View source for Kite's 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|Enharmonic unison (EU)]].
{| class="wikitable center-all"
|+
vowels for (P8, P5), up/down repurposed to mean aug/dim
|-
!d<sup>4</sup>
!ddd
!dd
!dim
!plain
!aug
!AA
!AAA
!A<sup>4</sup>
|-
| -eye<br>"ay-yay"
| -eyo
| -e
| -o
| -a
| -u
| -i
| -iyu
| -iyi<br>"ee-yee"
|}
{| class="wikitable center-all"
|+
vowels for single-pair pergens
|-
!quud
!trud
!dud
!down
!plain
!up
!dup
!trup
!quup
|-
| -eye
| -eyo
| -e
| -o
| -a
| -u
| -i
| -iyu
| -iyi
|}

{| class="wikitable center-all"
|+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==
{| class="wikitable center-all"
|+
bolded entries are tippy, meaning that ^ and v can easily swap<br>-iyu = triple-up or triple-aug, -eyo = triple-down or triple-dim<br>-uwi = uplift, -uwe = updrop, -owi = downlift, -owe = downdrop
!
! colspan="2" |pergen
!mapping
![[Enharmonic unison|EU(s)]] and cents
!vowels
!perchain and/or genchain(s)
!tipping points
|-
!1
|[[List of uniform solfeges for pergens##1 (P8, P5) whole|(P8, P5)]]
|whole
|(1 1...) (0 1...)
|vA1, ^ = 100¢ + 7c
| -a -u -o (-i -e)
|Da - Sa
|
|-
!2
|[[List of uniform solfeges for pergens##2 (P8/2, P5) halves|(P8/2, P5)]]
|halves
|(2 2...) (0 1...)
|'''^^d2, ^ = 6c'''
| -a -u -o
|'''Da - Po/Shu- Da'''
|7\12 = 700¢
|-
!3
|[[List of uniform solfeges for pergens##3 (P8, P4/2) half-4th|(P8, P4/2)]]
|half-4th
|(1 2...) (0 -2...)
|vvm2, ^ = 50¢ - 2.5c
| -a -u -o
|Da - Ru/No - Fa
|
|-
!4
|[[List of uniform solfeges for pergens##4 (P8, P5/2) half-5th|(P8, P5/2)]]
|half-5th
|(1 1...) (0 2...)
|vvA1, ^ = 50¢ + 3.5c
| -a -u -o
|Da - Nu/Mo - Sa
|
|-
!5
|[[List of uniform solfeges for pergens##5 (P8/2, P4/2) half-all|(P8/2, P4/2)]]<br>true double
|half-all
|(2 4...) (0 -2...)
|vvm2, \\A1<br>^=50¢-2.5c, /=50¢+3.5c
| -a -u -o -i -e<br>-uwi -owe
|Da - Ru/No - Fa<br>Fuwi/Sowe - Fli/Le - Duwi/Rowe
|
|-
! colspan="8" |third-splits
|-
!6
|[[List of uniform solfeges for pergens##6 (P8/3, P5) thirds|(P8/3, P5)]]
|thirds
|(3 3...) (0 1...)
|'''^<sup>3</sup>d2, ^ = 4c'''
|  -a -u -o
|'''Da - Mo - Flu - Da'''
|7\12 = 700¢
|-
!7
|[[List of uniform solfeges for pergens##7 (P8, P4/3) third-4th|(P8, P4/3)]]
|third-4th
|(1 2...) (0 -3...)
|v<sup>3</sup>A1, ^ = 33¢ + 2.33c
|  -a -u -o
|Da - Ro - Nu - Fa
|
|-
!8
|[[List of uniform solfeges for pergens##8 (P8, P5/3) third-5th|(P8, P5/3)]]
|third-5th
|(1 1...) (0 3...)
|v<sup>3</sup>m2, ^ = 33¢ - 1.67c
|  -a -u -o
|Da - Ru - Fo - Sa
|
|-
!9
|[[List of uniform solfeges for pergens##9 (P8, P11/3) third-11th|(P8, P11/3)]]
|third-11th
|(1 3...) (0 -3...)
|v<sup>3</sup>M2, ^ = 67¢ + 0.67c
|  -a -u -o
|Da - Fu - Do - Fa
|
|-
!10
|[[List of uniform solfeges for pergens##10 (P8/3, P4/2) thirds half-4th|(P8/3, P4/2)]]
|thirds<br>half-4th
|(3 6...) (0 -2...)
|vvm2, \<sup>6</sup>A2, ^\\\A1, v\\\M2<br>^=50¢-2.5c, /=50¢+1.5c
|  -a -u -o -i -e<br>-owi -uwe
|Muwe - Se - Luwe<br>Da - Ru/No - Fa<br>Flowi - Thi - Frowi
|
|-
!11
|[[List of uniform solfeges for pergens##11 (P8/3, P5/2) thirds, half-5th|(P8/3, P5/2)]]
|thirds<br>half-5th
|(3 3...) (0 2...)
|vvA1, \<sup>6</sup>m3, ^\\\m2, v\\\M2<br>^=50¢+3.5c, /=50¢-0.5c
|  -a -u -o -i -e<br>-owi -uwe
|Mowi - Si - Towi<br>Da - Nu/Mo - Sa<br>Fluwe - De - Nuwe
|
|-
! rowspan="2" |12
|[[List of uniform solfeges for pergens##12 (P8/2, P4/3) halves third-4th|(P8/2, P4/3)]]
|halves<br>third-4th
|(2 4...) (0 -3...)
|v<sup>3</sup>A1, \<sup>6</sup>d4, ^\\m2, vv\\M2<br>^=33¢+2.33c, /=67¢-1.33c
|  -a -u -o -i -e<br>-uwi -owe -owi -uwe
|Da - Ro - Nu - Fa<br>Fuwi/Sowe - Si/Fluwe -<br>- Lowi/The - Thuwi/Dowe
|
|-
|
|
|
|v<sup>3</sup>A1, '''\<sup>6</sup>d<sup>3</sup>4''', v\\m2, ^^\\d2<br>^=33¢+2.33c, '''/=33¢-3.67c'''
|  -a -u -o -i -e<br>-owi -uwe
|Da - Ro - Nu - Fa<br>'''Powi/Shuwe - Fle - Li - Towi'''
|13\22 = 709¢
|-
!13
|(P8/2, P5/3)
|halves<br>third-5th
|(2 2...) (0 3...)
|v<sup>3</sup>m2, '''/<sup>6</sup>d<sup>3</sup>2''', v\\A1, vv//d2<br>^=33¢-1.67c, /=33¢+4.33c
| -a -u -o -i -e<br>-owi -uwe
|Da - Ru - Fo - Sa<br>'''Puwe/Showi - Fli - Te - Frowi'''
|15\26 = 692¢
|-
!14
|(P8/2, P11/3)
|halves<br>third-11th
|(2 6...) (0 -3...)
|v<sup>6</sup>M2, ^ = 33¢ + c/3
| -a -u -o -i -e<br>-iyu -eyo
|Da - Fi - De - Fa<br>Fiyu/Seyo - Do - Fu - Thiyu/Deyo
|
|-
!15
|(P5/3, P4/3)<br>true double
|third-all
|(3 6...) (0 -3...)
|v<sup>3</sup>A1, \<sup>3</sup>m2<br>^=33¢+2.33c, /=33¢-1.67c
|  -a -u -o -i -e<br>-uwi -owe -owi -uwe
|Mowi - Fuwi - Si - Lowi<br>Da - Ro - Nu - Fa<br>Fluwe - The - Dowe - Fruwe
|
|-
! colspan="8" |quarter-splits
|-
!16
|[[List of uniform solfeges for pergens##16 (P8/4, P5) quarters|(P8/4, P5)]]
|quarters
|(4 4...) (0 1...)
|'''^<sup>4</sup>d2, ^ = 3c'''
|  -a -u -o -i -e
|'''Da - Nu - Pe/Shi - Lo - Da'''
|7\12 = 700¢
|-
!17
|[[List of uniform solfeges for pergens##17 (P8, P4/4) quarter-4th|(P8, P4/4)]]
|quarter-4th
|(1 2...) (0 -4...)
|'''^<sup>4</sup>dd2''', \\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
|[[List of uniform solfeges for pergens##18 (P8, P5/4) quarter-5th|(P8, P5/4)]]
|quarter-5th
|(1 1...) (0 4...)
|v<sup>4</sup>A1, ^ = 25¢ + 1.75c
|<nowiki>-a -u -o -i -e</nowiki>
|Da - Ro - Ni/Me - Fu - Sa
|
|-
!19
|[[List of uniform solfeges for pergens##19 (P8, P11/4) quarter-11th|(P8, P11/4)]]
|quarter-11th
|(1 3...) (0 -4...)
|'''v<sup>4</sup>dd3''', \\A1, vv\m2, vv/d2
| -a -u -o -i -e
|'''Da - Mu - Fli/Le - Fro - Fa'''
|10\17 = 706¢
|-
!20
|[[List of uniform solfeges for pergens##20 (P8, P12/4) quarter-12th|(P8, P12/4)]]
|quarter-12th
|(1 0...) (0 4...)
|v<sup>4</sup>m2
| -a -u -o -i -e
|Da - Fo - Li/The - Ru - Sa
|
|-
!21
|(P8/4, P4/2)
|(true double)
|
|
|
|
|
|-
!22
|[[List of uniform solfeges for pergens##22 (P8/2, M2/4) halves quarter-tone|(P8/2, M2/4)]]
|halves<br>quarter-tone
|(2 3...) (0 2...)
|v<sup>4</sup>M2, ^ = 50¢ + c/2
|  -a -u -o -i -e
|Da - Du - Di/Re - Ro - Ra<br>Fi/Se - So - Sa - Su - Si/Le
|
|-
!23
|(P8/2, P4/4)
|(true double)
|
|
|
|
|
|-
!24
|(P8/2, P5/4)
|(true double)
|
|
|
|
|
|-
! colspan="8" |fifth-splits
|-
!33
|[[List of uniform solfeges for pergens##33 (P8/5, P5) fifths|(P8/5, P5)]]
|fifths
|(5 5...) (0 1...)
|v<sup>5</sup>m2, ^ = 20¢ - c
|  -a -u -o -i -e
|Da - Ri - Fo - Su - The - Da
|
|-
!34
|[[List of uniform solfeges for pergens##34 (P8, P4/5) fifth-4th|(P8, P4/5)]]
|fifth-4th
|(1 2...) (0 5...)
|'''^<sup>5</sup>d2, ^ = 2.4c'''
|  -a -u -o -i -e
|'''Da - Fri - Ro - Nu - Me - Fa'''
|7\12 = 700¢
|-
!35
|[[List of uniform solfeges for pergens##35 (P8, P5/5) fifth-5th|(P8, P5/5)]]
|fifth-5th
|(1 1...) (0 5...)
|v<sup>5</sup>A2, ^ = 60¢ + 1.8c
|  -a -u -o -i -e
|Da - Ro - Me - Ni - Fu - Sa
|
|-
!36
|[[List of uniform solfeges for pergens##36 (P8, P11/5) fifth-11th|(P8, P11/5)]]
|fifth-11th
|(1 3...) (0 -5...)
|v<sup>5</sup>A1, ^ = 20¢ + 1.4c
|  -a -u -o -i -e
|Da - Ni - So - Thu - Re - Fa
|
|-
!37
|[[List of uniform solfeges for pergens##37 (P8, P12/5) fifth-12th|(P8, P12/5)]]
|fifth-12th
|(1 0...) (0 5...)
|'''^<sup>5</sup>dd2, \<sup>5</sup>d<sup>3</sup>4,''' ^^\d2, v\\m2<br>'''^=20¢+3.8c, /=40¢-4.4c'''
|  -a -u -o -i -e
|'''Da - Mo - Fle - Ti - Nu - Sa'''
|11\19 = 695¢,<br>13\22 = 709¢
|-
!38
|[[List of uniform solfeges for pergens##38 (P8, ccP4/5) fifth-coco-4th|(P8, ccP4/5)]]
|fifth-coco-4th
|(1 4...) (0 -5...)
|v<sup>5</sup>M2, ^ = 40¢ + 0.4c
|  -a -u -o -i -e
|Da - Fi - Do - Fu - De - Fa
|
|-
! colspan="8" |sixth-splits
|-
!64
|(P8/6, P5)
|sixths
|(6 6...) (0 1...)
|'''^<sup>6</sup>d2, ^ = 2c'''
| -a -u -o -i -e<br>-iyu -eyo
|'''Da - Ro - Me - Peyo/Shiyu -<br>- Li - Thu - Da'''
|7\12 = 700¢
|-
!65
|(P8, P4/6)
|sixth-4th
|(1 2...) (0 -6...)
|v<sup>3</sup>A1, \\m2, 
|  -a -u -o -i -e<br>-uwi -owe -owi -uwe
|Da - Duwi/Fruwe - Ro - Ri/Ne -<br>- Nu - Mowi/Fowe - Fa
|
|-
! rowspan="2" |66
|(P8, P5/6)
|sixth-5th
|(1 1...) (0 6...)
|v<sup>3</sup>m2, \\A1
|  -a -u -o -i -e<br>-owi -uwe
|Da - Frowi - Ru - Ni/Me -<br>- Fo - Puwe - Sa
|
|-
|
|
|
|^<sup>6</sup>d<sup>4</sup>3, \<sup>3</sup>m2, vv\\A1
|  -a -u -o -i -e<br>-uwi -owe
|Da - Fru - Ri - Nuwi/Mowe -<br>- Fe - Po - Sa
|31edo
|-
!67
|(P8, P11/6)
|sixth-11th
|(1 3...) (0 -6...)
|vvA1, \<sup>3</sup>M2
|  -a -u -o -i -e<br>-owi -uwe
|Da - Nuwe - Fi - Flu/Lo -<br>- De - Rowi - Fa
|
|-
!68
|(P8, P12/6)
|sixth-12th
|(1 0...) (0 6...)
|vvm2, \<sup>3</sup>M2
|  -a -u -o -i -e<br>-owi -uwe
|Da - Nowi - Se - Lu/Tho -<br>- Di - Muwe - Sa
|
|-
!69
|(P8, ccP4/6)
|sixth-coco-4th
|(1 4...) (0 -6...)
|v<sup>6</sup>M2, ^ = 17¢ - 0.83c
| -a -u -o -i -e<br>-iyu -eyo
|Da - Fo - The - Neyo/Riyu -<br>- Si - Du - Fa
|
|-
!70
|(P8, ccP5/6)
|sixth-coco-5th
|(1 -1...) (0 -6...)
|v<sup>6</sup>A1
|  -a -u -o -i -e<br>-iyu -eyo
|Da - Fu - Thi - Niyu/Meyo -<br>- Le - Ro - Sa
|
|-
! colspan="8" |seventh-splits
|-
!96
|(P8/7, P5)
|sevenths
|(7 7...) (0 1...)
|v<sup>7</sup>A1, ^ = 14¢ + c
| -a -u -o -i -e<br>-iyu -eyo
|Da - Re - Niyu - Fu -<br>- So - Leyo - Thi - Da
|
|-
!97
|(P8, P4/7)
|
|
|
|
|
|
|-
!98
|(P8, P5/7)
|seventh-5th
|(1 1...) (0 7...)
|'''^<sup>7</sup>d2''', ^ = (12/7)c
| -a -u -o -i -e<br>-iyu -eyo
|'''Da - Friyu - Ro - Ni -<br>- Me - Fu - Peyo - Sa'''
|7\12 = 700¢
|-
!99
|(P8, P11/7)
|seventh-11th
|(1 3...) (0 -7...)
|v<sup>7</sup>m2, ^ = 14¢ - (5/7)c
| -a -u -o -i -e<br>-iyu -eyo
|Da - Riyu - Fo - Si -<br>- The - Du - Neyo - Fa 
|
|-
!100
|(P8, P12/7)
|seventh-12th
|(1 0...) (0 7...)
|v<sup>7</sup>A2, ^ = 43¢ - (9/7)c
|  -a -u -o -i -e<br>-iyu -eyo
|Da - Meyo - Fu - Le -<br>- Thi - Ro - Niyu - Sa
|
|-
!101
|(P8, ccP4/7)
|
|
|
|
|<nowiki>-</nowiki><br>-
|
|-
!102
|(P8, ccP5/7)
|
|
|
|
|<nowiki>-</nowiki><br>-
|
|-
!103
|(P8, c<sup>3</sup>P4/7)
|seventh-trico-4th
|(1 5...) (0 -7...)
|v<sup>7</sup>M2, ^ = 29¢ + 0.29c
| -a -u -o -i -e<br>-iyu -eyo
|Da - Fiyu - Do - Fi -<br>- De - Fu - Deyo - Fa
|
|-
! colspan="8" |eighth-splits
|-
!160
|(P8/8, P5)
|eighths
|(8 8...) (0 1...)
|v<sup>8</sup>AA2
| -a -u -o -i -e<br>-iyu -iyi -eyo -eye
|Da - Ro - Me - Peyo -<br>- AugSeye/DimFiyi -<br>- Shiyu - Fli - Thu - Da
|
|-
!
|
|
|
|
|
|
|
|-
!
|
|
|
|
|
|
|
|-
! colspan="8" |ninth-splits
|-
!
|
|
|
|
|
|
|
|-
!
|
|
|
|
|
|
|
|-
!
|
|
|
|
|
|
|
|}
{| class="wikitable center-all"
|+
Multi-edo pergens -- genchain is always De Do Da Du Di
! colspan="2" |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 -<br>- 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.
{| class="wikitable center-all"
|+
MOS scales and good pergens for them (bolded = requires more than 5 vowels)
!MOS scale
! colspan="2" |primary example
!secondary examples
|-
!Pentatonic
! colspan="2" |
!
|-
|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
! colspan="2" |
!
|-
|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
! colspan="2" |
!
|-
|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
! colspan="2" |
!
|-
|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
! colspan="2" |
!
|-
|1L 8s
|(P8, P4/4) [9]
|quarter-4th nonatonic
|fifth-4th, sixth-4th, sixth-5th, seventh-4th/5th, eighth-4th/5th
|-
|2L 7s
|(P8, c<sup>3</sup>P5/8) [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
! colspan="2" |
!
|-
|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)

{| class="wikitable center-all"
|+
'''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#
|}
{| class="wikitable center-all"
|+
'''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
|-
|d<sup>3</sup>5
|...
|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
|...
|A<sup>3</sup>4
|-
|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#
|}
{| class="wikitable center-all"
|+
2L3s MOS scales (L = m3, s = M2), L/s = (300-3c)/(200+2c)
![[Genchain mode numbering|GMN]] name
! colspan="2" |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
|}
{| class="wikitable center-all"
|+
5L2s MOS scales (L = M2, s = m2), L/s = (200+2c)/(100-5c)
![[Genchain mode numbering|GMN]] name
! colspan="2" |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
|}
{| class="wikitable center-all"
|+
5L7s MOS scales (L = A1/^1, s = m2/vM2), L/s = (100+7c)/(100-5c)<br>if P5 < 700¢, swap L and s to get 7L5s
![[Genchain mode numbering|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) '''<u>or</u>''' ^A4/vd5 (solfege #2) = 600¢
*G = P5 = 700¢ + c, mingen = vA1/^m2 (solfege #1) '''<u>or</u>''' ^A1/vm2 (solfege #2) = 100¢ + c
*EU = ^^d2 (solfege #1) = 0¢ '''<u>or</u>''' 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¢)===
{| class="wikitable center-all"
|+
'''solfege #1 (P5 > 700¢) (-a = plain, -u = up, -o = down)'''
|-
! colspan="2" |genspan ('''gen = P5''')
!-6
!-5
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
!6
|-
! rowspan="3" |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#
|-
| colspan="15" |
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
'''solfege #1 (P5 > 700¢) (-a = plain, -u = up, -o = down) [[mingen]] format'''
|-
! colspan="2" |genspan ('''gen = vA1/^m2''')
!-6
!-5
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
!6
|-
! rowspan="3" |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#
|-
| colspan="15" |
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
2L6s MOS scales using solfege #1 (L = m3/vvA2, s = vA1/^m2)

if P5 > 5\8 = 750¢, swap L and s to get 6L2s
![[Genchain mode numbering|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
|}

{| class="wikitable center-all"
|+
2L8s MOS scales using solfege #1 (L = vM2/^d3, s = vA1/^m2)

if P5 > 3\5 = 720¢, swap L and s to get 8L2s
![[Genchain mode numbering|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
|}

{| class="wikitable center-all"
|+
10L2s MOS scales using solfege #1 (L = vA1/^m2, s = vvA1/m2)
![[Genchain mode numbering|GMN]] name
!scale
!1sn
! colspan="2" |2nds
! colspan="2" |3rds
!4th
!tritone
!5th
! colspan="2" |6ths
! colspan="2" |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¢)===
{| class="wikitable center-all"
|+
'''solfege #2 (P5 < 700¢) (-a = plain, -u = up, -o = down)'''
|-
! colspan="2" |genspan ('''gen = P5''')
!-6
!-5
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
!6
|-
! rowspan="3" |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#
|-
| colspan="15" |
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
'''solfege #2 (P5 < 700¢) (-a = plain, -u = up, -o = down) [[mingen]] format'''
|-
! colspan="2" |genspan (gen = ^A1/vm2)
!-6
!-5
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
!6
|-
! rowspan="3" |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#
|-
| colspan="15" |
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
2L6s MOS scales using solfege #2 (L = m3/^^A2, s = ^A1/vm2)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
2L8s MOS scales using solfege #2 (L = ^M2/vd3, s = ^A1/vm2)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
2L10s MOS scales using solfege #2 (L = ^^A1/m2, s = ^A1/vm2)
![[Genchain mode numbering|GMN]] name
!scale
!1sn
! colspan="2" |2nds
! colspan="2" |3rds
!4th
!tritone
!5th
! colspan="2" |6ths
! colspan="2" |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
|}
{| class="wikitable center-all"
|+
12L2s MOS scales using solfege #2 (L = ^A1/vm2, s = ^1) -- P5 must be < 700¢, or s will be < 0¢
![[Genchain mode numbering|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
*<nowiki># = 100¢ + 7c</nowiki>

Doesn't tip.
{| class="wikitable center-all"
|+
'''solfege #3 (-a = plain, -u = up, -o = down)'''
|-
! colspan="2" |genspan ('''gen = P5''')
!-6
!-5
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
!6
|-
! rowspan="3" |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#
|-
| colspan="15" |
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
'''solfege #3 (-a = plain, -u = up, -o = down) [[mingen]] format'''
|-
! colspan="2" |genspan ('''gen = ^1 = vM2''')
!-6
!-5
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
!6
|-
! rowspan="3" |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#
|-
| colspan="15" |
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
10L2s MOS scales using solfege #3 (L = ^A1 = vM2, s = m2 = rhymes)

if P5 < 7\12 = 700¢, swap L and s to get 2L10s
![[Genchain mode numbering|GMN]] name
!scale
!1sn
! colspan="2" |2nds
! colspan="2" |3rds
!4th
!tritone
!5th
! colspan="2" |6ths
! colspan="2" |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¢)

{| class="wikitable center-all"
|+
'''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
|}
{| class="wikitable center-all"
|+
4L1s MOS scales (L = ^M2/vm3 = no rhyme, s = M2 = rhymes)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
5L4s MOS scales (L = M2 = rhymes, s = ^1/vm2 = no rhyme)

if P5 < 5\9 = 667¢, swap L and s to get 4L5s
![[Genchain mode numbering|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)

{| class="wikitable center-all"
|+
'''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.
{| class="wikitable center-all"
|+
3L4s MOS scales (L = M2 = rhymes, s = ~2 = no rhyme)

if P5 < 4\7 = 686¢, swap L and s to get 4L3s
![[Genchain mode numbering|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.
{| class="wikitable center-all"
|+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
![[Genchain mode numbering|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¢)

{| class="wikitable center-all"
|+
'''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
|-
! rowspan="3" |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
|-
| colspan="24" |
|-
! rowspan="3" |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) '''<u>or</u>''' ^M3/vvd4 (solfege #2) = 400¢
*G = P5 = 700¢ + c '''<u>or</u>''' vvA1/^m2 (mingen for solfege #1) '''<u>or</u>''' ^^A1/vm2 (mingen for solfege #2) = 100¢ - c
*EU = ^<sup>3</sup>d2 = 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¢)===
{| class="wikitable center-all"
|+
'''solfege #1 (-a = plain, -u = up, -o = down)'''
|-
! colspan="2" |genspan (gen = P5)
!-2
!-1
!0
!1
!2
|-
! rowspan="3" |down

genchain

perspan = 1
!solfege
|Ro
|Lo
|Mo
|To
|Po
|-
!intervals
|vM2
|vM6
|vM3
|vM7
|vA4
|-
!notes
|vD
|vA
|vE
|vB
|vF#
|-
| colspan="7" |
|-
! rowspan="3" |plain

genchain

perspan = 0
!solfege
|Tha
|Fa
|'''Da'''
|Sa
|Ra
|-
!intervals
|m7
|P4
|'''P1'''
|P5
|M2
|-
!notes
|Bb
|F
|'''C'''
|G
|D
|-
| colspan="7" |
|-
! rowspan="3" |up

genchain

perspan = -1
!solfege
|Shu
|Fru
|Flu
|Nu
|Thu
|-
!intervals
|^d5
|^m2
|^m6
|^m3
|^m7
|-
!notes
|^Gb
|^Db
|^Ab
|^Eb
|^Bb
|}
{| class="wikitable center-all"
|+
'''solfege #1 (-a = plain, -u = up, -o = down) [[mingen]] format'''
|-
! colspan="2" |genspan (gen = vvA1/^m2)
!2
!1
!0
!-1
!-2
|-
! rowspan="3" |Fa's

genchain

perspan = 1
!solfege
|Shu
|Fa
|Mo
|Nu
|Ra
|-
!intervals
|^d5
|P4
|vM3
|^m3
|M2
|-
!notes
|^Gb
|F
|vE
|^Eb
|D
|-
| colspan="7" |
|-
! rowspan="3" |Da's

genchain

perspan = 0
!solfege
|Ro
|Fru
|'''Da'''
|To
|Thu
|-
!intervals
|vM2
|^m2
|'''P1'''
|vM7
|^m7
|-
!notes
|vD
|^Db
|'''C'''
|vB
|^Bb
|-
| colspan="7" |
|-
! rowspan="3" |Sa's

genchain

perspan = -1
!solfege
|Tha
|Lo
|Flu
|Sa
|Po
|-
!intervals
|m7
|vM6
|^m6
|P5
|vA4
|-
!notes
|Bb
|vA
|^Ab
|G
|vF#
|}
{| class="wikitable center-all"
|+
'''extended solfege #1 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
! colspan="2" |genspan (gen = P5)
!-6
!-5
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
!6
|-
! rowspan="3" |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
|-
| colspan="15" |
|-
! rowspan="3" |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#
|-
| colspan="15" |
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
'''extended solfege #1 (-a = plain, -u = up, -o = down, -i = dup, -e = dud) [[mingen]] format'''
|-
! colspan="2" |genspan (gen = vvA1/^m2)
!6
!5
!4
!3
!2
!1
!0
!-1
!-2
!-3
!-4
!-5
!-6
|-
! rowspan="3" |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
|-
| colspan="15" |
|-
! rowspan="3" |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#
|-
| colspan="15" |
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
3L3s MOS scales (L = ^m3/vvA2, s = ^m2/vvA1)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
3L6s MOS scales (L = M2 = rhymes, s = ^m2/vvA1)
![[Genchain mode numbering|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
|}

{| class="wikitable center-all"
|+
3L9s MOS scales (L = vA1/^^m2, s = ^m2/vvA1)
![[Genchain mode numbering|GMN]] name
!scale
!1sn
! colspan="2" |2nds
! colspan="2" |3rds
!4th
!tritone
!5th
! colspan="2" |6ths
! colspan="2" |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¢)===
{| class="wikitable center-all"
|+
'''solfege #2 (-a = plain, -u = up, -o = down)'''
|-
! colspan="2" |genspan (gen = P5)
!-2
!-1
!0
!1
!2
|-
! rowspan="3" |up

genchain

perspan = 1
!solfege
|Ru
|Lu
|Mu
|Tu
|Pu
|-
!intervals
|^M2
|^M6
|^M3
|^M7
|^A4
|-
!notes
|^D
|^A
|^E
|^B
|^F#
|-
| colspan="7" |
|-
! rowspan="3" |plain

genchain

perspan = 0
!solfege
|Tha
|Fa
|'''Da'''
|Sa
|Ra
|-
!intervals
|m7
|P4
|'''P1'''
|P5
|M2
|-
!notes
|Bb
|F
|'''C'''
|G
|D
|-
| colspan="7" |
|-
! rowspan="3" |down

genchain

perspan = -1
!solfege
|Sho
|Fro
|Flo
|No
|Tho
|-
!intervals
|vd5
|vm2
|vm6
|vm3
|vm7
|-
!notes
|vGb
|vDb
|vAb
|vEb
|vBb
|}
{| class="wikitable center-all"
|+
'''solfege #2 (-a = plain, -u = up, -o = down) [[mingen]] format'''
|-
! colspan="2" |genspan (gen = ^^A1/vm2)
!2
!1
!0
!-1
!-2
|-
! rowspan="3" |Fa's

genchain

perspan = 1
!solfege
|Sho
|Fa
|Mu
|No
|Ra
|-
!intervals
|vd5
|P4
|^M3
|vm3
|M2
|-
!notes
|vGb
|F
|^E
|vEb
|D
|-
| colspan="7" |
|-
! rowspan="3" |Da's

genchain

perspan = 0
!solfege
|Ru
|Fro
|'''Da'''
|Tu
|Tho
|-
!intervals
|^M2
|vm2
|'''P1'''
|^M7
|vm7
|-
!notes
|^D
|vDb
|'''C'''
|^B
|vBb
|-
| colspan="7" |
|-
! rowspan="3" |Sa's

genchain

perspan = -1
!solfege
|Tha
|Lu
|Flo
|Sa
|Pu
|-
!intervals
|m7
|^M6
|vm6
|P5
|^A4
|-
!notes
|Bb
|^A
|vAb
|G
|^F#
|}
{| class="wikitable center-all"
|+
'''extended solfege #2 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
! colspan="2" |genspan (gen = P5)
!-6
!-5
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
!6
|-
! rowspan="3" |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
|-
| colspan="15" |
|-
! rowspan="3" |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#
|-
| colspan="15" |
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
'''extended solfege #2 (-a = plain, -u = up, -o = down, -i = dup, -e = dud) [[mingen]] format'''
|-
! colspan="2" |genspan (gen = ^^A1/vm2)
!6
!5
!4
!3
!2
!1
!0
!-1
!-2
!-3
!-4
!-5
!-6
|-
! rowspan="3" |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
|-
| colspan="15" |
|-
! rowspan="3" |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#
|-
| colspan="15" |
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
3L3s MOS scales (L = ^^A2/vm3, s = ^^A1/vm2)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
3L6s MOS scales (L = M2 = rhymes, s = ^^A1/vm2)

if P5 < 5\9 = 667¢, swap L and s to get 6L3s
![[Genchain mode numbering|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
|}

{| class="wikitable center-all"
|+
9L3s MOS scales (L = ^A1/vvm2, s = ^^A1/vm2)
![[Genchain mode numbering|GMN]] name
!scale
!1sn
! colspan="2" |2nds
! colspan="2" |3rds
!4th
!tritone
!5th
! colspan="2" |6ths
! colspan="2" |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 = v<sup>3</sup>A1 = 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)

{| class="wikitable center-all"
|+
'''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
{| class="wikitable center-all"
|+
'''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
|}
{| class="wikitable center-all"
|+
1L6s MOS scales (L = M2 = rhymes, s = vM2/^^m2 = no rhyme)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
7L1s MOS scales (L = vM2/^^m2, s = ^1/vvA1 = same degree)
![[Genchain mode numbering|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 = v<sup>3</sup>m2 = 0¢
*^ = (100¢ - 5c) / 3

MOS scales covered:

*5 = 1L4s (for 4L1s use pergen #3, half-4th)
*6 = 5L1s
*11 = 5L6s
*16 = 5L11s

{| class="wikitable center-all"
|+
'''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
|}
{| class="wikitable center-all"
|+
1L4s MOS scales (L = ^^M2/vm3, s = ^M2/vvm3)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
5L1s MOS scales (L = ^M2/vvm3, s = ^1/vvM2)
![[Genchain mode numbering|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 = v<sup>3</sup>M2 = 0¢
*^ = 67¢ + 0.67c

MOS scales covered:

*5 = 2L3s
*7 = 2L5s
*9 = 2L7s
*11 = 2L9s
*etc. up to 19 = 17L2s
{| class="wikitable center-all"
|+
'''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#
|}
{| class="wikitable center-all"
|+
2L7s MOS scales (L = ^m3/vv4, s = vvM2/^1)
![[Genchain mode numbering|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, \<sup>6</sup>A2, ^\<sup>3</sup>A1 = 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¢)
{| class="wikitable center-all"
|+
'''solfege (-a = plain, -u = up, -o = down, i = lift, -e = drop)'''
|-
! colspan="2" |genspan (gen = ^M2 = vm3)
!5
!4
!3
!2
!1
!0
!-1
!-2
!-3
!-4
!-5
|-
! rowspan="3" |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
|-
| colspan="13" |
|-
! rowspan="3" |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
|-
| colspan="13" |
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
'''solfege (-a = plain, -u = up, -o = down, i = lift, -e = drop''') mingen format
|-
! colspan="2" |genspan (gen = \M2 = v//A1)
!-5
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
|-
! rowspan="3" |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
|-
| colspan="13" |
|-
! rowspan="3" |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
|-
| colspan="13" |
|-
! rowspan="3" |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, \<sup>6</sup>m3, ^\\\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¢)

* 
{| class="wikitable center-all"
|+
'''solfege (-a = plain, -u = up, -o = down, i = lift, -e = drop)'''
|-
! colspan="2" |genspan (gen = ^M2 = vm3)
!-5
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
|-
! rowspan="3" |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
|-
| colspan="13" |
|-
! rowspan="3" |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#
|-
| colspan="13" |
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
'''solfege (-a = plain, -u = up, -o = down, i = lift, -e = drop)''' mingen format
|-
! colspan="2" |genspan (gen = /1 = ^\\m2)
!5
!4
!3
!2
!1
!0
!-1
!-2
!-3
!-4
!-5
|-
! rowspan="3" |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
|-
| colspan="13" |
|-
! rowspan="3" |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
|-
| colspan="13" |
|-
! rowspan="3" |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: v<sup>3</sup>A1, \<sup>6</sup>d4, ^\\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¢)

* 
{| class="wikitable center-all"
|+
'''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
|-
! rowspan="3" |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
|-
| colspan="22" |
|-
! rowspan="3" |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

==<nowiki>#</nowiki>16 (P8/4, P5) quarters==
There are two solfeges. Use solfege #1 if P5 > 700¢, and use solfege #2 if P5 < 700¢.
*P = ^m3/v<sup>3</sup>A2 (solfege #1) '''<u>or</u>''' vm3/^<sup>3</sup>A2 (solfege #2) = 300¢
*G = P5 = 700¢ + c, mingen = vvA1/^^m2 (solfege #1) '''<u>or</u>''' ^^A1/vvm2 (solfege #2) = 100¢ + c
*EU = ^<sup>4</sup>d2 = 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¢)===
{| class="wikitable center-all"
|+
'''solfege #1 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
! colspan="2" |genspan (gen = P5)
!-3
!-2
!-1
!0
!1
!2
!3
|-
! rowspan="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
|-
| colspan="9" |
|-
! rowspan="3" |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
|-
| colspan="9" |
|-
! rowspan="3" |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#
|-
| colspan="9" |
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
'''solfege #1 (-a = plain, -u = up, -o = down, -i = dup, -e = dud) [[mingen]] format'''
|-
! colspan="2" |genspan (gen = vvA1/^^m2)
!-3
!-2
!-1
!0
!1
!2
!3
|-
! rowspan="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#
|-
| colspan="9" |
|-
! rowspan="3" |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
|-
| colspan="9" |
|-
! rowspan="3" |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
|-
| colspan="9" |
|-
! rowspan="3" |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.
{| class="wikitable center-all"
|+
4L4s MOS scales (L = vM2 , s = vvA1/^^m2) using solfege #1

if P5 > 5\8 = 750¢, swap L and s
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
8L4s MOS scales (L = vvA1/^^m2, s = vvvA1/^m2) using solfege #1
![[Genchain mode numbering|GMN]] name
!scale
!1sn
! colspan="2" |2nds
! colspan="2" |3rds
!4th
!tritone
!5th
! colspan="2" |6ths
! colspan="2" |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¢)===
{| class="wikitable center-all"
|+
'''solfege #2 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
! colspan="2" |genspan (gen = P5)
!-3
!-2
!-1
!0
!1
!2
!3
|-
! rowspan="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
|-
| colspan="9" |
|-
! rowspan="3" |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
|-
| colspan="9" |
|-
! rowspan="3" |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#
|-
| colspan="9" |
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
'''solfege #2 (-a = plain, -u = up, -o = down, -i = dup, -e = dud) [[mingen]] format'''
|-
! colspan="2" |genspan (gen = ^^A1/vvm2)
!-3
!-2
!-1
!0
!1
!2
!3
|-
! rowspan="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#
|-
| colspan="9" |
|-
! rowspan="3" |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
|-
| colspan="9" |
|-
! rowspan="3" |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
|-
| colspan="9" |
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
4L4s MOS scales (L = ^M2, s = ^^A1/vvm2) using solfege #2
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
4L8s MOS scales (L = ^<sup>3</sup>A1/vm2, s = ^^A1/vvm2) using solfege #2
![[Genchain mode numbering|GMN]] name
!scale
!1sn
! colspan="2" |2nds
! colspan="2" |3rds
!4th
!tritone
!5th
! colspan="2" |6ths
! colspan="2" |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
|}
{| class="wikitable center-all"
|+
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
![[Genchain mode numbering|GMN]] name
!scale
!1sn
!
!2nd
!
! colspan="2" |3rds
!
!4th
!tritone
!5th
!
! colspan="2" |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 = v<sup>3</sup>AA1 = v\M2 = v/A1 = 125¢ - c/4
*EU's = ^<sup>4</sup>dd2, \\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.

{| class="wikitable center-all"
|+
'''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
|}
{| class="wikitable center-all"
|+
1L7s MOS scales (L = ^m3 = v/A2, s = ^m2 = v/A1)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
1L8s MOS scales (L = M2 = rhymes, s = ^m2 = v/A1)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
9L1s MOS scales (L = ^m2 = v/A1, s = vA1 = ^\m2) Sa must be > 5\9 = 667¢
![[Genchain mode numbering|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.

==<nowiki>#</nowiki>18 (P8, P5/4) quarter-5th==
*G = vM2 = ^<sup>3</sup>m2 = 175¢ + c/4
*EU = v<sup>4</sup>A1 = 0¢
*^ = 25¢ + 1.75c

MOS scales covered:

*7 = 6L1s
*13 = 7L6s
*20 = 7L13s (and 13L7s when P5 > 3\5 = 720¢)

{| class="wikitable center-all"
|+
'''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
|}
{| class="wikitable center-all"
|+
6L1s MOS scales (L = vM2/^<sup>3</sup>m2, s = ~2) if P5 < 4\7, swap L & s
![[Genchain mode numbering|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
|}

==<nowiki>#</nowiki>19 (P8, P11/4) quarter-11th==
*G = ^M3 = v<sup>3</sup>4 = v\4 = v/d4 = ^//m3 = 425¢ - c/4
*EU's = v<sup>4</sup>dd3, \\A1, vv\m2, vv/d2, etc.
*^ = 25¢ - 4.25c
*/ = 50¢ + 3.5c
MOS scales covered:

*5 = 3L2s
*8 = 3L5s
*11 = 3L8s

{| class="wikitable center-all"
|+
'''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#
|}

{| class="wikitable center-all"
|+
3L2s MOS scales (L = ~3 = ^^A2 = vvd4, s = vm2 = ^/1)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
3L5s MOS scales (L = vm3 = ^/M2, s = vm2 = ^/1)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
3L8s MOS scales (L = M2 = rhymes, s = vm2 = ^/1 = ^\A1 = no rhyme)
![[Genchain mode numbering|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
|}
==<nowiki>#</nowiki>20 (P8, P12/4) quarter-12th==

*G = v4 = ^<sup>3</sup>M3 = 475¢ + c/4
*EU = v<sup>4</sup>m2 = 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)

{| class="wikitable center-all"
|+
'''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.
{| class="wikitable center-all"
|+
3L2s MOS scales (L = ^^M2 = vvm3, s = ^M2)

if P5 > 720¢, swap L and s to get 2L3s
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
5L3s MOS scales (L = ^M2 = v<sup>3</sup>m3, s = ^1 = v<sup>3</sup>m2)
![[Genchain mode numbering|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
|}
==<nowiki>#</nowiki>22 (P8/2, M2/4) halves quarter-tone==
*P = ^^4 = vv5 = 600¢
*G = ^1 = v<sup>3</sup>M2 = 50¢ + c/2
*EU = v<sup>4</sup>M2 = 0¢
*^ = 50¢ + c/2

MOS scales covered:

*16 = 2L14s
*18 = 2L16s
*20 = 2L18s
*22 = 2L20s
*24 = 2L22s or 22L2s
{| class="wikitable center-all"
|+
'''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
|-
! rowspan="3" |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#
|-
| colspan="24" |
|-
! rowspan="3" |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
|}

{| class="wikitable center-all"
|+
2L20s MOS scales (L = m2 =  rhymes, s = ^1/v<sup>3</sup>M2 = no rhyme)
![[Genchain mode numbering|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
|}

==<nowiki>#</nowiki>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 = v<sup>3</sup>m3 = 240¢
*G = P5 = 700¢ + c, mingen = ^1 = v<sup>4</sup>m2 = 20¢ - c
*EU = v<sup>5</sup>m2 = 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¢)

{| class="wikitable center-all"
|+
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
! colspan="2" |genspan (gen = P5)
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
|-
! rowspan="3" |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
|-
| colspan="10" |
|
|-
! rowspan="3" |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#
|-
| colspan="10" |
|
|-
! rowspan="3" |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
|-
| colspan="10" |
|
|-
! rowspan="3" |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
|-
| colspan="10" |
|
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud) [[mingen]] format'''
|-
! colspan="2" |genspan (gen = ^1)
!4
!3
!2
!1
!0
!-1
!-2
!-3
!-4
|-
! rowspan="3" |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
|-
| colspan="11" |
|-
! rowspan="3" |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
|-
| colspan="11" |
|-
! rowspan="3" |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
|-
| colspan="11" |
|-
! rowspan="3" |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
|-
| colspan="11" |
|-
! rowspan="3" |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#
|}

{| class="wikitable center-all"
|+
5L5s MOS scales (L = ^M2/v<sup>4</sup>m3, s = ^1 = v<sup>4</sup>m2)
![[Genchain mode numbering|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
|}

{| class="wikitable center-all"
|+
5L10s MOS scales (L = M2 = rhymes, s = ^1/v<sup>4</sup>m2 = no rhyme)

if P5 < 8\15 = 640¢, swap L and s to get 10L5s
![[Genchain mode numbering|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
|}

==<nowiki>#</nowiki>34 (P8, P4/5) fifth-4th==

*G = ^^m2 = v<sup>3</sup>A1 = 100¢ - c/5
*EU = ^<sup>5</sup>d2 = 0¢
*^ = 2.4c

MOS scales covered:
*10 = 1L9s
*11 = 1L10s
*12 = 1L11s (all but 2 modes)

{| class="wikitable center-all"
|+
'''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
|}
{| class="wikitable center-all"
|+
1L9s MOS scales (L = ^^m3/v<sup>3</sup>A2, s = ^^m2/v<sup>3</sup>A1)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
1L10s MOS scales (L = M2 = rhymes, s = ^^m2/v<sup>3</sup>A1 = no rhyme)
![[Genchain mode numbering|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
|}

==<nowiki>#</nowiki>35 (P8, P5/5) fifth-5th==

*G = vM2 = ^<sup>4</sup>d1 = 140¢ + c/5
*EU = v<sup>5</sup>A2 = 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¢)

{| class="wikitable center-all"
|+
'''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
|}
{| class="wikitable center-all"
|+
1L7s MOS scales (L = ^^m2/v<sup>3</sup>M3, s = vM2/^<sup>4</sup>d1)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
8L1s MOS scales (L = vM2/^<sup>4</sup>d1, s = vvM2/^<sup>3</sup>d1)
![[Genchain mode numbering|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
|}

==<nowiki>#</nowiki>36 (P8, P11/5) fifth-11th==
This pergen can be thought of as "half-down5th".

*G = ^^m3 = v<sup>3</sup>M3 = 340¢ - c/5
*EU = v<sup>5</sup>A1 = 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

{| class="wikitable center-all"
|+
'''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
|}

{| class="wikitable center-all"
|+
4L3s MOS scales (L = vM2 = ^<sup>4</sup>m2, s = vvM2 = ^<sup>3</sup>m2)
![[Genchain mode numbering|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
|}
==<nowiki>#</nowiki>37 (P8, P12/5) fifth-12th==
This pergen can be thought of as "half-dudaug5th".
*G = vM3 = ^\d4 = //A2 = 380¢ + c/5
*EU's = ^<sup>5</sup>dd2, \<sup>5</sup>d<sup>3</sup>4, ^^\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)

{| class="wikitable center-all"
|+
'''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
|}
{| class="wikitable center-all"
|+
3L4s MOS scales (L = ^m3 = v/A2 = \\d4, s = ^/1 = vvA1 = \m2)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
3L7s MOS scales (L = ^/M2 = vvA2 = \m3, s = ^/1 = vvA1 = \m2)
![[Genchain mode numbering|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
|}
==<nowiki>#</nowiki>38 (P8, ccP4/5) fifth-coco-4th==
*G = ^^4 = v<sup>3</sup>5 = 580¢ - c/5
*EU = v<sup>5</sup>M2 = 0¢
*^ = 40¢ + 0.4c

MOS scales covered:
*5 = 2L3s
*7 = 2L5s
*9 = 2L7s
*11 = 2L9s
*etc. up to 31 = 2L29s and 29L2s

{| class="wikitable center-all"
|+
'''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#
|}
{| class="wikitable center-all"
|+
2L7s MOS scales (L = v4 = ^<sup>4</sup>m3, s = ^1 = v<sup>4</sup>M2)
![[Genchain mode numbering|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. 

<u>Multi-edo pergens only make sense musically if the edo's approximation of the 5th has a relative error < 25%</u>. 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.
{| class="wikitable center-all"
|+
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
{| class="wikitable center-all"
|+
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
! colspan="2" |genspan (gen = ^1)
!-2
!-1
!0
!1
!2
|-
! rowspan="3" |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
|-
| colspan="7" |
|-
! rowspan="3" |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
|-
| colspan="7" |
|-
! rowspan="3" |Da's

genchain

perspan = 0
!solfege
|De
|Do
|'''Da'''
|Du
|Di
|-
!intervals
|vv8
|v8
|'''P1'''
|^1
|^^1
|-
!notes
|vvC
|vC
|'''C'''
|^C
|^^C
|-
| colspan="7" |
|-
! rowspan="3" |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
|-
| colspan="7" |
|-
! rowspan="3" |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:
{| class="wikitable center-all"
|+
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
! colspan="2" |genspan (gen = vM3)
!2
!1
!0
!-1
!-2
|-
! rowspan="3" |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
|-
|
|
|
|
|
|
|
|-
! rowspan="3" |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
|-
|
|
|
|
|
|
|
|-
! rowspan="3" |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
|-
|
|
|
|
|
|
|
|-
! rowspan="3" |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
|-
|
|
|
|
|
|
|
|-
! rowspan="3" |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
|}
{| class="wikitable center-all"
|+
5L5s MOS scales (L = vM2/vm3, s = ^1)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
5L10s MOS scales (L = vM2/vm3, s = ^1)
if s > 1\15 = 80¢, swap L and s to get 10L5s
![[Genchain mode numbering|GMN]] name
!scale
!1sn
!
!
!2nd
! colspan="2" |3rds
!4th
! colspan="2" |tritones
!5th
! colspan="2" |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
{| class="wikitable center-all"
|+
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
! colspan="2" |genspan (gen = ^1)
!-2
!-1
!0
!1
!2
|-
! rowspan="3" |Fa's

genchain

perspan = 3
!solfege
|Fe
|Fo
|Fa
|Fu
|Fi
|-
!intervals
|vv4
|v4
|P4
|^4
|^^4
|-
!notes
|vvF
|vF
|F
|^F
|^^F
|-
| colspan="7" |
|-
! rowspan="3" |Ma's

genchain

perspan = 2
!solfege
|Me
|Mo
|Ma
|Mu
|Mi
|-
!intervals
|vvM3
|vM3
|M3
|^M3
|^^M3
|-
!notes
|vvE
|vE
|E
|^E
|^^E
|-
| colspan="7" |
|-
! rowspan="3" |Ra's

genchain

perspan = 1
!solfege
|Re
|Ro
|Ra
|Ru
|Ri
|-
!intervals
|vvM2
|vM2
|M2
|^M2
|^^M2
|-
!notes
|vvD
|vD
|D
|^D
|^^D
|-
| colspan="7" |
|-
! rowspan="3" |Da's

genchain

perspan = 0
!solfege
|De
|Do
|'''Da'''
|Du
|Di
|-
!intervals
|vv8
|v8
|'''P1'''
|^1
|^^1
|-
!notes
|vvC
|vC
|'''C'''
|^C
|^^C
|-
| colspan="7" |
|-
! rowspan="3" |Ta's

genchain

perspan = -1
!solfege
|Te
|To
|Ta
|Tu
|Ti
|-
!intervals
|vvM7
|vM7
|M7
|^M7
|^^M7
|-
!notes
|vvB
|vB
|B
|^B
|^^B
|-
| colspan="7" |
|-
! rowspan="3" |La's

genchain

perspan = -2
!solfege
|Le
|Lo
|La
|Lu
|Li
|-
!intervals
|vvM6
|vM6
|M6
|^M6
|^^M6
|-
!notes
|vvA
|vA
|A
|^A
|^^A
|-
| colspan="7" |
|-
! rowspan="3" |Sa's

genchain

perspan = -3
!solfege
|Se
|So
|Sa
|Su
|Si
|-
!intervals
|vv5
|v5
|P5
|^5
|^^5
|-
!notes
|vvG
|vG
|G
|^G
|^^G
|}
{| class="wikitable center-all"
|+
7L7s MOS scales (L = vM2/vm2, s = ^1)
![[Genchain mode numbering|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
|}
{| class="wikitable center-all"
|+
7L14s MOS scales (L = vvM2/vvm2, s = ^1)
if s > 1\21 = 57¢, swap L and s to get 14L7s
![[Genchain mode numbering|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
|}
[[Category:Solfege]]