16
5ths	Sa Se Si	v5 P5 ^5	17-19
6ths	Lu Lo La Le Li	vm6 m6 ~6 M6 ^M6	20-24
7ths	Tu To Ta Te Ti	vm7 m7 ~7 M7 ^M7	25-29
8ves	Du Do	v8 P8	30-31

Beware: Mi, Fa, So, La and Ti all have new meanings!

Example scales

Major scale	Do	Re	Me	Fo	Se	Le	Te	Do
Minor scale	Do	Re	Mo	Fo	Se	Lo	To	Do
Upmajor scale	Do	Re	Mi	Fo	Se	Li	Ti	Do
Downminor scale	Do	Re	Mu	Fo	Se	Lu	Tu	Do
Mid scale	Do	Re	Ma	Fo	Se	La	Ta	Do

Learning suggestion

Even with many familiar consonants and a consistent vowel sequence, it can take a while to master 35 syllables. One might want to divide-and-conquer. Start with using this simple solfege:

Da - Ra - Ma - Fa - Sa - La - Ta - Da

Each syllable is a catch-all term. For example, Ra covers Ri, Re, Ra, Ro and Ru. Using this solfege helps with unlearning the syllables Mi, Fa, So, La and Ti, which are still present but have a changed meaning.

Once this is fully internalized, add in the other 4 vowels.

The circle of fifths

The 5 vowels create 5 chains of fifths. The 2 tritones with duplicate names each connect 2 pairs of chains. Thus there are only 3 fifths that don't rhyme:

• Do - Se (P1 to P5)
• Da - Si (^1 to ^5)
• Du - Sa (v1 to v5)

The 33 note names in circle-of-5ths order (read left-to-right, top-row-to-bottom-row)

1sn	5th	2nd	6th	3rd	7th	4th	1sn
Do	Se	Re	Le	Me	Te	Fe (Su)
	Su	Ru	Lu	Mu	Tu	Fu	Du
	Sa	Ra	La	Ma	Ta	Fa	Da
	Si	Ri	Li	Mi	Ti	Fi (So)
	So	Ro	Lo	Mo	To	Fo	Do

Because the chains mostly connect up, it's fairly easy to find the note a 4th or 5th above any note. It always rhymes (except the three 5ths from D- to S-), and the consonant is as would be expected from conventional interval arithmetic. Thus Re plus a 4th is Se, Ro plus a 5th is Lo, etc. And in the example scales above, the 3rd, 6th and 7th always rhyme, as do the tonic and 4th, as do the 2nd and 5th.

However going a 5th up from an aug or upaug 4th would go to an aug or upaug 8ve, which doesn't exist in this solfege. Therefore one must rename the 4th as a dim 5th, then go up to a minor 2nd. Thus Fe + 5th = Su + 5th = Ru. Dim 5ths may also need renaming: So + 4th = Fi + 4th = Ti.

Andrew Heathwaite's solfege

Andrew Heathwaite's solfege is a subset of his 41edo solfege. It expands on the conventional Do - Di/Ra - Re - Ri/Me - Mi - Fa - Fi/Se - So - Si/Le - La - Li/Te - Ti - Do. As a result there are 6 different vowel sequences.

31edo	solfege names	ups and downs names	edosteps
unisons	Do Di	P1 ^1	0-1
2nds	Ro Ra Ru Re Ri	vm2 m2 ~2 M2 ^M2	2-6
3rds	Ma Me Mu Mi Mo	vm3 m3 ~3 M3 ^M3	7-11
4ths	Fe Fa Fu Fi	v4 P4 ^4 A4	12-15
5ths	Se Su So (or Sol) Si	d5 v5 P5 ^5	16-19
6ths	Lo Le Lu La Li	vm6 m6 ~6 M6 ^M6	20-24
7ths	Ta Te Tu Ti To	vm7 m7 ~7 M7 ^M7	25-29
8ves	Da Do	v8 P8	30-31

See also: 17edo Solfege, 22edo Solfege, 29edo Solfege and 41edo Solfege.

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

Example scales

Major scale	Do	Re	Mi	Fa	Sol	La	Ti	Do
Minor scale	Do	Re	Me	Fa	Sol	Le	Te	Do
Upmajor scale	Do	Re	Mo	Fa	Sol	Li	To	Do
Downminor scale	Do	Re	Ma	Fa	Sol	Lo	Ta	Do
Mid scale	Do	Re	Mu	Fa	Sol	Lu	Tu	Do

The major and minor scales are the same as conventional solfege.