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41edo solfege

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Kite Giedraitis's Solfege

Overview

Kite's solfege uses the conventional consonants D, R, M, F, S, L and T. But most consonants have an alternate form that indicates flattening or sharpening. The vowels are unconventional: u = up, a = plain, o = down and i = mid.

41edo solfege names ups and downs names
unisons Da Du P1 ^1
2nds Fro Fra Fru Ri Ro Ra Ru vm2 m2 ^m2 ~2 vM2 M2 ^M2
3rds No Na Nu Mi Mo Ma Mu vm3 m3 ^m3 ~3 vM3 M3 ^M3
4ths Fo Fa Fu v4 P4 ^4
tritones Fi/Sho Po/Sha Pa/Shu Pu/Si ~4/vd5 vA4/d5 A4/^d5 ^A4/~5
5ths So Sa Su v5 P5 ^5
6ths Flo Fla Flu Li Lo La Lu vm6 m6 ^m6 ~6 vM6 M6 ^M6
7ths Tho Tha Thu Ti To Ta Tu vm7 m7 ^m7 ~7 vM7 M7 ^M7
8ves Do Da (Du) v8 P8 (^8)

Th- is unvoiced as in think. The idea of 12 consonants is inspired by Erv Wilson's solfege (see below). However Kite added a 13th consonant: P- indicates a sharpened 4th. Mnemonic: Sha sharpens to Sa and Tha sharpens to Ta, so if Fa were spelled Pha, it would sharpen to Pa.

The seven 2nds illustrate the solfege's logic:

  • Fro = flat-Re-down = vm2
  • Fra = flat-Re-plain = m2
  • Fru = flat-Re-up = ^m2
  • Ri = Re-mid = ~2
  • Ro = Re-down = vM2
  • Ra = Re-plain = M2
  • Ru = Re-up = ^M2

The vowels relate to color notation: -a = wa, -o = yo or zo, -u = gu or ru, and -i = ila. The zogu 5th is Sha because the -o and -u in zogu cancel to make -a.

Example scales

Plain major scale Da Ra Ma Fa Sa La Ta Da
Plain minor scale Da Ra Na Fa Sa Fla Tha Da
Downmajor scale Da Ra Mo Fa Sa Lo To Da
Upminor scale Da Ra Nu Fa Sa Flu Thu Da
Upmajor scale Da Ra Mu Fa Sa Lu Tu Da
Downminor scale Da Ra No Fa Sa Flo Tho Da
Mid scale Da Ra Mi Fa Sa Li Ti Da

Octave Complements

To find the octave complement of any interval:

  • change the degree as usual: 2nd <--> 7th, 3rd <--> 6th, and 4th <--> 5th
  • change the quality as usual: major <--> minor, aug <--> dim, but perfect and mid are unchanged
  • change the vowel as expected: -o <--> -u, but -a and -i are unchanged

For example, Fro = minor-Re-down becomes major-Ti-up = Tu. The rule for changing the quality means the ~4 and the ~5 must be either Fi & Si or else Pi & Shi. The former is chosen to ensure that the 6 mid intervals Ri Mi Fi Si Li Ti all use the conventional (unaltered) consonants.

The Circle of Fifths

The 13 -a notes form a chain of 5ths running from the dim 5th to the aug 4th:

Sha - Fra - Fla - Na - Tha - Fa - Da - Sa - Ra - La - Ma - Ta - Pa

The aug 4th Pa is also the updim 5th Shu, which is the starting point for another 13-note chain of 5ths, all -u notes. Since Pu = Si, this leads to a 6-note chain of -i notes. This in turn leads to a 13-note -o chain, which leads back to the -a chain. 13 -a notes + 13 -u notes + 13 -o notes + 6 -i notes = 45 names = 41 notes with duplicate names for the 4 tritones.

To summarize, the 4 vowels create 4 separate chains of 5ths, and the 4 tritones with duplicate names connect those 4 chains into one 41-note circle. This is one rationale for the 13th consonant, for it supplies most of the duplicate names. (The other is to get symmetry.)

The 45 note names in circle-of-5ths order
(read left-to-right, top-row-to-bottom-row)
d5 m2 m6 m3 m7 P4 P1 P5 M2 M6 M3 M7 A4 (d5)
Da Sa Ra La Ma Ta Pa (Shu)
Shu Fru Flu Nu Thu Fu Du Su Ru Lu Mu Tu Pu (Si)
Si Ri Li Mi Ti Fi (Sho)
Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po (Sha)
Sha Fra Fla Na Tha Fa Da

Adding/subtracting 4ths, 5ths and major 2nds

Because the aforementioned 4 chains connect up, it's very easy to find the note a 4th or 5th above any note. It always rhymes, and the consonant is as would be expected from conventional interval arithmetic. Ra plus a 4th is Sa, Fro plus a 5th is Flo, etc. Thus in the example scales above, the 3rd, 6th and 7th always rhyme, as do the tonic, 2nd, 4th and 5th.

However the note a 5th above an aug or mid 4th would be an aug or mid 8ve, which doesn't exist in this solfege. Therefore one must rename the aug/mid 4th to a dim/mid 5th. Thus Po + 5th = Sha + 5th = Fra. Dim/mid 5ths may also need renaming: Sha + 4th = Po + 4th = To.

A few minor exceptions arise with the -i notes. Conventionally, M7 + 5th = A4, and indeed Ta + 5th = Pa. But Ti + 5th = Fi not Pi. Likewise Fa + 4th = Tha, a minor 7th as expected, but Fi + 4th = Ti not Thi. These exceptions are not an issue as long as you remember that there is no Pi or Thi in the solfege.

The same rule for 4ths and 5ths mostly holds for plain major 2nds. Keep the vowel, and change the consonant as expected. Ra + M2 = Ma. Again, aug/dim intervals must be renamed: Fi + M2 = Sho + M2 = Flo. Note that Fi to Si is a minor 2nd. Beware, this rule breaks down entirely for major and mid 7ths, due to the lack of aug and mid 8ves:

  • Tu + M2 = Ri (^M7 + M2 = ~2)
  • Ta + M2 = Fru (M7 + M2 = ^m2)
  • To + M2 = Fra (vM7 + M2 = m2)
  • Ti + M2 = Fro (~7 + M2 = vm2)

Learning suggestion

Even with many familiar consonants and a consistent vowel sequence, it can take a while to master 45 syllables. One might want to divide-and-conquer by first learning the consonants. Start with using this 12-edo-like solfege:

Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da

Once this is fully internalized, add in the vowels. This approach also helps with unlearning the syllables Do, Mi, So and Ti, which are still present but have a changed meaning.

Andrew Heathwaite's Solfege

Andrew's solfege expands on the conventional Do - Di/Ra - Re - Ri/Me - Mi - Fa - Fi/Se - Sol - Si/Le - La - Li/Te - Ti - Do. As a result there are 6 different vowel sequences.

41edo solfege names ups and downs names
unisons Do Di P1 ^1
2nds Ro Rih Ra Ru Reh Re Ri vm2 m2 ^m2 ~2 vM2 M2 ^M2
3rds Ma Meh Me Mu Mi Maa Mo vm3 m3 ^m3 ~3 vM3 M3 ^M3
4ths Fe Fa Fih v4 P4 ^4
tritones Fu Fi Se Su ~4/vd5 vA4/d5 A4/^d5 ^A4/~5
5ths Sih So (or Sol) Si v5 P5 ^5
6ths Lo Leh Le Lu La Laa Li vm6 m6 ^m6 ~6 vM6 M6 ^M6
7ths Ta Teh Te Tu Ti Taa To vm7 m7 ^m7 ~7 vM7 M7 ^M7
8ves Da Do (Di) v8 P8 (^8)

See also: 31edo solfege, which is a subset of this solfege.

Example scales

Plain major scale Do Re Maa Fa Sol Laa Taa Do
Plain minor scale Do Re Meh Fa Sol Leh Teh Do
Downmajor scale Do Re Mi Fa Sol La Ti Do
Upminor 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 downmajor and upminor scales are the same as conventional solfege.

Erv Wilson's Solfege

Erv's solfege uses unconventional consonants and vowels. From page 54 of http://www.anaphoria.com/41notes.pdf:

41edo solfege names ups and downs names
unisons Ka Ki P1 ^1
2nds Su So Se Si Nu Na Ni vm2 m2 ^m2 ~2 vM2 M2 ^M2
3rds Fu Fa Fi Bu Bo Be Bi vm3 m3 ^m3 ~3 vM3 M3 ^M3
4ths Du Da Di v4 P4 ^4
tritones Gu Go Ge Gi ~4/vd5 vA4/d5 A4/^d5 ^A4/~5
5ths Ju Ja Ji v5 P5 ^5
6ths Tu To Te Ti Pu Pa Pi vm6 m6 ^m6 ~6 vM6 M6 ^M6
7ths Lu La Li Ru Ro Re Ri vm7 m7 ^m7 ~7 vM7 M7 ^M7
8ves Ku Ka (Ki) v8 P8 (^8)

Vowel sequences: -u -a -i for the 7 notes of the Dorian scale and -u -o -e -i for the other 5 notes.

Example scales

Plain dorian scale Ka Na Fa Da Ja Pa La Ka
Plain major scale Ka Na Be Da Ja Pa Re Ka
Plain minor scale Ka Na Fa Da Ja To La Ka
Downmajor scale Ka Na Bi Da Ja Pi Ri Ka
Upminor scale Ka Na Bo Da Ja Pu Ro Ka
Upmajor scale Ka Na Fi Da Ja Te Li Ka
Downminor scale Ka Na Fu Da Ja Tu Lu Ka
Mid scale Ka Na Bu Da Ja Ti Ru Ka

The only single-vowel scales are the dorian scale, and subsets of it.

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