Xenharmonic Wiki

User:TallKite/List of Solfeges

< User:TallKite

This page is a work in progress!

To do: check all edo pages for others' solfeges, done up to 19

include subset solfeges (8 of 24, 9/18 of 36, 16 of 48, 15/20 of 60, others? 11 of 22? 13 of 26?)

discuss advantages and disadvantages of lots of enharmonic equivalences (the "extra" notes)

discuss performerr vs composer solfeges? example: subset solfege and 12-edo numeric solfege, the ultimate performer solfege

maybe break up into 2 pages?

  • microtonal solfeges page discusses BC, uniform and numeric solfeges
  • list of solfeges page has all edos and pergens, with all 3 types of solfeges

Classification

Numeric solfeges are for small edos that aren't heptatonic-friendly, like 5, 6, and 8-11. All other edos use the conventional consonants D R M F S L T.

BC (backwards-compatible) solfeges are for mid-sized edos like 17 and 19. They expand on the conventional Do Re Mi (and Do Di/Ra Re RiMa Mi) and use traditional vowels plus new ones.

Uniform solfeges are for larger edos like 41 and 53. They use a uniform vowel sequence for all degrees. They add 6 altered consonants: Fr- N- P- Sh- Fl- and Th-. Uniform diatonic solfeges don't add them.

Uniform solfeges

Uniform solfeges are a type of solfege developed by Kite Giedraitis. They are closely related to his ups and downs notation. A uniform solfege lets one perform basic interval arithmetic directly within the solfege, without having to translate to note names or interval names and back. They use a uniform vowel sequence for each degree, hence the name. They use the conventional consonants D R M F S L T. But all consonants except D have an alternate form that indicates flattening or sharpening:

  • Fr- = flat Re = minor 2nd (mnemonic: F stands for flat)
  • N- = flat Mi = minor 3rd
  • P- = sharp Fa = aug 4th (mnemonic: Sh- sharpens to S-, and Th- sharpens to T-, so if Fa were spelled Pha, it would sharpen to Pa)
  • Sh- = flat So = dim 5th
  • Fl- = flat La = minor 6th (mnemonic: F stands for flat)
  • Th- = flat Ti = minor 7th

Sharpening and flattening refers to adding/subtracting the lawa unison Lw1. In edos 7, 14, 21, 28 and 35, there is no need for the altered consonants, since Lw1 is tempered out. Some other edos (12, ??) also omit them.

The vowel sequence varies depending on the edo or pergen. There is always -a for plain, and almost always -u for up and -o for down. Larger edos also have either -i for mid, or -i for dup (double-up) and -e for dud (double-down). Pergens are similar, see below.

the three vowel sequences
3 vowels 14-22, etc, -o = down -a = plain -u = up
4 vowels 31, 41 -i = mid -o = down -a = plain -u = up -i = mid
5 vowels 53, 60 -e = dud -o = down -a = plain -u = up -i = dup

These 5 vowels cover all the more popular edos up to 60. Which edos aren't covered? The number of vowels a uniform solfege needs equals the edo's sharpness or penta-sharpness, whichever is larger. Thus an edo with a (penta)sharpness of 6 or higher needs 6 or more vowels and isn't covered. Every edo above 60 is such an edo. The excluded edos are the less efficient ones, with a fairly inaccurate 5th for their size. Thus they tend to be the less popular edos.

A 6th vowel could of course be added, which would cover most edos up to 72edo. Perhaps -uh for the mid/betweens ring of 72edo?

Examples

  • 12edo: Da Fra Ra Na Ma Fa Pa/Sha Sa Fla La Tha Ta Da
  • 21edo: Da Du Ro Ra Ru Mo Ma Mu Fo Fa Fu So Sa Su Lo La Lu To Ta Tu Do Da

Edos 5, 7 and 12 have only -a. 10edo has -a and -o but no -u.

Superflat edos have a very flat 5th. A uniform solfege can still be used, but the size of the interval won't match what its name implies very well.

In sharp-1 edos, to up an interval means to augment it. Thus Fu = Pa and So = Sha. Fru = Ra and Fra = Ro.

In flat-1 edos, to up an interval means to diminish it. Fo = Pa and Su = Sha. Fro = Ra and Fra = Ru.

In sharp-2 and sharp-4 edos, mid is spelled as downmajor, downaug for the 4th, and downperfect for the 5th.

In edos with an even penta-sharpness, there are "in-between" notes with two names. For example, 4\19 (Ru/No) is named as both a 2nd and a 3rd.

Example Scales

(The prime limits assumes a larger edo in which both 81/80 and 64/63 are 1 edostep.)

3-limit Plain major scale Da Ra Ma Fa Sa La Ta Da
Plain minor scale Da Ra Na Fa Sa Fla Tha Da
5-limit Downmajor scale Da Ra Mo Fa Sa Lo To Da
Upminor scale Da Ra Nu Fa Sa Flu Thu Da
7-limit Upmajor scale Da Ra Mu Fa Sa Lu Tu Da
Downminor scale Da Ra No Fa Sa Flo Tho Da

Suggestion for learning

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

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

This helps with unlearning the syllables Do, Mi, So and Ti, which are still present but have a changed meaning. (For those familiar with the full 17-name solfege, note that Ra, Ri, Fi, Si and Li are often present but changed.)

Next add in the 6 altered consonants, making a 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 other vowels, and learn how to respell the various tritones.

Octave Complement

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 and aug <--> dim, but perfect and mid are unchanged.
  • get the new consonant from the quality and degree.
  • change the vowel as expected: -u <--> -o, but -a is unchanged. If -e is used, -i <--> -e, otherwise -i is unchanged.

For example, Fru = minor-Re-up becomes major-Ti-down = To.

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

Each vowel creates a separate chains of 5ths, usually starting with Sh- and ending with P-. But each P- note is enharmonically equivalent to some Sh- note (or S- or F- note). In 12n edos, the vowel of the equivalent note is the same, the chain becomes a circle, and there are multiple circles of 5ths. In other edos, the vowel changes, and the duplicate names connect these separate chains into one circle. (See 34edo for an exception.) This is one rationale for the 13th consonant P-, for it supplies the needed duplicate names.

For example, 31edo uses 3 vowels. Since Pa = Sho, the end of the -a chain connects to the start of the -o chain. Since Po = Fu, the -o chain connects to the -u chain. Since Pu = Sha, the -u chain connects back to the -a chain, making a circle of 31 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

Thus as long as one spells the tritone correctly, all 5ths rhyme. This makes interval arithmetic very easy.

Adding/subtracting 4ths and 5ths

The note a 4th or 5th above any note 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, consider the aug 4th, a P- note. The note a 5th above it would be an augmented 8ve, which doesn't exist in a uniform solfege. Therefore one must rename the tritone as a dim or mid 5th. Thus in 31edo Pa + 5th = Sho + 5th = Fro. Likewise, Sho and Sha need renaming when adding a 4th: Sha + 4th = Pu + 4th = Tu.

Adding/subtracting other intervals

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. But an aug 4th must be renamed as a 5th. Beware, this rule breaks down entirely for major and mid 7ths (the T- notes), due to the lack of aug and mid 8ves.

In general, one can add or subtract any conventional (i.e. plain) interval from any note, and the result will be as expected. But only if the expected answer exists in the solfege. It must exist on the 13-note chain of 5ths from dim5 to aug4. In other words, the expected answer must not be augmented or diminished, unless it's an aug4 or a dim5. (Otherwise, one must use an enharmonic equivalent.) For example, one can easily add a M3 to any note other than a L-, M-, T- or P- note. Thus Ro + M3 = Po and Na + M3 = Sa, but La + M3 is a Fr- note. Beware, sometimes a chain is not 13 notes long, and when adding to or subtracting, the expected answer must exist on the shorter chain. For example, in 31edo, the -u chain runs from P4 to A4.

One can often easily add/subtract an unconventional (upped or downed) interval as well. The ups and downs add up and cancel out as expected. Thus Ra + vM2 = Mo and Ru + vM2 = Ma. Obviously the vowel will change. Again, the expected answer must exist in the solfege. 3-vowel solfeges lack double-ups and double-downs. 4-vowel solfeges lack double-upmajor and double-downminor. 5-vowel solfeges lack triple-ups and triple-downs.

Correlations with colorspeak

-u/-o can mean not only up/down, but also under/over, meaning in the ratio's denominator or numerator. A colorspeak review:

  • ya (5-limit): yo/gu = 5-over/5-under = subtract/add 81/80
  • za (2.3.7): zo/ru = 7-over/7-under = subtract/add 64/63
  • ila (2.3.11): ilo/lu = 11-over/11-under = subtract/add 729/704
  • tha (2.3.13): tho/thu = 13-over/13-under = subtract/add 27/26

(In colorspeak, the last two commas could instead be 33/32 and 1053/1024, but these are over commas, and they must be under to keep the -o/-u correlation.)

If 81/80 maps to 1 edostep, then yo/gu = down/up = -o/-u. Likewise with the other commas. The table below shows that almost every edo has at least one such correlation. Parentheses are used when the prime's relative error is high, e.g. 12edo's prime 11.

colorspeak correlations for all 25 diatonic edos that have uniform solfeges with 5 vowels or less
12 17 19 22 24 26 27 29 31 32 33 34 36 38 39 40 41 43 45 46 48 50 53 55 60
ya (yo) yo yo yo yo (yo) yo yo (yo) yo yo
(gu) gu gu gu gu (gu) gu gu (gu) gu gu
za zo zo zo zo zo zo zo zo zo (zo) zo zo zo zo zo
ru ru ru ru ru ru ru ru ru (ru) ru ru ru ru ru
ila (ilo) ilo ilo ilo (ilo) (ilo) ilo ilo
(lu) lu lu lu (lu) (lu) lu lu
tha tho tho tho tho tho tho tho tho (tho)
thu thu thu thu thu thu thu thu (thu)

About the edo list

This list only includes edos that have uniform solfeges, which are edos with both sharpness and penta-sharpness of 5 or less. However, smaller edos are included with numeric solfeges. Excluded edos: 1-4, 30, 37, 42, 44, 47, 49, 51-52, 54, 56-59, and everything under 5 or over 60. A total of 43 edos, and 41 uniform solfeges.

7 consonants 7 consonants + P- 13 consonants BC numeric
-a 7 5 12 5 7 12 5 6

8 9

10 11

-o -a -u 12 14 21 10 15 16 17 19 22 24

26 29 31 36

-i -o -a -u 20 25 27 41
-e -o -a -u -i 28 35 40 48 53 60

5edo

various solfeges
5edo 0 1 2 3 4 5
notes C D / Eb E / F G / Ab A / Bb C
intervals P1 M2 / m3 M3 / P4 P5 / m6 M6 / m7 P8
numeric solfege Wa Tu Ti Fo Fa Wa
BC solfege Do Re / Me Fa So La / Te Do
uniform solfege Da Ra / Na Fa Sa La / Tha Da
uniform circle of fifths
0 3 1 4 2 5
-a Da Sa Ra La
-a Na Tha Fa Da

6edo

BC & numeric solfeges
6edo 0 1 2 3 4 5 6
notes C D E F# / Gb G# / Ab A# / Bb C
intervals P1 M2 M3 A4 / d5 A5 / m6 A6 / m7 P8
BC solfege (12edo subset) Do Re Mi Fi / Se Si / Le Li / Te Do
numeric solfege Wa Tu Ti Fo Fa Si Wa

7edo

BC & uniform solfeges
7edo 0 1 2 3 4 5 6 7
notes C D E F G A B C
intervals P1 P2 P3 P4 P5 P6 P7 P8
BC solfege Do Re Mi Fa So La Ti Do
uniform solfege Da Ra Ma Fa Sa La Ta Da
circle of fifths
0 4 1 5 2 6 3 7
BC Do So Re La Mi Ti Fa Do
uniform Da Sa Ra La Ma Ta Fa Da

8edo

numeric solfege
8edo 0 1 2 3 4 5 6 7 8
solfege Wa Tu Ti Fo Fa Si Se E Wa

9edo

numeric solfege
9edo 0 1 2 3 4 5 6 7 8 9
solfege Wa Tu Ti Fo Fa Si Se E Na Wa
uniform solfege (-a = plain)
9edo 0 1 2 3 4 5 6 7 8 9
cents 0 133 267 400 533 667 800 933 1067 1200
notes C D Db/E Eb/F# F G Gb/A Ab/B Bb C
intervals P1 M2 m2/M3 m3/A4 P4 P5 d5/M6 m6/M7 m7 P8
solfege Da Ra Fra/Ma Na/Pa Fa Sa Sha/La Fla/Ta Tha Da

Of qustionable merit. Circle of 5ths: Da Sa Ra La/Sha Ma/Fra Ta/Fla Pa/Na Tha Fa Da

10edo

numeric solfege
10edo 0 1 2 3 4 5 6 7 8 9 10
solfege Wa Tu Ti Fo Fa Si Se E Na Te Wa
uniform solfege (-a = plain, -o = down)
10edo 0 1 2 3 4 5 6 7 8 9 10
cents 0 120 240 360 480 600 720 840 960 1080 1200
notes C vD D / Eb vE F vF# / vG G vA A / Bb vB C
intervals P1 ~2 M2 / m3 ~3 P4 ~4 / ~5 P5 ~6 M6 / m7 ~7 P8
solfege Da Ro Ra / Na Mo Fa Po / So Sa Lo La / Tha To Da
extra names Du / Fru Nu Ma Fu / Shu Fla Flu Thu / Do
circles of fifths
plain circle down circle
0 6 2 8 4 10 1 7 3 9 5 1
-a Da Sa Ra La -o Ro Lo Mo To Po
-a Na Tha Fa Da -o So Ro

11edo

numeric solfege, see also edos 8-10
11edo 0 1 2 3 4 5 6 7 8 9 10 11
solfege Wa Tu Ti Fo Fa Si Se E Na Te Le Wa
uniform solfege (-a = plain, -u = up, -o = down, -i = mid)
11edo 0 1 2 3 4 5 6 7 8 9 10 11
cents 0 109 218 327 436 545 655 764 873 982 1091 1200
notes C C
intervals P1 ^1/M2 ~2/M3 m2/~3 m3/v4 P4/v5 ^4/P5 ^5/M6 ~6/M7 m6/~7 m7/v8 P8
solfege Da Du/Ra Ri/Ma Fra/Mi Na/Fo Fa/So Fu/Sa Su/La Li/Ta Fla/Ti Tha/Do Da

Of qustionable merit. Circle of 5ths: Da Sa/Fu Ra/Du La/Su Ma/Ri Ta/Li Mi/Fra Ti/Fla Na/Fo Tha/Do Fa/So Da

someone's solfege from 11edo page, a subset of 22edo
11edo 0 1 2 3 4 5 6 7 8 9 10 11
solfege Do Ra Re Me Mo Fu Su Lo La Ta Ti Do

12edo

conventional solfege (-i = sharp, -e = flat, -a = flat Re)
12edo 0 1 2 3 4 5 6 7 8 9 10 11 12
notes C C# / Db D D# / Eb E F F# / Gb G G# / Ab A A# / Bb B C
intervals P1 A1 / m2 M2 A2 / m3 M3 P4 A4 / d5 P5 A5 / m6 M6 A6 / m7 M7 P8
solfege Do Di / Ra Re Ri / Me Mi Fa Fi / Se So Si / Le La Li / Te Ti Do
circle of fifths (asymmetrical and major-centric)
0 7 2 9 4 11 6 1 8 3 10 5 12
Do So Re La Mi Ti Fi Di Si Ri Li
Se Ra Le Me Te Fa Da
perfect major aug / minor perfect
uniform solfege #1 (-a = plain = perfect/major, -u = aug, -o = dim/minor) (7 consonants)
12edo 0 1 2 3 4 5 6 7 8 9 10 11 12
notes C C# / Db D D# / Eb E F F# / Gb G G# / Ab A A# / Bb B C
intervals P1 A1 / m2 M2 A2 / m3 M3 P4 A4 / d5 P5 A5 / m6 M6 A6 / m7 M7 P8
solfege Da Du / Ro Ra Ru / Mo Ma Fa Fu / So Sa Su / Lo La Lu / To Ta Da
extras Fo Mu Do Tu
circle of fifths (asymmetrical and major-centric)
0 7 2 9 4 11 6 1 8 3 10 5 12
-a Da Sa Ra La Ma Ta
-o So Ro Lo Mo To
-u Fu Du Su Ru Lu
-a Fa Da
uniform solfege #2 (-a = plain = perfect/major, -u = aug)
12edo 0 1 2 3 4 5 6 7 8 9 10 11 12
notes C C# / Db D D# / Eb E F F# / Gb G G# / Ab A A# / Bb B C
intervals P1 A1 / m2 M2 A2 / m3 M3 P4 A4 / d5 P5 A5 / m6 M6 A6 / m7 M7 P8
solfege Da Du / Fra Ra Ru / Na Ma Fa Pa / Sha Sa Su / Fla La Lu / Tha Ta Da
extras Fo Mu Do
circle of fifths (asymmetrical and major-centric)
0 7 2 9 4 11 6 1 8 3 10 5 12
-a Da Sa Ra La Ma Ta Pa
-u Du Su Ru Lu
-a Sha Fra Fla Na Tha Fa Da

13b-edo

uniform solfege (-a = plain, -u = up, -o = down) (no Pa or Sha)
13edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13
notes C ^C/D ^D/E vDb/^E Db/vEb Eb/vF F G ^G/A ^A/B vAb/^B Ab/vBb Bb/vC C
intervals P1 ^1/M2 ^M2/M3 vm2/^M3 m2/vm3 m3/v4 P4 P5 ^5/M6 ^M6/M7 vm6/^M7 m6/vm7 m7/v8 P8
solfege Da Du/Ra Ru/Ma Fro/Mu Fra/No Na/Fo Fa Sa Su/La Lu/Ta Flo/Tu Fla/Tho Tha/Do Da
circle of fifths
0 7 1 8 2 9 3 10 4 11 5 12 6 13
-a Da Sa Ra La Ma Ta
-u Du Su Ru Lu Mu Tu
-o Fro Flo No Tho Fo Do
-a Fra Fla Na Tha Fa Da

14edo

uniform solfege (-a = plain, -u = up, -o = down), see also 21edo
14edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
notes C ^C/vD D ^D/vE E ^E/vF F ^F/vG G ^G/vA A ^A/vB B ^B/vC C
intervals P1 ^1/v2 P2 ^2/v3 P3 ^3/v4 P4 ^4/v5 P5 ^5/v6 P6 ^6/v7 P7 ^7/v8 P8
uniform solfege Da Du/Ro Ra Ru/Mo Ma Mu/Fo Fa Fu/So Sa Su/Lo La Lu/To Ta Tu/Do Da
circles of fifths
plain circle up/down circle
0 8 2 10 4 12 6 14 7 1 9 3 11 5 13 7
-a Da Sa Ra La Ma Ta Fa Da -u Fu Du Su Ru Lu Mu Tu Fu
-o So Ro Lo Mo To Fo Do So

15edo

uniform solfege (-u = up, -o = down, -a = plain)
15edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
cents 0 80 160 240 320 400 480 560 640 720 800 880 960 1040 1120 1200
notes C ^Db vD D / Eb ^Eb vE E / F ^F / ^Gb vF# / vG G / Ab ^Ab vA A / Bb ^Bb vB C
intervals P1 ^m2 vM2 M2 / m3 ^m3 vM3 M3 / P4 ^4 / ^d5 vA4 / v5 P5 / m6 ^m6 vM6 M6 / m7 ^m7 vM7 P8
solfege Da Fru Ro Ra / Na Nu Mo Fa Fu / Shu Po / So Sa Flu Lo La / Tha Thu To Da
extras Du Do
circles of fifths
plain circle up circle down circle
0 9 3 12 6 15 1 10 4 13 7 1 2 11 5 14 8 2
Da Sa Ra La Fru Flu Nu Thu Fu Ro Lo Mo To Po
Na Tha Fa Da Shu Fru So Ro
Kite's diatonic solfege (-i = minor, -u = upminor, -o = downmajor, -a = major), see 20edo, 22edo
15edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
cents 0 80 160 240 320 400 480 560 640 720 800 880 960 1040 1120 1200
notes C ^Db vD D/Eb ^Eb vE E/F ^F vG G/Ab ^Ab vA A/Bb ^Bb vB C
intervals P1 ^m2 vM2 M2/m3 ^m3 vM3 M3/P4 ^4 v5 P5/m6 ^m6 vM6 M6/m7 ^m7 vM7 P8
solfege Da Ru Ro Ra/Mi Mu Mo Ma/Fa Fu So Sa/Li Lu Lo La/Ti Tu To Da

circles of 5ths: Fu Ru Lu Mu Tu Fu --- Da Sa/Li Ra/Mi La/Ti Ma/Fa Da --- So Ro Lo Mo To So

someone's BC solfege from the 15edo page
15edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
notes C ^C vD D ^Eb vE F ^F vG G ^Ab vA Bb ^Bb vB C
intervals P1 ^1 vM2 M2 ^m3 vM3 P4 ^4 v5 P5 ^m6 vM6 m7 ^m7 vM7 P8
solfege Do Di Ru Re Me Mi Fa Fu Su So Le La Ta Tu Ti Do

16edo

uniform solfege (-a = major/minor/perfect, -u = up/dim, -o = down/aug)
16edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
cents 0 75 150 225 300 375 450 525 600 675 750 825 900 975 1050 1125 1200
notes C Cb/D# D Db E Eb Ebb/F# F Fb/G# G Gb/A# A Ab B Bb Bbb/C# C
intervals P1 d1/A2 M2 m2 M3 m3 d3/A4 P4 d4/A5 P5 d5/A6 M6 m6 M7 m7 d7/A8 P8
solfege Da Du/Ro Ra Fra Ma Na Nu/Pa Fa Fu/So Sa Sha/Lo La Fla Ta Tha Thu/Do Da
extras Fro Ru No Mu Fo Su Flo Lu Tho Tu
circle of fifths
0 9 2 11 4 13 6 15 8 1 10 3 12 5 14 7 16
-a Da Sa Ra La Ma Ta Pa
-u Nu Thu Fu Du
-o Do So Ro Lo
-a Sha Fra Fla Na Tha Fa Da
perfect major in-between minor perfect
Kite's BC solfege (-i = sharp, -e = flat, -a = sharp Mi and Ti, flat Re), see also 12edo
16edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
notes C Cb/D# D Db/E# E Eb F# F Fb/G# G Gb/A# A Ab/B# B Bb C# C
intervals P1 d1/A2 M2 m2/A3 M3 m3 A4 P4 d4/A5 P5 d5/A6 M6 m6/A7 M7 m7 A8 P8
solfege Do De/Ri Re Ra/Ma Mi Me Fi Fa Fe/Si So Se/Li La Le/Ta Ti Te Di Do

17edo

uniform solfege (-a = plain, -u = up, -o = down)
17edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
notes C ^C / Db vD D ^D / Eb vE E F ^F / Gb F# / vG G Ab vA A ^A / Bb vB B / vC C
intervals P1 ^1 / m2 ~2 M2 ^M2 / m3 ~3 M3 P4 ~4 / d5 A4 / ~5 P5 m6 ~6 M6 ^M6 / m7 ~7 M7 / v8 P8
solfege Da Du / Fra Ro Ra Na Mo Ma Fa Fu / Sha Pa / So Sa Fla Lo La Tha To Ta / Do Da
extras Fru No Ru Nu Fo Su Flu Tho Lu Thu
circle of fifths
0 10 3 13 6 16 9 2 12 5 15 8 1 11 4 14 7 17
-a Da Sa Ra La Ma Ta Pa
-o Do So Ro Lo Mo To
-u (Fru) (Flu) (Nu) (Thu) Fu Du
-a Sha Fra Fla Na Tha Fa Da
perfect major mid minor perfect
Andrew's BC solfege (-u = mid)
17edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
notes C ^C / Db C# / vD D ^D / Eb D# / vE E F ^F / Gb F# / vG G ^G / Ab G# / vA A ^A / Bb A# / vB B C
intervals P1 ^1 / m2 A1 / ~2 M2 ^M2 / m3 A2 / ~3 M3 P4 ~4 / d5 A4 / ~5 P5 ^5 / m6 A5 / ~6 M6 ^M6 / m7 A6 / ~7 M7 P8
solfege Do Da / Ra Di / Ru Re Ro / Me Ri / Mu Mi Fa Fu / Se Fi / Su So Sa / Le Si / Lu La Lo / Te Li / Tu Ti Do

18b-edo

uniform solfege (-a = plain, -u = up, -o = down)
18edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
notes C ^C

vD

D ^D

vDb

Db

E

^E

vEb

Eb ^Eb / ^F#

vF

F ^F

vG

G ^G

vGb / vA

A ^A

vAb

Ab

B

^B

vBb

Bb ^Bb

vC

C
intervals P1 ^1

vM2

M2 ~2 m2

M3

~3 m3 ^m3 / ^A4

v4

P4 ^4

v5

P5 ^5

vd5 / vM6

M6 ~6 m6

M7

~7 m7 ^m7

v8

P8
solfege Da Du

Ro

Ra Ru

Fro

Fra

Ma

Mu

No

Na Nu / Pu

Fo

Fa Fu

So

Sa Su

Sho / Lo

La Lu

Flo

Fla

Ta

Tu

Tho

Tha Thu

Do

Da
extras Pa Sha
circles of fifths
plain circle up/down circle
0 10 2 12 4 14 6 16 8 18 9 1 11 3 13 5 15 7 17 9
-a Da Sa Ra La Ma Ta -u Fu Du Su Ru Lu Mu Tu Pu/Nu Thu Fu
-a Fra Fla Na Tha Fa Da -o So Ro Lo/Sho Fro Flo No Tho Fo Do So

19edo

traditional solfege
19edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
notes C C#/Dbb Db D D#/Ebb Eb E E#/Fb F F# Gb G G#/Abb Ab A A#/Bbb Bb B B#/Cb C
intervals P1 A1/d2 m2 M2 A2/d3 m3 M3 A3/d4 P4 A4 d5 P5 A5/d6 m6 M6 A6/d7 m7 M7 A7/d8 P8
solfege Do Di/Ro Ra Re Ri/Ma Me Mi Mo/Fe Fa Fi Se So Si/Lo Le La Li/Ta Te Ti To/Da Do
uniform solfege (-a = plain, -u = up, -o = down)
19edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
notes C C#/Dbb Db D D#/Ebb Eb E E#/Fb F F#/Gbb Fx/Gb G G#/Abb Ab A A#/Bbb Bb B B#/Cb C
intervals P1 A1/d2 m2 M2 A2/d3 m3 M3 A3/d4 P4 A4/dd5 AA4/d5 P5 A5/d6 m6 M6 A6/d7 m7 M7 A7/d8 P8
solfege Da Du/Fro Fra Ra Ru/No Na Ma Mu/Fo Fa Pa/Sho Pu/Sha Sa Su/Flo Fla La Lu/Tho Tha Ta Tu/Do Da
extras Po Fu So Shu
circle of fifths
0 11 3 14 6 17 9 1 12 4 15 7 18 10 2 13 5 16 8 19
-a Da Sa Ra La Ma Ta Pa
-o Sho Fro Flo No Tho Fo Do
-u Du Su Ru Lu Mu Tu Pu
-a Sha Fra Fla Na Tha Fa Da
perfect major in-between minor perfect
Kite's diatonic solfege (-a = plain = perfect/major/A4, -u = up = aug, -o = down = dim/minor)
19edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
notes C C#/Dbb Db D D#/Ebb Eb E E#/Fb F F# Gb G G#/Abb Ab A A#/Bbb Bb B B#/Cb C
intervals P1 A1/d2 m2 M2 A2/d3 m3 M3 A3/d4 P4 A4 d5 P5 A5/d6 m6 M6 A6/d7 m7 M7 A7/d8 P8
solfege Da Du Ro Ra Ru Mo Ma Mu Fa/Po Fu/Pa So Sa Su Lo La Lu To Ta Tu/Do Da
extras Fo Sho Pu Shu

Da Sa Ra La Ma Ta Pa/Fu Du Su Ru Lu Mu Tu/Do So Ro Lo Mo To Po/Fa Da

20edo

uniform solfege (-a = plain, -u = up, -o = down, -i = mid)
20edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
cents 0 60 120 180 240 300 360 420 480 540 600 660 720 780 840 900 960 1020 1080 1140 1200
notes C ^Db vvD vD D/Eb ^Eb vvE vE F ^F/^Gb ^^F/vvG vF#/vG G ^Ab vvA vA A/Bb ^Bb vvB vB C
intervals P1 ^m2 ~2 vM2 M2/m3 ^m3 ~3 vM3 P4 ^4/^d5 ~4/~5 vA4/v5 P5 ^m6 ~6 vM6 M6/m7 ^m7 ~7 vM7 P8
solfege Da Fru Ri Ro Ra/Na Nu Mi Mo Fa Fu/Shu Fi/Si Po/So Sa Flu Li Lo La/Tha Thu Ti To Da
extras Du Ma Fla Do
circles of fifths
plain circle up circle mid circle down circle
0 12 4 16 8 20 1 13 5 17 9 1 2 14 6 18 10 2 2 11 5 14 8 2
Da Sa Ra La Fru Flu Nu Thu Fu Ri Li Mi Ti Pi Ro Lo Mo To Po
Na Tha Fa Da Shu Fru Si Ri So Ro
Kite's diatonic solfege (-i = minor, -u = upminor, -e = mid, -o = downmajor, -a = major), see 15edo, 22edo
20edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
notes C/Db ^Db vvD vD D/Eb ^Eb vvE vE E/F ^F ^^F/vvG vG G/Ab ^Ab vvA vA A/Bb ^Bb vvB vB B/C
intervals P1/m2 ^m2 ~2 vM2 M2/m3 ^m3 ~3 vM3 M3/P4 ^4 ~4/~5 v5 P5/m6 ^m6 ~6 vM6 M6/m7 ^m7 ~7 vM7 M7/P8
solfege Da/Ri Ru Re Ro Ra/Mi Mu Me Mo Ma/Fa Fu Fe/Se So Sa/Li Lu Le Lo La/Ti Tu Te To Ta/Da

21edo

uniform solfege (-a = plain, -u = up, -o = down), see also 14edo
21edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
notes C ^C vD D ^D vE E ^E vF F ^F vG G ^G vA A ^A vB B ^B vC C
intervals P1 ^1 v2 P2 ^2 v3 P3 ^3 v4 P4 ^4 v5 P5 ^5 v6 P6 ^6 v7 P7 ^7 v8 P8
solfege Da Du Ro Ra Ru Mo Ma Mu Fo Fa Fu So Sa Su Lo La Lu To Ta Tu Do Da
circles of fifths
plain circle up circle down circle
0 12 3 15 6 18 9 21 1 13 4 16 7 19 10 1 2 14 5 17 8 20 11 2
Da Sa Ra La Ma Ta Fa Da Du Su Ru Lu Mu Tu Fu Du Do So Ro Lo Mo To Fo Do

22edo

uniform solfege (-u = up, -o = down, -a = plain)
22edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
notes C Db ^Db vD D Eb ^Eb vE E F ^F/Gb vF#/^Gb F#/vG G Ab ^Ab vA A Bb ^Bb vB B C
intervals P1 m2 ^m2 vM2 M2 m3 ^m3 vM3 M3 P4 ^4/d5 vA4/^d5 A4/v5 P5 m6 ^m6 vM6 M6 m7 ^m7 vM7 M7 P8
solfege Da Du

Fra

Fru Ro Ra Na Nu Mo Ma Fa Fu

Sha

Po

Shu

Pa

So

Sa Fla Flu Lo La Tha Thu To Ta

Do

Da
extras Fro No Ru Fo Mu

Sho

Pu

Flo

Su Tho Lu Tu
circle of fifths
0 13 4 17 8 21 12 3 16 7 20 11 2 15 6 19 10 1 14 5 18 9 22
-a Da Sa Ra La Ma Ta Pa
-o Do So Ro Lo Mo To Po
-u Shu Fru Flu Nu Thu Fu Du
-a Sha Fra Fla Na Tha Fa Da
perfect major downmajor upminor minor perfect
Kite's diatonic solfege (-i = minor, -u = upminor, -o = downmajor, -a = major), see 15edo
22edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
notes C ^C/Db ^Db vD D Eb ^Eb vE E F ^F vF#/^Gb vG G Ab ^Ab vA A Bb ^Bb vB B/vC C
intervals P1 ^1/m2 ^m2 vM2 M2 m3 ^m3 vM3 M3 P4 ^4 vA4/^d5 v5 P5 m6 ^m6 vM6 M6 m7 ^m7 vM7 M7/v8 P8
solfege Da Du/Ri Ru Ro Ra Mi Mu Mo Ma Fa Fu Po/Shu So Sa Li Lu Lo La Ti Tu To Ta/Do Da
circle of 5ths (1 non-rhyming 5th, Ti-Fa)
0 13 4 17 8 21 12 3 16 7 20 11 2 15 6 19 10 1 14 5 18 9 22
-a Da Sa Ra La Ma Ta
-o Do So Ro Lo Mo To Po
-u Shu Ru Lu Mu Tu Fu Du
-i Ri Li Mi Ti
-a Fa Da
Andrew's BC solfege
22edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
notes C Db ^Db vD D Eb ^Eb vE E F ^F/Gb vF#/^Gb F#/vG G Ab ^Ab vA A Bb ^Bb vB B C
intervals P1 m2 ^m2 vM2 M2 m3 ^m3 vM3 M3 P4 ^4/d5 vA4/^d5 A4/v5 P5 m6 ^m6 vM6 M6 m7 ^m7 vM7 M7 P8
solfege Do Di Ra Ru Re Ma Me Mi Mo Fa Fu Fi Su Sol Lo Le La Li Ta Tu Ti Da Do

23edo

uniform solfege (-a = major/minor/perfect, -u = up/dim, -o = down/aug)
23edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
notes C Cb D# D Db Dbb

E#

E Eb Ebb F# F Fb G# G Gb A# A Ab Abb

B#

B Bb Bbb C# C
intervals P1 d1 A2 M2 m2 d2

A3

M3 m3 d3 A4 P4 d4 A5 P5 d5 A6 M6 m6 d6

A7

M7 m7 d7 A8 P8
solfege Da Du Ro Ra Fra Fru

Mo

Ma Na Nu Fo

Pa

Fa Fu So Sa Su

Sha

Lo La Fla Flu

To

Ta Tha Thu Do Da
extras Fro Ru No Mu Pu Sho Flo Lu Tho Tu
circle of fifths
0 13 3 16 6 19 9 22 12 2 15 5 18 8 21 11 1 14 4 17 7 20 10 23
-a Da Sa Ra La Ma Ta Pa
-o Fo Do So Ro Lo Mo To
-u Fru Flu Nu Thu Fu Du Su
-a Sha Fra Fla Na Tha Fa Da

24edo

uniform solfege (-u = up, -a = plain, -o = down), see also 29edo, 36edo
24edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
notes C ^C

vDb

Db ^Db

vD

D ^D

vEb

Eb ^Eb

vE

E ^E

vF

F ^F

vF# vGb

F#

Gb

^F#

^Gb vG

G ^G

vAb

Ab ^Ab

vA

A ^A

vBb

Bb ^Bb

vB

B ^B

vC

C
intervals P1 ^1

vm2

m2 ~2 M2 ^M2

vm3

m3 ~3 M3 ^M3

v4

P4 ~4

vd5

A4

d5

~5

v5

P5 ^5

vm6

m6 ~6 M6 ^M6

vm7

m7 ~7 M7 ^M7

v8

P8
solfege Da Du

Fro

Fra Fru

Ro

Ra Ru

No

Na Nu

Mo

Ma Mu

Fo

Fa Fu

Po

Sho

Pa

Sha

Pu

Shu So

Sa Su

Flo

Fla Flu

Lo

La Lu

Tho

Tha Thu

To

Ta Tu

Do

Da

Fru, Nu, Flu andThu are included to complete the -u circle, so you can do interval arithmetic within it.

circles of fifths
plain

circle

0 14 4 18 8 22 12 2 16 6 20 10 24
-a Da Sa Ra La Ma Ta Pa
-a Sha Fra Fla Na Tha Fa Da
1 15 5 19 9 23 13 3 17 7 21 11 1
up

circle

-u Du Su Ru Lu Mu Tu Pu
-u Shu Fru Flu Nu Thu Fu Du
down

circle

-o Fro Flo No Tho Fo Do So Ro Lo Mo To Po
-o Sho Fro
Kite's diatonic solfege (-i -e -a -o -u = ^M M ~ m vm), see 31edo
24edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
notes C ^C

vDb

Db vD D ^D

vEb

Eb vE E ^E

vF

F ^F

vGb

F#

Gb

^F#

vG

G ^G

vAb

Ab vA A ^A

vBb

Bb vB B ^B

vC

C
intervals P1 ^1

vm2

m2 ~2 M2 ^M2

vm3

m3 ~3 M3 ^M3

v4

P4 ^4

vd5

A4

d5

^A4

v5

P5 ^5

vm6

m6 ~6 M6 ^M6

vm7

m7 ~7 M7 ^M7

v8

P8
solfege Do Da

Ru

Ro Ra Re Ri

Mu

Mo Ma Me Mi

Fu

Fo Fa

Su

Fe

So

Fi

Sa

Se Si

Lu

Lo La Le Li

Tu

To Ta Te Ti

Du

Do
  • plain circle: Do Se Re Le Me Te Fe/So Ro Lo Mo To Fo Do
  • mid/inbetween circle: Da/Ru Si/Lu Ri/Mu Li/Tu Mi/Fu Ti/Du Fi/Sa Ra La Ma Ta Fa/Su Da/Ru

25edo

uniform solfege (-a = plain, -u = up, -o = down, -i = dup/dud = downmid/upmid)
25edo edosteps solfege names ups and downs names
unisons 0-1 Da Du/Fru P1 ^1/^m2 C ^C/^Db
2nds 1-5 Du/Fru Fri Ri Ro Ra/Na ^1/^m2 v~2 ^~2 vM2 M2/m3 ^C/^Db ^^Db vvD vD D/Eb
3rds 5-9 Ra/Na Nu Ni Mi Mo M2/m3 ^m3 v~3 ^~3 vM3 D/Eb ^Eb ^^Eb vvE vE
4ths 10 Fa P4 F
tritones 11-14 Fu/Shu Fi/Shi Pi/Si Po/So ^4/^d5 v~4/v~5 ^~4/^~5 vA4/v5 ^F/^Gb ^^F/^^Gb vvF#/vvG vF#/vG
5ths 15 Sa P5 G
6ths 16-20 Flu Fli Li Lo La/Tha ^m6 v~6 ^~6 vM6 M6/m7 ^Ab ^^Ab vvA vA A/Bb
7ths 20-24 La/Tha Thu Thi Ti To/Do M6/m7 ^~7 vM7/v8 A/Bb ^Bb ^^Bb vvB vB/vC
8ves 24-25 (26) To/Do Da (Du) vM7/v8 P8 (^8) vB/vC C (^C)
Uniform solfege (-a = plain, -u = up, -o = down, -i = mid) (duplicate names are bolded)
25edo edosteps solfege names ups and downs names
unisons 0-1 Da Du P1 ^1 C ^C
2nds 1-5 Fru Fri Ri Ro Ra ^m2 v~2 ^~2 vM2 M2 ^Db ^^Db vvD vD D
3rds 5-9 Na Nu Ni Mi Mo m3 ^m3 v~3 ^~3 vM3 Eb ^Eb ^^Eb vvE vE
4ths 10 Fa P4 F
tritones 11-14 Fu/Shu Fi/Shi Pi/Si Po/So ^4/^d5 v~4/v~5 ^~4/^~5 vA4/v5 ^F/^Gb ^^F/^^Gb vvF#/vvG vF#/vG
5ths 15 Sa P5 G
6ths 16-20 Flu Fli Li Lo La ^m6 v~6 ^~6 vM6 M6 ^Ab ^^Ab vvA vA A
7ths 20-24 Tha Thu Thi Ti To m7 ^~7 vM7 Bb ^Bb ^^Bb vvB vB
8ves 24-25 (26) Do Da (Du) v8 P8 (^8) vC C (^C)
  • plain ring: Da Sa Ra/Na La/Tha Fa Da
  • up ring: Fu/Shu Du/Fru Flu Nu Thu Fu/Shu
  • downmid ring: Fi/Shi Fri Fli Ni Thi Fi/Shi
  • upmid ring: Pi/Si Ri Li Mi Ti Pi/Si
  • down ring: Po/So Ro Lo Mo To/Do Po/So
circles of fifths
plain circle
plain

circle

0 15 5 20 10 25
Da Sa Ra La
Na Tha Fa Da
up

circle

1 16 6 21 11 1
Fru Flu Nu Thu Fu Du
Du Shu Fru
downmid

circle

2 17 7 22 12 2
Fri Fli Ni Thi Fi
Shi Fri
upmid

circle

3 18 8 23 13 3
Ri Li Mi Ti Pi
Si Ri
down

circle

4 19 9 24 14 4
Ro Lo Mo To Po
So Ro

26edo

uniform solfege (-a = major/minor/perfect, -u = aug, -o = dim)
26edo edosteps solfege ups and downs names
unisons 0-1 Da Du P1 A1 C C#
2nds 2-5 Fro Fra Ra Ru d2 m2 M2 A2 Dbb Db D D#
3rds 6-9 No Na Ma Mu d3 m3 M3 A3 Ebb Eb E E#
4ths 10-12 Fo Fa Fu/Pa d4 P4 A4 Fb F F#
tritone 13 Pu/Sho AA4/dd5 Fx/Gbb
5ths 14-16 Sha/So Sa Su d5 P5 A5 Gb G G#
6ths 17-20 Flo Fla La Lu d6 m6 M6 A6 Abb Ab A A#
7ths 21-24 Tho Tha Ta Tu d7 m7 M7 A7 Bbb Bb B B#
8ves 25-26 (27) Do Da (Du) d8 P8 (A8) Cb C (C#)

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

Kite's diatonic solfege (-o = downminor = dim, -i = minor, -a = major/perfect, -u = upmajor = aug)
26edo edosteps Kite's Phylingual's ups and downs names
unisons 0-1 Da Du Do Di P1 A1 C C#
2nds 2-5 Ro Ri Ra Ru Rih Ru Re Ri d2 m2 M2 A2 Dbb Db D D#
3rds 6-9 Mo Mi Ma Mu Ma Me Muh/Mi Maa d3 m3 M3 A3 Ebb Eb E E#
4ths 10-12 Fo Fa Fu/Pa Fe Fa Fu d4 P4 A4 Fb F F#
tritone 13 Pu/Sho Fi/Se AA4/dd5 Fx/Gbb
5ths 14-16 Sha/So Sa Su Su So Si d5 P5 A5 Gb G G#
6ths 17-20 Lo Li La Lu Leh Le/Lu La Li d6 m6 M6 A6 Abb Ab A A#
7ths 21-24 To Ti Ta Tu Ta Te Tu/Ti To d7 m7 M7 A7 Bbb Bb B B#
8ves 25-26 (27) Do Da (Du) Da Do (Di) d8 P8 (A8) Cb C (C#)

circle of 5ths: Da Sa Ra La Ma Ta Pa/Fu Du Su Ru Lu Mu Tu Pu/Sho Ro Lo Mo To Fo Do So Ri Li Mi Ti Fa Da

27edo

uniform solfege (-a = plain, -u = up, -o = down, -i = mid)
27edo edosteps solfege names ups and downs names
unisons 0-1 Da Du/Fra P1 ^1/m2 C ^C/Db
2nds 1-5 Du/Fra Fru Ri Ro Ra ^1/m2 ^m2 ~2 vM2 M2 ^C/Db ^Db vvD vD D
3rds 6-10 Na Nu Mi Mo Ma m3 ^m3 ~3 vM3 M3 Eb ^Eb vvE vE E
4ths 11 Fa P4 F
tritones 12-15 Fu/Sha Fi/Shu Po/Si Pa/So ^4/b5 ~4/^d5 vA4/~5 A4/v5 ^F/Gb ^^F/^Gb vF#/vvG F#/vG
5ths 16 Sa P5 G
6ths 17-21 Fla Flu Li Lo La m6 ^m6 ~6 vM6 M6 Ab ^Ab vvA vA A
7ths 22-26 Tha Thu Ti To Ta/Do m7 ^m7 ~7 vM7 M7/v8 Bb ^Bb vvB vB B/vC
8ves 26-27 (28) Ta/Do Da (Du) M7/v8 P8 (^8) B/vC C (^C)

circle of 5ths: Da Sa Ra La Ma Ta/Do Pa/So Ro Lo Mo To Po/Si Ri Li Mi Ti Fi/Shu Fru Flu Nu Thu Fu/Sha Du/Fra Fla Na Tha Fa Da

Du and Do aren't necessary, but only one D- note seems too few since all the other degrees have 5 notes.

28edo

uniform solfege (-a = plain, -u = up, -o = down, -i = double-up, -e = double-down)
28edo edosteps solfege names ups and downs names
unisons 0-2 Da Du Di/Re P1 ^1 ^^1/vv2 C ^C ^^C/vvD
2nds 2-6 Di/Re Ro Ra Ru Ri/Me ^^1/vv2 v2 P2 ^2 ^^2/vv3 ^^C/vvD vD D ^D ^^D/vvE
3rds 6-10 Ri/Me Mo Ma Mu Mi/Fe ^^2/vv3 v3 P3 ^3 ^^3/vv4 ^^D/vvE vE E ^E ^^E/vvF
4ths 10-14 Mi/Fe Fo Fa Fu Fi/Se ^^3/vv4 v4 P4 ^4 ^^4/vv5 ^^E/vvF vF F ^F ^^F/vvG
5ths 14-18 Fi/Se So Sa Su Si/Le ^^4/vv5 v5 P5 ^5 ^^5/vv6 ^^F/vvG vG G ^G ^^G/vvA
6ths 18-22 Si/Le Lo La Lu Li/Te ^^5/vv6 v6 P6 ^6 ^^6/vv7 ^^G/vvA vA A ^A ^^A/vvB
7ths 22-26 Li/Te To Ta Tu Ti/De ^^6/vv7 v7 P7 ^7 ^^7/vv8 ^^A/vvB vB B ^B ^^B/vvC
8ves 26-28 (29 30) Ti/De Do Da (Du Di) ^^7/vv8 v8 P8 (^8 ^^8) ^^B/vvC vC C (^C ^^C)
circles of fifths
plain circle 0 16 4 20 8 24 12 28
Da Sa Ra La Ma Ta Fa Da
up circle 1 17 5 21 9 25 13 1
Du Su Ru Lu Mu Tu Fu Du
down circle 27 15 3 19 7 23 11 27
Do So Ro Lo Mo To Fo Do
in-between circle 2 18 6 22 10 26 14 2
Di Si Ri Li Mi Ti Fi Di
Re Le Me Te Fe De Se Re

29edo

uniform solfege (-a = plain, -u = up, -o = down), see also 24edo, 36edo
29edo edosteps solfege names ups and downs names
unisons 0-1 Da Du/Fro P1 ^1/vm2 C ^C/vDb
2nds 1-6 Du/Fro Fra Fru Ro Ra Ru/No ^1/vm2 m2 ^m2 vM2 M2 ^M2/vm3 ^C/vDb Db ^Db vD D ^D/vEb
3rds 6-11 Ru/No Na Nu Mo Ma Mu/Fo ^M2/vm3 m3 ^m3 vM3 M3 ^M3/v4 ^D/vEb Eb ^Eb vE E ^E/vF
4ths 11-13 Mu/Fo Fa Fu ^M3/v4 P4 ^4 ^E/vF F ^F
tritones 14-15 Po/Sha Pa/Shu vA4/d5 A4/^d5 vF#/Gb F#/^Gb
5ths 16-18 So Sa Su/Flo v5 P5 ^5/vm6 vG G ^G/vAb
6ths 18-23 Su/Flo Fla Flu Lo La Lu/Tho ^5/vm6 m6 ^m6 vM6 M6 ^M6/vm7 ^G/vAb Ab ^Ab vA A ^A/vBb
7ths 23-28 Lu/Tho Tha Thu To Ta Tu/Do ^M6/vm7 m7 ^m7 vM7 M7 ^M7/v8 ^A/vBb Bb ^Bb vB B ^B/vC
8ves 28-29 (30) Tu/Do Da (Du) ^M7/v8 P8 (^8) ^B/vC C (^C)

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

Phylingual's solfege
29edo edosteps solfege names ups and downs names
unisons 0-1 Do Di P1 ^1 C ^C
2nds 2-6 Rih Ra Ru Re Raw m2 ^m2 vM2 M2 ^M2 Db ^Db vD D ^D
3rds 7-11 Meh Me Mi Maa Maw m3 ^m3 vM3 M3 ^M3 Eb ^Eb vE E ^E
4ths 12-14 Fa Fu Fi P4 ^4 ^^4 F ^F ^^F
5ths 15-18 Se Su So Saw vv5 v5 P5 ^5 vvG vG G ^G
6ths 19-23 Leh Le La Laa Law m6 ^m6 vM6 M6 ^M6 Ab ^Ab vA A ^A
7ths 24-27 Teh Te Ti Taa m7 ^m7 vM7 M7 Bb ^Bb vB B
8ves 28-29 (30) Da Do (Di) v8 P8 (^8) vC C (^C)

31edo

uniform solfege (-a = plain, -u = up, -o = down)
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 (32) Do Da (Du) v8 P8 (^8) vC C (^C)

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

Kite's bright-to-dim solfege (-i -e -a -o -u = ^M M ~ m vm), see 24edo
31edo solfege names ups and downs names edosteps
unisons Do Da P1 ^1 C ^C 0-1
2nds Ru Ro Ra Re Ri vm2 m2 ~2 M2 ^M2 vDb Db vD D ^D 2-6
3rds Mu Mo Ma Me Mi vm3 m3 ~3 M3 ^M3 vEb Eb vE E ^E 7-11
4ths Fu Fo Fa v4 P4 ^4 vF F ^F 12-14
tritones Fe/Su Fi/So A4/vd5 ^A4/d5 F#/vGb ^F#/Gb 15-16
5ths Sa Se Si v5 P5 ^5 vG G ^G 17-19
6ths Lu Lo La Le Li vm6 m6 ~6 M6 ^M6 vAb Ab vA A ^A 20-24
7ths Tu To Ta Te Ti vm7 m7 ~7 M7 ^M7 vBb Bb vB B ^B 25-29
8ves Du Do (Da) v8 P8 (^8) vC C (^C) 30-31 (32)

As a circle of 5ths:

Do Se Re Le Me Te Fe/Su Ru Lu Mu Tu Fu Du Sa Ra La Ma Ta Fa Da Si Ri Li Mi Ti Fi/So Ro Lo Mo To Fo Do

Kite's solfege (-u -a -e -i -o = Upmajor mAjor nEutral mInor dOwnminor)
31edo solfege names ups and downs names edosteps
unisons Da Du P1 ^1 C ^C 0-1
2nds Ro Ri Re Ra Ru vm2 m2 ~2 M2 ^M2 vDb Db vD D ^D 2-6
3rds Mo Mi Me Ma Mu vm3 m3 ~3 M3 ^M3 vEb Eb vE E ^E 7-11
4ths Fo Fi Fe v4 P4 ^4 vF F ^F 12-14
tritones Fa/So Fu/Si A4/vd5 ^A4/d5 F#/vGb ^F#/Gb 15-16
5ths Se Sa Su v5 P5 ^5 vG G ^G 17-19
6ths Lo Li Le La Lu vm6 m6 ~6 M6 ^M6 vAb Ab vA A ^A 20-24
7ths To Ti Te Ta Tu vm7 m7 ~7 M7 ^M7 vBb Bb vB B ^B 25-29
8ves De Da (Du) v8 P8 (^8) vC C (^C) 30-31 (32)

circle of 5ths: Da Sa Ra La Ma Ta Fa/So Ro Lo Mo To Fo De Se Re Le Me Te Fe Du Su Ru Lu Mu Tu Fu/Si Ri Li Mi Ti Fi Da

Andrew's solfege
31edo edosteps solfege names ups and downs names
unisons 0-1 Do Di P1 ^1 C ^C
2nds 2-6 Ro Ra Ru Re Ri vm2 m2 ~2 M2 ^M2 vDb Db vD D ^D
3rds 7-11 Ma Me Mu Mi Mo vm3 m3 ~3 M3 ^M3 vEb Eb vE E ^E
4ths 12-15 Fe Fa Fu Fi v4 P4 ^4 A4 vF F ^F F#
5ths 16-19 Se Su So (or Sol) Si d5 v5 P5 ^5 Gb vG G ^G
6ths 20-24 Lo Le Lu La Li vm6 m6 ~6 M6 ^M6 vAb Ab vA A ^A
7ths 25-29 Ta Te Tu Ti To vm7 m7 ~7 M7 ^M7 vBb Bb vB B ^B
8ves 30-31 (32) Da Do (Di) v8 P8 (^8) vC C (^C)

32edo

uniform solfege (-a = plain, -u = up, -o = down, -i = dup/dud = downmid/upmid)
32edo edosteps solfege names ups and downs names
unisons 0-1 Da Du/Fra P1 ^1/m2 C ^C/Db
2nds 1-6 Du/Fra Fru Fri Ri Ro Ra ^1/m2 ^m2 v~2 ^~2 vM2 M2 ^C/Db ^Db ^^Db vvD vD D
3rds 7-12 Na Nu Ni Mi Mo Ma m3 ^m3 v~2 ^~3 vM3 M3 Eb ^Eb ^^Eb vvE vE E
4ths 13 Fa P4 F
tritones 14-18 Fu/Sha Fi/Shu Pi/Shi Po/Si Pa/So ^4/d5 v~4/^d5 ^~4/v~5 vA4/^~5 A4/v5 ^F/Gb ^^F/^Gb vvF#/^^Gb vF#/vvG F#/vG
5ths 19 Sa P5 G
6ths 20-25 Fla Flu Fli Li Lo La m6 ^m6 v~6 ^~6 vM6 M6 Ab ^Ab ^^Ab vvA vA A
7ths 26-31 Tha Thu Thi Ti To Ta/Do m7 ^m7 v~7 ^~7 vM7 M7/v8 Bb ^Bb ^^Bb vvB vB B/vC
8ves 31-32 (33) Ta/Do Da (Du) M7/v8 P8 (^8) B/vC C (^C)

Da Sa Ra La Ma Ta/Do Pa/So Ro Lo Mo To Po/Si Ri Li Mi Ti Pi/Shi Fri Fli Ni Thi Fi/Shu Fru Flu Nu Thu Fu/Sha Du/Fra Fla Na Tha Fa Da

Du and Do aren't necessary, but only one D- note seems too few since all the other degrees have 5 notes.

33edo

uniform solfege (-a = major/minor/perfect, -u = aug, -o = dim, -i = double-aug, -e = double-dim)
33edo edosteps solfege ups and downs names
unisons 0-2 Da Du Di/Fre P1 A1 AA1/dd2 C C# Cx
2nds 2-7 Di/Fre Fro Fra Ra Ru Ri/Ne AA1/dd2 d2 m2 M2 A2 AA2/dd3 Dbbb Dbb Db D D# Dx/Ebbb
3rds 7-12 Ri/Ne No Na Ma Mu Mi/Fe AA2/dd3 d3 m3 M3 A3 AA3/dd4 Dx/Ebbb Ebb Eb E E# Ex/Fbb
4ths 12-15 Mi/Fe Fo Fa Fu/Pa AA3/dd4 d4 P4 A4 Ex/Fbb Fb F F#
tritone 16-17 Fi/Pu/She Pi/Sho/Se AA4/ddd5 AAA4/dd5 Fx/Gbbb Fx#/Gbb
5ths 18-21 Sha/So Sa Su Si/Fle d5 P5 A5 AA5/dd6 Gb G G# Gx/Abbb
6ths 21-26 Si/Fle Flo Fla La Lu Li/The AA5/dd6 d6 m6 M6 A6 AA6/dd7 Gx/Abbb Abb Ab A A# Ax/Bbbb
7ths 26-31 Li/The Tho Tha Ta Tu Ti/De AA6/dd7 d7 m7 M7 A7 AA7/dd8 Ax/Bbbb Bbb Bb B B# Bx/Cbb
8ves 31-33 (34-35) Ti/De Do Da (Du Di) AA7/dd8 d8 P8 (A8 AA8) Bx/Cbb Cb C (C# Cx)

Da Sa Ra La Ma Ta Pa/Fu Du Su Ru Lu Mu Tu Pu/Fi/She Di/Fre Si/Fle Ri/Ne Li/The Mi/Fe Ti/De Pi/Se/Sho Fro Flo No Tho Fo Do So/Sha Fra Fla Na Tha Fa Da

34edo

uniform solfege (-a = plain, -u = up, -o = down, -i = mid) in-between notes are bolded
34edo edosteps solfege names ups and downs names
unisons 0-1 Da Du=Fro P1 ^1=vm2 C ^C=vDb
2nds 1-7 Fro Fra Fru Ri Ro Ra Ru=No vm2 m2 ^m2 ~2 vM2 M2 ^M2=vm3 vDb Db ^Db vvD vD D ^D=vEb
3rds 7-13 No Na Nu Mi Mo Ma Mu=Fo vm3 m3 ^m3 ~3 vM3 M3 ^M3=v4 vEb Eb ^Eb vvE vE E ^E=vF
4ths 13-15 Fo Fa Fu v4 P4 ^4 vF F ^F
tritones 16-18 Fi/Sha Po/Shu Pa/Si ~4/d5 vA4/^d5 A4/~5 ^^F/Gb vF#/^Gb F#/vvG
5ths 19-21 So Sa Su=Flo v5 P5 ^5=vm6 vG G ^G=vAb
6ths 21-27 Flo Fla Flu Li Lo La Lu=Tho vm6 m6 ^m6 ~6 vM6 M6 ^M6=vm7 vAb Ab ^Ab vvA vA A ^A=vBb
7ths 27-33 Tho Tha Thu Ti To Ta Tu=Do vm7 m7 ^m7 ~7 vM7 M7 ^M7=v8 vBb Bb ^Bb vvB vB B ^B=vC
8ves 33-34 (35) Do Da (Du) v8 P8 (^8) vC C (^C)
circles of fifths
plain/mid

circle

0 20 6 26 12 32 18 4 24 10 30 16 2 22 8 28 14 34
-a Da Sa Ra La Ma Ta Pa
-i Si Ri Li Mi Ti Fi
-a Sha Fra Fla Na Tha Fa Da
perfect major mid minor perfect
up/down

circle

17 3 23 9 29 15 1 21 7 27 13 33 19 5 25 11 31 17
-o Po
-u Shu Fru Flu Nu Thu Fu Du Su Ru Lu Mu Tu
-o Fro Flo No Tho Fo Do So Ro Lo Mo To Po
-u Shu
upminor in-between downmajor

35edo

uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
35edo edosteps solfege names ups and downs names
unisons 0-2 Da Du Di P1 ^1 ^^1 C ^C ^^C
2nds 3-7 Re Ro Ra Ru Ri vv2 v2 P2 ^2 ^^2 vvD vD D ^D ^^D
3rds 8-12 Me Mo Ma Mu Mi vv3 v3 P3 ^3 ^^3 vvE vE E ^E ^^E
4ths 13-17 Fe Fo Fa Fu Fi vv4 v4 P4 ^4 ^^4 vvF vF F ^F ^^F
5ths 18-22 Se So Sa Su Si vv5 v5 P5 ^5 ^^5 vvG vG G ^G ^^G
6ths 23-27 Le Lo La Lu Li vv6 v6 P6 ^6 ^^6 vvA vA A ^A ^^A
7ths 28-32 Te To Ta Tu Ti vv7 v7 P7 ^7 ^^7 vvB vB B ^B ^^B
8ves 33-35 (36 37) De Do Da (Du Di) vv8 v8 P8 (^8 ^^8) vvC vC C (^C ^^C)
circles of fifths
plain circle 0 20 5 25 10 30 15 35
Da Sa Ra La Ma Ta Fa Da
up circle 1 21 6 26 11 31 16 1
Du Su Ru Lu Mu Tu Fu Du
dup circle 2 22 7 27 12 32 17 2
Di Si Ri Li Mi Ti Fi Di
down circle 34 19 4 24 9 29 14 34
Do So Ro Lo Mo To Fo Do
dud circle 33 18 3 23 8 28 13 33
De Se Re Le Me Te Fe De

36edo

uniform solfege (-a = plain, -u = up, -o = down), see also 24edo, 29edo
36edo edosteps solfege names ups and downs names
unisons 0-1 Da Du P1 ^1 C ^C
2nds 2-7 Fro Fra Fru Ro Ra Ru vm2 m2 ^m2 vM2 M2 ^M2 vDb Db ^Db vD D ^D
3rds 8-13 No Na Nu Mo Ma Mu vm3 m3 ^m3 vM3 M3 ^M3 vEb Eb ^Eb vE E ^E
4ths 14-16 Fo Fa Fu v4 P4 ^4 vF F ^F
tritones 17-19 Po/Sho Pa/Sha Pu/Shu vA4/vd5 A4/d5 ^A4/^d5 vF#/vGb F#/Gb ^F#/^Gb
5ths 20-22 So Sa Su v5 P5 ^5 vG G ^G
6ths 23-28 Flo Fla Flu Lo La Lu vm6 m6 ^m6 vM6 M6 ^M6 vAb Ab ^Ab vA A ^A
7ths 29-34 Tho Tha Thu To Ta Tu vm7 m7 ^m7 vM7 M7 ^M7 vBb Bb ^Bb vB B ^B
8ves 35-36 (37) Do Da (Du) v8 P8 (^8) vC C (^C)
circles of fifths
plain

circle

0 21 6 27 12 33 18 3 24 9 30 15 36
Da Sa Ra La Ma Ta Pa
Sha Fra Fla Na Tha Fa Da
up

circle

1 22 7 28 13 34 19 4 25 10 31 16 1
Du Su Ru Lu Mu Tu Pu
Shu Fru Flu Nu Thu Fu Du
down

circle

35 20 5 26 11 32 17 2 23 8 29 14 35
Do So Ro Lo Mo To Po
Sho Fro Flo No Tho Fo Do

38edo

uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud), contains 19edo's solfege, but with u --> i and o --> e
38edo edosteps solfege names ups and downs names
unisons 0-2 Da Du Di/Fre P1 ^1 ^^1/vvm2 C ^C ^^C/vvDb
2nds 2-8 Di/Fre Fro Fra Ro Ra Ru Ri/Ne ^^1/vvm2 vm2 m2 ~2 M2 ^M2 ^^M2/vvm3 ^^C/vvDb vDb Db vD D ^D ^^D/vvEb
3rds 8-14 Ri/Ne No Na Mo Ma Mu Mi/Fe ^^M2/vvm3 vm3 m3 ~3 M3 ^M3 ^^M3/vv4 ^^D/vvEb vEb Eb vE E ^E ^^E/vvF
4ths 14-17 Mi/Fe Fo Fa Fu/Po ^^M3/vv4 v4 P4 ~4 ^^E/vvF vF F ^F
tritones 18-20 Pa/She Pu/Sho Pi/Sha A4/vvd5 ^A4/vd5 ^^A4/d5 F#/vvGb ^F#/vGb ^^F#/Gb
5ths 21-24 So Sa Su Si/Fle ~5 P5 ^5 ^^5/vvm6 vG G ^G ^^G/vvAb
6ths 24-30 Si/Fle Flo Fla Lo La Lu Li/The ^^5/vvm6 vm6 m6 ~6 M6 ^M6 ^^M6/vvm7 ^^G/vvAb vAb Ab vA A ^A ^^A/vvBb
7ths 30-36 Li/The Tho Tha To Ta Tu Ti/De ^^M6/vvm7 vm7 m7 ~7 M7 ^M7 ^^M7/vv8 ^^A/vvBb vBb Bb vB B ^B ^^B/vvC
8ves 36-38 Ti/De Do Da (Du Di) ^^M7/vv8 v8 P8 (^8 ^^8) ^^B/vvC vC C (^C ^^C)
circles of fifths
plain/

dup/

dud

circle

0 22 6 28 12 34 18 2 24 8 30 14 36 20 4 26 10 32 16 38
-a Da Sa Ra La Ma Ta Pa
-e She Fre Fle Ne The Fe De
-i Di Si Ri Li Mi Ti Pi
-a Sha Fra Fla Na Tha Fa Da
perfect major in-between minor perfect
up/

down

circle

1 23 7 29 13 35 19 3 25 9 31 15 37 21 5 27 11 33 17 1
-u Du Su Ru Lu Mu Tu Pu
-o Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po
-u Fu Du
upperfect upmajor downminor downperfect mid upperfect

39edo

uniform solfege (-a = plain, -u = up, -o = down, -i = dup/dud = downmid/upmid) in-between notes are bolded
39edo edosteps solfege names ups and downs names
unisons 0-1 Da Du=Fro P1 ^1=vm2 C ^C=vDb
2nds 1-8 Fro Fra Fru Fri Ri Ro Ra Ru=No vm2 m2 ^m2 v~2 ^~2 vM2 M2 ^M2=vm3 vDb Db ^Db ^^Db vvD vD D ^D=vEb
3rds 8-15 No Na Nu Ni Mi Mo Ma Mu=Fo vm3 m3 ^m3 v~3 ^~3 vM3 M3 ^M3=v4 vEb Eb ^Eb ^^Eb vvE vE E ^E=vF
4ths 15-17 Fo Fa Fu v4 P4 ^4 vF F ^F
tritones 18-21 Fi/Sha Pi/Shu Po/Shi Pa/Si v~4/d5 ^~4/^d5 vA4/v~5 A4/^~5 ^^F/Gb vvF#/^Gb vF#/^^Gb F#/vvG
5ths 22-24 So Sa Su=Flo v5 P5 ^5=vm6 vG G ^G=vAb
6ths 24-31 Flo Fla Flu Fli Li Lo La Lu=Tho vm6 m6 ^m6 v~6 ^~6 vM6 M6 ^M6=vm7 vAb Ab ^Ab ^^Ab vvA vA A ^A=vBb
7ths 31-38 Tho Tha Thu Thi Ti To Ta Tu=Do vm7 m7 ^m7 v~7 ^~7 vM7 M7 ^M7=v8 vBb Bb ^Bb ^^Bb vvB vB B ^B=vC
8ves 38-39 (40) Do Da (Du) v8 P8 (^8) vC C (^C)

Da Sa Ra La Ma Ta Pa/Si Ri Li Mi Ti Pi/Shu Fru Flu Nu Thu Fu Du/Fro Su/Flo Ru/No Lu/Tho Mu/Fo Tu/Do So Ro Lo Mo To Po/Shi Fri Fli Ni Thi Fi/Sha Fra Fla Na Tha Fa Da

40edo

uniform solfege (-a = major/minor/perfect, -u = aug, -o = dim, -i = double-aug, -e = double-dim)
40edo edosteps solfege ups and downs names
unisons 0-2 Da Du Di P1 A1 AA1 C C# Cx
2nds 3-8 Fre Fro Fra Ra Ru Ri dd2 d2 m2 M2 A2 AA2 Dbbb Dbb Db D D# Dx
3rds 9-14 Ne No Na Ma Mu Mi dd3 d3 m3 M3 A3 AA3 Ebbb Ebb Eb E E# Ex
4ths 15-18 Fe Fo Fa Fu/Pa dd4 d4 P4 A4 Fbb Fb F F#
tritone 19-21 Fi/Pu Pi/She Sho/Se AA4 AAA4/ddd5 dd5 Fx Fx#/Gbbb Gbb
5ths 22-25 Sha/So Sa Su Si d5 P5 A5 AA5 Gb G G# Gx
6ths 26-31 Fle Flo Fla La Lu Li dd6 d6 m6 M6 A6 AA6 Abbb Abb Ab A A# Ax
7ths 32-37 The Tho Tha Ta Tu Ti dd7 d7 m7 M7 A7 AA7 Bbbb Bbb Bb B B# Bx
8ves 38-40 (41-42) De Do Da (Du Di) dd8 d8 P8 (A8 AA8) Cbb Cb C (C# Cx)

Da Sa Ra La Ma Ta Pa/Fu Du Su Ru Lu Mu Tu Pu/Fi Di Si Ri Li Mi Ti Pi/She Fre Fle Ne The Fe De Se/Sho Fro Flo No Tho Fo Do So/Sha Fra Fla Na Tha Fa Da

41edo

Kite's solfege (-a = plain, -u = up, -o = down, -i = mid), see also 53edo
41edo edosteps Da Ra Mo names ups and downs names
unisons 0-1 Da Du P1 ^1 C ^C
2nds 2-8 Fro Fra Fru Ri Ro Ra Ru vm2 m2 ^m2 ~2 vM2 M2 ^M2 vDb Db ^Db vvD vD D ^D
3rds 9-15 No Na Nu Mi Mo Ma Mu vm3 m3 ^m3 ~3 vM3 M3 ^M3 vEb Eb ^Eb vvE vE E ^E
4ths 16-18 Fo Fa Fu v4 P4 ^4 vF F ^F
tritones 19-22 Fi/Sho Po/Sha Pa/Shu Pu/Si ~4/vd5 vA4/d5 A4/^d5 ^A4/~5 ^^F/vGb vF#/Gb F#/^Gb ^F#/vvG
5ths 23-25 So Sa Su v5 P5 ^5 vG G ^G
6ths 26-32 Flo Fla Flu Li Lo La Lu vm6 m6 ^m6 ~6 vM6 M6 ^M6 vAb Ab ^Ab vvA vA A ^A
7ths 33-39 Tho Tha Thu Ti To Ta Tu vm7 m7 ^m7 ~7 vM7 M7 ^M7 vBb Bb ^Bb vvB vB B ^B
8ves 40-41 (42) Do Da (Du) v8 P8 (^8) vC C (^C)

Da Sa Ra La Ma Ta Pa/Shu Fru Flu Nu Thu Fu Du Su Ru Lu Mu Tu Pu/Si Ri Li Mi Ti Fi/Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po/Sha Fra Fla Na Tha Fa Da

  • plain segment: Da Sa Ra La Ma Ta Pa/Shu
  • up segment: Shu Fru Flu Nu Thu Fu Du Su Ru Lu Mu Tu Pu/Si
  • mid segment: Si Ri Li Mi Ti Fi/Sho
  • down segment: Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po/Sha
  • plain segment: Sha Fra Fla Na Tha Fa Da
Andrew's solfege
41edo edosteps solfege names ups and downs names
unisons 0-1 Do Di P1 ^1 C ^C
2nds 2-8 Ro Rih Ra Ru Reh Re Ri vm2 m2 ^m2 ~2 vM2 M2 ^M2 vDb Db ^Db vvD vD D ^D
3rds 9-15 Ma Meh Me Mu Mi Maa Mo vm3 m3 ^m3 ~3 vM3 M3 ^M3 vEb Eb ^Eb vvE vE E ^E
4ths 16-20 Fe Fa Fih Fu Fi v4 P4 ^4 ~4 vA4 vF F ^F ^^F vF#
5ths 21-25 Se Su Sih So (or Sol) Si ^d5 ~5 v5 P5 ^5 ^Gb vvG vG G ^G
6ths 26-32 Lo Leh Le Lu La Laa Li vm6 m6 ^m6 ~6 vM6 M6 ^M6 vAb Ab ^Ab vvA vA A ^A
7ths 33-39 Ta Teh Te Tu Ti Taa To vm7 m7 ^m7 ~7 vM7 M7 ^M7 vBb Bb ^Bb vvB vB B ^B
8ves 40-41 (42) Da Do (Di) v8 P8 (^8) vC C (^C)

43edo

uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud), in-betweener's duplicate names are bolded
43edo edosteps solfege names ups and downs names
unisons 0-2 Da Du Di=Fre P1 ^1 ^^1 C ^C ^^C
2nds 2-9 Fre Fro Fra Fru Ro Ra Ru Ri=Ne vvm2 vm2 m2 ^m2 vM2 M2 ^M2 ^^M2 vvDb vDb Db ^Db vD D ^D ^^D
3rds 9-16 Ne No Na Nu Mo Ma Mu Mi=Fe vvm3 vm3 m3 ^m3 vM3 M3 ^M3 ^^M3 vvEb vEb Eb ^Eb vE E ^E ^^E
4ths 16-19 Fe Fo Fa Fu vv4 v4 P4 ^4 vvF vF F ^F
tritones 20-23 Po/She Pa/Sho Pu/Sha Pi/Shu vA4/vvd5 A4/vd5 ^A4/d5 ^^A4/^d5 vF#/vvGb F#/vGb ^F#/Gb ^^F#/^Gb
5ths 24-27 So Sa Su Si=Fle v5 P5 ^5 ^^5 vG G ^G ^^G
6ths 27-34 Fle Flo Fla Flu Lo La Lu Li=The vvm6 vm6 m6 ^m6 vM6 M6 ^M6 ^^M6 vvAb vAb Ab ^Ab vA A ^A ^^A
7ths 34-41 The Tho Tha Thu To Ta Tu Ti=De vvm7 vm7 m7 ^m7 vM7 M7 ^M7 ^^M7 vvBb vBb Bb ^Bb vB B ^B ^^B
8ves 41-43 De Do Da (Du Di) vv8 v8 P8 (^8 ^^8) vvC vC C (^C ^^C)

Da Sa Ra La Ma Ta Pa/Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po/She Di/Fre Si/Fle Ri/Ne Li/The Mi/Fe Ti/De Pi/Shu Fru Flu Nu Thu Fu Du Su Ru Lu Mu Tu Pu/Sha Fra Fla Na Tha Fa Da

  • plain segment: Da Sa Ra La Ma Ta Pa/Sho
  • down segment: Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po/She
  • dup/dud/inbetween segment: She Di/Fre Si/Fle Ri/Ne Li/The Mi/Fe Ti/De Pi/Shu
  • up segment: Shu Fru Flu Nu Thu Fu Du Su Ru Lu Mu Tu Pu/Sha
  • plain segment: Sha Fra Fla Na Tha Fa Da

45edo

uniform solfege (-a = plain, -u = up, -o = down, -i = dup = aug, -e = dud = dim)
45edo edosteps solfege names ups and downs names
unisons 0-2 Da Du Di P1 ^1 A1 C ^C C#
2nds 3-9 Fre Fro Fra Ro Ra Ru Ri d2 vm2 m2 ~2 M2 ^M2 A2 Dbb vDb Db vD D ^D D#
3rds 10-16 Ne No Na Mo Ma Mu Mi d3 vm3 m3 ~3 M3 ^M3 A3 Ebb vEb Eb vE E ^E E#
4ths 17-20 Fe Fo Fa Fu/Po d4 v4 P4 ~4 Fb vF F ^F
tritones 21-24 Fi/Pa Pu/She Pi/Sho Sha/Se A4 ^A4/dd5 AA4/vd5 d5 F# ^F#/Gbb Fx/vGb Gb
5ths 25-28 So Sa Su Si ~5 P5 ^5 A5 vG G ^G G#
6ths 29-35 Fle Flo Fla Lo La Lu Li d6 vm6 m6 ~6 M6 ^M6 A6 Abb vAb Ab vA A ^A A#
7ths 36-42 The Tho Tha To Ta Tu Ti d7 vm7 m7 ^~7 M7 ^M7 A7 Bbb vBb Bb vB B ^B B#
8ves 43-45 (46 47) De Do Da (Du Di) d8 v8 P8 (^8 A8) Cb vC C (^C C#)

Da Sa Ra La Ma Ta Pa/Fi Di Si Ri Li Mi Ti Pi/Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po/Fu Du Su Ru Lu Mu Tu Pu/She Fre Fle Ne The Fe De Se/Sha Fra Fla Na Tha Fa Da

  • plain segment: Da Sa Ra La Ma Ta Pa/Fi
  • dup/aug segment: Fi Di Si Ri Li Mi Ti Pi/Sho
  • down segment: Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po/Fu
  • up segment: Fu Du Su Ru Lu Mu Tu Pu/She
  • dud/dim segment: She Fre Fle Ne The Fe De Se/Sha
  • plain segment: Sha Fra Fla Na Tha Fa Da

46edo

Could use 5 vowels by using -e for dud/upmid.

uniform solfege (-a = plain, -u = up, -o = down, -i = dup/dud = downmid/upmid)
46edo edosteps solfege names ups and downs names
unisons 0-1 Da Du P1 ^1 C ^C
2nds 2-9 Fro Fra Fru Fri Ri Ro Ra Ru vm2 m2 ^m2 v~2 ^~2 vM2 M2 ^M2 vDb Db ^Db ^^Db vvD vD D ^D
3rds 10-17 No Na Nu Ni Mi Mo Ma Mu vm3 m3 ^m3 v~3 ^~3 vM3 M3 ^M3 vEb Eb ^Eb ^^Eb vvE vE E ^E
4ths 18-20 Fo Fa Fu v4 P4 ^4 vF F ^F
tritones 21-25 Fi/Sho Pi/Sha Po/Shu Pa/Shi Pu/Si v~4/vd5 ^~4/d5 vA4/^d5 A4/v~5 ^A4/^~5 ^^F/vGb vvF#/Gb vF#/^Gb F#/^^Gb ^F#/vvG
5ths 26-28 So Sa Su v5 P5 ^5 vG G ^G
6ths 29-36 Flo Fla Flu Fli Li Lo La Lu vm6 m6 ^m6 v~6 ^~6 vM6 M6 ^M6 vAb Ab ^Ab ^^Ab vvA vA A ^A
7ths 37-44 Tho Tha Thu Thi Ti To Ta Tu vm7 m7 ^m7 v~7 ^~7 vM7 M7 ^M7 vBb Bb ^Bb ^^Bb vvB vB B ^B
8ves 45-46 (47) Do Da (Du) v8 P8 (^8) vC C (^C)

Da Sa Ra La Ma Ta Pa/Shi Fri Fli Ni Thi Fi/Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po/Shu Fru Flu Nu Thu Fu Du Su Ru Lu Mu Tu Pu/Si Ri Li Mi Ti Pi/Sha Fra Fla Na Tha Fa Da

  • plain segment: Da Sa Ra La Ma Ta Pa/Shi
  • dup/downmid segment: Shi Fri Fli Ni Thi Fi/Sho
  • down segment: Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po/Shu
  • up segment: Shu Fru Flu Nu Thu Fu Du Su Ru Lu Mu Tu Pu/Si
  • dud/upmid segment: Si Ri Li Mi Ti Pi/Sha
  • plain segment: Sha Fra Fla Na Tha Fa Da

48edo

uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
48edo edosteps solfege names ups and downs names
unisons 0-2 Da Du Di/Fre P1 ^1 ^^1/vvm2 C ^C ^^C/vvDb
2nds 2-10 Di/Fre Fro Fra Fru Fri/Re Ro Ra Ru Ri/Ne ^^1/vvm2 vm2 m2 ^m2 ~2 vM2 M2 ^M2 ^^M2/vvm3 ^^C/vvDb vDb Db ^Db ^^Db/vvD vD D ^D ^^D/vvEb
3rds 10-18 Ri/Ne No Na Nu Ni/Me Mo Ma Mu Mi/Fe ^^M2/vvm3 vm3 m3 ^m3 ~3 vM3 M3 ^M3 ^^M3/vv4 ^^D/vvEb vEb Eb ^Eb ^^Eb/vvE vE E ^E ^^E/vvF
4ths 18-21 Mi/Fe Fo Fa Fu ^^M3/vv4 v4 P4 ^4 ^^E/vvF vF F ^F
tritones 22-26 Fi/Pe/She Po/Sho Pa/Sha Pu/Shu Pi/Shi/Se ^^4/vvA4/vvd5 vA4/vd5 A4/d5 ^A4/^d5 ^^A4/^^d5/vv5 ^^F/vvF#/vvGb vF#/vGb F#/Gb ^F#/^Gb ^^F#/^^Gb/vvG
5ths 27-30 So Sa Su Si/Fle v5 P5 ^5 ^^5/vvm6 vG G ^G ^^G/vvAb
6ths 30-38 Si/Fle Flo Fla Flu Fli/Le Lo La Lu Li/The ^^5/vvm6 vm6 m6 ^m6 ~6 vM6 M6 ^M6 ^^M6/vvm7 ^^G/vvAb vAb Ab ^Ab ^^Ab/vvA vA A ^A ^^A/vvBb
7ths 38-46 Li/The Tho Tha Thu Thi/Te To Ta Tu Ti/De ^^M6/vvm7 vm7 m7 ^m7 ~7 vM7 M7 ^M7 ^^M7/vv8 ^^A/vvBb vBb Bb ^Bb ^^Bb/vvB vB B ^B ^^B/vvC
8ves 46-48 Ti/De Do Da (Du Di) ^^M7/vv8 v8 P8 (^8 ^^8) ^^B/vvC vC C (^C ^^C)
uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud), inbetween names are bolded
48edo edosteps solfege names ups and downs names
unisons 0-2 Da Du Di=Fre P1 ^1 ^^1 C ^C ^^C
2nds 2-10 Fre Fro Fra Fru Fri/Re Ro Ra Ru Ri=Ne vvm2 vm2 m2 ^m2 ~2 vM2 M2 ^M2 ^^M2 vvDb vDb Db ^Db ^^Db/vvD vD D ^D ^^D
3rds 10-18 Ne No Na Nu Ni/Me Mo Ma Mu Mi=Fe vvm3 vm3 m3 ^m3 ~3 vM3 M3 ^M3 ^^M3 vvEb vEb Eb ^Eb ^^Eb/vvE vE E ^E ^^E
4ths 18-22 Fe Fo Fa Fu Fi=Pe/She vv4 v4 P4 ^4 ~4 vvF vF F ^F ^^F
tritones 22-26 Pe/She Po/Sho Pa/Sha Pu/Shu Pi/Shi=Se ~4/vvd5 vA4/vd5 A4/d5 ^A4/^d5 ^^A4/~5 vvF#/vvGb vF#/vGb F#/Gb ^F#/^Gb ^^F#/^^Gb
5ths 26-30 Se So Sa Su Si=Fle ~5 v5 P5 ^5 ^^5 vvG vG G ^G ^^G
6ths 30-38 Fle Flo Fla Flu Fli/Le Lo La Lu Li=The vvm6 vm6 m6 ^m6 ~6 vM6 M6 ^M6 ^^M6 vvAb vAb Ab ^Ab ^^Ab/vvA vA A ^A ^^A
7ths 38-46 The Tho Tha Thu Thi/Te To Ta Tu Ti=De vvm7 vm7 m7 ^m7 ~7 vM7 M7 ^M7 ^^M7 vvBb vBb Bb ^Bb ^^Bb/vvB vB B ^B ^^B
8ves 46-48 De Do Da (Du Di) vv8 v8 P8 (^8 ^^8) vvC vC C (^C ^^C)

Fri/Ni/Fli/Thi are included to make the -i circle complete, so that one can do interval arithmetic within it.

circles of fifths
plain

circle

0 28 8 36 16 44 24 4 32 12 40 20 48
Da Sa Ra La Ma Ta Pa
Sha Fra Fla Na Tha Fa Da
up

circle

1 29 9 37 17 45 25 5 33 13 41 21 1
Du Su Ru Lu Mu Tu Pu
Shu Fru Flu Nu Thu Fu Du
down

circle

47 27 7 35 15 43 23 3 31 11 39 19 47
Do So Ro Lo Mo To Po
Sho Fro Flo No Tho Fo Do
mid /

inbetween

circle

2 30 10 38 18 46 26 6 34 14 42 22 2
Di Si Ri Li Mi Ti Pi
Shi Fri Fli Ni Thi Fi Di
Fre Fle Ne The Fe De Se Re Le Me Te Pe
She Fre
in-between mid

50edo

uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
50edo edosteps solfege names ups and downs names
unisons 0-2 Da Du Di P1 ^1 ^^1 C ^C ^^C
2nds 3-10 Fre Fro Fra Fru Ro Ra Ru Ri vvm2 vm2 m2 ^m2 vM2 M2 ^M2 ^^M2 vvDb vDb Db ^Db vD D ^D ^^D
3rds 11-18 Ne No Na Nu Mo Ma Mu Mi vvm3 vm3 m3 ^m3 vM3 M3 ^M3 ^^M3 vvEb vEb Eb ^Eb vE E ^E ^^E
4ths 19-22 Fe Fo Fa Fu vv4 v4 P4 ^4 vvF vF F ^F
tritones 23-27 Fi/Po Pa/She Pu/Sho Pi/Sha Shu/Se ^^4/vA4 A4/vvd5 ^A4/vd5 ^^A4/d5 ^d5/vv5 ^^F/vF# F#/vvGb ^F#/vGb ^^F#/Gb ^Gb/vvG
5ths 28-31 So Sa Su Si v5 P5 ^5 ^^5 vG G ^G ^^G
6ths 32-39 Fle Flo Fla Flu Lo La Lu Li vvm6 vm6 m6 ^m6 vM6 M6 ^M6 ^^M6 vvAb vAb Ab ^Ab vA A ^A ^^A
7ths 40-47 The Tho Tha Thu To Ta Tu Ti vvm7 vm7 m7 ^m7 vM7 M7 ^M7 ^^M7 vvBb vBb Bb ^Bb vB B ^B ^^B
8ves 48-50 De Do Da (Du Di) vv8 v8 P8 (^8 ^^8) vvC vC C (^C ^^C)

Da Sa Ra La Ma Ta Pa/She Fre Fle Ne The Fe De Se/Shu Fru Flu Nu Thu Fu Du Su Ru Lu Mu Tu Pu/Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po/Fi Di Si Ri Li Mi Ti Pi/Sha Fra Fla Na Tha Fa Da

  • plain segment: Da Sa Ra La Ma Ta Pa/She
  • dud segment: She Fre Fle Ne The Fe De Se/Shu
  • up segment: Shu Fru Flu Nu Thu Fu Du Su Ru Lu Mu Tu Pu/Sho
  • down segment: Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po/Fi
  • dup segment: Fi Di Si Ri Li Mi Ti Pi/Sha
  • plain segment: Sha Fra Fla Na Tha Fa Da

53edo

uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
53edo edosteps solfege names ups and downs names
unisons 0-2 Da Du Di/Fre P1 ^1 ^^1/vvm2
2nds 2-11 Di/Fre Fro Fra Fru Fri Re Ro Ra Ru Ri/Ne ^^1/vvm2 vm2 m2 ^m2 v~2 ^~2 vM2 M2 ^M2 ^^M2/vvm3
3rds 11-20 Ri/Ne No Na Nu Ni Me Mo Ma Mu Mi/Fe ^^M2/vvm3 vm3 m3 ^m3 v~3 ^~3 vM3 M3 ^M3 ^^M3/vv4
4ths 20-23 Mi/Fe Fo Fa Fu ^^M3/vv4 v4 P4 ^4
tritones 24-29 Fi/She Pe/Sho Po/Sha Pa/Shu Pu/Shi Pi/Se v~4/vvd5 ^~4/vd5 vA4/d5 A4/^d5 ^A4/v~5 ^^A4/^~5
5ths 30-33 So Sa Su Si/Fle v5 P5 ^5 ^^5/vvm6
6ths 33-42 Si/Fle Flo Fla Flu Fli Le Lo La Lu Li/The ^^5/vvm6 vm6 m6 ^m6 v~6 ^~6 vM6 M6 ^M6 ^^M6/vvm7
7ths 42-51 Li/The Tho Tha Thu Thi Te To Ta Tu Ti/De ^^M6/vvm7 vm7 m7 ^m7 v~7 ^~7 vM7 M7 ^M7 ^^M7/vv8
8ves 51-53 (54 55) Ti/De Do Da (Du Di) ^^M7/vv8 v8 P8 (^8 ^^8)

Da Sa Ra La Ma Ta Pa/Shu Fru Flu Nu Thu Fu Du Su Ru Lu Mu Tu Pu/Shi Fri Fli Ni Thi Fi/She Di/Fre Si/Fle Ri/Ne Li/The Mi/Fe Ti/De Pi/Se Re Le Me Te Pe/Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po/Sha Fra Fla Na Tha Fa Da

  • plain segment: Da Sa Ra La Ma Ta Pa/Shu
  • up segment: Shu Fru Flu Nu Thu Fu Du Su Ru Lu Mu Tu Pu/Shi
  • dup segment: Shi Fri Fli Ni Thi Fi/She
  • dup/dud segment: Fi/She Di/Fre Si/Fle Ri/Ne Li/The Mi/Fe Ti/De Pi/Se
  • dud segment: Se Re Le Me Te Pe/Sho
  • down segment: Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po/Sha
  • plain segment: Sha Fra Fla Na Tha Fa Da
Phylingual's solfege
53edo edosteps solfege names ups and downs names
unisons 0-2 Do Di Daw P1 ^1 ^^1
2nds 3-11 Ro Rih Ra Ru Ruh Reh Re Ri Raw vm2 m2 ^m2 v~2 ^~2 vM2 M2 ^M2 ^^M2
3rds 12-20 Ma Meh Me Mu Muh Mi Maa Mo Maw vm3 m3 ^m3 v~3 ^~3 vM3 M3 ^M3 ^^M3
4ths 21-26 Fe Fa Fih Fu Fuh Fi v4 P4 ^4 v~4 ^~4 vA4
5ths 27-33 Se Suh Su Sih So (or Sol) Si Saw ^d5 v~5 ^~5 v5 P5 ^5 ^^5
6ths 34-42 Lo Leh Le Lu Luh La Laa Li Law vm6 m6 ^m6 v~6 ^~6 vM6 M6 ^M6 ^^M6
7ths 43-51 Ta Teh Te Tu Tuh Ti Tih To Taw vm7 m7 ^m7 v~7 ^~7 vM7 M7 ^M7 ^^M7
8ves 52-(55) Da Do (Di Daw) v8 P8 (^8 ^^8)

55edo

uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
55edo edosteps solfege names ups and downs names
unisons 0-2 Da Du Di P1 ^1 ^^1 C ^C ^^C
2nds 3-11 Fre Fro Fra Fru Re Ro Ra Ru Ri vvm2 vm2 m2 ^m2 ~2 vM2 M2 ^M2 ^^M2 vvDb vDb Db ^Db vvD vD D ^D ^^D
3rds 12-20 Ne No Na Nu Me Mo Ma Mu Mi vvm3 vm3 m3 ^m3 ~3 vM3 M3 ^M3 ^^M3 vvEb vEb Eb ^Eb vvE vE E ^E ^^E
4ths 21-25 Fe Fo Fa Fu Fi/Pe vv4 v4 P4 ^4 ~4 vvF vF F ^F ^^F
tritones 26-29 Po/She Pa/Sho Pu/Sha Pi/Shu vA4/vvd5 A4/vd5 ^A4/d5 ^^A4/^d5 vF#/vvGb F#/vGb ^F#/Gb ^^F#/^Gb
5ths 30-34 Se So Sa Su Si ~5 v5 P5 ^5 ^^5 vvG vG G ^G ^^G
6ths 35-43 Fle Flo Fla Flu Le Lo La Lu Li vvm6 vm6 m6 ^m6 ~6 vM6 M6 ^M6 ^^M6 vvAb vAb Ab ^Ab vvA vA A ^A ^^A
7ths 44-52 The Tho Tha Thu Te To Ta Tu Ti vvm7 vm7 m7 ^m7 ~7 vM7 M7 ^M7 ^^M7 vvBb vBb Bb ^Bb vvB vB B ^B ^^B
8ves 53-55 De Do Da (Du Di) vv8 v8 P8 (^8 ^^8) vvC vC C (^C ^^C)

Da Sa Ra La Ma Ta Pa/Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po/She Fre Fle Ne The Fe De Se Re Le Me Te Pe/Fi Di Si Ri Li Mi Ti Pi/Shu Fru Flu Nu Thu Fu Du Su Ru Lu Mu Tu Pu/Sha Fra Fla Na Tha Fa Da

  • plain segment: Da Sa Ra La Ma Ta Pa/Sho
  • down segment: Sho Fro Flo No Tho Fo Do So Ro Lo Mo To Po/She
  • dud segment: She Fre Fle Ne The Fe De Se Re Le Me Te Pe/Fi
  • dup segment: Fi Di Si Ri Li Mi Ti Pi/Shu
  • up segment: Shu Fru Flu Nu Thu Fu Du Su Ru Lu Mu Tu Pu/Sha
  • plain segment: Sha Fra Fla Na Tha Fa Da

60edo

uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
60edo edosteps solfege names ups and downs names
unisons 0-2 Da Du Di P1 ^1 ^^1 C ^C ^^C
2nds 3-12 Fre Fro Fra Fru Fri Re Ro Ra Ru Ri vvm2 vm2 m2 ^m2 v~2 ^~2 vM2 M2 ^M2 ^^M2 vvDb vDb Db ^Db ^^Db vvD vD D ^D ^^D
3rds 13-22 Ne No Na Nu Ni Me Mo Ma Mu Mi vvm3 vm3 m3 ^m3 v~3 ^~3 vM3 M3 ^M3 ^^M3 vvEb vEb Eb ^Eb ^^Eb vvE vE E ^E ^^E
4ths 23-27 Fe Fo Fa Fu Fi vv4 v4 P4 ^4 v~4 vvF vF F ^F ^^F
tritones 28-32 Pe/She Po/Sho Pa/Sha Pu/Shu Pi/Shi ^~4/vvd5 vA4/vd5 A4/d5 ^A4/^d5 ^^A4/v~5 vvF#/vvGb vF#/vGb F#/Gb ^F#/^Gb ^^F#/^^Gb
5ths 33-37 Se So Sa Su Si ^~5 v5 P5 ^5 ^^5 vvG vG G ^G ^^G
6ths 38-47 Fle Flo Fla Flu Fli Le Lo La Lu Li vvm6 vm6 m6 ^m6 v~6 ^~6 vM6 M6 ^M6 ^^M6 vvAb vAb Ab ^Ab ^^Ab vvA vA A ^A ^^A
7ths 48-57 The Tho Tha Thu Thi Te To Ta Tu Ti vvm7 vm7 m7 ^m7 v~7 ^~7 vM7 M7 ^M7 ^^M7 vvBb vBb Bb ^Bb ^^Bb vvB vB B ^B ^^B
8ves 58-60 De Do Da (Du Di) vv8 v8 P8 (^8 ^^8) vvC vC C (^C ^^C)
circles of fifths
plain

circle

0 35 10 45 20 55 30 5 40 15 50 25 60
Da Sa Ra La Ma Ta Pa
Sha Fra Fla Na Tha Fa Da
up

circle

1 36 11 46 21 56 31 6 41 16 51 26 1
Du Su Ru Lu Mu Tu Pu
Shu Fru Flu Nu Thu Fu Du
down

circle

59 34 9 44 19 54 29 64 39 74 49 84 59
Do So Ro Lo Mo To Po
Sho Fro Flo No Tho Fo Do
dup

circle

2 37 12 47 22 57 32 7 42 17 52 27 2
Di Si Ri Li Mi Ti Pi
Shi Fri Fli Ni Thi Fi Di
dud circle 58 33 8 43 18 53 28 3 38 13 48 23 58
De Se Re Le Me Te Pe
She Fre Fle Ne The Fe De

Rank-2 Uniform Solfeges by Pergen

Rank-2 temperaments have an infinite number of notes, so a solfege can only cover a fraction of them. But often one only uses enough notes to make a MOS scale. Pergens tell us how to use ups and downs to notate them, and the same consonants and vowels can be used. Instead of circles of 5ths, there are fifthchains. Each fifthchain requires its own vowel, so there is a maximum of 5 fifthchains.

Genchains are distinct from fifthchains. Each pergen has one or more genchains, each of which contains one or more fifthchains. However if the octave is split in halves or quarters, the half-octave requires two names, and the pergen needs an additional vowel. The 13 consonants and 5 vowels cover about 20 pergens. Of course, the genchains can only extend so far with only 13 consonants. But in general, it's enough to cover all the modes of any reasonably-sized MOS scale.

Sometimes -i and -e mean lift/drop not dup/dud. If so, note that there are no words for uplift, downlift, etc. -i never means mid, so there are only two vowel sequences, not three:

the two vowel sequences
3 vowels -o = down -a = plain -u = up
5 vowels -e = dud or drop -o = down -a = plain -u = up -i = dup or lift

In the MOS scale tables, any note that changes from one mode to the next is bolded.

The EU (enharmonic unison) can be added to or subtracted from any note or interval to get an equivalent note or interval.

A pergen's solfege can suggest an edo's solfege. For example, 22edo supports (P8, P4/3), and the pergen's solfege has 27 notes in it. Since the generator is 3\22, simply apply the genchain to every 3rd edostep of 22edo. The extra 5 names make duplicate names.to do:

  • explain c is P5 - 700¢
  • explain the 1st mode always has Sa and not Fa, and the last mode always has Fa and not Sa.
  • make a table of pergens and what MOS scales each one covers
  • discuss using numeric solfeges with non-diatonic-friendly MOSes
  • for each pergen, list the entire genchain in melodic order, if possible?
  • explain temperament naming: can use Aug and Dim syllables to extend the genchains, can use -a- for an omitted prime.

List of MOS scales

Some combos of pergens and MOS scales require a very sharp or flat 5th. Just as with superflat edos, a uniform solfege can still be used, but the sound of the interval won't match what its name implies. Better to use a different pergen.

MOS scales and good pergens for them (bolded = requires more than 5 vowels)
MOS scale primary example secondary examples
Pentatonic
1L 4s (P8, P5/3) [5] third-5th pentatonic third-4th, quarter-4th, quarter-5th
2L 3s (P8, P5) [5] unsplit pentatonic third-11th
3L 2s (P8, P12/4) [5] quarter-12th pentatonic quarter-11th
4L 1s (P8, P4/2) [5] half-4th pentatonic
Hexatonic
1L 5s (P8, P4/3) [6] third-4th hexatonic quarter-4th, quarter-5th, fifth-4th, fifth-5th
2L 4s (P8/2, P5) [6] half-8ve hexatonic
3L 3s (P8/3, P5) [6] third-8ve hexatonic
4L 2s (P8/2, P4/2) [6] half-everything hexatonic
5L 1s (P8, P5/3) [6] third-5th hexatonic
Heptatonic
1L 6s (P8, P4/3) [7] third-4th heptatonic quarter-4th, fifth-4th, fifth-5th, sixth-4th, sixth-5th
2L 5s (P8, P11/3) [7] third-11th heptatonic fifth-coco-4th, sixth-coco-5th
3L 4s (P8, P5/2) [7] half-5th heptatonic fifth-12th
4L 3s (P8, P11/5) [7] fifth-11th heptatonic sixth-12th
5L 2s (P8, P5) [7] unsplit heptatonic sixth-coco-4th
6L 1s (P8, P5/4) [7] quarter-5th heptatonic
Octotonic
1L 7s (P8, P4/4) [8] quarter-4th octotonic fifth-4th, fifth-5th, sixth-4th, sixth-5th, seventh-4th, seventh-5th
2L 6s (P8/2, P5) [8] half-8ve octotonic
3L 5s (P8, P11/4) [8] quarter-11th octotonic seventh-cc4th, seventh-cc5th
4L 4s (P8/4, P5) [8] quarter-8ve octotonic
5L 3s (P8, P12/4) [8] quarter-12th octotonic (very lopsided, unless 5th is quite flat)
6L 2s (P8/2, P4/3) [8] half-8ve third-4th octotonic
7L 1s (P8, P4/3) [8] third-4th octotonic
Nonatonic
1L 8s (P8, P4/4) [9] quarter-4th nonatonic fifth-4th, sixth-4th, sixth-5th, seventh-4th/5th, eighth-4th/5th
2L 7s (P8, c3P5/8) [9] eighth-trico-5th nonatonic third-11th, fifth-coco-4th
3L 6s (P8/3, P5) [9] third-8ve nonatonic third-8ve half-5th
4L 5s (P8, P12/7) [9] seventh-12th nonatonic sixth-11th
5L 4s (P8, P4/2) [9] half-4th nonatonic (lopsided unless 4th is sharp), seventh-11th
6L 3s (P8/3, P4/2) [9] third-8ve half-4th nonatonic
7L 2s (P8, ccP5/6)[9] sixth-coco-5th nonatonic (lopsided unless 5th is sharp)
8L 1s (P8, P5/5) [9] fifth-5th nonatonic
Decatonic
1L 9s (P8, P5/6) [10] sixth-5th decatonic fifth-4th, sixth-4th, seventh-4th/5th, eighth-4th/5th, ninth-4th/5th
2L 8s (P8/2, P5) [10] half-8ve decatonic half-8ve quartertone, half-8ve third-11th
3L 7s (P8, P12/5) [10] fifth-12th decatonic eighth-cc4th, eighth-cc5th
4L 6s (P8/2, P4/2) [10] half-everything decatonic
5L 5s (P8/2, P5) [10] half-8ve decatonic (lopsided unless 5th is quite flat)
6L 4s (P8/2, P5/3) [10] half-8ve third-5th decatonic
7L 3s (P8, P5/2) [10] half-5th decatonic ninth-coco-5th
8L 2s (P8/2, P4/4) [10] half-8ve quarter-4th decatonic half-8ve quarter-12th
9L 1s (P8, P4/2) [10] quarter-4th decatonic

#1 (P8, P5) unsplit

  • G = P5 = 700¢ + c
  • EU = vA1 = 0¢ (extended solfege only)
  • ^ = # = 100 + 7c (extended solfege only)

MOS scales covered:

  • 5 = 2L3s (1\2 < P5 < 3\5) (for 3L2s, use P11/4 or P12/4, to avoid P5 > 3\5= 720¢)
  • 7 = 5L2s (4\7 < P5 < 3\5) (for 2L5s, perhaps use P11/3 or ccP4/5, to avoid P5 < 4\7 = 686¢)
  • 12 = 7L5s or 5L7s (4\7 < P5 < 3\5) (extended solfege only)
uniform solfege (-a = plain)
genspan -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
solfege Sha Fra Fla Na Tha Fa Da Sa Ra La Ma Ta Pa
intervals d5 m2 m6 m3 m7 P4 P1 P5 M2 M6 M3 M7 A4
notes Gb Db Ab Eb Bb F C G D A E B F#
extended uniform solfege (-a = plain, -u = up = aug, -o = down = dim)
genspan -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
solfege Sho Fro Flo No Tho Fo Do So/Sha Fra Fla Na Tha Fa Da Sa Ra La Ma Ta Pa/Fu Du Su Ru Lu Mu Tu Pu
intervals dd5 d2 d6 d3 d7 d4 d8 d5 m2 m6 m3 m7 P4 P1 P5 M2 M6 M3 M7 A4 A1 A5 A2 A6 A3 A7 AA4
notes Gbb Dbb Abb Ebb Bbb Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# Fx
2L3s MOS scales (L = m3, s = M2), L/s = (300-3c)/(200+2c)
GMN name scale 0 1 2 3 4 5
1st 2L3s ssLsL Ionian Da Ra Ma Sa La Da
2nd 2L3s sLssL Mixolydian Da Ra Fa Sa La Da
3rd 2L3s sLsLs Dorian Da Ra Fa Sa Tha Da
4th 2L3s LssLs Aolian Da Na Fa Sa Tha Da
5th 2L3s LsLss Phrygian Da Na Fa Fla Tha Da
5L2s MOS scales (L = M2, s = m2), L/s = (200+2c)/(100-5c)
GMN name scale 1sn 2nd 3rd 4th 5th 6th 7th 8ve
1st 5L2s LLLsLLs Lydian Da Ra Ma Pa Sa La Ta Da
2nd 5L2s LLsLLLs Ionian Da Ra Ma Fa Sa La Ta Da
3rd 5L2s LLsLLsL Mixolydian Da Ra Ma Fa Sa La Tha Da
4th 5L2s LsLLLsL Dorian Da Ra Na Fa Sa La Tha Da
5th 5L2s LsLLsLL Aolian Da Ra Na Fa Sa Fla Tha Da
6th 5L2s sLLLsLL Phrygian Da Fra Na Fa Sa Fla Tha Da
7th 5L2s sLLsLLL Locrian Da Fra Na Fa Sha Fla Tha Da
5L7s MOS scales (L = A1/^1, s = m2/vM2) using the extended solfege, L/s = (100+7c)/(100-5c) if P5 > 700¢, swap L and s to get 7L5s
GMN name scale 0 1 2 3 4 5 6 7 8 9 10 11 12
1st 5L7s LsLsLssLsLss Da Du Ra Ru Ma Mu Pa/Fu Sa Su La Lu Ta Da
2nd 5L7s LsLssLsLsLss Da Du Ra Ru Ma Fa Pa/Fu Sa Su La Lu Ta Da
3rd 5L7s LsLssLsLssLs Da Du Ra Ru Ma Fa Pa/Fu Sa Su La Tha Ta Da
4th 5L7s LssLsLsLssLs Da Du Ra Na Ma Fa Pa/Fu Sa Su La Tha Ta Da
5th 5L7s LssLsLssLsLs Da Du Ra Na Ma Fa Pa/Fu Sa Fla La Tha Ta Da
6th 5L7s sLsLsLssLsLs Da Fra Ra Na Ma Fa Pa Sa Fla La Tha Ta Da
7th 5L7s sLsLssLsLsLs Da Fra Ra Na Ma Fa Sha Sa Fla La Tha Ta Da
8th 5L7s sLsLssLsLssL Da Fra Ra Na Ma Fa Sha/So Sa Fla La Tha Do Da
9th 5L7s sLssLsLsLssL Da Fra Ra Na Fo Fa Sha/So Sa Fla La Tha Do Da
10th 5L7s sLssLsLssLsL Da Fra Ra Na Fo Fa Sha/So Sa Fla Tho Tha Do Da
11th 5L7s ssLsLsLssLsL Da Fra No Na Fo Fa Sha/So Sa Fla Tho Tha Do Da
12th 5L7s ssLsLssLsLsL Da Fra No Na Fo Fa Sha/So Flo Fla Tho Tha Do Da

Meantone keyboards were usually tuned to the 4th mode (a fifthchain from Eb to G#).

The sequence of scales starts off with 6 sharps and ends with 7 flats and 3 double-flats:

  • C C# D D# E E# F# G G# A A# B C
  • C C# D D# E F F# G G# A A# B C
  • C C# D D# E F F# G G# A Bb B C
  • and so on until it ends with
  • C Db Ebb Eb Fb F Gb Abb Ab Bbb Bb Cb C

12edo's uniform solfege #2 is a merging of the 2nd through 7th modes.

If the solfege is further extended with -i = dup and -e = dud, it can cover the 19-note MOS scales 12L7s and 7L12s.

#2 (P8/2, P5) half-8ve

There are two solfeges. Use solfege #1 if P5 > 700¢, and use solfege #2 if P5 < 700¢.

  • P = vA4/^d5 (solfege #1) or ^A4/vd5 (solfege #2) = 600¢
  • G = P5 = 700¢ + c
  • or vA1/^m2 (solfege #1) = 100¢ + c
  • or ^A1/vm2 (solfege #2) = 100¢ + c
  • EU = ^^d2 (solfege #1) = 0¢
  • or vvd2 (solfege #2) = 0¢
  • ^ = 6 ⋅ |c|

MOS scales covered:

  • 8 = 2L6s (either solfege) or 6L2s (solfege #1 only, P5 > 5\8 = 750¢)
  • 10 = 2L8s (either solfege) or 8L2s (solfege #1 only, P5 > 3\5 = 720¢)
  • 12 = 10L2s (solfege #1 only) or 2L10s (solfege #2 only)
  • 14 = 12L2s (solfege #2 only)

Solfege #1 (P5 > 700¢)

uniform solfege #1 (P5 > 700¢) (-a = plain, -u = up, -o = down)
genspan (gen = P5) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
plain

genchain

perspan = 0

solfege Sha Fra Fla Na Tha Fa Da Sa Ra La Ma Ta Pa
intervals d5 m2 m6 m3 m7 P4 P1 P5 M2 M6 M3 M7 A4
notes Gb Db Ab Eb Bb F C G D A E B F#
up/down

genchain

perspan = ±1

solfege Do So Ro Lo Mo To Po/Shu Fru Flu Nu Thu Fu Du
intervals v8 v5 vM2 vM6 vM3 vM7 vA4/^d5 ^m2 ^m6 ^m3 ^m7 ^4 ^1
notes vC vG vD vA vE vB vF#/^Gb ^Db ^Ab ^Eb ^Bb ^F ^C
uniform solfege #1 (P5 > 700¢) (-a = plain, -u = up, -o = down)
genspan (gen = vA1/^m2) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Da's

genchain

perspan = 0

solfege Sha So Fla Lo Tha To Da Fru Ra Nu Ma Fu Pa
intervals d5 v5 m6 vM6 m7 vM7 P1 ^m2 M2 ^m3 M3 ^4 A4
notes Gb vG Ab vA Bb vB C ^Db D ^Eb E ^F F#
Sa's

genchain

perspan = ±1

solfege Do Fra Ro Na Mo Fa Po/Shu Sa Flu La Thu Ta Du
intervals v8 m2 vM2 m3 vM3 P4 vA4/^d5 P5 ^m6 M6 ^m7 M7 ^1
notes vC Db vD Eb vE F vF#/^Gb G ^Ab A ^Bb B ^C
2L6s MOS scales using solfege #1 (L = m3/vvA2, s = vA1/^m2) if P5 > 5\8 = 750¢, swap L and s to get 6L2s
GMN name scale 0 1 2 3 4 5 6 7 8
1st 2L6s sssL-sssL Da Fru Ra Nu Po/Shu Sa Flu La Da
2nd 2L6s ssLs-ssLs Da Fru Ra Fa Po/Shu Sa Flu To Da
3rd 2L6s sLss-sLss Da Fru Mo Fa Po/Shu Sa Tha To Da
4th 2L6s Lsss-Lsss Da Na Mo Fa Po/Shu Lo Tha To Da
2L8s MOS scales using solfege #1 (L = vM2/^d3, s = vA1/^m2) if P5 > 3\5 = 720¢, swap L and s to get 8L2s
GMN name scale 1sn 2nd 3rd tritone 6th 7th 8ve
1st 2L8s ssssL-ssssL Da Fru Ra Nu Ma Po/Shu Sa Flu La Thu Da
2nd 2L8s sssLs-sssLs Da Fru Ra Nu Fa Po/Shu Sa Flu La To Da
3rd 2L8s ssLss-ssLss Da Fru Ra Mo Fa Po/Shu Sa Flu Tha To Da
4th 2L8s sLsss-sLsss Da Fru Na Mo Fa Po/Shu Sa Lo Tha To Da
5th 2L8s Lssss-Lssss Da Ro Na Mo Fa Po/Shu Fla Lo Tha To Da
10L2s MOS scales using solfege #1 (L = vA1/^m2, s = vvA1/m2)
GMN name scale 1sn 2nds 3rds 4th tritone 5th 6ths 7ths 8ve
1st 10L2s LLLLLs-LLLLLs Da Fru Ra Nu Ma Fu Shu Sa Flu La Thu Ta Da
2nd 10L2s LLLLsL-LLLLsL Da Fru Ra Nu Ma Fa Po/Shu Sa Flu La Thu To Da
3rd 10L2s LLLsLL-LLLsLL Da Fru Ra Nu Mo Fa Po/Shu Sa Flu La Tha To Da
4th 10L2s LLsLLL-LLsLLL Da Fru Ra Na Mo Fa Po/Shu Sa Flu Lo Tha To Da
5th 10L2s LsLLLL-LsLLLL Da Fru Ro Na Mo Fa Po/Shu Sa Fla Lo Tha To Da
6th 10L2s sLLLLL-sLLLLL Da Fra Ro Na Mo Fa Po So Fla Lo Tha To Da

Solfege #2 (P5 < 700¢)

uniform solfege #2 (P5 < 700¢) (-a = plain, -u = up, -o = down)
genspan (gen = P5) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
plain

genchain

perspan = 0

solfege Sha Fra Fla Na Tha Fa Da Sa Ra La Ma Ta Pa
intervals d5 m2 m6 m3 m7 P4 P1 P5 M2 M6 M3 M7 A4
notes Gb Db Ab Eb Bb F C G D A E B F#
up/down

genchain

perspan = ±1

solfege Du Su Ru Lu Mu Tu Pu/Sho Fro Flo No Tho Fo Do
intervals ^1 ^5 ^M2 ^M6 ^M3 ^M7 ^A4/vd5 vm2 vm6 vm3 vm7 v4 v8
notes ^C ^G ^D ^A ^E ^B ^F#/vGb vDb vAb vEb vBb vF vC
uniform solfege #2 (P5 < 700¢) (-a = plain, -u = up, -o = down)
genspan (gen = ^A1/vm2) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Da's

genchain

perspan = 0

solfege Sha Su Fla Lu Tha Tu Da Fro Ra No Ma Fo Pa
intervals d5 ^5 m6 ^M6 m7 ^M7 P1 vm2 M2 vm3 M3 v4 A4
notes Gb ^G Ab ^A Bb ^B C vDb D vEb E vF F#
Sa's

genchain

perspan = ±1

solfege Du Fra Ru Na Mu Fa Pu/Sho Sa Flo La Tho Ta Do
intervals ^1 m2 ^M2 m3 ^M3 P4 ^A4/vd5 P5 vm6 M6 vm7 M7 v8
notes ^C Db ^D Eb ^E F ^F#/vGb G vAb A vBb B vC
2L6s MOS scales using solfege #2 (L = m3/^^A2, s = ^A1/vm2)
GMN name scale 0 1 2 3 4 5 6 7 8
1st 2L6s sssL-sssL Da Fro Ra No Pu/Sho Sa Flo La Da
2nd 2L6s ssLs-ssLs Da Fro Ra Fa Pu/Sho Sa Flo Tu Da
3rd 2L6s sLss-sLss Da Fro Mu Fa Pu/Sho Sa Tha Tu Da
4th 2L6s Lsss-Lsss Da Na Mu Fa Pu/Sho Lu Tha Tu Da
2L8s MOS scales using solfege #2 (L = ^M2/vd3, s = ^A1/vm2)
GMN name scale 1sn 2nd 3rd tritone 6th 7th 8ve
1st 2L8s ssssL-ssssL Da Fro Ra No Ma Pu/Sho Sa Flo La Tho Da
2nd 2L8s sssLs-sssLs Da Fro Ra No Fa Pu/Sho Sa Flo La Tu Da
3rd 2L8s ssLss-ssLss Da Fro Ra Mu Fa Pu/Sho Sa Flo Tha Tu Da
4th 2L8s sLsss-sLsss Da Fro Na Mu Fa Pu/Sho Sa Lu Tha Tu Da
5th 2L8s Lssss-Lssss Da Ru Na Mu Fa Pu/Sho Fla Lu Tha Tu Da
2L10s MOS scales using solfege #2 (L = ^^A1/m2, s = ^A1/vm2)
GMN name scale 1sn 2nds 3rds 4th tritone 5th 6ths 7ths 8ve
1st 2L10s sssssL-sssssL Da Fro Ra No Ma Fo Pu/Sho Sa Flo La Tho Ta Da
2nd 2L10s ssssLs-ssssLs Da Fro Ra No Ma Fa Pu/Sho Sa Flo La Tho Tu Da
3rd 2L10s sssLss-sssLss Da Fro Ra No Mu Fa Pu/Sho Sa Flo La Tha Tu Da
4th 2L10s ssLsss-ssLsss Da Fro Ra Na Mu Fa Pu/Sho Sa Flo Lu Tha Tu Da
5th 2L10s sLssss-sLssss Da Fro Ru Na Mu Fa Pu/Sho Sa Fla Lu Tha Tu Da
6th 2L10s Lsssss-Lsssss Da Fra Ru Na Mu Fa Pu/Sho Su Fla Lu Tha Tu Da
12L2s MOS scales using solfege #2 (L = ^A1/vm2, s = ^1) -- P5 must be < 700¢, or s will be < 0¢
GMN name scale 1sn 2nd 3rd 4th 5th 6th 7th 8ve
1st 12L2s LLLLLLs-LLLLLLs Da Fro Ra No Ma Fo Pa Pu/Sho Sa Flo La Tho Ta Do Da
2nd 12L2s LLLLLsL-LLLLLsL Da Fro Ra No Ma Fo Fa Pu/Sho Sa Flo La Tho Ta Tu Da
3rd 12L2s LLLLsLL-LLLLsLL Da Fro Ra No Ma Mu Fa Pu/Sho Sa Flo La Tho Tha Tu Da
4th 12L2s LLLsLLL-LLLsLLL Da Fro Ra No Na Mu Fa Pu/Sho Sa Flo La Lu Tha Tu Da
5th 12L2s LLsLLLL-LLsLLLL Da Fro Ra Ru Na Mu Fa Pu/Sho Sa Flo Fla Lu Tha Tu Da
6th 12L2s LsLLLLL-LsLLLLL Da Fro Fra Ru Na Mu Fa Pu/Sho Sa Su Fla Lu Tha Tu Da
7th 12L2s sLLLLLL-sLLLLLL Da Du Fra Ru Na Mu Fa Pu/Sho Sha Su Fla Lu Tha Tu Da

#3 (P8, P4/2) half-4th

  • G = ^M2/vm3 = 250¢ - c/2
  • EU = vvm2 = 0¢
  • ^ = 50¢ - 2.5c

MOS scales covered:

  • 5 = 4L1s (for 1L4s use pergen #8, third-5th)
  • 9 = 5L4s or 4L5s (P5 < 5\9 = 667¢)
  • 14 = 9L5s or 5L9s (P5 < 4\7 = 686¢)
uniform solfege (-a = plain, -u = up, -o = down)
genspan 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13
solfege Flu Sha Nu Fra Thu Fla Fu

Sho

Na Du

Fro

Tha Su

Flo

Fa Ru

No

Da Lu

Tho

Sa Mu

Fo

Ra Tu

Do

La Pu

So

Ma Ro Ta Lo Pa Mo
intervals ^m6 d5 ^m3 m2 ^m7 m6 ^4

vd5

m3 ^1

vm2

m7 ^5

vm6

P4 ^M2

vm3

P1 ^M6

vm7

P5 ^M3

v4

M2 ^M7

v8

M6 ^A4

v5

M3 vM2 M7 vM6 A4 vM3
notes ^Ab Gb ^Eb Db ^Bb Ab ^F

vGb

Eb ^C

vDb

Bb ^G

vAb

F ^D

vEb

C ^A

vBb

G ^E

vF

D ^B

vC

A ^F#

vG

E vD B vA F# vE
4L1s MOS scales (L = ^M2/vm3 = no rhyme, s = M2 = rhymes)
GMN name scale 0 1 2 3 4 5
1st 4L1s sLLLL Da Ra Mu/Fo Sa Lu/Tho Da
2nd 4L1s LsLLL Da Ru/No Mu/Fo Sa Lu/Tho Da
3rd 4L1s LLsLL Da Ru/No Fa Sa Lu/Tho Da
4th 4L1s LLLsL Da Ru/No Fa Su/Flo Lu/Tho Da
5th 4L1s LLLLs Da Ru/No Fa Su/Flo Tha Da
5L4s MOS scales (L = M2 = rhymes, s = ^1/vm2 = no rhyme) if P5 < 5\9 = 667¢, swap L and s to get 4L5s
GMN name scale 0 1 2 3 4 5 6 7 8 9
1st 5L4s LLsLsLsLs Da Ra Ma Mu/Fo Pu/So Sa La Lu/Tho Tu/Do Da
2nd 5L4s LsLLsLsLs Da Ra Ru/No Mu/Fo Pu/So Sa La Lu/Tho Tu/Do Da
3rd 5L4s LsLsLLsLs Da Ra Ru/No Mu/Fo Fa Sa La Lu/Tho Tu/Do Da
4th 5L4s LsLsLsLLs Da Ra Ru/No Mu/Fo Fa Sa Su/Flo Lu/Tho Tu/Do Da
5th 5L4s LsLsLsLsL Da Ra Ru/No Mu/Fo Fa Sa Su/Flo Lu/Tho Tha Da
6th 5L4s sLLsLsLsL Da Du/Fro Ru/No Mu/Fo Fa Sa Su/Flo Lu/Tho Tha Da
7th 5L4s sLsLLsLsL Da Du/Fro Ru/No Na Fa Sa Su/Flo Lu/Tho Tha Da
8th 5L4s sLsLsLLsL Da Du/Fro Ru/No Na Fa Fu/Sho Su/Flo Lu/Tho Tha Da
9th 5L4s sLsLsLsLL Da Du/Fro Ru/No Na Fa Fu/Sho Su/Flo Fla Tha Da

A similar table can be made for 5L9s. The same solfege can be used for 9L5s, but Sa will be < 4\7 = 686¢.

#4 (P8, P5/2) half-5th (list alternate pergens)

  • G = ^m3/vM3 = ~3 = 350¢ + c/2
  • EU = vvA1 = 0¢
  • ^ = 50¢ + 3.5c

MOS scales covered:

  • 7 = 3L4s (and 4L3s if P5 < 4\7 = 686¢)
  • 10 = 7L3s (and 3L7s if P5 > 3\5 = 720¢)
  • 13 = 10L3s (if P5 > 3\5 = 720¢) and 3L10s (if P5 > 8\13)
uniform solfege (-a = plain, -u = up, -o = down)
genspan -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
solfege No Sha Tho Fra Fo Fla Do Na So

Shu

Tha Ro

Fru

Fa Lo

Flu

Da Mo

Nu

Sa To

Thu

Ra Po

Fu

La Du Ma Su Ta Ru Pa Lu
intervals vm3 d5 vm7 m2 v4 m6 v8 m3 ~5 m7 ~2 P4 ~6 P1 ~3 P5 ~7 M2 ~4 M6 ^1 M3 ^5 M7 ^M2 A4 ^M6
notes vEb Gb vBb Db vF Ab vC Eb ^Gb

vG

Bb ^Db

vD

F ^Ab

vA

C ^Eb

vE

G ^Bb

vB

D ^F

vF#

A ^C E ^G B ^D F# ^A

for 7-note scales, up notes aren't needed, because every up note can be sung as a down note.

3L4s MOS scales (L = M2 = rhymes, s = ~2 = no rhyme) if P5 < 4\7 = 686¢, swap L and s to get 4L3s
GMN name scale 1sn 2nd 3rd 4th 5th 6th 7th 8ve
1st 3L4s LsLsLss Da Ra Mo Po Sa La To Da
2nd 3L4s LsLssLs Da Ra Mo Po Sa Lo To Da
3rd 3L4s LssLsLs Da Ra Mo Fa Sa Lo To Da
4th 3L4s sLsLsLs Da Ro Mo Fa Sa Lo To Da
5th 3L4s sLsLssL Da Ro Mo Fa Sa Lo Tha Da
6th 3L4s sLssLsL Da Ro Mo Fa So Lo Tha Da
7th 3L4s ssLsLsL Da Ro Na Fa So Lo Tha Da

For 10-note scales, both up notes and down notes are needed.

7L3s MOS scales (L = ^m2 = vM2 = different degree, s = ^1 = vA1 = same degree) if P5 > 3\5 = 720¢, swap L and s to get 3L7s
GMN name scale 0 1 2 3 4 5 6 7 8 9 10
1st 7L3s sLLsLLsLLL Da Du Ra Nu/Mo Ma Fu/Po Sa Su La Thu/To Da
2nd 7L3s sLLsLLLsLL Da Du Ra Nu/Mo Ma Fu/Po Sa Flu/Lo La Thu/To Da
3rd 7L3s sLLLsLLsLL Da Du Ra Nu/Mo Fa Fu/Po Sa Flu/Lo La Thu/To Da
4th 7L3s LsLLsLLsLL Da Fru/Ro Ra Nu/Mo Fa Fu/Po Sa Flu/Lo La Thu/To Da
5th 7L3s LsLLsLLLsL Da Fru/Ro Ra Nu/Mo Fa Fu/Po Sa Flu/Lo Tha Thu/To Da
6th 7L3s LsLLLsLLsL Da Fru/Ro Ra Nu/Mo Fa Shu/So Sa Flu/Lo Tha Thu/To Da
7th 7L3s LLsLLsLLsL Da Fru/Ro Na Nu/Mo Fa Shu/So Sa Flu/Lo Tha Thu/To Da
8th 7L3s LLsLLsLLLs Da Fru/Ro Na Nu/Mo Fa Shu/So Sa Flu/Lo Tha Do Da
9th 7L3s LLsLLLsLLs Da Fru/Ro Na Nu/Mo Fa Shu/So Fla Flu/Lo Tha Do Da
10th 7L3s LLLsLLsLLs Da Fru/Ro Na Fo Fa Shu/So Fla Flu/Lo Tha Do Da

#5 (P8/2, P4/2) half-everything (incomplete)

It has only 4 fifthchains, but two of them require double names. Hmm, must think about this...

#6 (P8/3, P5) third-8ve

There are two solfeges. Use solfege #1 if P5 > 700¢, and use solfege #2 if P5 < 700¢.

  • P = vM3/^^d4 (solfege #1) or ^M3/vvd4 (solfege #2) = 400¢
  • G = P5 = 700¢ + c or vvA1/^m2 (solfege #1) or ^^A1/vm2 (solfege #2) = 100¢ - c
  • EU = ^3d2 = 0¢
  • ^ = 4 ⋅ |c|

MOS scales covered:

  • 6 = 3L3s (either solfege)
  • 9 = 3L6s (either solfege) or 6L3s (solfege #2 only)
  • 12 = 3L9s (extended solfege #1 only) or 9L3s (extended solfege #2 only)
  • 15 = 12L3s (extended solfege #1 only) or 3L12s (extended solfege #1 only, P5 > 3\5 = 720¢)
  • 18 = 15L3s (extended solfege #1 only) (P5 > 3\5 = 720¢, if P5 > 11\18 = 733¢, you get 3L15s)
  • 21= 12L9s (extended solfege #2 only)
  • 21 = 18L3s (extended solfege #1 only) (P5 > 3\5 = 720¢, if P5 > 13\21 = 743¢, you get 3L18s)

Solfege #1 (P5 > 700¢)

solfege #1 (-a = plain, -u = up, -o = down)
genspan (gen = P5) -2 -1 0 1 2
down

genchain

perspan = 1

solfege Ro Lo Mo To Po
intervals vM2 vM6 vM3 vM7 vA4
notes vD vA vE vB vF#
plain

genchain

perspan = 0

solfege Tha Fa Da Sa Ra
intervals m7 P4 P1 P5 M2
notes Bb F C G D
up

genchain

perspan = -1

solfege Shu Fru Flu Nu Thu
intervals ^d5 ^m2 ^m6 ^m3 ^m7
notes ^Gb ^Db ^Ab ^Eb ^Bb
solfege #1 (-a = plain, -u = up, -o = down)
genspan (gen = vvA1/^m2) 2 1 0 -1 -2
Fa's

genchain

perspan = 1

solfege Shu Fa Mo Nu Ra
intervals ^d5 P4 vM3 ^m3 M2
notes ^Gb F vE ^Eb D
Da's

genchain

perspan = 0

solfege Ro Fru Da To Thu
intervals vM2 ^m2 P1 vM7 ^m7
notes vD ^Db C vB ^Bb
Sa's

genchain

perspan = -1

solfege Tha Lo Flu Sa Po
intervals m7 vM6 ^m6 P5 vA4
notes Bb vA ^Ab G vF#
extended solfege #1 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan (gen = P5) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
down

genchain

perspan = 1

solfege Tho Fo Do So Ro Lo Mo To Po/Shi Fri Fli Ni Thi
intervals vm7 v4 v1 v5 vM2 vM6 vM3 vM7 vA4/^^d5 ^^m2 ^^m6 ^^m3 ^^m7
notes vBb vF vC vG vD vA vE vB vF#/^^Gb ^^Db ^^Ab ^^Eb ^^Bb
plain

genchain

perspan = 0

solfege Sha Fra Fla Na Tha Fa Da Sa Ra La Ma Ta Pa
intervals d5 m2 m6 m3 m7 P4 P1 P5 M2 M6 M3 M7 A4
notes Gb Db Ab Eb Bb F C G D A E B F#
up

genchain

perspan = -1

solfege Re Le Me Te Pe/Shu Fru Flu Nu Thu Fu Du Su Ru
intervals vvM2 vvM6 vvM3 vvM7 vvA4/^d5 ^m2 ^m6 ^m3 ^m7 ^4 ^1 ^5 ^M2
notes vvD vvA vvE vvB vvF#/^Gb ^Db ^Ab ^Eb ^Bb ^F ^C ^G ^D
extended solfege #1 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan (gen = vvA1/^m2) 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6
Fa's

genchain

perspan = 1

solfege Tho Le Fla So Pe/Shu Fa Mo Nu Ra Fri Du Ta Thi
intervals vm7 vvM6 m6 v5 vvA4/^d5 P4 vM3 ^m3 M2 ^^m2 ^1 M7 ^^m7
notes vBb vvA Ab vG vvF#/^Gb F vE ^Eb D ^^Db ^C B ^^Bb
Da's

genchain

perspan = 0

solfege Sha Fo Me Na Ro Fru Da To Thu La Fli Su Pa
intervals d5 v4 vvM3 m3 vM2 ^m2 P1 vM7 ^m7 M6 ^^m6 ^5 A4
notes Gb vF vvE Eb vD ^Db C vB ^Bb A ^^Ab ^G F#
Sa's

genchain

perspan = -1

solfege Re Fra Do Te Tha Lo Flu Sa Po/Shi Fu Ma Ni Ru
intervals vvM2 m2 v1 vvM7 m7 vM6 ^m6 P5 vA4/^^d5 ^4 M3 ^^m3 ^M2
notes vvD Db vC vvB Bb vA ^Ab G vF#/^^Gb ^F E ^^Eb ^D
3L3s MOS scales (L = ^m3/vvA2, s = ^m2/vvA1)
GMN name scale 1sn 3rd 6th 8ve
1st 3L3s Ls-Ls-Ls Da Nu Mo Sa Flu To Da
2nd 3L3s sL-sL-sL Da Fru Mo Fa Flu Lo Da
3L6s MOS scales (L = M2 = rhymes, s = ^m2/vvA1)
GMN name scale 1sn 2nd 3rd 4th 5th 6th 7th 8ve
1st 3L6s Lss-Lss-Lss Da Ra Nu Mo Po Sa Flu Thu To Da
2nd 3L6s sLs-sLs-sLs Da Fru Nu Mo Fa Sa Flu Lo To Da
3rd 3L6s ssL-ssL-ssL Da Fru Ro Mo Fa Shu Flu Lo Tha Da
3L9s MOS scales (L = vA1/^^m2, s = ^m2/vvA1)
GMN name scale 1sn 2nds 3rds 4th tritone 5th 6ths 7ths 8ve
1st 3L9s Lsss-Lsss-Lsss Da Fri Ra Nu Mo Fu Po/Shi Sa Flu La Thu To Da
2nd 3L9s sLss-sLss-sLss Da Fru Ra Nu Mo Fa Po Sa Flu Lo Thu To Da
3rd 3L9s ssLs-ssLs-ssLs Da Fru Ro Nu Mo Fa Shu Sa Flu Lo Tha To Da
4th 3L9s sssL-sssL-sssL Da Fru Ro Na Mo Fa Pe/Shu So Flu Lo Tha Te Da

Similar tables can be made for 15- and 18-note scales.

Solfege #2 (P5 < 700¢)

solfege #2 (-a = plain, -u = up, -o = down)
genspan (gen = P5) -2 -1 0 1 2
up

genchain

perspan = 1

solfege Ru Lu Mu Tu Pu
intervals ^M2 ^M6 ^M3 ^M7 ^A4
notes ^D ^A ^E ^B ^F#
plain

genchain

perspan = 0

solfege Tha Fa Da Sa Ra
intervals m7 P4 P1 P5 M2
notes Bb F C G D
down

genchain

perspan = -1

solfege Sho Fro Flo No Tho
intervals vd5 vm2 vm6 vm3 vm7
notes vGb vDb vAb vEb vBb
solfege #2 (-a = plain, -u = up, -o = down)
genspan (gen = ^^A1/vm2) 2 1 0 -1 -2
Fa's

genchain

perspan = 1

solfege Sho Fa Mu No Ra
intervals vd5 P4 ^M3 vm3 M2
notes vGb F ^E vEb D
Da's

genchain

perspan = 0

solfege Ru Fro Da Tu Tho
intervals ^M2 vm2 P1 ^M7 vm7
notes ^D vDb C ^B vBb
Sa's

genchain

perspan = -1

solfege Tha Lu Flo Sa Pu
intervals m7 ^M6 vm6 P5 ^A4
notes Bb ^A vAb G ^F#
extended solfege #2 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan (gen = P5) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
up/dud

genchain

perspan = 1

solfege Thu Fu Du Su Ru Lu Mu Tu Pu/She Fre Fle Ne The
intervals ^m7 ^4 ^1 ^5 ^M2 ^M6 ^M3 ^M7 ^A4/vvd5 vvm2 vvm6 vvm3 vvm7
notes Bb ^F ^C ^G ^D ^A ^E ^B ^F#/vvGb vvDb vvAb vvEb vvBb
plain

genchain

perspan = 0

solfege Sha Fra Fla Na Tha Fa Da Sa Ra La Ma Ta Pa
intervals d5 m2 m6 m3 m7 P4 P1 P5 M2 M6 M3 M7 A4
notes Gb Db Ab Eb Bb F C G D A E B F#
down/dup

genchain

perspan = -1

solfege Ri Li Mi Ti Pi/Sho Fro Flo No Tho Fo Do So Ro
intervals ^^M2 ^^M6 ^^M3 ^^M7 ^^A4/vd5 vm2 vm6 vm3 vm7 v4 v1 v5 vM2
notes ^^D ^^A ^^E ^^B ^^F#/vGb vDb vAb vEb vBb vF vC vG vD
extended solfege #2 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan (gen = ^^A1/vm2) 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6
Fa's

genchain

perspan = 1

solfege Thu Li Fla Su Pi/Sho Fa Mu No Ra Fre Do Ta The
intervals ^m7 ^^M6 m6 ^5 ^^A4/vd5 P4 ^M3 vm3 M2 vvm2 v1 M7 vvm7
notes ^Bb ^^A Ab ^G ^^F#/vGb F ^E vEb D vvDb vC B vvBb
Da's

genchain

perspan = 0

solfege Sha Fu Mi Na Ru Fro Da Tu Tho La Fle So Pa
intervals d5 ^4 ^^M3 m3 ^M2 vm2 P1 ^M7 vm7 M6 vvm6 v5 A4
notes Gb ^F ^^E Eb ^D vDb C ^B vBb A vvAb vG F#
Sa's

genchain

perspan = -1

solfege Ri Fra Du Ti Tha Lu Flo Sa Pu/She Fo Ma Ne Ro
intervals ^^M2 m2 ^1 ^^M7 m7 ^M6 vm6 P5 ^A4/vvd5 v4 M3 vvm3 vM2
notes ^^D Db ^C ^^B Bb ^A vAb G ^F#/vvGb vF E vvEb vD
3L3s MOS scales (L = ^^A2/vm3, s = ^^A1/vm2)
GMN name scale 1sn 3rd 6th 8ve
1st 3L3s Ls-Ls-Ls Da No Mu Sa Flo Tu Da
2nd 3L3s sL-sL-sL Da Fro Mu Fa Flo Lu Da
3L6s MOS scales (L = M2 = rhymes, s = ^^A1/vm2) if P5 < 5\9 = 667¢, swap L and s to get 6L3s
GMN name scale 1sn 2nd 3rd 4th 5th 6th 7th 8ve
1st 3L6s Lss-Lss-Lss Da Ra No Mu Pu Sa Flo Tho Tu Da
2nd 3L6s sLs-sLs-sLs Da Fro No Mu Fa Sa Flo Lu Tu Da
3rd 3L6s ssL-ssL-ssL Da Fro Ru Mu Fa Sho Flo Lu Tha Da
9L3s MOS scales (L = ^A1/vvm2, s = ^^A1/vm2)
GMN name scale 1sn 2nds 3rds 4th tritone 5th 6ths 7ths 8ve
1st 9L3s sLLL-sLLL-sLLL Da Fre Ra No Mu Fo Pu/She Sa Flo La Tho Tu Da
2nd 9L3s LsLL-LsLL-LsLL Da Fro Ra No Mu Fa Pu Sa Flo Lu Tho Tu Da
3rd 9L3s LLsL-LLsL-LLsL Da Fro Ru No Mu Fa Sho Sa Flo Lu Tha Tu Da
4th 9L3s LLLs-LLLs-LLLs Da Fro Ru Na Mu Fa Pi/Sho Su Flo Lu Tha Ti Da

#7 (P8, P4/3) third-4th

  • G = vM2/^^m2 = ^~2 = 167¢ - c/3
  • EU = v3A1 = 0¢
  • ^ = (100¢ + 7c) / 3

MOS scales covered:

  • 7 = 1L6s (for 6L1s use quarter-5th)
  • 8 = 7L1s or 1L7s
  • 15 = 7L8s (all but 2 modes) (4\7 < P5 < 3\5)
uniform solfege (-a = plain, -u = up, -o = down)
genspan 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13
solfege Tho Fla Shu Fo Na Fru Do Tha Flu So Fa Nu Ro Da Thu Lo Sa Fu Mo Ra Du To La Su Po Ma Ru
intervals vm7 m6 ^d5 v4 m3 ^m2 v8 m7 ^m6 v5 P4 ^m3 vM2 P1 ^m7 vM6 P5 ^4 vM3 M2 ^1 vM7 M6 ^5 vA4 M3 ^M2
notes vBb Ab ^Gb vF Eb ^Db vC Bb ^Ab vG F ^Eb vD C ^Bb vA G ^F vE D ^C vB A ^G vF# E ^D
uniform solfege in melodic order (Po and Shu switch places when P5 > 13\22 = 709¢)
index 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
genspan 0 -7 8 1 -6 -13 9 2 -5 -12 10 3 -4 -11 11 4 -3 -10 12 5 -2 -9 13 6 -1 -8 7 0
solfege Da Du Fru Ro Ra Ru Na Nu Mo Ma Fo Fa Fu Po Shu So Sa Su Fla Flu Lo La Tho Tha Thu To Do Da
intervals P1 ^1 ^m2 vM2 M2 ^M2 m3 ^m3 vM3 M3 v4 P4 ^4 vA4 ^d5 v5 P5 ^5 m6 ^m6 vM6 M6 vm7 m7 ^m7 vM7 v8 P1
notes C ^C ^Db vD D ^D Eb ^Eb vE E vF F ^F vF# ^Gb vG G ^G Ab ^Ab vA A vBb Bb ^Bb vB vC C
1L6s MOS scales (L = M2 = rhymes, s = vM2/^^m2 = no rhyme)
GMN name scale 1sn 2nd 3rd 4th 5th 6th 7th 8ve
1st 1L6s Lssssss Da Ra Mo Fu Sa Lo Thu Da
2nd 1L6s sLsssss Da Ro Mo Fu Sa Lo Thu Da
3rd 1L6s ssLssss Da Ro Nu Fu Sa Lo Thu Da
4th 1L6s sssLsss Da Ro Nu Fa Sa Lo Thu Da
5th 1L6s ssssLss Da Ro Nu Fa So Lo Thu Da
6th 1L6s sssssLs Da Ro Nu Fa So Flu Thu Da
7th 1L6s ssssssL Da Ro Nu Fa So Flu Tha Da
7L1s MOS scales (L = vM2/^^m2, s = ^1/vvA1 = same degree)
GMN name scale 0 1 2 3 4 5 6 7 8
1st 7L1s sLLLLLLL Da Du Ra Mo Fu Sa Lo Thu Da
2nd 7L1s LsLLLLLL Da Ro Ra Mo Fu Sa Lo Thu Da
3rd 7L1s LLsLLLLL Da Ro Nu Mo Fu Sa Lo Thu Da
4th 7L1s LLLsLLLL Da Ro Nu Fa Fu Sa Lo Thu Da
5th 7L1s LLLLsLLL Da Ro Nu Fa So Sa Lo Thu Da
6th 7L1s LLLLLsLL Da Ro Nu Fa So Flu Lo Thu Da
7th 7L1s LLLLLLsL Da Ro Nu Fa So Flu Tha Thu Da
8th 7L1s LLLLLLLs Da Ro Nu Fa So Flu Tha Do Da

A similar table can be made for 7L8s, but it will lack the 1st and 15th modes.

#8 (P8, P5/3) third-5th

  • G = ^M2/vvm3 = 233¢ + c/3
  • EU = v3m2 = 0¢
  • ^ = (100¢ - 5c) / 3

MOS scales covered:

  • 5 = 1L4s (for 4L1s use pergen #3, half-4th)
  • 6 = 5L1s
  • 11 = 5L6s
  • 16 = 5L11s
uniform solfege (-a = plain, -u = up, -o = down)
-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Fra Nu Sho Fla Thu Fro Na Fu Flo Tha Du No Fa Su Tho Da Ru Fo Sa Lu Do Ra Mu So La Tu Ro Ma Pu Lo Ta
m2 ^m3 vd5 m6 ^m7 vm2 m3 ^4 vm6 m7 ^1 vm3 P4 ^5 vm7 P1 ^M2 v4 P5 ^M6 v8 M2 ^M3 v5 M6 ^M7 vM2 M3 ^A4 vM6 M7
Db ^Eb vGb Ab ^Bb vDb Eb ^F vAb Bb ^C vEb F ^G vBb C ^D vF G ^A vC D ^E vG A ^B vD E ^F# vA B
1L4s MOS scales (L = ^^M2/vm3, s = ^M2/vvm3)
GMN name scale 0 1 2 3 4 5
1st 1L4s ssssL Da Ru Fo Sa Lu Da
2nd 1L4s sssLs Da Ru Fo Sa Tho Da
3rd 1L4s ssLss Da Ru Fo Su Tho Da
4th 1L4s sLsss Da Ru Fa Su Tho Da
5th 1L4s Lssss Da No Fa Su Tho Da
5L1s MOS scales (L = ^M2/vvm3, s = ^1/vvM2)
GMN name scale 0 1 2 3 4 5 6
1st 5L1s LLLLLs Da Ru Fo Sa Lu Do Da
2nd 5L1s LLLLsL Da Ru Fo Sa Lu Tho Da
3rd 5L1s LLLsLL Da Ru Fo Sa Su Tho Da
4th 5L1s LLsLLL Da Ru Fo Fa Su Tho Da
5th 5L1s LsLLLL Da Ru No Fa Su Tho Da
6th 5L1s sLLLLL Da Du No Fa Su Tho Da

Similar tables can be made for every mode of 5L6s and 5L11s.

#9 (P8, P11/3) third-11th

  • G = ^4/vv5 = 567¢ - c/3
  • EU = v3M2 = 0¢
  • ^ = (200¢ + 2c) / 3 (quite large, a literal third-tone)

MOS scales covered:

  • 5 = 2L3s
  • 7 = 2L5s
  • 9 = 2L7s
  • 11 = 2L9s
  • etc. up to 19 = 17L2s
uniform solfege (-a = plain, -u = up, -o = down)
18 ... 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 ... -18
Sha ... Fla No Flu Na Tho Nu Tha Fo Thu Fa Do Fu Da So Du Sa Ro Su Ra Lo Ru La Mo Lu Ma ... Pa
d5 ... m6 vm3 ^m6 m3 vm7 ^m3 m7 v4 ^m7 P4 v8 ^4 P1 v5 ^1 P5 vM2 ^5 M2 vM6 ^M2 M6 vM3 ^M6 M3 ... A4
Gb ... Ab vEb ^Ab Eb vBb ^Eb Bb vF ^Bb F vC ^F C vG ^C G vD ^G D vA ^D A vE ^A E ... F#
2L7s MOS scales (L = ^m3/vv4, s = vvM2/^1)
GMN name scale 0 1 2 3 4 5 6 7 8 9
1st 2L7s ssssLsssL Da Du Ro Ra Ru So Sa Su Lo Da
2nd 2L7s sssLssssL Da Du Ro Ra Fu So Sa Su Lo Da
3rd 2L7s sssLsssLs Da Du Ro Ra Fu So Sa Su Do Da
4th 2L7s ssLssssLs Da Du Ro Fa Fu So Sa Su Do Da
5th 2L7s ssLsssLss Da Du Ro Fa Fu So Sa Thu Do Da
6th 2L7s sLssssLss Da Du Fo Fa Fu So Sa Thu Do Da
7th 2L7s sLsssLsss Da Du Fo Fa Fu So Tha Thu Do Da
8th 2L7s LssssLsss Da Nu Fo Fa Fu So Tha Thu Do Da
9th 2L7s LsssLssss Da Nu Fo Fa Fu Tho Tha Thu Do Da

When the 5th is anywhere near just, the L/s ratio is huge. The notes tend to cluster tightly together. This is why the L step is a 3rd or a 4th, and the s step is a 2nd or even a unison. Thus this 9-note scale never using all 7 degrees, but only 4 or 5 degrees.

#16 (P8/4, P5) quarter-8ve

There are two solfeges. Use solfege #1 if P5 > 700¢, and use solfege #2 if P5 < 700¢.

  • P = ^m3/v3A2 (solfege #1) or vm3/^3A2 (solfege #2) = 300¢
  • G = P5 = 700¢ + c or vvA1/^^m2 (solfege #1) or ^^A1/vvm2 (solfege #2) = 100¢ + c
  • EU = ^4d2 = 0¢
  • ^ = 3 ⋅ |c|

MOS scales covered:

  • 8 = 4L4s (either solfege)
  • 12 = 8L4s (solfege #1 only) or 4L8s (solfege #2 only)
  • 16 = 12L4s (solfege #2 only) or 4L12s (solfege #2 only)

Solfege #1 (P5 > 700¢)

solfege #1 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan (gen = P5) -3 -2 -1 0 1 2 3
up

genchain

perspan = 1

solfege Shu Fru Flu Nu Thu Fu Du
intervals ^d5 ^m2 ^m6 ^m3 ^m7 ^4 ^1
notes ^Gb ^Db ^Ab ^Eb ^Bb ^F ^C
plain

genchain

perspan = 0

solfege Na Tha Fa Da Sa Ra La
intervals m3 m7 P4 P1 P5 M2 M6
notes Eb Bb F C G D A
down

genchain

perspan = -1

solfege Do So Ro Lo Mo To Po
intervals v8 v5 vM2 vM6 vM3 vM7 vA4
notes vC vG vD vA vE vB vF#
dup/dud

genchain

perspan = ±2

solfege Le Me Te Pe/Shi Fri Fli Ni
intervals vvM6 vvM3 vvM7 vvA4/^^d5 ^^m2 ^^m6 ^^m3
notes vvA vvE vvB vvF#/^^Gb ^^Db ^^Ab ^^Eb
solfege #1 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan (gen = vvA1/^^m2) -3 -2 -1 0 1 2 3
Nu's

genchain

perspan = 1

solfege Do Fru Ro Nu Mo Fu Po
intervals v8 ^m2 vM2 ^m3 vM3 ^4 vA4
notes vC ^Db vD ^Eb vE ^F vF#
Da's

genchain

perspan = 0

solfege Le Tha Te Da Fri Ra Ni
intervals vvM6 m7 vvM7 P1 ^^m2 M2 ^^m3
notes vvA Bb vvB C ^^Db D ^^Eb
Lo's

genchain

perspan = -1

solfege Shu So Flu Lo Thu To Du
intervals ^d5 v5 ^m6 vM6 ^m7 vM7 ^1
notes ^Gb vG ^Ab vA ^Bb vB ^C
Sa's

genchain

perspan = ±2

solfege Na Me Fa Pe/Shi Sa Fli La
intervals m3 vvM3 P4 vvA4/^^d5 P5 ^^m6 M6
notes Eb vvE F vvF#/^^Gb G ^^Ab A

Note that solfege #1 doesn't work for 16-note MOS scales, because those require that P5 be < 700¢. So the outer two columns (genspan 3 or -3) aren't used much. Use solfege #2 for 16-note MOS scales.

4L4s MOS scales (L = vM2 , s = vvA1/^^m2) using solfege #1 if P5 > 5\8 = 750¢, swap L and s
GMN name scale 1sn 2nd 3rd tritone 6th 7th 8ve
1st 4L4s sL-sL-sL-sL Da Fri Nu Mo Pe/Shi Sa Lo Thu Da
2nd 4L4s Ls-Ls-Ls-Ls Da Ro Nu Fa Pe/Shi Flu Lo Te Da
8L4s MOS scales (L = vvA1/^^m2, s = vvvA1/^m2) using solfege #1
GMN name scale 1sn 2nds 3rds 4th tritone 5th 6ths 7ths 8ve
1st 8L4s LLs-LLs-LLs-LLs Da Fri Ra Nu Mo Fu Pe/Shi Sa Fli Lo Thu To Da
2nd 8L4s LsL-LsL-LsL-LsL Da Fri Ro Nu Mo Fa Pe/Shi Sa Flu Lo Thu Te Da
3rd 8L4s sLL-sLL-sLL-sLL Da Fru Ro Nu Me Fa Pe/Shi So Flu Lo Tha Te Da

Solfege #2 (P5 < 700¢)

solfege #2 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan (gen = P5) -3 -2 -1 0 1 2 3
down

genchain

perspan = 1

solfege Sho Fro Flo No Tho Fo Do
intervals vd5 vm2 vm6 vm3 vm7 v4 v1
notes vGb vDb vAb vEb vBb vF vC
plain

genchain

perspan = 0

solfege Na Tha Fa Da Sa Ra La
intervals m3 m7 P4 P1 P5 M2 M6
notes Eb Bb F C G D A
up

genchain

perspan = -1

solfege Du Su Ru Lu Mu Tu Pu
intervals ^8 ^5 ^M2 ^M6 ^M3 ^M7 ^A4
notes ^C ^G ^D ^A ^E ^B ^F#
dup/dud

genchain

perspan = ±2

solfege Li Mi Ti Pi/She Fre Fle Ne
intervals ^^M6 ^^M3 ^^M7 ^^A4/vvd5 vvm2 vvm6 vvm3
notes ^^A ^^E ^^B ^^F#/vvGb vvDb vvAb vvEb
solfege #2 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan (gen = ^^A1/vvm2) -3 -2 -1 0 1 2 3
No's

genchain

perspan = 1

solfege Du Fro Ru No Mu Fo Pu
intervals ^8 vm2 ^M2 vm3 ^M3 v4 ^A4
notes ^C vDb ^D vEb ^E vF ^F#
Da's

genchain

perspan = 0

solfege Li Tha Ti Da Fre Ra Ne
intervals ^^M6 m7 ^^M7 P1 vvm2 M2 vvm3
notes ^^A Bb ^^B C vvDb D vvEb
Lu's

genchain

perspan = -1

solfege Sho Su Flo Lu Tho Tu Do
intervals vd5 ^5 vm6 ^M6 vm7 ^M7 v1
notes vGb ^G vAb ^A vBb ^B vC
Sa's

genchain

perspan = ±2

solfege Na Mi Fa Pi/She Sa Fle La
intervals m3 ^^M3 P4 ^^A4/vvd5 P5 vvm6 M6
notes Eb ^^E F ^^F#/vvGb G vvAb A
4L4s MOS scales (L = ^M2, s = ^^A1/vvm2) using solfege #2
GMN name scale 1sn 2nd 3rd tritone 6th 7th 8ve
1st 4L4s sL-sL-sL-sL Da Fre No Mu Pi/She Sa Lu Tho Da
2nd 4L4s Ls-Ls-Ls-Ls Da Ru No Fa Pi/She Flo Lu Ti Da
4L8s MOS scales (L = ^3A1/vm2, s = ^^A1/vvm2) using solfege #2
GMN name scale 1sn 2nds 3rds 4th tritone 5th 6ths 7ths 8ve
1st 8L4s ssL-ssL-ssL-ssL Da Fre Ra No Mu Fo Pi/She Sa Fle Lu Tho Tu Da
2nd 8L4s sLs-sLs-sLs-sLs Da Fre Ru No Mu Fa Pi/She Sa Flo Lu Tho Ti Da
3rd 8L4s Lss-Lss-Lss-Lss Da Fro Ru No Mi Fa Pi/She Su Flo Lu Tha Ti Da
12L4s MOS scales (L = ^^A1/vvm2 = different consonant, s = ^1 = same consonant) using solfege #2 if P5 < 9\16 = 675¢, swap L and s for 4L12s
GMN name scale 1sn 2nd 3rds 4th tritone 5th 6ths 7th 8ve
1st 12L4s LLLs-LLLs-LLLs-LLLs Da Fre Ra Ne No Mu Fo Pu Pi/She Sa Fle La Lu Tho Tu Do Da
2nd 12L4s LLsL-LLsL-LLsL-LLsL Da Fre Ra Ru No Mu Fo Fa Pi/She Sa Fle Flo Lu Tho Tu Ti Da
3rd 12L4s LsLL-LsLL-LsLL-LsLL Da Fre Fro Ru No Mu Mi Fa Pi/She Sa Su Flo Lu Tho Tha Ti Da
4th 12L4s sLLL-sLLL-sLLL-sLLL Da Du Fro Ru No Na Mi Fa Pi/She Sho Su Flo Lu Li Tha Ti Da

#17 (P8, P4/4) quarter-4th

  • G = ^m2 = v3AA1 = v\M2 = v/A1 = 125¢ - c/4
  • EU's = ^4dd2, \\m2, ^^\d2, vv\A1, etc.
  • ^ = 25¢ + 4.75c
  • / = 50¢ - 2.5c

MOS scales covered:

  • 8 = 1L7s
  • 9 = 1L8s
  • 10 = 9L1s (all but 2 modes)
  • 11 = 10L1s (all but 4 modes) Sa must be > 3\5 = 720¢
  • etc.
uniform solfege (-a = plain, -u = up, -o = down, -i = lift, -e = drop)
genspan 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8
solfege Tha Lo Si

Fle

Shu Fa Mo Ri

Ne

Fru Da To Li

The

Flu Sa Po Mi

Fe

Nu Ra
intervals m7 vM6 /5

\m6

^d5 P4 vM3 /M2

\m3

^m2 P1 vM7 /M6

\m7

^m6 P5 vA4 /M3

\4

^m3 M2
notes Bb vA /G

\Ab

^Gb F vE /D

\Eb

^Db C vB /A

\Bb

^Ab G vF# /E

\F

^Eb D
1L7s MOS scales (L = ^m3 = v/A2, s = ^m2 = v/A1)
GMN name scale 0 1 2 3 4 5 6 7 8
1st 1L7s Lsssssss Da Nu Mi/Fe Po Sa Flu Li/The To Da
2nd 1L7s sLssssss Da Fru Mi/Fe Po Sa Flu Li/The To Da
3rd 1L7s ssLsssss Da Fru Ri/Ne Po Sa Flu Li/The To Da
4th 1L7s sssLssss Da Fru Ri/Ne Mo Sa Flu Li/The To Da
5th 1L7s ssssLsss Da Fru Ri/Ne Mo Fa Flu Li/The To Da
6th 1L7s sssssLss Da Fru Ri/Ne Mo Fa Shu Li/The To Da
7th 1L7s ssssssLs Da Fru Ri/Ne Mo Fa Shu Si/Fle To Da
8th 1L7s sssssssL Da Fru Ri/Ne Mo Fa Shu Si/Fle Lo Da
1L8s MOS scales (L = M2 = rhymes, s = ^m2 = v/A1)
GMN name scale 1sn 2nd 3rd 4th 5th 6th 7th 8ve
1st 1L8s Lssssssss Da Ra Nu Mi/Fe Po Sa Flu Li/The To Da
2nd 1L8s sLsssssss Da Fru Nu Mi/Fe Po Sa Flu Li/The To Da
3rd 1L8s ssLssssss Da Fru Ri/Ne Mi/Fe Po Sa Flu Li/The To Da
4th 1L8s sssLsssss Da Fru Ri/Ne Mo Po Sa Flu Li/The To Da
5th 1L8s ssssLssss Da Fru Ri/Ne Mo Fa Sa Flu Li/The To Da
6th 1L8s sssssLsss Da Fru Ri/Ne Mo Fa Shu Flu Li/The To Da
7th 1L8s ssssssLss Da Fru Ri/Ne Mo Fa Shu Si/Fle Li/The To Da
8th 1L8s sssssssLs Da Fru Ri/Ne Mo Fa Shu Si/Fle Lo To Da
9th 1L8s ssssssssL Da Fru Ri/Ne Mo Fa Shu Si/Fle Lo Tha Da
9L1s MOS scales (L = ^m2 = v/A1, s = vA1 = ^\m2) Sa must be > 5\9 = 667¢
GMN name scale 1sn 2nd 3rd 4th tritone 5th 6th 7th 8ve
1st 9L1s sLLLLLLLLL Da ??? Ra Nu Mi/Fe Po Sa Flu Li/The To Da
2nd 9L1s LsLLLLLLLL Da Fru Ra Nu Mi/Fe Po Sa Flu Li/The To Da
3rd 9L1s LLsLLLLLLL Da Fru Ri/Ne Nu Mi/Fe Po Sa Flu Li/The To Da
4th 9L1s LLLsLLLLLL Da Fru Ri/Ne Mo Mi/Fe Po Sa Flu Li/The To Da
5th 9L1s LLLLsLLLLL Da Fru Ri/Ne Mo Fa Po Sa Flu Li/The To Da
6th 9L1s LLLLLsLLLL Da Fru Ri/Ne Mo Fa Shu Sa Flu Li/The To Da
7th 9L1s LLLLLLsLLL Da Fru Ri/Ne Mo Fa Shu Si/Fle Flu Li/The To Da
8th 9L1s LLLLLLLsLL Da Fru Ri/Ne Mo Fa Shu Si/Fle Lo Li/The To Da
9th 9L1s LLLLLLLLsL Da Fru Ri/Ne Mo Fa Shu Si/Fle Lo Tha To Da
10th 9L1s LLLLLLLLLs Da Fru Ri/Ne Mo Fa Shu Si/Fle Lo Tha ??? Da

The first and last modes contain vA1=vC# and ^d8=^Cb respectively, but the solfege has no names for those.

#18 (P8, P5/4) quarter-5th

  • G = vM2 = ^3m2 = 175¢ + c/4
  • EU = v4A1 = 0¢
  • ^ = 25¢ + 1.75c

MOS scales covered:

  • 7 = 6L1s
  • 13 = 7L6s
uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan -20 ... -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 ... 20
solfege Fra ... Na Fo Shi

Se

Flu Tha Do Fri

Re

Nu Fa So Fli

Le

Thu Da Ro Ni

Me

Fu Sa Lo Thi

Te

Du Ra Mo Fi

Pe

Su La ... Ta
intervals m2 ... m3 v4 ~5 ^m6 m7 v8 ~2 ^m3 P4 v5 ~6 ^m7 P1 vM2 ~3 ^4 P5 vM6 ~7 ^1 M2 vM3 ~4 ^5 M6 ... M7
notes Db ... Eb vF ^^Gb

vvG

^Ab Bb vC ^^Db

vvD

^Eb F vG ^^Ab

vvA

^Bb C vD ^^Eb

vvE

^F G vA ^^Bb

vvB

^C D vE ^^F

vvF#

^G A ... B
6L1s MOS scales (L = vM2/^3m2, s = ~2) if P5 < 4\7, swap L & s
GMN name scale 1sn 2nd 3rd 4th 5th 6th 7th 8ve
1st 6L1s LLLLLLs Da Ro Ni/Me Fu Sa Lo Thi/Te Da
2nd 6L1s LLLLLsL Da Ro Ni/Me Fu Sa Lo Thu Da
3rd 6L1s LLLLsLL Da Ro Ni/Me Fu Sa Fli/Le Thu Da
4th 6L1s LLLsLLL Da Ro Ni/Me Fu So Fli/Le Thu Da
5th 6L1s LLsLLLL Da Ro Ni/Me Fa So Fli/Le Thu Da
6th 6L1s LsLLLLL Da Ro Nu Fa So Fli/Le Thu Da
7th 6L1s sLLLLLL Da Fri/Re Nu Fa So Fli/Le Thu Da

#19 (P8, P11/4) quarter-11th

  • G = ^M3 = v34 = v\4 = v/d4 = ^//m3 = 425¢ - c/4
  • EU's = v4dd3, \\A1, vv\m2, vv/d2, etc.
  • ^ = 25¢ - 4.25c
  • / = 50¢ + 3.5c

MOS scales covered:

  • 5 = 3L2s
  • 8 = 3L5s
  • 11 = 3L8s
uniform solfege (-a = plain, -u = up, -o = down, -i = lift, -e = drop)
genspan 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
solfege Shi

Se

Ru Tha Sho Fri

Re

Lu Fa Fro Fli

Le

Mu Da Flo Ni

Me

Tu Sa No Thi

Te

Pu Ra Tho Fi

Pe

intervals ~5 ^M2 m7 vd5 ~2 ^M6 P4 vm2 ~6 ^M3 P1 vm6 ~3 ^M7 P5 vm3 ~7 ^A4 M2 vm7 ~4
notes /Gb

\G

^D Bb vGb /Db

\D

^A F vDb /Ab

\A

^E C vAb /Eb

\E

^B G vEb /Bb

\B

^F# D vBb /F

\F#

3L2s MOS scales (L = ~3 = ^^A2 = vvd4, s = vm2 = ^/1)
GMN name scale 0 1 2 3 4 5
1st 3L2s LLsLs Da Ni/Me Sa Flo Tu Da
2nd 3L2s LsLLs Da Ni/Me Mu Flo Tu Da
3rd 3L2s LsLsL Da Ni/Me Mu Flo Fli/Le Da
4th 3L2s sLLsL Da Fro Mu Flo Fli/Le Da
5th 3L2s sLsLL Da Fro Mu Fa Fli/Le Da
3L5s MOS scales (L = vm3 = ^/M2, s = vm2 = ^/1)
GMN name scale plain down mid up plain down mid up plain
1st 3L5s LsLssLss Da No Ni/Me Pu Sa Flo Thi/Te Tu Da
2nd 3L5s LssLsLss Da No Ni/Me Mu Sa Flo Thi/Te Tu Da
3rd 3L5s LssLssLs Da No Ni/Me Mu Sa Flo Fli/Le Tu Da
4th 3L5s sLsLssLs Da Fro Ni/Me Mu Sa Flo Fli/Le Tu Da
5th 3L5s sLssLsLs Da Fro Ni/Me Mu Fa Flo Fli/Le Tu Da
6th 3L5s sLssLssL Da Fro Ni/Me Mu Fa Flo Fli/Le Lu Da
7th 3L5s ssLsLssL Da Fro Fri/Re Mu Fa Flo Fli/Le Lu Da
8th 3L5s ssLssLsL Da Fro Fri/Re Mu Fa Sho Fli/Le Lu Da
3L8s MOS scales (L = M2 = rhymes, s = vm2 = ^/1 = ^\A1 = no rhyme)
GMN name scale 1sn 2nd 4th 5th 7th 8ve
1st 3L8s LssLsssLsss Da Ra No Ni/Me Fi/Pe Pu Sa Flo Tho Thi/Te Tu Da
2nd 3L8s LsssLssLsss Da Ra No Ni/Me Mu Pu Sa Flo Tho Thi/Te Tu Da
3rd 3L8s LsssLsssLss Da Ra No Ni/Me Mu Pu Sa Flo Fli/Le Thi/Te Tu Da
4th 3L8s sLssLsssLss Da Fro No Ni/Me Mu Pu Sa Flo Fli/Le Thi/Te Tu Da
5th 3L8s sLsssLssLss Da Fro No Ni/Me Mu Fa Sa Flo Fli/Le Thi/Te Tu Da
6th 3L8s sLsssLsssLs Da Fro No Ni/Me Mu Fa Sa Flo Fli/Le Lu Tu Da
7th 3L8s ssLssLsssLs Da Fro Fri/Re Ni/Me Mu Fa Sa Flo Fli/Le Lu Tu Da
8th 3L8s ssLsssLssLs Da Fro Fri/Re Ni/Me Mu Fa Sho Flo Fli/Le Lu Tu Da
9th 3L8s ssLsssLsssL Da Fro Fri/Re Ni/Me Mu Fa Sho Flo Fli/Le Lu Tha Da
10th 3L8s sssLssLsssL Da Fro Fri/Re Ru Mu Fa Sho Flo Fli/Le Lu Tha Da
11th 3L8s sssLsssLssL Da Fro Fri/Re Ru Mu Fa Sho Shi/Se Fli/Le Lu Tha Da

#20 (P8, P12/4) quarter-12th (incomplete)

  • G = v4 = ^3M3 = 475¢ + c/4
  • EU = v4m2 = 0¢
  • ^ = 25¢ - 1.25c

MOS scales covered:

  • 5 = 3L2s
  • 7 = 5L2s (if P5 > 3\5 = 720¢)
  • 8 = 5L3s
  • 13 = 5L8s
  • 18 = 5L13s
uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
-17 ... -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 ... 17
Nu ... Na Flo Di

Fre

Fu Tha No Si

Fle

Du Fa Tho Ri

Ne

Su Da Fo Li

The

Ru Sa Do Mi

Fe

Lu Ra So Ti

De

Mu La ... Lo
^m3 ... m3 vm6 ^^1

vvm2

^4 m7 vm3 ^^5

vvm6

^1 P4 vm7 ^^M2

vvm3

^5 P1 v4 ^^M6

vvm7

^M2 P5 v8 ^^M3

vv4

^M6 M2 v5 ^^M7

vv8

^M3 M6 ... vM6
^Eb ... Eb vAb ^^C

vvDb

^F Bb vEb ^^G

vvAb

^C F vBb ^^D

vvEb

^G C vF ^^A

vvBb

^D G vC ^^E

vvF

^A D vG ^^B

vvC

^E A ... vA


#22 (P8/2, M2/4) half-8ve quarter-tone

  • P = ^^4 = vv5 = 600¢
  • G = ^1 = v3M2 = 50¢ + c/2
  • EU = v4M2 = 0¢
  • ^ = 50¢ + c/2

MOS scales covered:

  • 16 = 2L14s
  • 18 = 2L16s
  • 20 = 2L18s
  • 22 = 2L20s
  • 24 = 2L22s or 22L2s
uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
Da's

gen-

chain

per-span = 0

Shu Shi

Fle

Flo Fla Flu Fli

The

Tho Tha Thu Thi

De

Do Da Du Di

Re

Ro Ra Ru Ri

Me

Mo Ma Mu Mi

Pe

Po
^d5 ^^d5

vvm6

vm6 m6 ^m6 ^^m6

vvm7

vm7 m7 ^m7 ^^m7

vv8

v8 P1 ^1 ^^1

vvM2

vM2 M2 ^M2 ^^M2

vvM3

vM3 M3 ^M3 ^^M3

vvA4

vA4
^Gb ^^Gb

vvAb

vAb Ab ^Ab ^^Ab

vvBb

vBb Bb ^Bb ^^Bb

vvC

vC C ^C ^^C

vvD

vD D ^D ^^D

vvE

vE E ^E ^^E

vvF#

vF#
Sa's

gen-

chain

per-span = ±1

Fro Fra Fru Fri

Ne

No Na Nu Ni

Fe

Fo Fa Fu Fi

Se

So Sa Su Si

Le

Lo La Lu Li

Te

To Ta Tu
vm2 m2 ^m2 ^^m2

vvm3

vm3 m3 ^m3 ^^m3

vv4

v4 P4 ^4 ^^4

vv5

v5 P5 ^5 ^^5

vvM6

vM6 M6 ^M6 ^^M6

vvM7

vM7 M7 ^M7
vDb Db ^Db ^^Db

vvEb

vEb Eb ^Eb ^^Eb

vvF

vF F ^F ^^F

vvG

vG G ^G ^^G

vvA

vA A ^A ^^A

vvB

vB B ^B
2L20s MOS scales (L = m2 = rhymes, s = ^1/v3M2 = no rhyme)
GMN name scale 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
1st 2L20s ssssssssssL x2 Da Du Di

Re

Ro Ra Ru Ri

Me

Mo Ma Mu Mi

Pe

Fi

Se

So Sa Su Si

Le

Lo La Lu Li

Te

To Ta Da
2nd 2L20s sssssssssLs x2 Da Du Di

Re

Ro Ra Ru Ri

Me

Mo Ma Mu Fu Fi

Se

So Sa Su Si

Le

Lo La Lu Li

Te

To Do Da
3rd 2L20s ssssssssLss x2 Da Du Di

Re

Ro Ra Ru Ri

Me

Mo Ma Fa Fu Fi

Se

So Sa Su Si

Le

Lo La Lu Li

Te

Thi

De

Do Da
4th 2L20s sssssssLsss x2 Da Du Di

Re

Ro Ra Ru Ri

Me

Mo Fo Fa Fu Fi

Se

So Sa Su Si

Le

Lo La Lu Thu Thi

De

Do Da
5th 2L20s ssssssLssss x2 Da Du Di

Re

Ro Ra Ru Ri

Me

Ni

Fe

Fo Fa Fu Fi

Se

So Sa Su Si

Le

Lo La Tha Thu Thi

De

Do Da
6th 2L20s sssssLsssss x2 Da Du Di

Re

Ro Ra Ru Nu Ni

Fe

Fo Fa Fu Fi

Se

So Sa Su Si

Le

Lo Tho Tha Thu Thi

De

Do Da
7th 2L20s ssssLssssss x2 Da Du Di

Re

Ro Ra Na Nu Ni

Fe

Fo Fa Fu Fi

Se

So Sa Su Si

Le

Fli

The

Tho Tha Thu Thi

De

Do Da
8th 2L20s sssLsssssss x2 Da Du Di

Re

Ro No Na Nu Ni

Fe

Fo Fa Fu Fi

Se

So Sa Su Flu Fli

The

Tho Tha Thu Thi

De

Do Da
9th 2L20s ssLssssssss x2 Da Du Di

Re

Fri

Ne

No Na Nu Ni

Fe

Fo Fa Fu Fi

Se

So Sa Fla Flu Fli

The

Tho Tha Thu Thi

De

Do Da
10th 2L20s sLsssssssss x2 Da Du Fru Fri

Ne

No Na Nu Ni

Fe

Fo Fa Fu Fi

Se

So Flo Fla Flu Fli

The

Tho Tha Thu Thi

De

Do Da
11th 2L20s Lssssssssss x2 Da Fra Fru Fri

Ne

No Na Nu Ni

Fe

Fo Fa Fu Fi

Se

Shi

Fle

Flo Fla Flu Fli

The

Tho Tha Thu Thi

De

Do Da

#33 (P8/5, P5) fifth-8ve

If P5 > 3\5 = 720¢, swap up with down, and dup with dud, to get solfege #2.

  • P = ^^M2 = v3m3 = 240¢
  • G = P5 = 700¢ + c or ^1 = v4m2 = 20¢ - c
  • EU = v5m2 = 0¢
  • ^ = 20¢ - c

MOS scales covered:

  • 10 = 5L5s
  • 15 = 5L10s (and 10L5s if P5 < 8\15 = 640¢)
  • 20 = 5L15s (and 15L5s if P5 < 11\20 = 660¢)
  • 25 = 5L20s (and 20L5s if P5 < 14\25 = 672¢)
solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan (gen = P5) -4 -3 -2 -1 0 1 2 3 4
down

genchain

perspan = 2

solfege Fro Flo No Tho Fo Do So Ro Lo
intervals vm2 vm6 vm3 vm7 v4 v8 v5 vM2 vM6
notes vDb vAb vEb vBb vF vC vG vD vA
dup

genchain

perspan = 1

solfege Thi Fi Di Si Ri Li Mi Ti Pi
intervals ^^m7 ^^4 ^^1 ^^5 ^^M2 ^^M6 ^^M3 ^^M7 ^^A4
notes ^^Bb ^^F ^^C ^^G ^^D ^^A ^^E ^^B ^^F#
plain

genchain

perspan = 0

solfege Fla Na Tha Fa Da Sa Ra La Ma
intervals m6 m3 m7 P4 P1 P5 M2 M6 M3
notes Ab Eb Bb F C G D A E
dud

genchain

perspan = -1

solfege She Fre Fle Ne The Fe De Se Re
intervals vvd5 vvm2 vvm6 vvm3 vvm7 vv4 vv8 vv5 vvM2
notes vvGb vvDb vvAb vvEb vvBb vvF vvC vvG vvD
up

genchain

perspan = -2

solfege Nu Thu Fu Du Su Ru Lu Mu Tu
intervals ^m3 ^m7 ^4 ^1 ^5 ^M2 ^M6 ^M3 ^M7
notes ^Eb ^Bb ^F ^C ^G ^D ^A ^E ^B
solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan (gen = ^1) 4 3 2 1 0 -1 -2 -3 -4
Fa's

genchain

perspan = 2

solfege She Fi Fu Fa Fo Fe Mi Mu Ma
intervals vvd5 ^^4 ^4 P4 v4 vv4 ^^M3 ^M3 M3
notes vvGb ^^F ^F F vF vvF ^^E ^E E
Ra's

genchain

perspan = 1

solfege Nu Na No Ne Ri Ru Ra Ro Re
intervals ^m3 m3 vm3 vvm3 ^^M2 ^M2 M2 vM2 vvM2
notes ^Eb Eb vEb vvEb ^^D ^D D vD vvD
Da's

genchain

perspan = 0

solfege Fro Fre Di Du Da Do De Ti Tu
intervals vm2 vvm2 ^^1 ^1 P1 v8 vv8 ^^M7 ^M7
notes vDb vvDb ^^C ^C C vC vvC ^^B ^B
Tha's

genchain

perspan = -1

solfege Thi Thu Tha Tho The Li Lu La Lo
intervals ^^m7 ^m7 m7 vm7 vvm7 ^^M6 ^M6 M6 vM6
notes ^^Bb ^Bb Bb vBb vvBb ^^A ^A A vA
Sa's

genchain

perspan = -2

solfege Fla Flo Fle Si Su Sa So Se Pi
intervals m6 vm6 vvm6 ^^5 ^5 P5 v5 vv5 ^^A4
notes Ab vAb vvAb ^^G ^G G vG vvG ^^F#
5L5s MOS scales (L = ^M2/v4m3, s = ^1)
GMN name scale 1sn 2nd 4th 5th 7th 8ve
1st 5L5s Ls-Ls-Ls-Ls-Ls Da Ru Ri Fe Fo Sa Su Li The Do Da
2nd 5L5s sL-sL-sL-sL-sL Da Du Ri Ne Fo Fa Su Si The Tho Da
5L10s MOS scales (L = M2 = rhymes, s = ^1/v4m2 = no rhyme) if P5 < 8\15 = 640¢, swap L and s to get 10L5s
GMN name scale 1sn 2nd 3rd 4th 5th 6th 7th 8ve
1st 5L10s Lss-Lss-Lss-Lss-Lss Da Ra Ru Ri Mi Fe Fo So Sa Su Lu Li The De Do Da
2nd 5L10s sLs-sLs-sLs-sLs-sLs Da Du Ru Ri Ne Fe Fo Fa Sa Su Si Li The Tho Do Da
3rd 5L10s ssL-ssL-ssL-ssL-ssL Da Du Di Ri Ne No Fo Fa Fu Su Si Fle The Tho Tha Da

#34 (P8, P4/5) fifth-4th

  • G = ^^m2 = v3A1 = 100¢ - c/5
  • EU = ^5d2 = 0¢
  • ^ = 2.4c

MOS scales covered:

  • 10 = 1L9s
  • 11 = 1L10s
  • 12 = 1L11s (all but 2 modes)
uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
solfege Tha Le Flu So Shi Fa Me Nu Ro Fri Da Te Thu Lo Fli Sa Pe Fu Mo Ni Ra
intervals m7 vvM6 ^m6 v5 ^^d5 P4 vvM3 ^m3 vM2 ^^m2 P1 vvM7 ^m7 vM6 ^^m6 P5 vvA4 ^4 vM3 ^^m3 M2
notes Bb vvA ^Ab vG ^^Gb F vvE ^Eb vD ^^Db C vvB ^Bb vA ^^Ab G vvF# ^F vE ^^Eb D
1L9s MOS scales (L = ^^m3/v3A2, s = ^^m2/v3A1)
GMN name scale 0 1 2 3 4 5 6 7 8 9 10
1st 1L9s Lsssssssss Da Ni Mo Fu Pe Sa Fli Lo Thu Te Da
2nd 1L9s sLssssssss Da Fri Mo Fu Pe Sa Fli Lo Thu Te Da
3rd 1L9s ssLsssssss Da Fri Ro Fu Pe Sa Fli Lo Thu Te Da
4th 1L9s sssLssssss Da Fri Ro Nu Pe Sa Fli Lo Thu Te Da
5th 1L9s ssssLsssss Da Fri Ro Nu Me Sa Fli Lo Thu Te Da
6th 1L9s sssssLssss Da Fri Ro Nu Me Fa Fli Lo Thu Te Da
7th 1L9s ssssssLsss Da Fri Ro Nu Me Fa Shi Lo Thu Te Da
8th 1L9s sssssssLss Da Fri Ro Nu Me Fa Shi So Thu Te Da
9th 1L9s ssssssssLs Da Fri Ro Nu Me Fa Shi So Flu Te Da
10th 1L9s sssssssssL Da Fri Ro Nu Me Fa Shi So Flu Le Da
1L10s MOS scales (L = M2 = rhymes, s = ^^m2/v3A1 = no rhyme)
GMN name scale 1sn 2nd 3rd 4th 5th 6th 7th 8ve
1st 1L10s Lssssssssss Da Ra Ni Mo Fu Pe Sa Fli Lo Thu Te Da
2nd 1L10s sLsssssssss Da Fri Ni Mo Fu Pe Sa Fli Lo Thu Te Da
3rd 1L10s ssLssssssss Da Fri Ro Mo Fu Pe Sa Fli Lo Thu Te Da
4th 1L10s sssLsssssss Da Fri Ro Nu Fu Pe Sa Fli Lo Thu Te Da
5th 1L10s ssssLssssss Da Fri Ro Nu Me Pe Sa Fli Lo Thu Te Da
6th 1L10s sssssLsssss Da Fri Ro Nu Me Fa Sa Fli Lo Thu Te Da
7th 1L10s ssssssLssss Da Fri Ro Nu Me Fa Shi Fli Lo Thu Te Da
8th 1L10s sssssssLsss Da Fri Ro Nu Me Fa Shi So Lo Thu Te Da
9th 1L10s ssssssssLss Da Fri Ro Nu Me Fa Shi So Flu Thu Te Da
10th 1L10s sssssssssLs Da Fri Ro Nu Me Fa Shi So Flu Le Te Da
11th 1L10s ssssssssssL Da Fri Ro Nu Me Fa Shi So Flu Le Tha Da

#35 (P8, P5/5) fifth-5th

  • G = vM2 = ^4d1 = 140¢ + c/5
  • EU = v5A2 = 0¢
  • ^ = 60¢ + 1.8c

MOS scales covered:

  • 8 = 1L7s
  • 9 = 8L1s (and 1L8s if P5 < 5\9 = 667¢)
  • 10 = 9L1s if P5 < 5\9 = 667¢
  • 17 = 9L8s (and 8L9s if P5 > 10/17 = 706¢)
uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan -16 ... -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 ... 16
solfege Fru ... Tha Do Re Fri Nu Fa So Le Fli Thu Da Ro Me Ni Fu Sa Lo Te Thi Du Ra ... To
intervals ^m2 ... m7 v8 vvM2 ^^m2 ^m3 P4 v5 vvM6 ^^m6 ^m7 P1 vM2 vvM3 ^^m3 ^4 P5 vM6 vvM7 ^^m7 ^1 M2 ... vM7
notes ^Db ... Bb vC vvD ^^Db ^Eb F vG vvA ^^Ab ^Bb C vD vvE ^^Eb ^F G vA vvB ^^Bb ^C D ... vB
1L7s MOS scales (L = ^^m2/v3M3, s = vM2/^4d1)
GMN name scale 1sn 2nd 3rd tritone 6th 7th 8ve
1st 1L7s sssssssL Da Ro Me Ni Fu Sa Lo Te Da
2nd 1L7s ssssssLs Da Ro Me Ni Fu Sa Lo Thu Da
3rd 1L7s sssssLss Da Ro Me Ni Fu Sa Fli Thu Da
4th 1L7s ssssLsss Da Ro Me Ni Fu Le Fli Thu Da
5th 1L7s sssLssss Da Ro Me Ni So Le Fli Thu Da
6th 1L7s ssLsssss Da Ro Me Fa So Le Fli Thu Da
7th 1L7s sLssssss Da Ro Nu Fa So Le Fli Thu Da
8th 1L7s Lsssssss Da Fri Nu Fa So Le Fli Thu Da
8L1s MOS scales (L = vM2/^4d1, s = vvM2/^3d1)
GMN name scale 1sn 2nd 3rd 4th 5th 6th 7th 8ve
1st 8L1s LLLLLLLLs Da Ro Me Ni Fu Sa Lo Te Thi Da
2nd 8L1s LLLLLLLsL Da Ro Me Ni Fu Sa Lo Te Thu Da
3rd 8L1s LLLLLLsLL Da Ro Me Ni Fu Sa Lo Fli Thu Da
4th 8L1s LLLLLsLLL Da Ro Me Ni Fu Sa Le Fli Thu Da
5th 8L1s LLLLsLLLL Da Ro Me Ni Fu So Le Fli Thu Da
6th 8L1s LLLsLLLLL Da Ro Me Ni Fa So Le Fli Thu Da
7th 8L1s LLsLLLLLL Da Ro Me Nu Fa So Le Fli Thu Da
8th 8L1s LsLLLLLLL Da Ro Fri Nu Fa So Le Fli Thu Da
9th 8L1s sLLLLLLLL Da Re Fri Nu Fa So Le Fli Thu Da

#36 (P8, P11/5) fifth-11th

This pergen can be thought of as "half-down5th".

  • G = ^^m3 = v3M3 = 340¢ - c/5
  • EU = v5A1 = 0¢
  • ^ = 20¢ + 1.4c

MOS scales covered:

  • 7 = 4L3s if P5 > 4\7 = 686¢ (for 3L4s use half-5th solfege)
  • 11 = 7L4s
  • 18 = 7L11s and 11L7s
uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan -20 ... 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 ... -20
solfege Fla ... Tha Se Nu Do Fli Fa Re Thu So Ni Da Le Fu Ro Thi Sa Me Du Lo Fi Ra ... Ma
intervals m6 ... m7 ^~5 ^m3 v8 v~6 P4 ^~2 ^m7 v5 v~3 P1 ^~6 ^4 vM2 v~7 P5 ^~2 ^1 vM6 v~4 M2 ... M3
notes Ab ... Bb vvG ^Eb vC ^^Ab F vvD ^Bb vG ^^Eb C vvA ^F vD ^^Bb G vvE ^C vA ^^F D ... E
4L3s MOS scales (L = vM2 = ^4m2, s = vvM2 = ^3m2)
GMN name scale 1sn 2nd 3rd 4th 5th 6th 7th 8ve
1st 4L3s LLsLsLs Da Ro Me Fu Sa Le Thi Da
2nd 4L3s LsLLsLs Da Ro Ni Fu Sa Le Thi Da
3rd 4L3s LsLsLLs Da Ro Ni Fu So Le Thi Da
4th 4L3s LsLsLsL Da Ro Ni Fu So Le Thu Da
5th 4L3s sLLsLsL Da Re Ni Fu So Le Thu Da
6th 4L3s sLsLLsL Da Re Ni Fa So Le Thu Da
7th 4L3s sLsLsLL Da Re Ni Fa So Fli Thu Da

#37 (P8, P12/5) fifth-12th

This pergen can be thought of as "half-dudaug5th".

  • G = vM3 = ^\d4 = //A2 = 380¢ + c/5
  • EU's = ^5dd2, \5d34, ^^\d2, v\\m2, etc.
  • ^ = 20¢ + 3.8c
  • / = 40¢ - 4.4c

MOS scales covered:

  • 7 = 3L4s (P5 is 515-800¢), but better to use half-5th solfege
  • 10 = 3L7s (P5 is 600-800¢)
  • 13 = 3L10s (and 10L3s if P5 < 7\13)
uniform solfege (-a = plain, -u = up, -o = down, -i = lift, -e = drop)
genspan -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
solfege Ri Shu Tha Ro She Li Fru Fa Lo Fre Mi Flu Da Mo Fle Ti Nu Sa To Ne Pi Thu Ra Po The
intervals /M2 ^d5 m7 vM2 \d5 /M6 ^m2 P4 vM6 \m2 /M3 ^m6 P1 vM3 \m6 /M7 ^m3 P5 vM7 \m3 /A4 ^m7 M2 vA4 \m7
notes /D ^Gb Bb vD \Gb /A ^Db F vA \Db /E ^Ab C vE \Ab /B ^Eb G vB \Eb /F# ^Bb D vF# \Bb
3L4s MOS scales (L = ^m3 = v/A2 = \\d4, s = ^/1 = vvA1 = \m2)
GMN name scale 0 1 2 3 4 5 6 7
1st 3L4s LsLsLss Da Nu Mo Sa Fle To Ti Da
2nd 3L4s LsLssLs Da Nu Mo Sa Fle Flu Ti Da
3rd 3L4s LssLsLs Da Nu Mo Mi Fle Flu Ti Da
4th 3L4s sLsLsLs Da Fre Mo Mi Fle Flu Ti Da
5th 3L4s sLsLssL Da Fre Mo Mi Fle Flu Lo Da
6th 3L4s sLssLsL Da Fre Mo Mi Fa Flu Lo Da
7th 3L4s ssLsLsL Da Fre Fru Mi Fa Flu Lo Da
3L7s MOS scales (L = ^/M2 = vvA2 = \m3, s = ^/1 = vvA1 = \m2)
GMN name scale plain drop up down lift plain drop up down lift plain
1st 3L7s LssLssLsss Da Ne Nu Mo Pi Sa Fle Thu To Ti Da
2nd 3L7s LssLsssLss Da Ne Nu Mo Pi Sa Fle Flu To Ti Da
3rd 3L7s LsssLssLss Da Ne Nu Mo Mi Sa Fle Flu To Ti Da
4th 3L7s sLssLssLss Da Fre Nu Mo Mi Sa Fle Flu To Ti Da
5th 3L7s sLssLsssLs Da Fre Nu Mo Mi Sa Fle Flu Lo Ti Da
6th 3L7s sLsssLssLs Da Fre Nu Mo Mi Fa Fle Flu Lo Ti Da
7th 3L7s ssLssLssLs Da Fre Fru Mo Mi Fa Fle Flu Lo Ti Da
8th 3L7s ssLssLsssL Da Fre Fru Mo Mi Fa Fle Flu Lo Li Da
9th 3L7s ssLsssLssL Da Fre Fru Mo Mi Fa She Flu Lo Li Da
10th 3L7s sssLssLssL Da Fre Fru Ro Mi Fa She Flu Lo Li Da

#38 (P8, ccP4/5) fifth-coco-4th

  • G = ^^4 = v35 = 580¢ - c/5
  • EU = v5M2 = 0¢
  • ^ = 40¢ + 0.4c

MOS scales covered:

  • 5 = 2L3s
  • 7 = 2L5s
  • 9 = 2L7s
  • 11 = 2L9s
  • etc.
uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan 30 ... 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 ... -30
solfege Sha ... Tha Fe Thu Fo Thi Fa De Fu Do Fi Da Se Du So Di Sa Re Su Ro Si Ra ... Pa
intervals d5 ... m7 vv4 ^m7 v4 ^^m7 P4 vv8 ^4 v8 ^^4 P1 vv5 ^1 v5 ^^1 P5 vvM2 ^5 vM2 ^^5 M2 ... A4
notes Gb ... Bb vvF ^Bb vF ^^Bb F vvC ^F vC ^^F C vvG ^C vG ^^C G vvD ^G vD ^^G D ... F#
2L7s MOS scales (L = , s = ^1 = v4M2)
GMN name scale 0 1 2 3 4 5 6 7 8 9
1st 2L7s ssssLsssL Da Du Di Re Ro Se So Sa Su Da
2nd 2L7s sssLssssL Da Du Di Re Fi Se So Sa Su Da
3rd 2L7s sssLsssLs Da Du Di Re Fi Se So Sa Do Da
4th 2L7s ssLssssLs Da Du Di Fu Fi Se So Sa Do Da
5th 2L7s ssLsssLss Da Du Di Fu Fi Se So De Do Da
6th 2L7s sLssssLss Da Du Fa Fu Fi Se So De Do Da
7th 2L7s sLsssLsss Da Du Fa Fu Fi Se Thi De Do Da
8th 2L7s LssssLsss Da Fo Fa Fu Fi Se Thi De Do Da
9th 2L7s LsssLssss Da Fo Fa Fu Fi Thu Thi De Do Da

Multi-edo pergens of the form (P8/m, ^1)

pergen period EU perchain
(P8/2, ^1) A4 / d5 d2 Da - Pa/Sha - Da
(P8/3, ^1) M3 / d4 d2 Da - Ma - Fla - Da
(P8/4, ^1) m3 / A2 d2 Da - Na - Pa/Sha - La - Da
(P8/5, ^1) M2 / m3 d2 Da - Ra/Na - Ma/Fa - Sa/Fla - La/Tha- Da
(P8/6, ^1) M2 / d3 d2 Da - Ra - Ma - Pa/Sha - Fla - Tha - Da
(P8/7, ^1) M2 / m2 A1 Da - Ra - Ma - Fa - Sa - La - Ta - Da
(P8/8, ^1) ???
(P8/9, ^1) ???
(P8/10, ^1) ??? ??? Da - Fra - Ra/Na - Ma - Fa - Pa/Sha - Sa - Fla - La/Tha - Ta - Da
(P8/11, ^1) ???
(P8/12, ^1) A1 / m2 d2 Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da

(P8/5, ^1)

  • P = M2/m3 = 200¢
  • G = ^1 = c (stands for 81/80 in Blackwood)
  • EU = d2 = 0¢
  • ^ = c

MOS scales covered:

  • 10 = 5L5s
  • 15 = 5L10s or 10L5s
solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan (gen = ^1) -2 -1 0 1 2
Fa's

genchain

perspan = 2

solfege Me/Fe Mo/Fo Fa Fu Fi
intervals vvM3/vv4 vM3/v4 P4 ^4 ^^4
notes vvE/vvF vE/vF F ^F ^^F
Ra's

genchain

perspan = 1

solfege Re Ro Ra/Na Ru/Nu Ri/Ni
intervals vvM2 vM2 M2/m3 ^M2/^m3 ^^M2/^^m3
notes vvD vD D/Eb ^D/^Eb ^^D/^^Eb
Da's

genchain

perspan = 0

solfege De Do Da Du Di
intervals vv8 v8 P1 ^1 ^^1
notes vvC vC C ^C ^^C
Tha's

genchain

perspan = -1

solfege Le/The Lo/Tho La/Tha Thu Thi
intervals vvM6/vvm7 vM6/vm7 M6/m7 ^m7 ^^m7
notes vvA/vvBb vA/vBb A/Bb ^Bb ^^Bb
Sa's

genchain

perspan = -2

solfege Se So Sa Su/Flu Si/Fli
intervals vv5 v5 P5 ^5/^m6 ^^5/^^m6
notes vvG vG G ^G/^Ab ^^G/^^Ab

Blackwood has a vM3 generator:

solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan (gen = vM3) 2 1 0 -1 -2
Fa's

genchain

perspan = 2

solfege Re Lo Ma/Fa Du Fli
intervals vvM2 vM6 M3/P4 ^1 ^^m6
notes vvD vA E/F ^C ^^Ab
Ra's

genchain

perspan = 1

solfege De So Ra/Na Thu Fi
intervals vv8 v5 M2/m3 ^m7 ^^4
notes vvC vG D/Eb ^Bb ^^F
Da's

genchain

perspan = 0

solfege Le Mo Da Flu Ri/Ni
intervals vvM6 vM3 P1 ^m6 ^^M2/^^m3
notes vvA vE C ^Ab ^^D/^^Eb
Tha's

genchain

perspan = -1

solfege Se Ro La/Tha Fu Di
intervals vv5 vM2 M6/m7 ^4 ^^1
notes vvG vD A/Bb ^F ^^C
Sa's

genchain

perspan = -2

solfege Me Do Sa/Fla Ru/Nu Thi
intervals vvM3 v8 P5/m6 ^M2/^m3 ^^m7
notes vvE vC G/Ab ^D/^Eb ^^Bb
5L5s MOS scales (L = vM2/vm3, s = ^1)
GMN name scale 1sn 2nd 3rd 4th tritone 5th 6th 7th 8ve
1st 5L5s LsLsLsLsLs Da Ro Ra Mo Fa So Sa Lo Tha Do Da
2nd 5L5s sLsLsLsLsL Da Du Ra Nu Fa Fu Sa Flu Tha Thu Da
5L10s MOS scales (L = vM2/vm3, s = ^1) if s > 1\15 = 80¢, swap L and s to get 10L5s
GMN name scale 1sn 2nd 3rds 4th tritones 5th 6ths 7th 8ve
1st 5L10s Lss x5 Da Re Ro Ra Me Mo Fa Se So Sa Le Lo Tha De Do Da
2nd 5L10s sLs x5 Da Du Ro Ra Nu Mo Fa Fu So Sa Flu Lo Tha Thu Do Da
3rd 5L10s ssL x5 Da Du Di Ra Nu Ni Fa Fu Fi Sa Flu Fli Tha Thu Thi Da

(P8/7, ^1)

  • P = M2/m2 = 171¢
  • G = ^1 = c
  • EU = A1 = 0¢
  • ^ = c

MOS scales covered:

  • 14 = 7L7s
  • 21 = 7L14s and 14L7s
solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)
genspan (gen = ^1) -2 -1 0 1 2
Fa's

genchain

perspan = 3

solfege Fe Fo Fa Fu Fi
intervals vv4 v4 P4 ^4 ^^4
notes vvF vF F ^F ^^F
Ma's

genchain

perspan = 2

solfege Me Mo Ma Mu Mi
intervals vvM3 vM3 M3 ^M3 ^^M3
notes vvE vE E ^E ^^E
Ra's

genchain

perspan = 1

solfege Re Ro Ra Ru Ri
intervals vvM2 vM2 M2 ^M2 ^^M2
notes vvD vD D ^D ^^D
Da's

genchain

perspan = 0

solfege De Do Da Du Di
intervals vv8 v8 P1 ^1 ^^1
notes vvC vC C ^C ^^C
Ta's

genchain

perspan = -1

solfege Te To Ta Tu Ti
intervals vvM7 vM7 M7 ^M7 ^^M7
notes vvB vB B ^B ^^B
La's

genchain

perspan = -2

solfege Le Lo La Lu Li
intervals vvM6 vM6 M6 ^M6 ^^M6
notes vvA vA A ^A ^^A
Sa's

genchain

perspan = -3

solfege Se So Sa Su Si
intervals vv5 v5 P5 ^5 ^^5
notes vvG vG G ^G ^^G
7L7s MOS scales (L = vM2/vm2, s = ^1)
GMN name scale 1sn 2nd 3rd 4th 5th 6th 7th 8ve
1st 7L7s Ls x7 Da Ro Ra Mo Ma Fo Fa So Sa Lo La To Ta Do Da
2nd 7L7s sL x7 Da Du Ra Ru Ma Mu Fa Fu Sa Su La Lu Ta Thu Da
7L14s MOS scales (L = vvM2/vvm2, s = ^1) if s > 1\21 = 57¢, swap L and s to get 14L7s
GMN name scale 1sn 2nd 3rd 4th 5th 6th 7th 8ve
1st 7L14s Lss x7 Da Re Ro Ra Me Mo Ma Fe Fo Fa Se So Sa Le Lo La Te To Ta De Do Da
2nd 7L14s sLs x7 Da Du Ro Ra Ru Mo Ma Mu Fo Fa Fu So Sa Su Lo La Lu To Ta Tu Do Da
3rd 7L14s ssL x7 Da Du Di Ra Ru Ri Ma Mu Mi Fa Fu Fi Sa Su Si La Lu Li Ta Tu Ti Da

Pergens Summary

bolded entries are tippy, meaning that ^ and v can easiiy swap
pergen EU vowels perchain and/or genchain mapping notes
1 (P8, P5) vA1 -a -u -o aug / dim Da - Sa (1 1...) (0 1...) -i = AA, -e = dd
2 (P8/2, P5) ^^d2 -a -u -o Da - Po/Shu- Da (2 2...) (0 1...)
3 (P8, P4/2) vvm2 -a -u -o Da - Ru/No - Fa (1 2...) (0 -2...)
4 (P8, P5/2) vvA1 -a -u -o Da - Nu/Mo - Sa (1 1...) (0 2...)
6 (P8/3, P5) ^3d2 -a -u -o Da - Mo - Flu - Da (3 3...) (0 1...)
7 (P8, P4/3) v3A1 -a -u -o Da - Ro - Nu - Fa (1 2...) (0 -3...)
8 (P8, P5/3) v3m2 -a -u -o Da - Ru - Fo - Sa (1 1...) (0 3...)
9 (P8, P11/3) v3M2 -a -u -o Da - Fu - Do - Fa (1 3...) (0 -3...)
16 (P8/4, P5) ^4d2 -a -u -o -i -e Da - Nu - Pe/Shi - Lo - Da (4 4...) (0 1...)
17 (P8, P4/4) \\m2, ^^\d2, vv\A1 -a -u -o -i -e lift / drop Da - Fru - Ri/Ne - Mo - Fa (1 2...) (0 -4...)
18 (P8, P5/4) v4A1 -a -u -o -i -e Da - Ro - Ni/Me - Fu - Sa (1 1...) (0 4...)
19 (P8, P11/4) \\A1, vv\m2, vv/d2 -a -u -o -i -e lift / drop Da - Mu - Fli/Le - Fro - Fa (1 3...) (0 -4...)
20 (P8, P12/4) v4m2 -a -u -o -i -e Da - Fo - Li/The - Ru - Sa (1 0...) (0 4...)
22 (P8/2, M2/4) v4M2 -a -u -o -i -e Da - Fi/Se - Da

Da - Du - Di/Re - Ro - Ra

(2 3...) (0 2...)
33 (P8/5, P5) v5m2 -a -u -o -i -e Da - Ri - Fo - Su - The - Da (5 5...) (0 1...)
34 (P8, P4/5) ^5d2 -a -u -o -i -e Da - Fri - Ro - Nu - Me - Fa (1 2...) (0 5...)
35 (P8, P5/5) v5A2 -a -u -o -i -e Da - Ro - Me - Ni - Fu - Sa (1 1...) (0 5...)
36 (P8, P11/5) v5A1 -a -u -o -i -e Da - Ni - So - Thu - Re - Fa (1 3...) (0 -5...)
37 (P8, P12/5) ^^\d2, v\\m2 -a -u -o -i -e lift / drop Da - Mo - Fle - Ti - Nu - Sa (1 0...) (0 5...)
38 (P8, ccP4/5) v5M2 -a -u -o -i -e Da - Fi - Do - Fu - De - Fa (1 4...) (0 -5...)
Multi-edo pergens
pergen period EU perchain
(P8/2, ^1) A4 / d5 d2 Da - Pa/Sha - Da
(P8/3, ^1) M3 / d4 d2 Da - Ma - Fla - Da
(P8/4, ^1) m3 / A2 d2 Da - Na - Pa/Sha - La - Da
(P8/5, ^1) M2 / m3 d2 Da - Ra/Na - Ma/Fa - Sa/Fla - La/Tha- Da
(P8/6, ^1) M2 / d3 d2 Da - Ra - Ma - Pa/Sha - Fla - Tha - Da
(P8/7, ^1) M2 / m2 A1 Da - Ra - Ma - Fa - Sa - La - Ta - Da
(P8/10, ^1) ??? ??? Da - Fra - Ra/Na - Ma - Fa - Pa/Sha - Sa - Fla - La/Tha - Ta - Da
(P8/12, ^1) A1 / m2 d2 Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da
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