31edo solfege

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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.