List of uniform solfeges for pergens

In the MOS scale tables, any note that changes from one mode to the next is bolded. The mode numbers are defined such that the 1st mode always has Sa and not Fa, and the last mode always has Fa and not Sa.

See Uniform solfege and Enharmonic unison (EU).

vowels for (P8, P5), up/down repurposed to mean aug/dim

d4	ddd	dd	dim	plain	aug	AA	AAA	A4
-eye "ay-yay"	-eyo	-e	-o	-a	-u	-i	-iyu	-iyi "ee-yee"

vowels for single-pair pergens

quud	trud	dud	down	plain	up	dup	trup	quup
-eye	-eyo	-e	-o	-a	-u	-i	-iyu	-iyi

vowels for double-pair pergens

	down	plain	up
lift	-owi	-i	-uwi
plain	-o	-a	-u
drop	-owe	-e	-uwe

Any compound vowel with a "w" is for double-pair only. Mnemonic: w = "double-U" = double-pair.

Pergens Summary

bolded entries are tippy, meaning that ^ and v can easily swap
-iyu = triple-up or triple-aug, -eyo = triple-down or triple-dim
-uwi = uplift, -uwe = updrop, -owi = downlift, -owe = downdrop

	pergen		mapping	EU(s) and cents	vowels	perchain and/or genchain(s)	tipping points
1	(P8, P5)	whole	(1 1...) (0 1...)	vA1, ^ = 100¢ + 7c	-a -u -o (-i -e)	Da - Sa
2	(P8/2, P5)	halves	(2 2...) (0 1...)	^^d2, ^ = 6c	-a -u -o	Da - Po/Shu- Da	7\12 = 700¢
3	(P8, P4/2)	half-4th	(1 2...) (0 -2...)	vvm2, ^ = 50¢ - 2.5c	-a -u -o	Da - Ru/No - Fa
4	(P8, P5/2)	half-5th	(1 1...) (0 2...)	vvA1, ^ = 50¢ + 3.5c	-a -u -o	Da - Nu/Mo - Sa
5	(P8/2, P4/2) true double	half-all	(2 4...) (0 -2...)	vvm2, \\A1 ^=50¢-2.5c, /=50¢+3.5c	-a -u -o -i -e -uwi -owe	Da - Ru/No - Fa Fuwi/Sowe - Fli/Le - Duwi/Rowe
third-splits
6	(P8/3, P5)	thirds	(3 3...) (0 1...)	^3d2, ^ = 4c	-a -u -o	Da - Mo - Flu - Da	7\12 = 700¢
7	(P8, P4/3)	third-4th	(1 2...) (0 -3...)	v3A1, ^ = 33¢ + 2.33c	-a -u -o	Da - Ro - Nu - Fa
8	(P8, P5/3)	third-5th	(1 1...) (0 3...)	v3m2, ^ = 33¢ - 1.67c	-a -u -o	Da - Ru - Fo - Sa
9	(P8, P11/3)	third-11th	(1 3...) (0 -3...)	v3M2, ^ = 67¢ + 0.67c	-a -u -o	Da - Fu - Do - Fa
10	(P8/3, P4/2)	thirds half-4th	(3 6...) (0 -2...)	vvm2, \6A2, ^\\\A1, v\\\M2 ^=50¢-2.5c, /=50¢+1.5c	-a -u -o -i -e -owi -uwe	Muwe - Se - Luwe Da - Ru/No - Fa Flowi - Thi - Frowi
11	(P8/3, P5/2)	thirds half-5th	(3 3...) (0 2...)	vvA1, \6m3, ^\\\m2, v\\\M2 ^=50¢+3.5c, /=50¢-0.5c	-a -u -o -i -e -owi -uwe	Mowi - Si - Towi Da - Nu/Mo - Sa Fluwe - De - Nuwe
12	(P8/2, P4/3)	halves third-4th	(2 4...) (0 -3...)	v3A1, \6d4, ^\\m2, vv\\M2 ^=33¢+2.33c, /=67¢-1.33c	-a -u -o -i -e -uwi -owe -owi -uwe	Da - Ro - Nu - Fa Fuwi/Sowe - Si/Fluwe - - Lowi/The - Thuwi/Dowe
				v3A1, \6d34, v\\m2, ^^\\d2 ^=33¢+2.33c, /=33¢-3.67c	-a -u -o -i -e -owi -uwe	Da - Ro - Nu - Fa Powi/Shuwe - Fle - Li - Towi	13\22 = 709¢
13	(P8/2, P5/3)	halves third-5th	(2 2...) (0 3...)	v3m2, /6d32, v\\A1, vv//d2 ^=33¢-1.67c, /=33¢+4.33c	-a -u -o -i -e -owi -uwe	Da - Ru - Fo - Sa Puwe/Showi - Fli - Te - Frowi	15\26 = 692¢
14	(P8/2, P11/3)	halves third-11th	(2 6...) (0 -3...)	v6M2, ^ = 33¢ + c/3	-a -u -o -i -e -iyu -eyo	Da - Fi - De - Fa Fiyu/Seyo - Do - Fu - Thiyu/Deyo
15	(P5/3, P4/3) true double	third-all	(3 6...) (0 -3...)	v3A1, \3m2 ^=33¢+2.33c, /=33¢-1.67c	-a -u -o -i -e -uwi -owe -owi -uwe	Mowi - Fuwi - Si - Lowi Da - Ro - Nu - Fa Fluwe - The - Dowe - Fruwe
quarter-splits
16	(P8/4, P5)	quarters	(4 4...) (0 1...)	^4d2, ^ = 3c	-a -u -o -i -e	Da - Nu - Pe/Shi - Lo - Da	7\12 = 700¢
17	(P8, P4/4)	quarter-4th	(1 2...) (0 -4...)	^4dd2, \\m2, ^^\d2, vv\A1 ^=25¢+4.75c, /=50¢-2.5c	-a -u -o -i -e	Da - Fru - Ri/Ne - Mo - Fa	11\19 = 695¢
18	(P8, P5/4)	quarter-5th	(1 1...) (0 4...)	v4A1, ^ = 25¢ + 1.75c	-a -u -o -i -e	Da - Ro - Ni/Me - Fu - Sa
19	(P8, P11/4)	quarter-11th	(1 3...) (0 -4...)	v4dd3, \\A1, vv\m2, vv/d2	-a -u -o -i -e	Da - Mu - Fli/Le - Fro - Fa	10\17 = 706¢
20	(P8, P12/4)	quarter-12th	(1 0...) (0 4...)	v4m2	-a -u -o -i -e	Da - Fo - Li/The - Ru - Sa
21	(P8/4, P4/2)	(true double)
22	(P8/2, M2/4)	halves quarter-tone	(2 3...) (0 2...)	v4M2, ^ = 50¢ + c/2	-a -u -o -i -e	Da - Du - Di/Re - Ro - Ra Fi/Se - So - Sa - Su - Si/Le
23	(P8/2, P4/4)	(true double)
24	(P8/2, P5/4)	(true double)
fifth-splits
33	(P8/5, P5)	fifths	(5 5...) (0 1...)	v5m2, ^ = 20¢ - c	-a -u -o -i -e	Da - Ri - Fo - Su - The - Da
34	(P8, P4/5)	fifth-4th	(1 2...) (0 5...)	^5d2, ^ = 2.4c	-a -u -o -i -e	Da - Fri - Ro - Nu - Me - Fa	7\12 = 700¢
35	(P8, P5/5)	fifth-5th	(1 1...) (0 5...)	v5A2, ^ = 60¢ + 1.8c	-a -u -o -i -e	Da - Ro - Me - Ni - Fu - Sa
36	(P8, P11/5)	fifth-11th	(1 3...) (0 -5...)	v5A1, ^ = 20¢ + 1.4c	-a -u -o -i -e	Da - Ni - So - Thu - Re - Fa
37	(P8, P12/5)	fifth-12th	(1 0...) (0 5...)	^5dd2, \5d34, ^^\d2, v\\m2 ^=20¢+3.8c, /=40¢-4.4c	-a -u -o -i -e	Da - Mo - Fle - Ti - Nu - Sa	11\19 = 695¢, 13\22 = 709¢
38	(P8, ccP4/5)	fifth-coco-4th	(1 4...) (0 -5...)	v5M2, ^ = 40¢ + 0.4c	-a -u -o -i -e	Da - Fi - Do - Fu - De - Fa
sixth-splits
64	(P8/6, P5)	sixths	(6 6...) (0 1...)	^6d2, ^ = 2c	-a -u -o -i -e -iyu -eyo	Da - Ro - Me - Peyo/Shiyu - - Li - Thu - Da	7\12 = 700¢
65	(P8, P4/6)	sixth-4th	(1 2...) (0 -6...)	v3A1, \\m2,	-a -u -o -i -e -uwi -owe -owi -uwe	Da - Duwi/Fruwe - Ro - Ri/Ne - - Nu - Mowi/Fowe - Fa
66	(P8, P5/6)	sixth-5th	(1 1...) (0 6...)	v3m2, \\A1	-a -u -o -i -e -owi -uwe	Da - Frowi - Ru - Ni/Me - - Fo - Puwe - Sa
				^6d43, \3m2, vv\\A1	-a -u -o -i -e -uwi -owe	Da - Fru - Ri - Nuwi/Mowe - - Fe - Po - Sa	31edo
67	(P8, P11/6)	sixth-11th	(1 3...) (0 -6...)	vvA1, \3M2	-a -u -o -i -e -owi -uwe	Da - Nuwe - Fi - Flu/Lo - - De - Rowi - Fa
68	(P8, P12/6)	sixth-12th	(1 0...) (0 6...)	vvm2, \3M2	-a -u -o -i -e -owi -uwe	Da - Nowi - Se - Lu/Tho - - Di - Muwe - Sa
69	(P8, ccP4/6)	sixth-coco-4th	(1 4...) (0 -6...)	v6M2, ^ = 17¢ - 0.83c	-a -u -o -i -e -iyu -eyo	Da - Fo - The - Neyo/Riyu - - Si - Du - Fa
70	(P8, ccP5/6)	sixth-coco-5th	(1 -1...) (0 -6...)	v6A1	-a -u -o -i -e -iyu -eyo	Da - Fu - Thi - Niyu/Meyo - - Le - Ro - Sa
seventh-splits
96	(P8/7, P5)	sevenths	(7 7...) (0 1...)	v7A1, ^ = 14¢ + c	-a -u -o -i -e -iyu -eyo	Da - Re - Niyu - Fu - - So - Leyo - Thi - Da
97	(P8, P4/7)
98	(P8, P5/7)	seventh-5th	(1 1...) (0 7...)	^7d2, ^ = (12/7)c	-a -u -o -i -e -iyu -eyo	Da - Friyu - Ro - Ni - - Me - Fu - Peyo - Sa	7\12 = 700¢
99	(P8, P11/7)	seventh-11th	(1 3...) (0 -7...)	v7m2, ^ = 14¢ - (5/7)c	-a -u -o -i -e -iyu -eyo	Da - Riyu - Fo - Si - - The - Du - Neyo - Fa
100	(P8, P12/7)	seventh-12th	(1 0...) (0 7...)	v7A2, ^ = 43¢ - (9/7)c	-a -u -o -i -e -iyu -eyo	Da - Meyo - Fu - Le - - Thi - Ro - Niyu - Sa
101	(P8, ccP4/7)					- -
102	(P8, ccP5/7)					- -
103	(P8, c3P4/7)	seventh-trico-4th	(1 5...) (0 -7...)	v7M2, ^ = 29¢ + 0.29c	-a -u -o -i -e -iyu -eyo	Da - Fiyu - Do - Fi - - De - Fu - Deyo - Fa
eighth-splits
160	(P8/8, P5)	eighths	(8 8...) (0 1...)	v8AA2	-a -u -o -i -e -iyu -iyi -eyo -eye	Da - Ro - Me - Peyo - - AugSeye/DimFiyi - - Shiyu - Fli - Thu - Da
ninth-splits

Multi-edo pergens -- genchain is always De Do Da Du Di

pergen		mapping	EU	period	perchain	notes
(P8/5, ^1)	rank-2 5-edo	(5 8...) (0 0...)	m2	M2 / m3	Da - Ra/Na - Ma/Fa - Sa/Fla - La/Tha- Da	if Blackwood, ^ = 16/15
(P8/7, ^1)	rank-2 7-edo	(7 11...) (0 0...)	A1	M2 / m2	Da - Ra - Ma - Fa - Sa - La - Ta - Da	if Whitewood, ^ = 135/128
(P8/12, ^1)	rank-2 12-edo	(12 19...) (0 0...)	d2	A1 / m2	Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - - Sa - Fla - La - Tha - Ta - Da	if Compton, ^ = 81/80

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]	whole 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]	whole 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) whole

There are no ups and downs. The basic solfege has 13 notes. The extended solfege uses -u/-o to augment/diminish an -a interval. The solfege can be further extended with -i/-e meaning doubly augmented/diminished.

• G = P5, which = 700¢ + c for this and all other pergens
• 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)
• 19 = 12L7s and 7L12s (extended solfege only)

basic 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 solfege (-a = plain, -u = up = aug, -o = down = dim, and possibly -i = double-aug and -e = double-dim)

-20	...	-13	...	-11	-10	-9	-8	-7	-6	-5	-4	-3	-2	-1	0	1	2	3	4	5	6	7	8	9	10	11	...	13	...	20
She	...	Sho/Se	...	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	...	Pu/Fi	...	Pi
d35	...	dd5	...	d6	d3	d7	d4	d8	d5	m2	m6	m3	m7	P4	P1	P5	M2	M6	M3	M7	A4	A1	A5	A2	A6	A3	...	AA4	...	A34
Gbbb	...	Gbb	...	Abb	Ebb	Bbb	Fb	Cb	Gb	Db	Ab	Eb	Bb	F	C	G	D	A	E	B	F#	C#	G#	D#	A#	E#	...	Fx	...	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), 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 is a merging of the 2nd through 7th modes.

#2 (P8/2, P5) halves

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, mingen = vA1/^m2 (solfege #1) 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¢)

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

solfege #1 (P5 > 700¢) (-a = plain, -u = up, -o = down) mingen format

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¢)

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

solfege #2 (P5 < 700¢) (-a = plain, -u = up, -o = down) mingen format

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

Solfege #3 (EU = vvM2)

• P = ^4 = v5 = 600¢
• G = P5, mingen = ^1 = vM2 = 100¢ + c
• EU = vvM2 = 0¢
• ^ = 100¢ + c
• # = 100¢ + 7c

Doesn't tip.

solfege #3 (-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	Fro	Shu/Flo	Fru/No	Flu/Tho	Nu/Fo	Thu/Do	Fu/So	Du/Ro	Su/Lo	Ru/Mo	Lu/To	Mu/Po	Tu
	intervals	vm2	^d5/vm6	^m2/vm3	^m6/vm7	^m3/v4	^m7/v8	^4/v5	^1/vM2	^5/vM6	^M2/vM3	^M6/vM7	^M3/vA4	^M7
	notes	vDb	^Gb/vAb	^Db/vEb	^Ab/vBb	^Eb/vF	^Bb/vC	^F/vG	^C/vD	^G/vA	^D/vE	^A/vB	^E/vF#	^B

solfege #3 (-a = plain, -u = up, -o = down) mingen format

genspan (gen = ^1 = vM2)		-6	-5	-4	-3	-2	-1	0	1	2	3	4	5	6
Da's genchain perspan = 0	solfege	Sha	Shu/Flo	Fla	Flu/Tho	Tha	Thu/Do	Da	Du/Ro	Ra	Ru/Mo	Ma	Mu/Po	Pa
	intervals	d5	^d5/vm6	m6	^m6/vm7	m7	^m7/v8	P1	^1/vM2	M2	^M2/vM3	M3	^M3/vA4	A4
	notes	Gb	^Gb/vAb	Ab	^Ab/vBb	Bb	^Bb/vC	C	^C/vD	D	^D/vE	E	^E/vF#	F#
Sa's genchain perspan = ±1	solfege	Fro	Fra	Fru/No	Na	Nu/Fo	Fa	Fu/So	Sa	Su/Lo	La	Lu/To	Ta	Tu
	intervals	vm2	m2	^m2/vm3	m3	^m3/v4	P4	^4/v5	P5	^5/vM6	M6	^M6/vM7	M7	^M7
	notes	vDb	Db	^Db/vEb	Eb	^Eb/vF	F	^F/vG	G	^G/vA	A	^A/vB	B	^B

10L2s MOS scales using solfege #3 (L = ^A1 = vM2, s = m2 = rhymes) if P5 < 7\12 = 700¢, swap L and s to get 2L10s

GMN name	scale	1sn	2nds		3rds		4th	tritone	5th	6ths		7ths		8ve
1st 10L2s	LLLLLs-LLLLLs	Da	Du/Ro	Ra	Ru/Mo	Ma	Mu/Po	Fu/So	Sa	Su/Lo	La	Lu/To	Ta	Da
2nd 10L2s	LLLLsL-LLLLsL	Da	Du/Ro	Ra	Ru/Mo	Ma	Fa	Fu/So	Sa	Su/Lo	La	Lu/To	Thu/Do	Da
3rd 10L2s	LLLsLL-LLLsLL	Da	Du/Ro	Ra	Ru/Mo	Nu/Fo	Fa	Fu/So	Sa	Su/Lo	La	Tha	Thu/Do	Da
4th 10L2s	LLsLLL-LLsLLL	Da	Du/Ro	Ra	Na	Nu/Fo	Fa	Fu/So	Sa	Su/Lo	Flu/Tho	Tha	Thu/Do	Da
5th 10L2s	LsLLLL-LsLLLL	Da	Du/Ro	Fru/No	Na	Nu/Fo	Fa	Fu/So	Sa	Fla	Flu/Tho	Tha	Thu/Do	Da
6th 10L2s	sLLLLL-sLLLLL	Da	Fra	Fru/No	Na	Nu/Fo	Fa	Fu/So	Shu/Flo	Fla	Flu/Tho	Tha	Thu/Do	Da

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

• G = ^M2 = vm3 = 250¢ - c/2
• EU = vvm2 = 0¢
• ^ = 50¢ - 2.5c = 5G - P

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¢)

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

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

• G = ^m3 = vM3 = ~3 = 350¢ + c/2
• EU = vvA1 = 0¢
• ^ = 50¢ + 3.5c = 7G - 2P

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)

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-all

• P = ^/4 = v\5 = 600¢
• G = P4/2 = ^M2 = vm3 = 250¢ - c/2
• G' = P5/2 = /m3 = \M3 = 350¢ + c/2
• EU's: vvm2, \\A1
• ^ = 50¢ - 2.5c = 5G - P
• / = 50¢ + 3.5c = 3P - 7G

MOS scales covered:

• 6 = 4L2s
• 10 = 4L6s (and 6L4s when P5 > 3\5 = 720¢)
• 14 = 10L4s (and 4L10s when P5 < 4\7 = 686¢)
• 16 = 10L6s (P5 must be > 3\5 = 720¢)
• 18 = 14L4s (P5 must be < 4\7 = 686¢)
• 24 = 10L14s (and 14L10s when P5 < 7\12 = 700¢)

solfege (-a = plain, -u = up, -o = down, -i = lift, -e = drop, -uwi = uplift, -owe = downdrop)

genspan	13	...	9	8	7	6	5	4	3	2	1	0	-1	-2	-3	-4	-5	-6	-7	-8	-9	...	-13
plain genchain perspan = 0	Flu	...	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	...	Mo
	^m6	...	^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	...	vM3
	^Ab	...	^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	...	vE
lift/drop genchain perspan = ±1	Ne	...	Fe	Fruwi Nowe	De	Fluwi Thowe	Shi Se	Nuwi Fowe	Fri Re	Thuwi Dowe	Fli Le	Fuwi Sowe	Ni Me	Duwi Rowe	Thi Te	Suwi Lowe	Fi Pe	Ruwi Mowe	Di	Luwi Towe	Si	...	Li
	\m3	...	\4	^/m2 v\m3	\8	^/m6 v\m7	\5	^/m3 v\4	/m2 \M2	^/m7 v\8	/m6 \M6	^/4 v\5	/m3 \M3	^/1 v\M2	/m7 \M7	^/5 v\M6	/4 \A4	^/M2 v\M3	/1	^/M6 v\M7	/5	...	/M6
	\Eb	...	\F	^/Db v\Eb	\C	^/Ab v\Bb	/Gb \G	^/Eb v\F	/Db \D	^/Bb v\C	/Ab \A	^/F v\G	/Eb \E	^/C v\D	/Bb \B	^/G v\A	/F \F#	^/D v\E	/C	^/A v\B	/G	...	/A

#6 (P8/3, P5) thirds

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 (mingen for solfege #1) or ^^A1/vm2 (mingen for 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) mingen format

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) mingen format

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) mingen format

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) mingen format

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)

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

Implied 22edo 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

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

#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

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¢
• ^ = 67¢ + 0.67c

MOS scales covered:

• 5 = 2L3s
• 7 = 2L5s
• 9 = 2L7s
• 11 = 2L9s
• etc. up to 19 = 17L2s

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.

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

• P = ^\M3 = v\4 = 400¢
• G = ^M2 = vm3 = 250¢ - c/2, mingen = \M2 = 150¢ + c/2
• EU = vvm2, \⁶A2, ^\³A1 = 0¢
• ^ = 50¢ - 2.5c
• / = 50¢ + 1.5c

MOS scales covered:

• 9 = 6L3s
• 12 = 9L3s, P5 must be < 5\9 = 667¢
• 15 = 9L6s (and 6L9s when P5 > 3\5 = 720¢)

solfege (-a = plain, -u = up, -o = down, i = lift, -e = drop)

genspan (gen = ^M2 = vm3)		5	4	3	2	1	0	-1	-2	-3	-4	-5
drop genchain perspan = 1	solfege	Fe	Ruwe	De	Luwe	Se	Muwe	Re	Tuwe	Le	Puwe	Me
	intervals	\4	^\M2	\1	^\M6	\5	^\M3	\M2	^\M7	\M6	^\A4	\M3
	notes	\F	^\D	\C	^\A	\G	^\E	\D	^\B	\A	^\F#	\E
plain genchain perspan = 0	solfege	Du / Fro	Tha	Su / Flo	Fa	Ru / No	Da	Lu / Tho	Sa	Mu / Fo	Ra	Tu / Do
	intervals	^1 = vm2	m7	^5 = vm6	P4	^M2 = vm3	P1	^M6 = vm7	P5	^M3 = v4	M2	^M7 = v8
	notes	^C = vDb	Bb	^G = vAb	F	^D = vEb	C	^A = vBb	G	^E = vF	D	^B = vC
lift genchain perspan = -1	solfege	Fli	Showi	Ni	Frowi	Thi	Flowi	Fi	Nowi	Di	Thowi	Si
	intervals	/m6	v/d5	/m3	v/m2	/m7	v/m6	/4	v/m3	/1	v/m7	/5
	notes	/Ab	v/Gb	/Eb	v/Db	/Bb	v/Ab	/F	v/Eb	/C	v/Bb	/G

solfege (-a = plain, -u = up, -o = down, i = lift, -e = drop) mingen format

genspan (gen = \M2 = v//A1)		-5	-4	-3	-2	-1	0	1	2	3	4	5
Sa's genchain perspan = 1	solfege	Fli	Tha	De	Frowi	Ru / No	Muwe	Fi	Sa	Le	Thowi	Tu / Do
	intervals	/m6	m7	\1	v/m2	^M2 = vm3	^\M3	/4	P5	\M6	v/m7	^M7 = v8
	notes	/Ab	Bb	\C	v/Db	^D = vEb	^\E	/F	G	\A	v/Bb	^B = vC
Da's genchain perspan = 0	solfege	Fe	Showi	Su / Flo	Luwe	Thi	Da	Re	Nowi	Mu / Fo	Puwe	Si
	intervals	\4	v/d5	^5 = vm6	^\M6	/m7	P1	\M2	v/m3	^M3 = v4	^\A4	/5
	notes	\F	v/Gb	^G = vAb	^\A	/Bb	C	\D	v/Eb	^E = vF	^\F#	/G
Fa's genchain perspan = -1	solfege	Du / Fro	Ruwe	Ni	Fa	Se	Flowi	Lu / Tho	Tuwe	Di	Ra	Me
	intervals	^1 = vm2	^\M2	/m3	P4	\5	v/m6	^M6 = vm7	^\M7	/1	M2	\M3
	notes	^C = vDb	^\D	/Eb	F	\G	v/Ab	^A = vBb	^\B	/C	D	\E

#11 (P8/3, P5/2) thirds half-5th

• P = v/M3 = v\4 = 400¢
• G = ^m3 = vM3 = 350¢ + c/2, mingen = /1 = ^\\m2 = 50¢ - c/2
• EUs: vvA1, \⁶m3, ^\\\m2, v\\\M2 = 0¢
• ^ = 50¢ + 3.5c
• / = 50¢ - 0.5c

MOS scales covered:

• 9 = 3L6s
• 12 = 3L9s
• 15 = 3L12s (and 12L3s when P5 < 8\15 = 640¢)
• 18 = 3L15s (and 15L3s when P5 < 5\9 = 667¢)

solfege (-a = plain, -u = up, -o = down, i = lift, -e = drop)

genspan (gen = ^M2 = vm3)		-5	-4	-3	-2	-1	0	1	2	3	4	5
lift genchain perspan = 1	solfege	Thi	Rowi	Fi	Lowi	Di	Mowi	Si	Towi	Ri	Powi	Li
	intervals	/m7	v/M2	/4	v/M6	/1	v/M3	/5	^v/M7	/M2	v/A4	/M6
	notes	/Bb	v/D	/F	v/A	/C	v/E	/G	v/B	/D	v/F#	/A
plain genchain perspan = 0	solfege	Shu / So	Tha	Fru / Ro	Fa	Flu / Lo	Da	Nu / Mo	Sa	Thu / To	Ra	Fu / Po
	intervals	^d5 = v5	m7	^m2 = vM2	P4	^m6 = vM6	P1	^m3 = vM3	P5	^m7 = vM7	M2	^4 = vA4
	notes	^Gb = vG	Bb	^Db = vD	F	^Ab = vA	C	^Eb = vE	G	^Bb = vB	D	^F = vF#
drop genchain perspan = -1	solfege	Ne	Shuwe	The	Fruwe	Fe	Fluwe	De	Nuwe	Se	Thuwe	Re
	intervals	\m3	^\d5	\m7	^\m2	\4	^\m6	\1	^\m3	\5	^\m7	\M2
	notes	\Eb	^\Gb	\Bb	^\Db	\F	^\Ab	\C	^\Eb	\G	^\Bb	\D

solfege (-a = plain, -u = up, -o = down, i = lift, -e = drop) mingen format

genspan (gen = /1 = ^\\m2)		5	4	3	2	1	0	-1	-2	-3	-4	-5
Fa's genchain perspan = 1	solfege	Shu / So	Shuwe	Fi	Fa	Fe	Mowi	Nu / Mo	Nuwe	Ri	Ra	Re
	intervals	^d5 = v5	^\d5	/4	P4	\4	v/M3	^m3 = vM3	^\m3	/M2	M2	\M2
	notes	^Gb = vG	^\Gb	/F	F	\F	v/E	^Eb = vE	^\Eb	/D	D	\D
Da's genchain perspan = 0	solfege	Ne	Rowi	Fru / Ro	Fruwe	Di	Da	De	Towi	Thu / To	Thuwe	Li
	intervals	\m3	v/M2	^m2 = vM2	^\m2	/1	P1	\1	^v/M7	^m7 = vM7	^\m7	/M6
	notes	\Eb	v/D	^Db = vD	^\Db	/C	C	\C	v/B	^Bb = vB	^\Bb	/A
Sa's genchain perspan = -1	solfege	Thi	Tha	The	Lowi	Flu / Lo	Fluwe	Si	Sa	Se	Powi	Fu / Po
	intervals	/m7	m7	\m7	v/M6	^m6 = vM6	^\m6	/5	P5	\5	v/A4	^4 = vA4
	notes	/Bb	Bb	\Bb	v/A	^Ab = vA	^\Ab	/G	G	\G	v/F#	^F = vF#

#12 (P8/2, P4/3) halves third-4th

• P = ^/4 = v\5 = 600¢
• G = vM2 = ^^m2 = ^//1 = 167¢ - c/3
• EUs: v³A1, \⁶d4, ^\\m2, vv\\M2 = 0¢
• ^ = 33¢ + 2.33c
• / = 67¢ - 1.33c

MOS scales covered:

• 8 = 6L2s (and 2L6s when P5 > 5\8 = 750¢)
• 14 = 8L6s (and 6L8s when P5 < 4\7 = 686¢)
• 22 = 14L8s (and 8L14s when P5 > 13\22 = 709¢)
• 26 = 8L18s (P5 must be > 5\8 = 750¢)

solfege (-a = plain, -u = up, -o = down, i = lift, -e = drop, -uwi = uplift, -owe = downdrop, -owi = downlift, -uwe = updrop)

genspan	13	...	8	7	6	5	4	3	2	1	0	-1	-2	-3	-4	-5	-6	-7	-8	...	-13
plain genchain perspan = 0	Tho	...	Fru	Do	Tha	Flu	So	Fa	Nu	Ro	Da	Thu	Lo	Sa	Fu	Mo	Ra	Du	To	...	Ru
	vm7	...	^m2	v8	m7	^m6	v5	P4	^m3	vM2	P1	^m7	vM6	P5	^4	vM3	M2	^1	vM7	...	^M2
	vBb	...	^Db	vC	Bb	^Ab	vG	F	^Eb	vD	C	^Bb	vA	G	^F	vE	D	^C	vB	...	^D
lift/drop genchain perspan = ±1	Ni	...	Sowi Fle	Fi Shuwe	Nuwi Fowe	Rowi Ne	Di Fruwe	Thuwi Dowe	Lowi The	Si Fluwe	Fuwi Sowe	Mowi Fe	Ri Nuwe	Duwi Rowe	Towi De	Li Thuwe	Suwi Lowe	Powi Se	Mi Fuwe	...	Le
	/m3	...	v/5 \m6	/4 ^\d5	^/m3 v\4	v/M2 \m3	/1 ^\m2	^/m7 v\8	v/M6 \m7	/5 ^\m6	^/4 v\5	v/M3 \4	/M2 ^\m3	^/1 v\M2	v/M7 \8	/M6 ^\m7	^/5 v\M6	v/A4 \5	/M3 ^/4	...	\M6
	/Eb	...	v/G \Ab	/F ^\Gb	^/Eb v\F	v/D \Eb	/C ^\Db	^/Bb v\C	v/A \Bb	/G ^\Ab	^/F v\G	v/E \F	/D ^\Eb	^/C v\D	v/B \C	/A ^\Bb	^/G v\A	v/F# \G	/E ^\F	...	\A

1st 6L2s = LLLs-LLLs = Da Duwi/Rowe Ri Fe Fuwi/Sowe Sa Lo Thu Da

1st 8L6s = LLsLsLs-LLsLsLs = Da Duwi/Rowe Ra Ri Mo Fe Fu Fuwi/Sowe Sa Suwi/Lowe Lo Li Thu De Da

#16 (P8/4, P5) quarters

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, mingen = 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) mingen format

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) mingen format

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.

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
• 20 = 7L13s (and 13L7s when P5 > 3\5 = 720¢)

solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)

-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
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
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
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

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

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

MOS scales covered:

• 5 = 3L2s (and 2L3s if P5 > 3\5 = 720¢)
• 7 = 5L2s (only if P5 > 3\5 = 720¢ -- weird, ^ and v change direction, and m2 < 0¢)
• 8 = 5L3s (no 3L5s, because that forces P5 to be < 600¢)
• 13 = 5L8s (and 8L5s if P5 < 7\13 = 462¢)
• 18 = 5L13s (and 13L5s if P5 < 5\9 = 667¢)
• 23 = 5L18s and 18L5s (extended solfege only)

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

The next note in the genchain (genspan +18) is ^^A1/vvM2 = ^^C#/vvD. There's no solfege name for ^^A1, but vvM2 is Re. Naming an inbetween note with only one name extends the genchain to +22, Fle = vvm6 = vvAb, and to -22, Mi = ^^M3 = ^^E. This provides names for 5L18s and 18L5s.

3L2s MOS scales (L = ^^M2 = vvm3, s = ^M2) if P5 > 720¢, swap L and s to get 2L3s

GMN name	scale	1sn	2nd/3rd	4th	5th	6th/7th	8ve
1st 3L2s	sLsLL	Da	Ru	Fo	Sa	Li/The	Da
2nd 3L2s	sLLsL	Da	Ru	Fo	Su	Li/The	Da
3rd 3L2s	LsLsL	Da	Ri/Ne	Fo	Su	Li/The	Da
4th 3L2s	LsLLs	Da	Ri/Ne	Fo	Su	Tho	Da
5th 3L2s	LLsLs	Da	Ri/Ne	Fa	Su	Tho	Da

5L3s MOS scales (L = ^M2 = v³m3, s = ^1 = v³m2)

GMN name	scale	plain	up	dup/dud	down	plain	up	dup/dud	down	plain
1st 5L3s	LLsLLsLs	Da	Ru	Mi/Fe	Fo	Sa	Lu	Li/The	Do	Da
2nd 5L3s	LLsLsLLs	Da	Ru	Mi/Fe	Fo	Sa	Su	Li/The	Do	Da
3rd 5L3s	LsLLsLLs	Da	Ru	Ri/Ne	Fo	Sa	Su	Li/The	Do	Da
4th 5L3s	LsLLsLsL	Da	Ru	Ri/Ne	Fo	Sa	Su	Li/The	Tho	Da
5th 5L3s	LsLsLLsL	Da	Ru	Ri/Ne	Fo	Fa	Su	Li/The	Tho	Da
6th 5L3s	sLLsLLsL	Da	Du	Ri/Ne	Fo	Fa	Su	Li/The	Tho	Da
7th 5L3s	sLLsLsLL	Da	Du	Ri/Ne	Fo	Fa	Su	Si/Fle	Tho	Da
8th 5L3s	sLsLLsLL	Da	Du	Ri/Ne	No	Fa	Su	Si/Fle	Tho	Da

#22 (P8/2, M2/4) halves 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

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) fifths

For the pergen that equates P5 with 3\5, see (P8/5, ^1) below.

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, mingen = ^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) mingen format

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 = v⁴m2)

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)

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¢)

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

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)

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. up to 31 = 2L29s and 29L2s

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 = v4 = ^⁴m3, 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)

These pergens consist of multiple rings (copies of an edo) equally offset from one another. For example, Blackwood[15] tuned such that 5/4 is just has three 5-note rings. The offset is the difference between 5/4 and the nearest 5edo note (2\5), which is about 94¢. Thus the cents run 0, 94, 146, 240, 334, 386, etc. (146 = 1\5 - 94¢). Multi-edo pergens are named after the edo. For example, Blackwood is named "rank-2 5edo", meaning a rank-2 temperament that contains 5-edo.

Most pergens map the 5th to some nonzero number of generators, i.e., the 5th's genspan is nonzero. But multi-edo pergens map the 5th to zero generators and some number of periods. Thus in the mapping matrix, the 2nd number of the 2nd row is zero. In other words, the 5th is mapped to some note in the edo, and Sa is on the perchain not the genchain. (Incidentally, if Sa is on a genchain, but a different genchain than Da, the multigen is imperfect, e.g. (P8/2, M2/4).) Because both Da and Sa are on the perchain, the entire perchain uses the -a vowel. The genchains run De - Do - Da - Du - Di, Se - So - Sa - Su - Si, etc.

Multi-edo pergens only make sense musically if the edo's approximation of the 5th has a relative error < 25%. Otherwise there will be a more accurate Sa on another ring. For example, 4-edo with 34% error has 3/2 = 600¢, but an additional ring will add an interval between 600¢ and 750¢ that will be a better approximation. With 3-edo, error 24.5%, for 2\3 to be the best approximation, the generator must be more than twice the absolute error of 102¢, but less than half an edostep, leaving only the small range of 196-200¢. With 2-edo, only one ring can be added, because the 3rd ring will create a better 3/2.

If one were to add a better 3/2, and were to call that note Sa, the pergen would change from (P8/m, ^1) to (P8/m, P5).

In order for 10-edo's mapping to be valid, it must have an odd number somewhere in the top row and a nonzero number somewhere in the bottom row. They can't be in the same column. So rank-2 10-edo needs at least two more primes besides 2 and 3. This holds true for any multi-ring edo, like 14 or 15.

various rank-2 edos

edo	rel. error	generator range	mapping	notes / examples
2-edo	17%	204-300¢	(2 3...) (0 0...)	maximum of 4 notes, boring
3-edo	24.5%	196-200¢	(3 5...) (0 0...)	maximum of 6 notes, within 4¢ of 6-edo
4-edo	34%	none
5-edo	7.5%	36-120¢	(5 8...) (0 0...)	Sawa aka Blackwood
6-edo	49%	none
7-edo	9.5%	32-85¢	(7 11...) (0 0...)	Lawa aka Whitewood
8-edo	32%	none
9-edo	26.5%	none
10-edo	15%	36-60¢	(10 16...) (0 0...)	valid
11-edo	47.5%	none
12-edo	2%	4-50¢	(12 19...) (0 0...)	Lalawa aka Compton
13-edo	40%	none
14-edo	19%	32-43¢	(14 22...) (0 0...)	valid
15-edo	22.5%	36-40¢	(15 24...) (0 0...)	maximum of 2 rings, within 4¢ of 30-edo

(P8/5, ^1) aka Sawa

• 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) aka Lawa

• P = M2/m2 = 171¢
• G = ^1 = c (stands for 135/128 in Whitewood)
• 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	Tu	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