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User:TallKite/Solfeges: Difference between revisions

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'''<big>This page is a work in progress!</big>'''
'''<big>This page is a work in progress!</big>'''


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


include subset solfeges (8 of 24, 9/18 of 36, 16 of 48, 15/20 of 60, others? 11 of 22? 13 of 26?)
check all edo pages for others' solfeges, done up to 19
 
figure out the format for inbetween notes in edo tables: list once or list twice?
 
include subset solfeges? (8 of 24, 9/18 of 36, 16 of 48, 15/20 of 60, maybe 11 of 22? 13 of 26?)


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


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


maybe break up into 2 pages?
maybe break up into 2 pages?
Line 19: Line 23:
'''BC (backwards-compatible)''' solfeges are for mid-sized edos like 17 and 19. They expand on the conventional Do Re Mi (and Do Di/Ra Re RiMa Mi) and use traditional vowels plus new ones.
'''BC (backwards-compatible)''' solfeges are for mid-sized edos like 17 and 19. They expand on the conventional Do Re Mi (and Do Di/Ra Re RiMa Mi) and use traditional vowels plus new ones.


'''Uniform''' solfeges are for larger edos like 41 and 53. They use a uniform vowel sequence for all degrees. They add 6 altered consonants: Fr- N- P- Sh- Fl- and Th-. '''Uniform diatonic''' solfeges don't add them.
'''Uniform''' solfeges are for almost edos, especially large ones like 41 and 53. They are also for rank-2 temperaments. They use a uniform vowel sequence for all degrees. They add 6 altered consonants: Fr- N- P- Sh- Fl- and Th-. '''Uniform diatonic''' solfeges don't add them.


== Uniform solfeges ==
== Uniform solfeges ==
Line 62: Line 66:
These 5 vowels cover all the more popular edos up to 60. Which edos aren't covered? The number of vowels a uniform solfege needs equals the edo's [[sharpness]] or penta-sharpness, whichever is larger. Thus an edo with a (penta)sharpness of 6 or higher needs 6 or more vowels and isn't covered. Every edo above 60 is such an edo. The excluded edos are the less efficient ones, with a fairly inaccurate 5th for their size. Thus they tend to be the less popular edos.
These 5 vowels cover all the more popular edos up to 60. Which edos aren't covered? The number of vowels a uniform solfege needs equals the edo's [[sharpness]] or penta-sharpness, whichever is larger. Thus an edo with a (penta)sharpness of 6 or higher needs 6 or more vowels and isn't covered. Every edo above 60 is such an edo. The excluded edos are the less efficient ones, with a fairly inaccurate 5th for their size. Thus they tend to be the less popular edos.


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


=== Examples ===
=== Examples ===
Line 154: Line 158:
Da - Ra - Ma - Fa - Sa - La - Ta - Da
Da - Ra - Ma - Fa - Sa - La - Ta - Da


This helps with <u>un</u>learning the syllables Do, Mi, So and Ti, which are still present but have a changed meaning. (For those familiar with the full 17-name solfege, note that Ra, Ri, Fi, Si and Li are often present but changed.)
This helps with <u>un</u>learning the traditional vowels. Next add in the 6 altered consonants, making a 12-edo-like solfege:
 
Next add in the 6 altered consonants, making a 12-edo-like solfege:


Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da
Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da
Line 1,827: Line 1,829:
{| class="wikitable  center-all"
{| class="wikitable  center-all"
|+
|+
uniform solfege (-u = up, -o = down, -a = plain)
uniform solfege (-a = plain, -u = up, -o = down)
![[15edo]]
![[15edo]]
!0
!0
Line 3,944: Line 3,946:
{| class="wikitable  center-all"
{| class="wikitable  center-all"
|+
|+
uniform solfege  (-u = up, -o = down, -a = plain)
uniform solfege  (-a = plain, -u = up, -o = down)
![[22edo]]
![[22edo]]
!0
!0
Line 4,870: Line 4,872:
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
uniform solfege (-u = up, -a = plain, -o = down), see also 29edo, 36edo
uniform solfege (-a = plain, -u = up, -o = down), see also 29edo, 36edo
![[24edo]]
![[24edo]]
!0
!0
Line 7,706: Line 7,708:
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
Kite's solfege (-a = plain, -u = up, -o = down, -i = mid), see also 53edo
uniform solfege (-a = plain, -u = up, -o = down, -i = mid), see also 53edo
![[41edo]]
![[41edo]]
!edosteps
!edosteps
Line 9,093: Line 9,095:
|}
|}


== Rank-2 Uniform Solfeges by Pergen ==
== Bonus edo: 72edo ==
Rank-2 temperaments have an infinite number of notes, so a solfege can only cover a fraction of them. But often one only uses enough notes to make a MOS scale. [[Pergen|Pergens]] tell us how to use ups and downs to notate them, and the same consonants and vowels can be used. Instead of circles of 5ths, there are fifthchains. Each fifthchain requires its own vowel, so there is a maximum of 5 fifthchains.
This solfege uses two additional vowels.
 
Genchains are distinct from fifthchains. Each pergen has one or more genchains, each of which contains one or more fifthchains. However if the octave is split in halves or quarters, the half-octave requires two names, and the pergen needs an additional vowel. The 13 consonants and 5 vowels cover about 20 pergens. Of course, the genchains can only extend so far with only 13 consonants. But in general, it's enough to cover all the modes of any reasonably-sized MOS scale.
 
Sometimes -i and -e mean lift/drop not dup/dud. If so, note that there are no words for uplift, downlift, etc. -i never means mid, so there are only two vowel sequences, not three:
{| class="wikitable center-all"
{| class="wikitable center-all"
|+the two vowel sequences
|+
!3 vowels
uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud, -ih = trup, -uh = trud)
|
![[72edo]]
|<nowiki>-o = down</nowiki>
!edosteps
|<nowiki>-a = plain</nowiki>
! colspan="2" |solfege names
|<nowiki>-u = up</nowiki>
! colspan="4" |[[Ups and downs notation|ups and downs]] names
|
|-
|-
!5 vowels
!unisons
| -e = dud or drop
|0-2
|<nowiki>-o = down</nowiki>
| colspan="2" |Da Du Di
|<nowiki>-a = plain</nowiki>
| colspan="2" |P1 ^1 ^^1
|<nowiki>-u = up</nowiki>
| colspan="2" |C ^C ^^C
|  -i = dup or lift
|}In the MOS scale tables, any note that changes from one mode to the next is '''bolded'''.
 
The EI (enharmonic interval) can be added to or subtracted from any note or interval to get an equivalent note or interval.
 
A pergen's solfege can suggest an edo's solfege. For example, 22edo supports (P8, P4/3), and the pergen's solfege has 27 notes in it. Since the generator is 3\22, simply apply the genchain to every 3rd edostep of 22edo. The extra 5 names make duplicate names.to do:
 
* explain c is P5 - 700¢
* explain the 1st mode always has Sa and not Fa, and the last mode always has Fa and not Sa.
* make a table of pergens and what MOS scales each one covers
* discuss using numeric solfeges with non-diatonic-friendly MOSes
* for each pergen, list the entire genchain in melodic order, if possible?
* explain temperament naming: can use Aug and Dim syllables to extend the genchains, can use -a- for an omitted prime.
 
=== List of MOS scales ===
Some combos of pergens and MOS scales require a very sharp or flat 5th. Just as with superflat edos, a uniform solfege can still be used, but the sound of the interval won't match what its name implies. Better to use a different pergen.
{| 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
!
!
|3
| colspan="2" |Dih/Fruh
| colspan="2" |^<sup>3</sup>1 / v<sup>3</sup>m2
| colspan="2" |^<sup>3</sup>C / v<sup>3</sup>Db
|-
!2nds
|4-14
|Fre Fro Fra Fru Fri
|Ruh Re Ro Ra Ru Ri
|vvm2 vm2 m2 ^m2 v~2
|~2 ^~2 vM2 M2 ^M2 ^^M2
|vvDb vDb Db ^Db ^^Db
|v<sup>3</sup>D vvD vD D ^D ^^D
|-
!
!
|15
| colspan="2" |Rih/Nuh
| colspan="2" |^<sup>3</sup>M2 / v<sup>3</sup>m3
| colspan="2" |^<sup>3</sup>D / v<sup>3</sup>Eb
|-
!3rds
|16-26
|Ne No Na Nu Ni
|Muh Me Mo Ma Mu Mi
|vvm3 vm3 m3 ^m3 v~3
|~3 ^~3 vM3 M3 ^M3 ^^M3
|vvEb vEb Eb ^Eb ^^Eb
|v<sup>3</sup>E vvE vE E ^E ^^E
|-
!
!
|27
| colspan="2" |Mih/Fuh
| colspan="2" |^<sup>3</sup>M3 / v<sup>3</sup>4
| colspan="2" |^<sup>3</sup>E / v<sup>3</sup>F
|-
|-
|1L 4s
!4ths
|(P8, P5/3) [5]
|28-32
|third-5th pentatonic
| colspan="2" |Fe Fo Fa Fu Fi
|third-4th, quarter-4th, quarter-5th
| colspan="2" |vv4 v4 P4 ^4 v~4
| colspan="2" |vvF vF F ^F ^^F
|-
|-
|2L 3s
!tritones
|(P8, P5) [5]
|33-39
|unsplit pentatonic
| colspan="2" |Fih/Puh/Shuh Pe/She Po/Sho Pa/Sha
|third-11th
Pu/Shu Pi/Shi Pih/Shi/Suh
| colspan="2" |~4/v<sup>3</sup>d5 ^~4/vvd5 vA4/vd5 A4/d5
^A4/^d5 ^^A4/v~5 ^<sup>3</sup>A4/~5
| colspan="2" |^<sup>3</sup>F/v<sup>3</sup>F#/v<sup>3</sup>Gb vvF#/vvGb vF#/vGb F#/Gb
^F#/^Gb ^^F#/^^Gb ^<sup>3</sup>F#/^<sup>3</sup>Gb/v<sup>3</sup>G
|-
|-
|3L 2s
!5ths
|(P8, P12/4) [5]
|40-44
|quarter-12th pentatonic
| colspan="2" |Se So Sa Su Si
|quarter-11th
| colspan="2" |^~5 v5 P5 ^5 ^^5
|-
| colspan="2" |vvG vG G ^G ^^G
|4L 1s
|(P8, P4/2) [5]
|half-4th pentatonic
|
|-
|-
!Hexatonic
!
!
!
!
|45
| colspan="2" |Sih/Fluh
| colspan="2" |^<sup>3</sup>5 / v<sup>3</sup>m6
| colspan="2" |^<sup>3</sup>G / v<sup>3</sup>Ab
|-
|-
|1L 5s
!6ths
|(P8, P4/3) [6]
|46-56
|third-4th hexatonic
|Fle Flo Fla Flu Fli
|quarter-4th, quarter-5th, fifth-4th, fifth-5th
|Luh Le Lo La Lu Li
|vvm6 vm6 m6 ^m6 v~6
|~6 ^~6 vM6 M6 ^M6 ^^M6
|vvAb vAb Ab ^Ab ^^Ab
|v<sup>3</sup>A vvA vA A ^A ^^A
|-
!
|57
| colspan="2" |Lih/Thuh
| colspan="2" |^<sup>3</sup>M6 / v<sup>3</sup>m7
| colspan="2" |^<sup>3</sup>A / v<sup>3</sup>Bb
|-
!7ths
|58-68
|The Tho Tha Thu Thi
|Tuh Te To Ta Tu Ti
|vvm7 vm7 m7 ^m7 v~7
|~7 ^~7 vM7 M7 ^M7 ^^M7
|vvBb vBb Bb ^Bb ^^Bb
|v<sup>3</sup>B vvB vB B ^B ^^B
|-
!
|69
| colspan="2" |Tih/Duh
| colspan="2" |^<sup>3</sup>M7 / v<sup>3</sup>8
| colspan="2" |^<sup>3</sup>B / v<sup>3</sup>C
|-
!8ves
|70-72
| colspan="2" |De Do Da (Du Di Dih)
| colspan="2" |vv8 v8 P8 (^8 ^^8 ^<sup>3</sup>8)
| colspan="2" |vvC vC C (^C ^^C ^<sup>3</sup>C)
|}
{| class="wikitable center-all"
|+
'''circles of fifths'''
! rowspan="3" |plain
 
circle
!0
!42
!12
!54
!24
!66
!36
!6
!48
!18
!60
!30
!72
|-
|-
|2L 4s
|Da
|(P8/2, P5) [6]
|Sa
|half-8ve hexatonic
|Ra
|La
|Ma
|Ta
|Pa
|
|
|
|
|
|
|
|-
|-
|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
|
|
|
|
|
|Sha
|Fra
|Fla
|Na
|Tha
|Fa
|Da
|-
|-
!Heptatonic
| colspan="14" |
!
!
!
|-
|-
|1L 6s
! rowspan="3" |up
|(P8, P4/3) [7]
 
|third-4th heptatonic
circle
|quarter-4th, fifth-4th, fifth-5th, '''sixth-4th, sixth-5th'''
!1
|-
!43
|2L 5s
!13
|(P8, P11/3) [7]
!55
|third-11th heptatonic
!25
|fifth-coco-4th, '''sixth-coco-5th'''
!67
!37
!7
!49
!19
!61
!31
!1
|-
|-
|3L 4s
|Du
|(P8, P5/2) [7]
|Su
|half-5th heptatonic
|Ru
|fifth-12th
|Lu
|Mu
|Tu
|Pu
|
|
|
|
|
|
|-
|-
|4L 3s
|(P8, P11/5) [7]
|fifth-11th heptatonic
|'''sixth-12th'''
|-
|5L 2s
|(P8, P5) [7]
|unsplit heptatonic
|'''sixth-coco-4th'''
|-
|6L 1s
|(P8, P5/4) [7]
|quarter-5th heptatonic
|
|
|-
!Octotonic
!
!
!
|-
|1L 7s
|(P8, P4/4) [8]
|quarter-4th octotonic
|fifth-4th, fifth-5th, '''sixth-4th, sixth-5th, seventh-4th, seventh-5th'''
|-
|2L 6s
|(P8/2, P5) [8]
|half-8ve octotonic
|
|
|-
|3L 5s
|(P8, P11/4) [8]
|quarter-11th octotonic
|'''seventh-cc4th, seventh-cc5th'''
|-
|4L 4s
|(P8/4, P5) [8]
|quarter-8ve octotonic
|
|
|-
|5L 3s
|(P8, P12/4) [8]
|quarter-12th octotonic
|(very lopsided, unless 5th is quite flat)
|-
|6L 2s
|'''(P8/2, P4/3) [8]'''
|'''half-8ve third-4th octotonic'''
|
|
|
|
|Shu
|Fru
|Flu
|Nu
|Thu
|Fu
|Du
|-
|-
|7L 1s
| colspan="14" |
|(P8, P4/3) [8]
|third-4th octotonic
|
|-
|-
!Nonatonic
! rowspan="3" |down
!
 
!
circle
!
!71
!41
!11
!53
!23
!65
!35
!5
!47
!17
!59
!29
!71
|-
|-
|1L 8s
|Do
|(P8, P4/4) [9]
|So
|quarter-4th nonatonic
|Ro
|fifth-4th, '''sixth-4th, sixth-5th, seventh-4th/5th, eighth-4th/5th'''
|Lo
|Mo
|To
|Po
|
|
|
|
|
|
|-
|-
|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
|
|
|
|
|
|
|Sho
|Fro
|Flo
|No
|Tho
|Fo
|Do
|-
|-
!Decatonic
| colspan="14" |
!
!
!
|-
|-
|1L 9s
! rowspan="3" |dup
|'''(P8, P5/6) [10]'''
 
|'''sixth-5th decatonic'''
circle
|fifth-4th, '''sixth-4th, seventh-4th/5th, eighth-4th/5th, ninth-4th/5th'''
!2
!44
!14
!56
!26
!68
!38
!8
!50
!20
!62
!33
!2
|-
|-
|2L 8s
|Di
|(P8/2, P5) [10]
|Si
|half-8ve decatonic
|Ri
|half-8ve quartertone, '''half-8ve third-11th'''
|Li
|Mi
|Ti
|Pi
|
|
|
|
|
|
|-
|-
|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'''
|
|
|
|
|
|
|Shi
|Fri
|Fli
|Ni
|Thi
|Fi
|Di
|-
|-
|7L 3s
| colspan="14" |
|(P8, P5/2) [10]
|half-5th decatonic
|'''ninth-coco-5th'''
|-
|-
|8L 2s
! rowspan="3" |dud circle
|'''(P8/2, P4/4) [10]'''
!70
|'''half-8ve quarter-4th decatonic'''
!40
|'''half-8ve quarter-12th'''
!10
!52
!22
!64
!34
!4
!46
!16
!58
!28
!70
|-
|-
|9L 1s
|De
|(P8, P4/2) [10]
|Se
|quarter-4th decatonic
|Re
|Le
|Me
|Te
|Pe
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|She
|Fre
|Fle
|Ne
|The
|Fe
|De
|-
| colspan="14" |
|-
! rowspan="5" |trup/trud
circle
!3
!45
!15
!57
!27
!69
!39
!9
!51
!21
!63
!33
!3
|-
|Dih
|Sih
|Rih
|Lih
|Mih
|Tih
|Pih
|
|
|
|
|
|
|-
|
|
|
|
|
|
|Shih
|Frih
|Flih
|Nih
|Thih
|Fih
|Dih
|-
|Fruh
|Fluh
|Nuh
|Thuh
|Fuh
|Duh
|Suh
|Ruh
|Luh
|Muh
|Tuh
|Puh
|
|-
|
|
|
|
|
|
|
|
|
|
|
|Shuh
|Fluh
|}
|}


== #1 (P8, P5) unsplit ==
== Rank-2 Uniform Solfeges by Pergen ==
 
Rank-2 temperaments have an infinite number of notes, so a solfege can only cover a fraction of them. But often one only uses enough notes to make a MOS scale. [[Pergen|Pergens]] tell us how to use ups and downs to notate these temperaments, and the same consonants and vowels can be used. Instead of circles of 5ths, there are fifthchains. Each fifthchain requires its own vowel, so there is a maximum of 5 fifthchains.
* G = P5 = 700¢ + c
* EI = vA1 = 0¢ (extended solfege only)
* ^ = # = 100 + 7c (extended solfege only)


MOS scales covered:
Genchains are distinct from fifthchains. Each pergen has one or more genchains, each of which contains one or more fifthchains. However if the octave is split in halves or quarters, the half-octave requires two names, and the pergen needs an additional vowel. The 13 consonants and 5 vowels cover 21 pergens. Of course, the genchains can only extend so far with only 13 consonants. But in general, it's enough to cover all the modes of any reasonably-sized MOS scale.


* 5 = 2L3s (1\2 < P5 < 3\5) (for 3L2s, use P11/4 or P12/4, to avoid P5 > 3\5= 720¢)
This pdf '''[https://tallkite.com/misc_files/notation&#x20;guide&#x20;for&#x20;rank-2&#x20;pergens.pdf tallkite.com/misc_files/notation guide for rank-2 pergens.pdf]''' lists many pergens. The tuning of every interval and every accidental is defined in terms of c = P5 - 700¢. The EU ([[enharmonic unison]]) can be added to or subtracted from any note or interval to get an equivalent note or interval. The entire solfege can be derived from the pergen, the EU and the vowel sequence.
* 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)


{| class="wikitable center-all"
Sometimes -i and -e mean lift/drop not dup/dud. -i never means mid, so there are only two vowel sequences, not three:
|+
{| class="wikitable"
'''uniform solfege (-a = plain)'''
|+unsplit (no-pair) solfege
|-
!genspan
!-6
!-5
!-4
!-4
!-3
!-3
Line 9,390: Line 9,538:
!3
!3
!4
!4
!5
!6
|-
|-
!solfege
!d<sup>4</sup>
|Sha
!ddd
|Fra
!dd
|Fla
!dim
|Na
!plain
|Tha
!aug
|Fa
!AA
|'''Da'''
!AAA
|Sa
!A<sup>4</sup>
|Ra
|-
|La
| -eye
|Ma
"ay-yay"
|Ta
| -eyo
|Pa
| -e
|-
| -o
!intervals
| -a
|d5
| -u
|m2
| -i
|m6
| -iyu
|m3
| -iyi
|m7
"ee-yee"
|P4
|}
|'''P1'''
{| class="wikitable"
|P5
|+single-pair solfeges
|M2
!-4
|M6
!-3
|M3
!-2
|M7
|A4
|-
!notes
|Gb
|Db
|Ab
|Eb
|Bb
|F
|'''C'''
|G
|D
|A
|E
|B
|F#
|}
{| class="wikitable center-all"
|+
'''extended uniform solfege (-a = plain, -u = up = aug, -o = down = dim)'''
|-
!genspan
!-13
!-12
!-11
!-10
!-9
!-8
!-7
!-6
!-5
!-4
!-3
!-2
!-1
!-1
!0
!0
Line 9,461: Line 9,572:
!3
!3
!4
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
|-
|-
!solfege
!quud
|Sho
!trud
|Fro
!dud
|Flo
!down
|No
!plain
|Tho
!up
|Fo
!dup
|Do
!trup
|So/Sha
!quup
|Fra
|-
|Fla
| -eye
|Na
| -eyo
|Tha
| -e
|Fa
| -o
|'''Da'''
| -a
|Sa
| -u
|Ra
| -i
|La
| -iyu
|Ma
| -iyi
|Ta
|}
|Pa/Fu
{| class="wikitable"
|Du
|+double-pair solfeges
|Su
|
|Ru
!down
|Lu
!plain
|Mu
!up
|Tu
|-
|Pu
!lift
| -owi
| -i
| -uwi
|-
|-
!intervals
!plain
|dd5
| -o
|d2
| -a
|d6
| -u
|d3
|d7
|d4
|d8
|d5
|m2
|m6
|m3
|m7
|P4
|'''P1'''
|P5
|M2
|M6
|M3
|M7
|A4
|A1
|A5
|A2
|A6
|A3
|A7
|AA4
|-
|-
!notes
!drop
|Gbb
| -owe
|Dbb
| -e
|Abb
| -uwe
|Ebb
|Bbb
|Fb
|Cb
|Gb
|Db
|Ab
|Eb
|Bb
|F
|'''C'''
|G
|D
|A
|E
|B
|F#
|C#
|G#
|D#
|A#
|E#
|B#
|Fx
|}
|}
Any compound vowel with a "w" is for double-pair only. Mnemonic: w = double-u = double-pair.
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.
A pergen's solfege can suggest an edo's solfege. For example, 22edo supports (P8, P4/3), and the pergen's solfege has 27 notes in it. Since the generator is 3\22, simply apply the genchain to every 3rd edostep of 22edo. The extra 5 names make duplicate names. 
Every solfege syllable that ends in -o indicates a correlation with colorspeak. Thus temperaments that start with Mo have -o/-u = yo/gu, those that have 2nd syllable Tho have -o/-u = zo/ru, etc. 
To Do:
* make a table of pergens and what MOS scales each one covers
* discuss using numeric solfeges with non-diatonic-friendly MOSes
* for each pergen, list the entire genchain in melodic order, if possible?
=== 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"
{| class="wikitable center-all"
|+
|+
2L3s MOS scales (L = m3, s = M2), L/s = (300-3c)/(200+2c)
MOS scales and good pergens for them (bolded = requires more than 5 vowels)
![[Genchain mode numbering|GMN]] name
!MOS scale
! colspan="2" |scale
! colspan="2" |primary example
!0
!secondary examples
!1
!2
!3
!4
!5
|-
|-
!1st 2L3s
!Pentatonic
!ssLsL
!
!Ionian
!
|Da
!
|Ra
|'''Ma'''
|Sa
|La
|Da
|-
|-
!2nd 2L3s
|1L 4s
!sLssL
|(P8, P5/3) [5]
!Mixolydian
|third-5th pentatonic
|Da
|third-4th, quarter-4th, quarter-5th
|Ra
|'''Fa'''
|Sa
|'''La'''
|Da
|-
|-
!3rd 2L3s
|2L 3s
!sLsLs
|(P8, P5) [5]
!Dorian
|unsplit pentatonic
|Da
|third-11th
|'''Ra'''
|Fa
|Sa
|'''Tha'''
|Da
|-
|-
!4th 2L3s
|3L 2s
!LssLs
|(P8, P12/4) [5]
!Aolian
|quarter-12th pentatonic
|Da
|quarter-11th
|'''Na'''
|Fa
|'''Sa'''
|Tha
|Da
|-
|-
!5th 2L3s
|4L 1s
!LsLss
|(P8, P4/2) [5]
!Phrygian
|half-4th pentatonic
|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
!Hexatonic
!LLLsLLs
!
!Lydian
!
|Da
!
|Ra
|-
|Ma
|1L 5s
|'''Pa'''
|(P8, P4/3) [6]
|Sa
|third-4th hexatonic
|La
|quarter-4th, quarter-5th, fifth-4th, fifth-5th
|Ta
|Da
|-
|-
!2nd 5L2s
|2L 4s
!LLsLLLs
|(P8/2, P5) [6]
!Ionian
|half-8ve hexatonic
|Da
|
|Ra
|Ma
|'''Fa'''
|Sa
|La
|'''Ta'''
|Da
|-
|-
!3rd 5L2s
|3L 3s
!LLsLLsL
|(P8/3, P5) [6]
!Mixolydian
|third-8ve hexatonic
|Da
|
|Ra
|'''Ma'''
|Fa
|Sa
|La
|'''Tha'''
|Da
|-
|-
!4th 5L2s
|4L 2s
!LsLLLsL
|(P8/2, P4/2) [6]
!Dorian
|half-everything hexatonic
|Da
|
|Ra
|'''Na'''
|Fa
|Sa
|'''La'''
|Tha
|Da
|-
|-
!5th 5L2s
|5L 1s
!LsLLsLL
|(P8, P5/3) [6]
!Aolian
|third-5th hexatonic
|Da
|
|'''Ra'''
|Na
|Fa
|Sa
|'''Fla'''
|Tha
|Da
|-
|-
!6th 5L2s
!Heptatonic
!sLLLsLL
!
!Phrygian
!
|Da
!
|'''Fra'''
|Na
|Fa
|'''Sa'''
|Fla
|Tha
|Da
|-
|-
!7th 5L2s
|1L 6s
!sLLsLLL
|(P8, P4/3) [7]
!Locrian
|third-4th heptatonic
|Da
|quarter-4th, fifth-4th, fifth-5th, '''sixth-4th, sixth-5th'''
|Fra
|Na
|Fa
|'''Sha'''
|Fla
|Tha
|Da
|}
{| class="wikitable center-all"
|+
5L7s MOS scales (L = A1/^1, s = m2/vM2) using the extended solfege, L/s = (100+7c)/(100-5c)
 
if P5 > 700¢, swap L and s to get 7L5s
![[Genchain mode numbering|GMN]] name
!scale
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
|-
|-
!1st 5L7s
|2L 5s
!LsLsLssLsLss
|(P8, P11/3) [7]
|Da
|third-11th heptatonic
|Du
|fifth-coco-4th, '''sixth-coco-5th'''
|Ra
|Ru
|Ma
|'''Mu'''
|Pa/Fu
|Sa
|Su
|La
|Lu
|Ta
|Da
|-
|-
!2nd 5L7s
|3L 4s
!LsLssLsLsLss
|(P8, P5/2) [7]
|Da
|half-5th heptatonic
|Du
|fifth-12th
|Ra
|Ru
|Ma
|'''Fa'''
|Pa/Fu
|Sa
|Su
|La
|'''Lu'''
|Ta
|Da
|-
|-
!3rd 5L7s
|4L 3s
!LsLssLsLssLs
|(P8, P11/5) [7]
|Da
|fifth-11th heptatonic
|Du
|'''sixth-12th'''
|Ra
|'''Ru'''
|Ma
|Fa
|Pa/Fu
|Sa
|Su
|La
|'''Tha'''
|Ta
|Da
|-
|-
!4th 5L7s
|5L 2s
!LssLsLsLssLs
|(P8, P5) [7]
|Da
|unsplit heptatonic
|Du
|'''sixth-coco-4th'''
|Ra
|'''Na'''
|Ma
|Fa
|Pa/Fu
|Sa
|'''Su'''
|La
|Tha
|Ta
|Da
|-
|-
!5th 5L7s
|6L 1s
!LssLsLssLsLs
|(P8, P5/4) [7]
|Da
|quarter-5th heptatonic
|'''Du'''
|
|Ra
|Na
|Ma
|Fa
|Pa/Fu
|Sa
|'''Fla'''
|La
|Tha
|Ta
|Da
|-
|-
!6th 5L7s
!Octotonic
!sLsLsLssLsLs
!
|Da
!
|'''Fra'''
!
|Ra
|Na
|Ma
|Fa
|'''Pa'''
|Sa
|Fla
|La
|Tha
|Ta
|Da
|-
|-
!7th 5L7s
|1L 7s
!sLsLssLsLsLs
|(P8, P4/4) [8]
|Da
|quarter-4th octotonic
|Fra
|fifth-4th, fifth-5th, '''sixth-4th, sixth-5th, seventh-4th, seventh-5th'''
|Ra
|Na
|Ma
|Fa
|'''Sha'''
|Sa
|Fla
|La
|Tha
|'''Ta'''
|Da
|-
|-
!8th 5L7s
|2L 6s
!sLsLssLsLssL
|(P8/2, P5) [8]
|Da
|half-8ve octotonic
|Fra
|
|Ra
|-
|Na
|3L 5s
|'''Ma'''
|(P8, P11/4) [8]
|Fa
|quarter-11th octotonic
|Sha/So
|'''seventh-cc4th, seventh-cc5th'''
|Sa
|Fla
|La
|Tha
|'''Do'''
|Da
|-
|-
!9th 5L7s
|4L 4s
!sLssLsLsLssL
|(P8/4, P5) [8]
|Da
|quarter-8ve octotonic
|Fra
|
|Ra
|Na
|'''Fo'''
|Fa
|Sha/So
|Sa
|Fla
|'''La'''
|Tha
|Do
|Da
|-
|-
!10th 5L7s
|5L 3s
!sLssLsLssLsL
|(P8, P12/4) [8]
|Da
|quarter-12th octotonic
|Fra
|(very lopsided, unless 5th is quite flat)
|'''Ra'''
|Na
|Fo
|Fa
|Sha/So
|Sa
|Fla
|'''Tho'''
|Tha
|Do
|Da
|-
|-
!11th 5L7s
|6L 2s
!ssLsLsLssLsL
|'''(P8/2, P4/3) [8]'''
|Da
|'''half-8ve third-4th octotonic'''
|Fra
|
|'''No'''
|Na
|Fo
|Fa
|Sha/So
|'''Sa'''
|Fla
|Tho
|Tha
|Do
|Da
|-
|-
!12th 5L7s
|7L 1s
!ssLsLssLsLsL
|(P8, P4/3) [8]
|Da
|third-4th octotonic
|Fra
|
|No
|Na
|Fo
|Fa
|Sha/So
|'''Flo'''
|Fla
|Tho
|Tha
|Do
|Da
|}
Meantone keyboards were usually tuned to the 4th mode (a fifthchain from Eb to G#).
 
The sequence of scales starts off with 6 sharps and ends with 7 flats and 3 double-flats:
 
* C C# D D# E '''E#''' F# G G# A A# B C
* C C# D D# E '''F''' F# G G# A '''A#''' B C
* C C# D D# E F F# G G# A '''Bb''' B C
* and so on until it ends with
* C Db Ebb Eb Fb F Gb Abb Ab Bbb Bb Cb C
 
12edo's uniform solfege #2 is a merging of the 2nd through 7th modes.
 
If the solfege is further extended with -i = dup and -e = dud, it can cover the 19-note MOS scales 12L7s and 7L12s.
 
== #2 (P8/2, P5) half-8ve (decide on a solfege) ==
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
*  '''<u>or</u>''' vA1/^m2 (solfege #1) = 100¢ + c
*  '''<u>or</u>''' ^A1/vm2 (solfege #2) = 100¢ + c
* EI = ^^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"
|+
'''uniform solfege #1 (P5 > 700¢) (-a = plain, -u = up, -o = down)'''
|-
|-
! colspan="2" |genspan ('''gen = P5''')
!Nonatonic
!-6
!
!-5
!
!-4
!
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
!6
|-
|-
! rowspan="3" |plain
|1L 8s
 
|(P8, P4/4) [9]
genchain
|quarter-4th nonatonic
 
|fifth-4th, '''sixth-4th, sixth-5th, seventh-4th/5th, eighth-4th/5th'''
perspan = 0
!solfege
|Sha
|Fra
|Fla
|Na
|Tha
|Fa
|'''Da'''
|Sa
|Ra
|La
|Ma
|Ta
|Pa
|-
|-
!intervals
|2L 7s
|d5
|'''(P8, c<sup>3</sup>P5/8) [9]'''
|m2
|'''eighth-trico-5th nonatonic'''
|m6
|third-11th, fifth-coco-4th
|m3
|m7
|P4
|'''P1'''
|P5
|M2
|M6
|M3
|M7
|A4
|-
|-
!notes
|3L 6s
|Gb
|(P8/3, P5) [9]
|Db
|third-8ve nonatonic
|Ab
|'''third-8ve half-5th'''
|Eb
|Bb
|F
|'''C'''
|G
|D
|A
|E
|B
|F#
|-
|-
| colspan="15" |
|4L 5s
|'''(P8, P12/7) [9]'''
|'''seventh-12th nonatonic'''
|'''sixth-11th'''
|-
|-
! rowspan="3" |up/down
|5L 4s
 
|(P8, P4/2) [9]
genchain
|half-4th nonatonic
 
|(lopsided unless 4th is sharp), '''seventh-11th'''
perspan = ±1
!solfege
|Do
|So
|Ro
|Lo
|Mo
|To
|Po/Shu
|Fru
|Flu
|Nu
|Thu
|Fu
|Du
|-
|-
!intervals
|6L 3s
|v8
|'''(P8/3, P4/2) [9]'''
|v5
|'''third-8ve half-4th nonatonic'''
|vM2
|
|vM6
|vM3
|vM7
|vA4/^d5
|^m2
|^m6
|^m3
|^m7
|^4
|^1
|-
|-
!notes
|7L 2s
|vC
|'''(P8, ccP5/6)[9]'''
|vG
|'''sixth-coco-5th nonatonic'''
|vD
|(lopsided unless 5th is sharp)
|vA
|-
|vE
|8L 1s
|vB
|(P8, P5/5) [9]
|vF#/^Gb
|fifth-5th nonatonic
|^Db
|
|^Ab
|-
|^Eb
!Decatonic
|^Bb
!
|^F
!
|^C
!
|-
|1L 9s
|'''(P8, P5/6) [10]'''
|'''sixth-5th decatonic'''
|fifth-4th, '''sixth-4th, seventh-4th/5th, eighth-4th/5th, ninth-4th/5th'''
|-
|2L 8s
|(P8/2, P5) [10]
|half-8ve decatonic
|half-8ve quartertone, '''half-8ve third-11th'''
|-
|3L 7s
|(P8, P12/5) [10]
|fifth-12th decatonic
|eighth-cc4th, eighth-cc5th
|-
|4L 6s
|(P8/2, P4/2) [10]
|half-everything decatonic
|
|-
|5L 5s
|(P8/2, P5) [10]
|half-8ve decatonic
|(lopsided unless 5th is quite flat)
|-
|6L 4s
|'''(P8/2, P5/3) [10]'''
|'''half-8ve third-5th decatonic'''
|
|-
|7L 3s
|(P8, P5/2) [10]
|half-5th decatonic
|'''ninth-coco-5th'''
|-
|8L 2s
|'''(P8/2, P4/4) [10]'''
|'''half-8ve quarter-4th decatonic'''
|'''half-8ve quarter-12th'''
|-
|9L 1s
|(P8, P4/2) [10]
|quarter-4th decatonic
|
|}
|}
== #1 (P8, P5) unsplit ==
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"
{| class="wikitable center-all"
|+
|+
'''uniform solfege #1 (P5 > 700¢) (-a = plain, -u = up, -o = down)'''
'''basic solfege (-a = plain)'''
|-
|-
! colspan="2" |genspan ('''gen = vA1/^m2''')
!genspan
!-6
!-6
!-5
!-5
Line 10,104: Line 9,896:
!6
!6
|-
|-
! rowspan="3" |Da's
genchain
perspan = 0
!solfege
!solfege
|Sha
|Sha
|So
|Fra
|Fla
|Fla
|Lo
|Na
|Tha
|Tha
|To
|Fa
|'''Da'''
|'''Da'''
|Fru
|Sa
|Ra
|Ra
|Nu
|La
|Ma
|Ma
|Fu
|Ta
|Pa
|Pa
|-
|-
!intervals
!intervals
|d5
|d5
|v5
|m2
|m6
|m6
|vM6
|m3
|m7
|m7
|vM7
|P4
|'''P1'''
|'''P1'''
|^m2
|P5
|M2
|M2
|^m3
|M6
|M3
|M3
|^4
|M7
|A4
|A4
|-
|-
!notes
!notes
|Gb
|Gb
|vG
|Db
|Ab
|Ab
|vA
|Eb
|Bb
|Bb
|vB
|F
|'''C'''
|'''C'''
|^Db
|G
|D
|D
|^Eb
|A
|E
|E
|^F
|B
|F#
|F#
|}
{| class="wikitable center-all"
|+
'''extended solfege (-a = plain, -u = up = aug, -o = down = dim, and possibly -i = double-aug and -e = double-dim)'''
|-
|-
| colspan="15" |
!genspan
!-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
|-
|-
! rowspan="3" |Sa's
genchain
perspan = ±1
!solfege
!solfege
|She
|...
|Sho/Se
|...
|Flo
|No
|Tho
|Fo
|Do
|Do
|So/Sha
|Fra
|Fra
|Ro
|Fla
|Na
|Na
|Mo
|Tha
|Fa
|Fa
|Po/Shu
|'''Da'''
|Sa
|Sa
|Flu
|Ra
|La
|La
|Thu
|Ma
|Ta
|Ta
|Pa/Fu
|Du
|Du
|Su
|Ru
|Lu
|Mu
|...
|Pu/Fi
|...
|Pi
|-
|-
!intervals
!intervals
|v8
|d<sup>3</sup>5
|...
|dd5
|...
|d6
|d3
|d7
|d4
|d8
|d5
|m2
|m2
|vM2
|m6
|m3
|m3
|vM3
|m7
|P4
|P4
|vA4/^d5
|'''P1'''
|P5
|P5
|^m6
|M2
|M6
|M6
|^m7
|M3
|M7
|M7
|^1
|A4
|A1
|A5
|A2
|A6
|A3
|...
|AA4
|...
|A<sup>3</sup>4
|-
|-
!notes
!notes
|vC
|Gbbb
|...
|Gbb
|...
|Abb
|Ebb
|Bbb
|Fb
|Cb
|Gb
|Db
|Db
|vD
|Ab
|Eb
|Eb
|vE
|Bb
|F
|F
|vF#/^Gb
|'''C'''
|G
|G
|^Ab
|D
|A
|A
|^Bb
|E
|B
|B
|^C
|F#
|C#
|G#
|D#
|A#
|E#
|...
|Fx
|...
|Fx#
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
2L6s MOS scales using solfege #1 (L = m3/vvA2, s = vA1/^m2)
2L3s MOS scales (L = m3, s = M2), L/s = (300-3c)/(200+2c)
 
if P5 > 5\8 = 750¢, swap L and s to get 6L2s
![[Genchain mode numbering|GMN]] name
![[Genchain mode numbering|GMN]] name
!scale
! colspan="2" |scale
!0
!0
!1
!1
Line 10,219: Line 10,088:
!4
!4
!5
!5
!6
!7
!8
|-
|-
!1st 2L6s
!1st 2L3s
!sssL-sssL
!ssLsL
!Ionian
|Da
|Da
|Fru
|Ra
|Ra
|'''Nu'''
|'''Ma'''
|Po/Shu
|Sa
|La
|Da
|-
!2nd 2L3s
!sLssL
!Mixolydian
|Da
|Ra
|'''Fa'''
|Sa
|Sa
|Flu
|'''La'''
|'''La'''
|Da
|Da
|-
|-
!2nd 2L6s
!3rd 2L3s
!ssLs-ssLs
!sLsLs
!Dorian
|Da
|Da
|Fru
|'''Ra'''
|'''Ra'''
|'''Fa'''
|Fa
|Po/Shu
|Sa
|Sa
|'''Flu'''
|'''Tha'''
|'''To'''
|Da
|Da
|-
|-
!3rd 2L6s
!4th 2L3s
!sLss-sLss
!LssLs
!Aolian
|Da
|Da
|'''Fru'''
|'''Na'''
|'''Mo'''
|Fa
|Fa
|Po/Shu
|'''Sa'''
|'''Sa'''
|'''Tha'''
|Tha
|To
|Da
|Da
|-
|-
!4th 2L6s
!5th 2L3s
!Lsss-Lsss
!LsLss
!Phrygian
|Da
|Da
|'''Na'''
|Na
|Mo
|Fa
|Fa
|Po/Shu
|'''Fla'''
|'''Lo'''
|Tha
|Tha
|To
|Da
|Da
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
2L8s MOS scales using solfege #1 (L = vM2/^d3, s = vA1/^m2)
5L2s MOS scales (L = M2, s = m2), L/s = (200+2c)/(100-5c)
 
if P5 > 3\5 = 720¢, swap L and s to get 8L2s
![[Genchain mode numbering|GMN]] name
![[Genchain mode numbering|GMN]] name
!scale
! colspan="2" |scale
!1sn
!1sn
!2nd
!2nd
!
!3rd
!3rd
!
!4th
!tritone
!5th
!
!6th
!6th
!
!7th
!7th
!8ve
!8ve
|-
|-
!1st 2L8s
!1st 5L2s
!ssssL-ssssL
!LLLsLLs
!Lydian
|Da
|Da
|Fru
|Ra
|Ra
|Nu
|Ma
|'''Ma'''
|'''Pa'''
|Po/Shu
|Sa
|Sa
|Flu
|La
|La
|'''Thu'''
|Ta
|Da
|Da
|-
|-
!2nd 2L8s
!2nd 5L2s
!sssLs-sssLs
!LLsLLLs
!Ionian
|Da
|Da
|Fru
|Ra
|Ra
|'''Nu'''
|Ma
|'''Fa'''
|'''Fa'''
|Po/Shu
|Sa
|Sa
|Flu
|La
|'''La'''
|'''Ta'''
|'''To'''
|Da
|Da
|-
|-
!3rd 2L8s
!3rd 5L2s
!ssLss-ssLss
!LLsLLsL
!Mixolydian
|Da
|Da
|Fru
|Ra
|'''Ra'''
|'''Ma'''
|'''Mo'''
|Fa
|Fa
|Po/Shu
|Sa
|Sa
|'''Flu'''
|La
|'''Tha'''
|'''Tha'''
|To
|Da
|Da
|-
|-
!4th 2L8s
!4th 5L2s
!sLsss-sLsss
!LsLLLsL
!Dorian
|Da
|Da
|'''Fru'''
|Ra
|'''Na'''
|'''Na'''
|Mo
|Fa
|Fa
|Po/Shu
|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'''
|'''Sa'''
|'''Lo'''
|Fla
|Tha
|Tha
|To
|Da
|Da
|-
|-
!5th 2L8s
!7th 5L2s
!Lssss-Lssss
!sLLsLLL
!Locrian
|Da
|Da
|'''Ro'''
|Fra
|Na
|Na
|Mo
|Fa
|Fa
|Po/Shu
|'''Sha'''
|'''Fla'''
|Fla
|Lo
|Tha
|Tha
|To
|Da
|Da
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
10L2s MOS scales using solfege #1 (L = vA1/^m2, s = vvA1/m2)
5L7s MOS scales (L = A1/^1, s = m2/vM2) using the extended solfege, L/s = (100+7c)/(100-5c)
 
if P5 > 700¢, swap L and s to get 7L5s
![[Genchain mode numbering|GMN]] name
![[Genchain mode numbering|GMN]] name
!scale
!scale
!1sn
!0
! colspan="2" |2nds
!1
! colspan="2" |3rds
!2
!4th
!3
!tritone
!4
!5th
!5
! colspan="2" |6ths
!6
! colspan="2" |7ths
!7
!8ve
!8
|-
!9
!1st 10L2s
!10
!LLLLLs-LLLLLs
!11
!12
|-
!1st 5L7s
!LsLsLssLsLss
|Da
|Da
|Fru
|Du
|Ra
|Ra
|Nu
|Ru
|Ma
|Ma
|'''Fu'''
|'''Mu'''
|Shu
|Pa/Fu
|Sa
|Sa
|Flu
|Su
|La
|La
|Thu
|Lu
|'''Ta'''
|Ta
|Da
|Da
|-
|-
!2nd 10L2s
!2nd 5L7s
!LLLLsL-LLLLsL
!LsLssLsLsLss
|Da
|Da
|Fru
|Du
|Ra
|Ra
|Nu
|Ru
|'''Ma'''
|Ma
|'''Fa'''
|'''Fa'''
|Po/Shu
|Pa/Fu
|Sa
|Sa
|Flu
|Su
|La
|La
|'''Thu'''
|'''Lu'''
|'''To'''
|Ta
|Da
|Da
|-
|-
!3rd 10L2s
!3rd 5L7s
!LLLsLL-LLLsLL
!LsLssLsLssLs
|Da
|Da
|Fru
|Du
|Ra
|Ra
|'''Nu'''
|'''Ru'''
|'''Mo'''
|Ma
|Fa
|Fa
|Po/Shu
|Pa/Fu
|Sa
|Sa
|Flu
|Su
|'''La'''
|La
|'''Tha'''
|'''Tha'''
|To
|Ta
|Da
|Da
|-
|-
!4th 10L2s
!4th 5L7s
!LLsLLL-LLsLLL
!LssLsLsLssLs
|Da
|Da
|Fru
|Du
|'''Ra'''
|Ra
|'''Na'''
|'''Na'''
|Mo
|Ma
|Fa
|Fa
|Po/Shu
|Pa/Fu
|Sa
|Sa
|'''Flu'''
|'''Su'''
|'''Lo'''
|La
|Tha
|Tha
|To
|Ta
|Da
|Da
|-
|-
!5th 10L2s
!5th 5L7s
!LsLLLL-LsLLLL
!LssLsLssLsLs
|Da
|Da
|'''Fru'''
|'''Du'''
|'''Ro'''
|Ra
|Na
|Na
|Mo
|Ma
|Fa
|Fa
|Po/Shu
|Pa/Fu
|'''Sa'''
|Sa
|'''Fla'''
|'''Fla'''
|Lo
|La
|Tha
|Tha
|To
|Ta
|Da
|Da
|-
|-
!6th 10L2s
!6th 5L7s
!sLLLLL-sLLLLL
!sLsLsLssLsLs
|Da
|Da
|'''Fra'''
|'''Fra'''
|Ro
|Ra
|Na
|Na
|Mo
|Ma
|Fa
|Fa
|Po
|'''Pa'''
|'''So'''
|Sa
|Fla
|Fla
|Lo
|La
|Tha
|Tha
|To
|Ta
|Da
|Da
|}
=== Solfege #2 (P5 < 700¢) ===
{| class="wikitable center-all"
|+
'''uniform solfege #2 (P5 < 700¢) (-a = plain, -u = up, -o = down)'''
|-
|-
! colspan="2" |genspan ('''gen = P5''')
!7th 5L7s
!-6
!sLsLssLsLsLs
!-5
|Da
!-4
|Fra
!-3
|Ra
!-2
|Na
!-1
|Ma
!0
|Fa
!1
|'''Sha'''
!2
|Sa
!3
|Fla
!4
|La
!5
|Tha
!6
|'''Ta'''
|Da
|-
|-
! rowspan="3" |plain
!8th 5L7s
 
!sLsLssLsLssL
genchain
|Da
 
perspan = 0
!solfege
|Sha
|Fra
|Fra
|Fla
|Ra
|Na
|Na
|Tha
|'''Ma'''
|Fa
|Fa
|'''Da'''
|Sha/So
|Sa
|Sa
|Ra
|Fla
|La
|La
|Ma
|Tha
|Ta
|'''Do'''
|Pa
|Da
|-
|-
!intervals
!9th 5L7s
|d5
!sLssLsLsLssL
|m2
|Da
|m6
|Fra
|m3
|Ra
|m7
|Na
|P4
|'''Fo'''
|'''P1'''
|Fa
|P5
|Sha/So
|M2
|Sa
|M6
|Fla
|M3
|'''La'''
|M7
|Tha
|A4
|Do
|Da
|-
|-
!notes
!10th 5L7s
|Gb
!sLssLsLssLsL
|Db
|Da
|Ab
|Fra
|Eb
|'''Ra'''
|Bb
|Na
|F
|Fo
|'''C'''
|Fa
|G
|Sha/So
|D
|Sa
|A
|Fla
|E
|'''Tho'''
|B
|Tha
|F#
|Do
|Da
|-
|-
| colspan="15" |
!11th 5L7s
|-
!ssLsLsLssLsL
! rowspan="3" |up/down
|Da
 
|Fra
genchain
|'''No'''
 
|Na
perspan = ±1
|Fo
!solfege
|Fa
|Du
|Sha/So
|Su
|'''Sa'''
|Ru
|Fla
|Lu
|Mu
|Tu
|Pu/Sho
|Fro
|Flo
|No
|Tho
|Tho
|Fo
|Tha
|Do
|Do
|Da
|-
|-
!intervals
!12th 5L7s
|^1
!ssLsLssLsLsL
|^5
|Da
|^M2
|Fra
|^M6
|No
|^M3
|Na
|^M7
|Fo
|^A4/vd5
|Fa
|vm2
|Sha/So
|vm6
|'''Flo'''
|vm3
|Fla
|vm7
|Tho
|v4
|Tha
|v8
|Do
|-
|Da
!notes
|^C
|^G
|^D
|^A
|^E
|^B
|^F#/vGb
|vDb
|vAb
|vEb
|vBb
|vF
|vC
|}
|}
Meantone keyboards were usually tuned to the 4th mode (a fifthchain from Eb to G#).
The sequence of scales starts off with 6 sharps and ends with 7 flats and 3 double-flats:
* C C# D D# E '''E#''' F# G G# A A# B C
* C C# D D# E '''F''' F# G G# A '''A#''' B C
* C C# D D# E F F# G G# A '''Bb''' B C
* and so on until it ends with
* C Db Ebb Eb Fb F Gb Abb Ab Bbb Bb Cb C
12edo's uniform solfege #2 is a merging of the 2nd through 7th modes.
== #2 (P8/2, P5) half-8ve (decide on a solfege) ==
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
*  '''<u>or</u>''' vA1/^m2 (solfege #1) = 100¢ + c
*  '''<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"
{| class="wikitable center-all"
|+
|+
'''uniform solfege #2 (P5 < 700¢) (-a = plain, -u = up, -o = down)'''
'''solfege #1 (P5 > 700¢) (-a = plain, -u = up, -o = down)'''
|-
|-
! colspan="2" |genspan (gen = ^A1/vm2)
! colspan="2" |genspan ('''gen = P5''')
!-6
!-6
!-5
!-5
Line 10,615: Line 10,500:
!6
!6
|-
|-
! rowspan="3" |Da's
! rowspan="3" |plain


genchain
genchain
Line 10,622: Line 10,507:
!solfege
!solfege
|Sha
|Sha
|Su
|Fra
|Fla
|Fla
|Lu
|Na
|Tha
|Tha
|Tu
|Fa
|'''Da'''
|'''Da'''
|Fro
|Sa
|Ra
|Ra
|No
|La
|Ma
|Ma
|Fo
|Ta
|Pa
|Pa
|-
|-
!intervals
!intervals
|d5
|d5
|^5
|m2
|m6
|m6
|^M6
|m3
|m7
|m7
|^M7
|P4
|'''P1'''
|'''P1'''
|vm2
|P5
|M2
|M2
|vm3
|M6
|M3
|M3
|v4
|M7
|A4
|A4
|-
|-
!notes
!notes
|Gb
|Gb
|^G
|Db
|Ab
|Ab
|^A
|Eb
|Bb
|Bb
|^B
|F
|'''C'''
|'''C'''
|vDb
|G
|D
|D
|vEb
|A
|E
|E
|vF
|B
|F#
|F#
|-
|-
| colspan="15" |
| colspan="15" |
|-
|-
! rowspan="3" |Sa's
! rowspan="3" |up/down


genchain
genchain
Line 10,673: Line 10,558:
perspan = ±1
perspan = ±1
!solfege
!solfege
|Do
|So
|Ro
|Lo
|Mo
|To
|Po/Shu
|Fru
|Flu
|Nu
|Thu
|Fu
|Du
|Du
|Fra
|Ru
|Na
|Mu
|Fa
|Pu/Sho
|Sa
|Flo
|La
|Tho
|Ta
|Do
|-
|-
!intervals
!intervals
|v8
|v5
|vM2
|vM6
|vM3
|vM7
|vA4/^d5
|^m2
|^m6
|^m3
|^m7
|^4
|^1
|^1
|m2
|^M2
|m3
|^M3
|P4
|^A4/vd5
|P5
|vm6
|M6
|vm7
|M7
|v8
|-
|-
!notes
!notes
|vC
|vG
|vD
|vA
|vE
|vB
|vF#/^Gb
|^Db
|^Ab
|^Eb
|^Bb
|^F
|^C
|^C
|Db
|^D
|Eb
|^E
|F
|^F#/vGb
|G
|vAb
|A
|vBb
|B
|vC
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
2L6s MOS scales using solfege #2 (L = m3/^^A2, s = ^A1/vm2)
'''solfege #1 (P5 > 700¢) (-a = plain, -u = up, -o = down) [[mingen]] format'''
![[Genchain mode numbering|GMN]] name
|-
!scale
! colspan="2" |genspan ('''gen = vA1/^m2''')
!-6
!-5
!-4
!-3
!-2
!-1
!0
!0
!1
!1
Line 10,729: Line 10,620:
!5
!5
!6
!6
!7
!8
|-
|-
!1st 2L6s
! rowspan="3" |Da's
!sssL-sssL
 
|Da
genchain
|Fro
 
perspan = 0
!solfege
|Sha
|So
|Fla
|Lo
|Tha
|To
|'''Da'''
|Fru
|Ra
|Ra
|'''No'''
|Nu
|Pu/Sho
|Ma
|Sa
|Fu
|Flo
|Pa
|'''La'''
|Da
|-
|-
!2nd 2L6s
!intervals
!ssLs-ssLs
|d5
|Da
|v5
|Fro
|m6
|'''Ra'''
|vM6
|'''Fa'''
|m7
|Pu/Sho
|vM7
|Sa
|'''P1'''
|'''Flo'''
|^m2
|'''Tu'''
|M2
|Da
|^m3
|M3
|^4
|A4
|-
|-
!3rd 2L6s
!notes
!sLss-sLss
|Gb
|Da
|vG
|'''Fro'''
|Ab
|'''Mu'''
|vA
|Fa
|Bb
|Pu/Sho
|vB
|'''Sa'''
|'''C'''
|'''Tha'''
|^Db
|Tu
|D
|Da
|^Eb
|E
|^F
|F#
|-
| colspan="15" |
|-
|-
!4th 2L6s
! rowspan="3" |Sa's
!Lsss-Lsss
 
|Da
genchain
|'''Na'''
 
|Mu
perspan = ±1
!solfege
|Do
|Fra
|Ro
|Na
|Mo
|Fa
|Fa
|Pu/Sho
|Po/Shu
|'''Lu'''
|Sa
|Tha
|Flu
|Tu
|La
|Da
|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"
{| class="wikitable center-all"
|+
|+
2L8s MOS scales using solfege #2 (L = ^M2/vd3, s = ^A1/vm2)
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
![[Genchain mode numbering|GMN]] name
!scale
!scale
!1sn
!0
!2nd
!1
!
!2
!3rd
!3
!
!4
!tritone
!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
!6th
Line 10,800: Line 10,811:
!ssssL-ssssL
!ssssL-ssssL
|Da
|Da
|Fro
|Fru
|Ra
|Ra
|No
|Nu
|'''Ma'''
|'''Ma'''
|Pu/Sho
|Po/Shu
|Sa
|Sa
|Flo
|Flu
|La
|La
|'''Tho'''
|'''Thu'''
|Da
|Da
|-
|-
Line 10,814: Line 10,825:
!sssLs-sssLs
!sssLs-sssLs
|Da
|Da
|Fro
|Fru
|Ra
|Ra
|'''No'''
|'''Nu'''
|'''Fa'''
|'''Fa'''
|Pu/Sho
|Po/Shu
|Sa
|Sa
|Flo
|Flu
|'''La'''
|'''La'''
|'''Tu'''
|'''To'''
|Da
|Da
|-
|-
Line 10,828: Line 10,839:
!ssLss-ssLss
!ssLss-ssLss
|Da
|Da
|Fro
|Fru
|'''Ra'''
|'''Ra'''
|'''Mu'''
|'''Mo'''
|Fa
|Fa
|Pu/Sho
|Po/Shu
|Sa
|Sa
|'''Flo'''
|'''Flu'''
|'''Tha'''
|'''Tha'''
|Tu
|To
|Da
|Da
|-
|-
Line 10,842: Line 10,853:
!sLsss-sLsss
!sLsss-sLsss
|Da
|Da
|'''Fro'''
|'''Fru'''
|'''Na'''
|'''Na'''
|Mu
|Mo
|Fa
|Fa
|Pu/Sho
|Po/Shu
|'''Sa'''
|'''Sa'''
|'''Lu'''
|'''Lo'''
|Tha
|Tha
|Tu
|To
|Da
|Da
|-
|-
Line 10,856: Line 10,867:
!Lssss-Lssss
!Lssss-Lssss
|Da
|Da
|'''Ru'''
|'''Ro'''
|Na
|Na
|Mu
|Mo
|Fa
|Fa
|Pu/Sho
|Po/Shu
|'''Fla'''
|'''Fla'''
|Lu
|Lo
|Tha
|Tha
|Tu
|To
|Da
|Da
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
2L10s MOS scales using solfege #2 (L = ^^A1/m2, s = ^A1/vm2)
10L2s MOS scales using solfege #1 (L = vA1/^m2, s = vvA1/m2)
![[Genchain mode numbering|GMN]] name
![[Genchain mode numbering|GMN]] name
!scale
!scale
Line 10,882: Line 10,894:
!8ve
!8ve
|-
|-
!1st 2L10s
!1st 10L2s
!sssssL-sssssL
!LLLLLs-LLLLLs
|Da
|Da
|Fro
|Fru
|Ra
|Ra
|No
|Nu
|Ma
|Ma
|'''Fo'''
|'''Fu'''
|Pu/Sho
|Shu
|Sa
|Sa
|Flo
|Flu
|La
|La
|Tho
|Thu
|'''Ta'''
|'''Ta'''
|Da
|Da
|-
|-
!2nd 2L10s
!2nd 10L2s
!ssssLs-ssssLs
!LLLLsL-LLLLsL
|Da
|Da
|Fro
|Fru
|Ra
|Ra
|No
|Nu
|'''Ma'''
|'''Ma'''
|'''Fa'''
|'''Fa'''
|Pu/Sho
|Po/Shu
|Sa
|Sa
|Flo
|Flu
|La
|La
|'''Tho'''
|'''Thu'''
|'''Tu'''
|'''To'''
|Da
|Da
|-
|-
!3rd 2L10s
!3rd 10L2s
!sssLss-sssLss
!LLLsLL-LLLsLL
|Da
|Da
|Fro
|Fru
|Ra
|Ra
|'''No'''
|'''Nu'''
|'''Mu'''
|'''Mo'''
|Fa
|Fa
|Pu/Sho
|Po/Shu
|Sa
|Sa
|Flo
|Flu
|'''La'''
|'''La'''
|'''Tha'''
|'''Tha'''
|Tu
|To
|Da
|Da
|-
|-
!4th 2L10s
!4th 10L2s
!ssLsss-ssLsss
!LLsLLL-LLsLLL
|Da
|Da
|Fro
|Fru
|'''Ra'''
|'''Ra'''
|'''Na'''
|'''Na'''
|Mu
|Mo
|Fa
|Fa
|Pu/Sho
|Po/Shu
|Sa
|Sa
|'''Flo'''
|'''Flu'''
|'''Lu'''
|'''Lo'''
|Tha
|Tha
|Tu
|To
|Da
|Da
|-
|-
!5th 2L10s
!5th 10L2s
!sLssss-sLssss
!LsLLLL-LsLLLL
|Da
|Da
|'''Fro'''
|'''Fru'''
|'''Ru'''
|'''Ro'''
|Na
|Na
|Mu
|Mo
|Fa
|Fa
|Pu/Sho
|Po/Shu
|'''Sa'''
|'''Sa'''
|'''Fla'''
|'''Fla'''
|Lu
|Lo
|Tha
|Tha
|Tu
|To
|Da
|Da
|-
|-
!6th 2L10s
!6th 10L2s
!Lsssss-Lsssss
!sLLLLL-sLLLLL
|Da
|Da
|'''Fra'''
|'''Fra'''
|Ru
|Ro
|Na
|Na
|Mu
|Mo
|Fa
|Fa
|Pu/Sho
|Po
|'''Su'''
|'''So'''
|Fla
|Fla
|Lu
|Lo
|Tha
|Tha
|Tu
|To
|Da
|Da
|}
|}
=== Solfege #2 (P5 < 700¢) ===
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
12L2s MOS scales using solfege #2 (L = ^A1/vm2, s = ^1) -- P5 must be < 700¢, or s will be < 0¢
'''solfege #2 (P5 < 700¢) (-a = plain, -u = up, -o = down)'''
![[Genchain mode numbering|GMN]] name
|-
!scale
! colspan="2" |genspan ('''gen = P5''')
!1sn
!-6
!
!-5
!2nd
!-4
!
!-3
!3rd
!-2
!
!-1
!4th
!0
!
!1
!5th
!2
!
!3
!6th
!4
!
!5
!7th
!6
!
!8ve
|-
|-
!1st 12L2s
! rowspan="3" |plain
!LLLLLLs-LLLLLLs
 
|Da
genchain
|Fro
 
|Ra
perspan = 0
|No
!solfege
|Ma
|Sha
|Fo
|Fra
|'''Pa'''
|Fla
|Pu/Sho
|Na
|Sa
|Tha
|Flo
|Fa
|La
|'''Da'''
|Tho
|Sa
|Ta
|'''Do'''
|Da
|-
!2nd 12L2s
!LLLLLsL-LLLLLsL
|Da
|Fro
|Ra
|Ra
|No
|La
|Ma
|Ma
|'''Fo'''
|Ta
|'''Fa'''
|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
|Pu/Sho
|Sa
|Fro
|Flo
|Flo
|La
|No
|Tho
|Tho
|'''Ta'''
|Fo
|'''Tu'''
|Do
|Da
|-
|-
!3rd 12L2s
!intervals
!LLLLsLL-LLLLsLL
|^1
|Da
|^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
|Fro
|Ra
|Ra
|No
|No
|'''Ma'''
|Ma
|'''Mu'''
|Fo
|Fa
|Pa
|Pu/Sho
|Sa
|Flo
|La
|'''Tho'''
|'''Tha'''
|Tu
|Da
|-
|-
!4th 12L2s
!intervals
!LLLsLLL-LLLsLLL
|d5
|Da
|^5
|Fro
|m6
|Ra
|^M6
|'''No'''
|m7
|'''Na'''
|^M7
|Mu
|'''P1'''
|Fa
|vm2
|Pu/Sho
|M2
|Sa
|vm3
|Flo
|M3
|'''La'''
|v4
|'''Lu'''
|A4
|Tha
|Tu
|Da
|-
|-
!5th 12L2s
!notes
!LLsLLLL-LLsLLLL
|Gb
|Da
|^G
|Fro
|Ab
|'''Ra'''
|^A
|'''Ru'''
|Bb
|Na
|^B
|Mu
|'''C'''
|Fa
|vDb
|Pu/Sho
|D
|Sa
|vEb
|'''Flo'''
|E
|'''Fla'''
|vF
|Lu
|F#
|Tha
|Tu
|Da
|-
|-
!6th 12L2s
| colspan="15" |
!LsLLLLL-LsLLLLL
|Da
|'''Fro'''
|'''Fra'''
|Ru
|Na
|Mu
|Fa
|Pu/Sho
|'''Sa'''
|'''Su'''
|Fla
|Lu
|Tha
|Tu
|Da
|-
|-
!7th 12L2s
! rowspan="3" |Sa's
!sLLLLLL-sLLLLLL
 
|Da
genchain
|'''Du'''
 
perspan = ±1
!solfege
|Du
|Fra
|Fra
|Ru
|Ru
Line 11,117: Line 11,197:
|Fa
|Fa
|Pu/Sho
|Pu/Sho
|'''Sha'''
|Sa
|Su
|Flo
|Fla
|La
|Lu
|Tho
|Tha
|Ta
|Tu
|Do
|Da
|-
|}
 
=== Solfege #3 (EI = vvM2) ===
 
* P = ^4/v5 = 600¢
* G = ^1 = vM2 = 100¢ + c
* EI = vvM2 = 0¢
* ^ = 100¢ + c
* # = 100¢ + 7c
 
Doesn't tip.
{| class="wikitable center-all"
|+
'''uniform 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
!intervals
|d5
|^1
|m2
|m2
|m6
|^M2
|m3
|m3
|m7
|^M3
|P4
|P4
|'''P1'''
|^A4/vd5
|P5
|P5
|M2
|vm6
|M6
|M6
|M3
|vm7
|M7
|M7
|A4
|v8
|-
|-
!notes
!notes
|Gb
|^C
|Db
|Db
|Ab
|^D
|Eb
|Eb
|Bb
|^E
|F
|F
|'''C'''
|^F#/vGb
|G
|G
|D
|vAb
|A
|A
|E
|vBb
|B
|B
|F#
|vC
|-
|}
| colspan="15" |
{| class="wikitable center-all"
|-
|+
! rowspan="3" |up/down
2L6s MOS scales using solfege #2 (L = m3/^^A2, s = ^A1/vm2)
 
![[Genchain mode numbering|GMN]] name
genchain
!scale
 
!0
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"
|+
'''uniform solfege #3 (-a = plain, -u = up, -o = down)'''
|-
! colspan="2" |genspan ('''gen = vA1/^m2''')
!-6
!-5
!-4
!-3
!-2
!-1
!0
!1
!1
!2
!2
Line 11,274: Line 11,246:
!5
!5
!6
!6
!7
!8
|-
|-
! rowspan="3" |Da's
!1st 2L6s
 
!sssL-sssL
genchain
|Da
 
|Fro
perspan = 0
!solfege
|Sha
|Shu/Flo
|Fla
|Flu/Tho
|Tha
|Thu/Do
|'''Da'''
|Du/Ro
|Ra
|Ra
|Ru/Mo
|'''No'''
|Ma
|Pu/Sho
|Mu/Po
|Sa
|Pa
|Flo
|'''La'''
|Da
|-
|-
!intervals
!2nd 2L6s
|d5
!ssLs-ssLs
|^d5/vm6
|Da
|m6
|Fro
|^m6/vm7
|'''Ra'''
|m7
|'''Fa'''
|^m7/v8
|Pu/Sho
|'''P1'''
|Sa
|^1/vM2
|'''Flo'''
|M2
|'''Tu'''
|^M2/vM3
|Da
|M3
|^M3/vA4
|A4
|-
|-
!notes
!3rd 2L6s
|Gb
!sLss-sLss
|^Gb/vAb
|Da
|Ab
|'''Fro'''
|^Ab/vBb
|'''Mu'''
|Bb
|Fa
|^Bb/vC
|Pu/Sho
|'''C'''
|'''Sa'''
|^C/vD
|'''Tha'''
|D
|Tu
|^D/vE
|Da
|E
|^E/vF#
|F#
|-
|-
| colspan="15" |
!4th 2L6s
|-
!Lsss-Lsss
! rowspan="3" |Sa's
|Da
 
|'''Na'''
genchain
|Mu
 
perspan = ±1
!solfege
|Fro
|Fra
|Fru/No
|Na
|Nu/Fo
|Fa
|Fa
|Fu/So
|Pu/Sho
|Sa
|'''Lu'''
|Su/Lo
|Tha
|La
|Lu/To
|Ta
|Tu
|Tu
|-
|Da
!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"
{| class="wikitable center-all"
|+
|+
10L2s MOS scales using solfege #3 (L = ^A1 = vM2, s = m2 = rhymes)
2L8s MOS scales using solfege #2 (L = ^M2/vd3, s = ^A1/vm2)
 
if P5 < 7\12 = 700¢, swap L and s to get 2L10s
![[Genchain mode numbering|GMN]] name
![[Genchain mode numbering|GMN]] name
!scale
!scale
!1sn
!1sn
! colspan="2" |2nds
!2nd
! colspan="2" |3rds
!
!4th
!3rd
!
!tritone
!tritone
!5th
!
! colspan="2" |6ths
!6th
! colspan="2" |7ths
!
!7th
!8ve
!8ve
|-
|-
!1st 10L2s
!1st 2L8s
!LLLLLs-LLLLLs
!ssssL-ssssL
|Da
|Da
|Du/Ro
|Fro
|Ra
|Ra
|Ru/Mo
|No
|Ma
|'''Ma'''
|'''Mu/Po'''
|Pu/Sho
|Fu/So
|Sa
|Sa
|Su/Lo
|Flo
|La
|La
|Lu/To
|'''Tho'''
|'''Ta'''
|Da
|Da
|-
|-
!2nd 10L2s
!2nd 2L8s
!LLLLsL-LLLLsL
!sssLs-sssLs
|Da
|Da
|Du/Ro
|Fro
|Ra
|Ra
|Ru/Mo
|'''No'''
|'''Ma'''
|'''Fa'''
|'''Fa'''
|Fu/So
|Pu/Sho
|Sa
|Sa
|Su/Lo
|Flo
|La
|'''La'''
|'''Lu/To'''
|'''Tu'''
|'''Thu/Do'''
|Da
|Da
|-
|-
!3rd 10L2s
!3rd 2L8s
!LLLsLL-LLLsLL
!ssLss-ssLss
|Da
|Da
|Du/Ro
|Fro
|Ra
|'''Ra'''
|'''Ru/Mo'''
|'''Mu'''
|'''Nu/Fo'''
|Fa
|Fa
|Fu/So
|Pu/Sho
|Sa
|Sa
|Su/Lo
|'''Flo'''
|'''La'''
|'''Tha'''
|'''Tha'''
|Thu/Do
|Tu
|Da
|Da
|-
|-
!4th 10L2s
!4th 2L8s
!LLsLLL-LLsLLL
!sLsss-sLsss
|Da
|Da
|Du/Ro
|'''Fro'''
|'''Ra'''
|'''Na'''
|'''Na'''
|Nu/Fo
|Mu
|Fa
|Fa
|Fu/So
|Pu/Sho
|Sa
|'''Sa'''
|'''Su/Lo'''
|'''Lu'''
|'''Flu/Tho'''
|Tha
|Tha
|Thu/Do
|Tu
|Da
|Da
|-
|-
!5th 10L2s
!5th 2L8s
!LsLLLL-LsLLLL
!Lssss-Lssss
|Da
|Da
|'''Du/Ro'''
|'''Ru'''
|'''Fru/No'''
|Na
|Na
|Nu/Fo
|Mu
|Fa
|Fa
|Fu/So
|Pu/Sho
|'''Sa'''
|'''Fla'''
|'''Fla'''
|Flu/Tho
|Lu
|Tha
|Tha
|Thu/Do
|Tu
|Da
|-
!6th 10L2s
!sLLLLL-sLLLLL
|Da
|'''Fra'''
|Fru/No
|Na
|Nu/Fo
|Fa
|Fu/So
|'''Shu/Flo'''
|Fla
|Flu/Tho
|Tha
|Thu/Do
|Da
|Da
|}
|}
== #3 (P8, P4/2) half-4th ==
* G = ^M2/vm3 = 250¢ - c/2
* EI = vvm2 = 0¢
* ^ = 50¢ - 2.5c
MOS scales covered:
* 5 = 4L1s (for 1L4s use pergen #8, third-5th)
* 9 = 5L4s or 4L5s (P5 < 5\9 = 667¢)
* 14 = 9L5s or 5L9s (P5 < 4\7 = 686¢)
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
'''uniform solfege (-a = plain, -u = up, -o = down)'''
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
|-
|-
!genspan
!1st 2L10s
!13
!sssssL-sssssL
!12
|Da
!11
|Fro
!10
|Ra
!9
|No
!8
|Ma
!7
|'''Fo'''
!6
|Pu/Sho
!5
|Sa
!4
|Flo
!3
|La
!2
|Tho
!1
|'''Ta'''
!0
|Da
!-1
!-2
!-3
!-4
!-5
!-6
!-7
!-8
!-9
!-10
!-11
!-12
!-13
|-
|-
!solfege
!2nd 2L10s
|Flu
!ssssLs-ssssLs
|Sha
|Da
|Nu
|Fro
|Fra
|Ra
|Thu
|No
|Fla
|'''Ma'''
|Fu
|'''Fa'''
 
|Pu/Sho
Sho
|Na
|Du
 
Fro
|Tha
|Su
 
Flo
|Fa
|Ru
 
No
|'''Da'''
|Lu
 
Tho
|Sa
|Sa
|Mu
|Flo
 
Fo
|Ra
|Tu
 
Do
|La
|La
|Pu
|'''Tho'''
 
|'''Tu'''
So
|Da
|Ma
|Ro
|Ta
|Lo
|Pa
|Mo
|-
|-
!intervals
!3rd 2L10s
|^m6
!sssLss-sssLss
|d5
|Da
|^m3
|Fro
|m2
|Ra
|^m7
|'''No'''
|m6
|'''Mu'''
|^4
|Fa
 
|Pu/Sho
vd5
|Sa
|m3
|Flo
|^1
|'''La'''
 
|'''Tha'''
vm2
|Tu
|m7
|Da
|^5
 
vm6
|P4
|^M2
 
vm3
|'''P1'''
|^M6
 
vm7
|P5
|^M3
 
v4
|M2
|^M7
 
v8
|M6
|^A4
 
v5
|M3
|vM2
|M7
|vM6
|A4
|vM3
|-
|-
!notes
!4th 2L10s
|^Ab
!ssLsss-ssLsss
|Gb
|Da
|^Eb
|Fro
|Db
|'''Ra'''
|^Bb
|'''Na'''
|Ab
|Mu
|^F
|Fa
 
|Pu/Sho
vGb
|Sa
|Eb
|'''Flo'''
|^C
|'''Lu'''
 
|Tha
vDb
|Tu
|Bb
|Da
|^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
!5th 2L10s
!sLLLL
!sLssss-sLssss
|Da
|Da
|'''Ra'''
|'''Fro'''
|Mu/Fo
|'''Ru'''
|Sa
|Na
|Lu/Tho
|Mu
|Da
|Fa
|-
|Pu/Sho
!2nd 4L1s
!LsLLL
|Da
|'''Ru/No'''
|'''Mu/Fo'''
|Sa
|Lu/Tho
|Da
|-
!3rd 4L1s
!LLsLL
|Da
|Ru/No
|'''Fa'''
|'''Sa'''
|'''Sa'''
|Lu/Tho
|'''Fla'''
|Lu
|Tha
|Tu
|Da
|Da
|-
|-
!4th 4L1s
!6th 2L10s
!LLLsL
!Lsssss-Lsssss
|Da
|Da
|Ru/No
|'''Fra'''
|Ru
|Na
|Mu
|Fa
|Fa
|'''Su/Flo'''
|Pu/Sho
|'''Lu/Tho'''
|'''Su'''
|Da
|Fla
|-
|Lu
!5th 4L1s
|Tha
!LLLLs
|Tu
|Da
|Ru/No
|Fa
|Su/Flo
|'''Tha'''
|Da
|Da
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
5L4s MOS scales (L = M2 = rhymes, s = ^1/vm2 = no rhyme)
12L2s MOS scales using solfege #2 (L = ^A1/vm2, s = ^1) -- P5 must be < 700¢, or s will be < 0¢
 
if P5 < 5\9 = 667¢, swap L and s to get 4L5s
![[Genchain mode numbering|GMN]] name
![[Genchain mode numbering|GMN]] name
!scale
!scale
!0
!1sn
!1
!
!2
!2nd
!3
!
!4
!3rd
!5
!
!6
!4th
!7
!
!8
!5th
!9
!
!6th
!
!7th
!
!8ve
|-
|-
!1st 5L4s
!1st 12L2s
!LLsLsLsLs
!LLLLLLs-LLLLLLs
|Da
|Da
|Fro
|Ra
|Ra
|'''Ma'''
|No
|Mu/Fo
|Ma
|Pu/So
|Fo
|'''Pa'''
|Pu/Sho
|Sa
|Sa
|Flo
|La
|La
|Lu/Tho
|Tho
|Tu/Do
|Ta
|'''Do'''
|Da
|Da
|-
|-
!2nd 5L4s
!2nd 12L2s
!LsLLsLsLs
!LLLLLsL-LLLLLsL
|Da
|Da
|Fro
|Ra
|Ra
|'''Ru/No'''
|No
|Mu/Fo
|Ma
|'''Pu/So'''
|'''Fo'''
|'''Fa'''
|Pu/Sho
|Sa
|Sa
|Flo
|La
|La
|Lu/Tho
|Tho
|Tu/Do
|'''Ta'''
|'''Tu'''
|Da
|Da
|-
|-
!3rd 5L4s
!3rd 12L2s
!LsLsLLsLs
!LLLLsLL-LLLLsLL
|Da
|Da
|Fro
|Ra
|Ra
|Ru/No
|No
|Mu/Fo
|'''Ma'''
|'''Fa'''
|'''Mu'''
|Fa
|Pu/Sho
|Sa
|Sa
|'''La'''
|Flo
|Lu/Tho
|La
|Tu/Do
|'''Tho'''
|'''Tha'''
|Tu
|Da
|Da
|-
|-
!4th 5L4s
!4th 12L2s
!LsLsLsLLs
!LLLsLLL-LLLsLLL
|Da
|Da
|Fro
|Ra
|Ra
|Ru/No
|'''No'''
|Mu/Fo
|'''Na'''
|Mu
|Fa
|Fa
|Pu/Sho
|Sa
|Sa
|'''Su/Flo'''
|Flo
|Lu/Tho
|'''La'''
|'''Tu/Do'''
|'''Lu'''
|Tha
|Tu
|Da
|Da
|-
|-
!5th 5L4s
!5th 12L2s
!LsLsLsLsL
!LLsLLLL-LLsLLLL
|Da
|Da
|Fro
|'''Ra'''
|'''Ra'''
|Ru/No
|'''Ru'''
|Mu/Fo
|Na
|Mu
|Fa
|Fa
|Pu/Sho
|Sa
|Sa
|Su/Flo
|'''Flo'''
|Lu/Tho
|'''Fla'''
|'''Tha'''
|Lu
|Da
|-
!6th 5L4s
!sLLsLsLsL
|Da
|'''Du/Fro'''
|Ru/No
|'''Mu/Fo'''
|Fa
|Sa
|Su/Flo
|Lu/Tho
|Tha
|Tha
|Tu
|Da
|Da
|-
|-
!7th 5L4s
!6th 12L2s
!sLsLLsLsL
!LsLLLLL-LsLLLLL
|Da
|Da
|Du/Fro
|'''Fro'''
|Ru/No
|'''Fra'''
|'''Na'''
|Ru
|Na
|Mu
|Fa
|Fa
|Pu/Sho
|'''Sa'''
|'''Sa'''
|Su/Flo
|'''Su'''
|Lu/Tho
|Fla
|Lu
|Tha
|Tha
|Tu
|Da
|Da
|-
|-
!8th 5L4s
!7th 12L2s
!sLsLsLLsL
!sLLLLLL-sLLLLLL
|Da
|Da
|Du/Fro
|'''Du'''
|Ru/No
|Fra
|Ru
|Na
|Na
|Mu
|Fa
|Fa
|'''Fu/Sho'''
|Pu/Sho
|Su/Flo
|'''Sha'''
|'''Lu/Tho'''
|Su
|Tha
|Fla
|Da
|Lu
|-
!9th 5L4s
!sLsLsLsLL
|Da
|Du/Fro
|Ru/No
|Na
|Fa
|Fu/Sho
|Su/Flo
|'''Fla'''
|Tha
|Tha
|Tu
|Da
|Da
|}
|}
A similar table can be made for 5L9s. The same solfege can be used for 9L5s, but Sa will be < 4\7 = 686¢.


== #4 (P8, P5/2) half-5th (list alternate pergens) ==
=== Solfege #3 (EU = vvM2) ===
* G = ^m3/vM3 = ~3 = 350¢ + c/2
* EI = vvA1 = 0¢
* ^ = 50¢ + 3.5c


MOS scales covered:
* P = ^4/v5 = 600¢
 
* G = ^1 = vM2 = 100¢ + c
* 7 = 3L4s (and 4L3s if P5 < 4\7 = 686¢)
* EU = vvM2 = 0¢
* 10 = 7L3s (and 3L7s if P5 > 3\5 = 720¢)
* ^ = 100¢ + c
* 13 = 10L3s (if P5 > 3\5 = 720¢) and 3L10s (if P5 > 8\13)
* # = 100¢ + 7c


Doesn't tip.
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
'''uniform solfege (-a = plain, -u = up, -o = down)'''
'''solfege #3 (-a = plain, -u = up, -o = down)'''
|-
|-
!genspan
! colspan="2" |genspan ('''gen = P5''')
!-13
!-12
!-11
!-10
!-9
!-8
!-7
!-6
!-6
!-5
!-5
Line 11,900: Line 11,670:
!5
!5
!6
!6
!7
!8
!9
!10
!11
!12
!13
|-
|-
! rowspan="3" |plain
genchain
perspan = 0
!solfege
!solfege
|No
|Sha
|Sha
|Tho
|Fra
|Fra
|Fo
|Fla
|Fla
|Do
|Na
|Na
|So
Shu
|Tha
|Tha
|Ro
Fru
|Fa
|Fa
|Lo
Flu
|'''Da'''
|'''Da'''
|Mo
Nu
|Sa
|Sa
|To
Thu
|Ra
|Ra
|Po
Fu
|La
|La
|Du
|Ma
|Ma
|Su
|Ta
|Ta
|Ru
|Pa
|Pa
|Lu
|-
|-
!intervals
!intervals
|vm3
|d5
|d5
|vm7
|m2
|m2
|v4
|m6
|m6
|v8
|m3
|m3
|~5
|m7
|m7
|~2
|P4
|P4
|~6
|'''P1'''
|'''P1'''
|~3
|P5
|P5
|~7
|M2
|M2
|~4
|M6
|M6
|^1
|M3
|M3
|^5
|M7
|M7
|^M2
|A4
|A4
|^M6
|-
|-
!notes
!notes
|vEb
|Gb
|Gb
|vBb
|Db
|Db
|vF
|Ab
|Ab
|vC
|Eb
|Eb
|^Gb
vG
|Bb
|Bb
|^Db
vD
|F
|F
|^Ab
vA
|'''C'''
|'''C'''
|^Eb
vE
|G
|G
|^Bb
vB
|D
|D
|^F
vF#
|A
|A
|^C
|E
|E
|^G
|B
|B
|^D
|F#
|F#
|^A
|-
| 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
|}
|}
for 7-note scales, up notes aren't needed, because every up note can be sung as a down note.
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
3L4s MOS scales (L = M2 = rhymes, s = ~2 = no rhyme)
'''solfege #3 (-a = plain, -u = up, -o = down) [[mingen]] format'''
 
|-
if P5 < 4\7 = 686¢, swap L and s to get 4L3s
! colspan="2" |genspan ('''gen = vA1/^m2''')
![[Genchain mode numbering|GMN]] name
!-6
!scale
!-5
!1sn
!-4
!2nd
!-3
!3rd
!-2
!4th
!-1
!5th
!0
!6th
!1
!7th
!2
!8ve
!3
!4
!5
!6
|-
|-
!1st 3L4s
! rowspan="3" |Da's
!LsLsLss
 
|Da
genchain
 
perspan = 0
!solfege
|Sha
|Shu/Flo
|Fla
|Flu/Tho
|Tha
|Thu/Do
|'''Da'''
|Du/Ro
|Ra
|Ra
|Mo
|Ru/Mo
|Po
|Ma
|Sa
|Mu/Po
|'''La'''
|Pa
|To
|Da
|-
|-
!2nd 3L4s
!intervals
!LsLssLs
|d5
|Da
|^d5/vm6
|Ra
|m6
|Mo
|^m6/vm7
|'''Po'''
|m7
|Sa
|^m7/v8
|'''Lo'''
|'''P1'''
|To
|^1/vM2
|Da
|M2
|^M2/vM3
|M3
|^M3/vA4
|A4
|-
|-
!3rd 3L4s
!notes
!LssLsLs
|Gb
|Da
|^Gb/vAb
|'''Ra'''
|Ab
|Mo
|^Ab/vBb
|'''Fa'''
|Bb
|Sa
|^Bb/vC
|Lo
|'''C'''
|To
|^C/vD
|Da
|D
|^D/vE
|E
|^E/vF#
|F#
|-
| colspan="15" |
|-
|-
!4th 3L4s
! rowspan="3" |Sa's
!sLsLsLs
 
|Da
genchain
|'''Ro'''
 
|Mo
perspan = ±1
!solfege
|Fro
|Fra
|Fru/No
|Na
|Nu/Fo
|Fa
|Fa
|Fu/So
|Sa
|Sa
|Lo
|Su/Lo
|'''To'''
|La
|Da
|Lu/To
|Ta
|Tu
|-
|-
!5th 3L4s
!intervals
!sLsLssL
|vm2
|Da
|m2
|Ro
|^m2/vm3
|Mo
|m3
|Fa
|^m3/v4
|'''Sa'''
|P4
|Lo
|^4/v5
|'''Tha'''
|P5
|Da
|^5/vM6
|M6
|^M6/vM7
|M7
|^M7
|-
|-
!6th 3L4s
!notes
!sLssLsL
|vDb
|Da
|Db
|Ro
|^Db/vEb
|'''Mo'''
|Eb
|Fa
|^Eb/vF
|'''So'''
|F
|Lo
|^F/vG
|Tha
|G
|Da
|^G/vA
|-
|A
!7th 3L4s
|^A/vB
!ssLsLsL
|B
|Da
|^B
|Ro
|'''Na'''
|Fa
|So
|Lo
|Tha
|Da
|}
|}
For 10-note scales, both up notes and down notes are needed.
{| class="wikitable center-all"
{| 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
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
![[Genchain mode numbering|GMN]] name
!scale
!scale
!0
!1sn
!1
! colspan="2" |2nds
!2
! colspan="2" |3rds
!3
!4th
!4
!tritone
!5
!5th
!6
! colspan="2" |6ths
!7
! colspan="2" |7ths
!8
!8ve
!9
!10
|-
|-
!1st 7L3s
!1st 10L2s
!sLLsLLsLLL
!LLLLLs-LLLLLs
|Da
|Da
|Du
|Du/Ro
|Ra
|Ra
|Nu/Mo
|Ru/Mo
|Ma
|Ma
|Fu/Po
|'''Mu/Po'''
|Fu/So
|Sa
|Sa
|'''Su'''
|Su/Lo
|La
|La
|Thu/To
|Lu/To
|'''Ta'''
|Da
|Da
|-
|-
!2nd 7L3s
!2nd 10L2s
!sLLsLLLsLL
!LLLLsL-LLLLsL
|Da
|Da
|Du
|Du/Ro
|Ra
|Ra
|Nu/Mo
|Ru/Mo
|'''Ma'''
|'''Ma'''
|Fu/Po
|'''Fa'''
|Fu/So
|Sa
|Sa
|'''Flu/Lo'''
|Su/Lo
|La
|La
|Thu/To
|'''Lu/To'''
|'''Thu/Do'''
|Da
|Da
|-
|-
!3rd 7L3s
!3rd 10L2s
!sLLLsLLsLL
!LLLsLL-LLLsLL
|Da
|Da
|'''Du'''
|Du/Ro
|Ra
|Ra
|Nu/Mo
|'''Ru/Mo'''
|'''Fa'''
|'''Nu/Fo'''
|Fu/Po
|Fa
|Fu/So
|Sa
|Sa
|Flu/Lo
|Su/Lo
|La
|'''La'''
|Thu/To
|'''Tha'''
|Thu/Do
|Da
|Da
|-
|-
!4th 7L3s
!4th 10L2s
!LsLLsLLsLL
!LLsLLL-LLsLLL
|Da
|Da
|'''Fru/Ro'''
|Du/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'''
|'''Ra'''
|Nu/Mo
|'''Na'''
|Nu/Fo
|Fa
|Fa
|'''Shu/So'''
|Fu/So
|Sa
|Sa
|Flu/Lo
|'''Su/Lo'''
|'''Flu/Tho'''
|Tha
|Tha
| Thu/To
|Thu/Do
|Da
|Da
|-
|-
!7th 7L3s
!5th 10L2s
! LLsLLsLLsL
!LsLLLL-LsLLLL
|Da
|Da
|Fru/Ro
|'''Du/Ro'''
|'''Na'''
|'''Fru/No'''
|Nu/Mo
|Fa
| Shu/So
|Sa
|Flu/Lo
|Tha
|'''Thu/To'''
| Da
|-
!8th 7L3s
!LLsLLsLLLs
|Da
|Fru/Ro
|Na
|Na
|Nu/Mo
|Nu/Fo
|Fa
|Fa
|Shu/So
|Fu/So
|'''Sa'''
|'''Sa'''
|Flu/Lo
|'''Fla'''
|Flu/Tho
|Tha
|Tha
|'''Do'''
|Thu/Do
|Da
|Da
|-
|-
!9th 7L3s
!6th 10L2s
!LLsLLLsLLs
!sLLLLL-sLLLLL
|Da
|Da
|Fru/Ro
|'''Fra'''
|Fru/No
|Na
|Na
|'''Nu/Mo'''
|Nu/Fo
|Fa
|Fa
|Shu/So
|Fu/So
|'''Fla'''
|'''Shu/Flo'''
|Flu/Lo
|Fla
|Flu/Tho
|Tha
|Tha
|Do
|Thu/Do
|Da
|-
!10th 7L3s
!LLLsLLsLLs
|Da
|Fru/Ro
|Na
|'''Fo'''
|Fa
|Shu/So
|Fla
|Flu/Lo
|Tha
|Do
|Da
|Da
|}
|}
==#5 (P8/2, P4/2) half-everything (incomplete)==
== #3 (P8, P4/2) half-4th ==
It has only 4 fifthchains, but two of them require double names. Hmm, must think about this...


== #6 (P8/3, P5) third-8ve ==
* G = ^M2/vm3 = 250¢ - c/2
There are two solfeges. Use solfege #1 if P5 > 700¢, and use solfege #2 if P5 < 700¢.
* EU = vvm2 = 0¢
* P = vM3/^^d4 (solfege #1) '''<u>or</u>''' ^M3/vvd4 (solfege #2) = 400¢
* ^ = 50¢ - 2.5c = 5G - P
* G = P5 = 700¢ + c '''<u>or</u>''' vvA1/^m2 (solfege #1) '''<u>or</u>''' ^^A1/vm2 (solfege #2) = 100¢ - c
* EI = ^<sup>3</sup>d2 = 0¢
* ^ = 4 '''⋅''' |c|


MOS scales covered:
MOS scales covered:


* 6 = 3L3s (either solfege)
* 5 = 4L1s (for 1L4s use pergen #8, third-5th)
* 9 = 3L6s (either solfege) or 6L3s (solfege #2 only)
* 9 = 5L4s or 4L5s (P5 < 5\9 = 667¢)
* 12 = 3L9s (extended solfege #1 only) or 9L3s (extended solfege #2 only)
* 14 = 9L5s or 5L9s (P5 < 4\7 = 686¢)
* 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"
{| class="wikitable center-all"
|+
|+
'''solfege #1 (-a = plain, -u = up, -o = down)'''
'''solfege (-a = plain, -u = up, -o = down)'''
|-
|-
! colspan="2" |genspan (gen = P5)
!genspan
!13
!12
!11
!10
!9
!8
!7
!6
!5
!4
!3
!2
!1
!0
!-1
!-2
!-2
!-1
!-3
!0
!-4
!1
!-5
!2
!-6
!-7
!-8
!-9
!-10
!-11
!-12
!-13
|-
|-
! rowspan="3" |down
!solfege
|Flu
|Sha
|Nu
|Fra
|Thu
|Fla
|Fu


genchain
Sho
|Na
|Du


perspan = 1
Fro
!solfege
|Tha
|Su
 
Flo
|Fa
|Ru
 
No
|'''Da'''
|Lu
 
Tho
|Sa
|Mu
 
Fo
|Ra
|Tu
 
Do
|La
|Pu
 
So
|Ma
|Ro
|Ro
|Ta
|Lo
|Lo
|Pa
|Mo
|Mo
|To
|Po
|-
|-
!intervals
!intervals
|vM2
|^m6
|vM6
|d5
|vM3
|^m3
|vM7
|m2
|vA4
|^m7
|-
|m6
!notes
|^4
|vD
|vA
|vE
|vB
|vF#
|-
| colspan="7" |
|-
! rowspan="3" |plain


genchain
vd5
|m3
|^1


perspan = 0
vm2
!solfege
|Tha
|Fa
|'''Da'''
|Sa
|Ra
|-
!intervals
|m7
|m7
|^5
vm6
|P4
|P4
|^M2
vm3
|'''P1'''
|'''P1'''
|^M6
vm7
|P5
|P5
|^M3
v4
|M2
|M2
|-
|^M7
!notes
|Bb
|F
|'''C'''
|G
|D
|-
| colspan="7" |
|-
! rowspan="3" |up


genchain
v8
|M6
|^A4


perspan = -1
v5
!solfege
|M3
|Shu
|vM2
|Fru
|M7
|Flu
|vM6
|Nu
|A4
|Thu
|vM3
|-
!intervals
|^d5
|^m2
|^m6
|^m3
|^m7
|-
|-
!notes
!notes
|^Gb
|^Db
|^Ab
|^Ab
|Gb
|^Eb
|^Eb
|Db
|^Bb
|^Bb
|}
|Ab
{| class="wikitable center-all"
|^F
|+
 
'''solfege #1 (-a = plain, -u = up, -o = down)'''
vGb
|-
|Eb
! colspan="2" |genspan (gen = vvA1/^m2)
|^C
!2
!1
!0
!-1
!-2
|-
! rowspan="3" |Fa's


genchain
vDb
|Bb
|^G


perspan = 1
vAb
!solfege
|Shu
|Fa
|Mo
|Nu
|Ra
|-
!intervals
|^d5
|P4
|vM3
|^m3
|M2
|-
!notes
|^Gb
|F
|F
|vE
|^D
|^Eb
 
vEb
|'''C'''
|^A
 
vBb
|G
|^E
 
vF
|D
|D
|-
|^B
| colspan="7" |
|-
! rowspan="3" |Da's


genchain
vC
|A
|^F#


perspan = 0
vG
!solfege
|E
|Ro
|Fru
|'''Da'''
|To
|Thu
|-
!intervals
|vM2
|^m2
|'''P1'''
|vM7
|^m7
|-
!notes
|vD
|vD
|^Db
|B
|'''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
|vA
|^Ab
|F#
|G
|vE
|vF#
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
'''extended solfege #1 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
4L1s MOS scales (L = ^M2/vm3 = no rhyme, s = M2 = rhymes)
|-
![[Genchain mode numbering|GMN]] name
! colspan="2" |genspan (gen = P5)
!scale
!-6
!-5
!-4
!-3
!-2
!-1
!0
!0
!1
!1
Line 12,489: Line 12,198:
!4
!4
!5
!5
!6
|-
|-
! rowspan="3" |down
!1st 4L1s
 
!sLLLL
genchain
|Da
 
|'''Ra'''
perspan = 1
|Mu/Fo
!solfege
|Sa
|Tho
|Lu/Tho
|Fo
|Da
|Do
|-
|So
!2nd 4L1s
|Ro
!LsLLL
|Lo
|Da
|Mo
|'''Ru/No'''
|To
|'''Mu/Fo'''
|Po/Shi
|Sa
|Fri
|Lu/Tho
|Fli
|Da
|Ni
|Thi
|-
|-
!intervals
!3rd 4L1s
|vm7
!LLsLL
|v4
|Da
|v1
|Ru/No
|v5
|'''Fa'''
|vM2
|'''Sa'''
|vM6
|Lu/Tho
|vM3
|Da
|vM7
|vA4/^^d5
|^^m2
|^^m6
|^^m3
|^^m7
|-
|-
!notes
!4th 4L1s
|vBb
!LLLsL
|vF
|Da
|vC
|Ru/No
|vG
|Fa
|vD
|'''Su/Flo'''
|vA
|'''Lu/Tho'''
|vE
|Da
|vB
|vF#/^^Gb
|^^Db
|^^Ab
|^^Eb
|^^Bb
|-
|-
| colspan="15" |
!5th 4L1s
|-
!LLLLs
! rowspan="3" |plain
|Da
 
|Ru/No
genchain
|Fa
|Su/Flo
|'''Tha'''
|Da
|}
{| class="wikitable center-all"
|+
5L4s MOS scales (L = M2 = rhymes, s = ^1/vm2 = no rhyme)


perspan = 0
if P5 < 5\9 = 667¢, swap L and s to get 4L5s
!solfege
![[Genchain mode numbering|GMN]] name
|Sha
!scale
|Fra
!0
|Fla
!1
|Na
!2
|Tha
!3
|Fa
!4
|'''Da'''
!5
|Sa
!6
!7
!8
!9
|-
!1st 5L4s
!LLsLsLsLs
|Da
|Ra
|Ra
|'''Ma'''
|Mu/Fo
|Pu/So
|Sa
|La
|La
|Ma
|Lu/Tho
|Ta
|Tu/Do
|Pa
|Da
|-
|-
!intervals
!2nd 5L4s
|d5
!LsLLsLsLs
|m2
|Da
|m6
|Ra
|m3
|'''Ru/No'''
|m7
|Mu/Fo
|P4
|'''Pu/So'''
|'''P1'''
|Sa
|P5
|La
|M2
|Lu/Tho
|M6
|Tu/Do
|M3
|Da
|M7
|A4
|-
|-
!notes
!3rd 5L4s
|Gb
!LsLsLLsLs
|Db
|Da
|Ab
|Ra
|Eb
|Ru/No
|Bb
|Mu/Fo
|F
|'''Fa'''
|'''C'''
|Sa
|G
|'''La'''
|D
|Lu/Tho
|A
|Tu/Do
|E
|Da
|B
|F#
|-
|-
| colspan="15" |
!4th 5L4s
|-
!LsLsLsLLs
! rowspan="3" |up
|Da
 
|Ra
genchain
|Ru/No
 
|Mu/Fo
perspan = -1
|Fa
!solfege
|Sa
|Re
|'''Su/Flo'''
|Le
|Lu/Tho
|Me
|'''Tu/Do'''
|Te
|Da
|Pe/Shu
|Fru
|Flu
|Nu
|Thu
|Fu
|Du
|Su
|Ru
|-
|-
!intervals
!5th 5L4s
|vvM2
!LsLsLsLsL
|vvM6
|Da
|vvM3
|'''Ra'''
|vvM7
|Ru/No
|vvA4/^d5
|Mu/Fo
|^m2
|Fa
|^m6
|Sa
|^m3
|Su/Flo
|^m7
|Lu/Tho
|^4
|'''Tha'''
|^1
|Da
|^5
|^M2
|-
|-
!notes
!6th 5L4s
|vvD
!sLLsLsLsL
|vvA
|Da
|vvE
|'''Du/Fro'''
|vvB
|Ru/No
|vvF#/^Gb
|'''Mu/Fo'''
|^Db
|Fa
|^Ab
|Sa
|^Eb
|Su/Flo
|^Bb
|Lu/Tho
|^F
|Tha
|^C
|Da
|^G
|^D
|}
{| class="wikitable center-all"
|+
'''extended solfege #1 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
|-
! colspan="2" |genspan (gen = vvA1/^m2)
!7th 5L4s
!6
!sLsLLsLsL
!5
|Da
!4
|Du/Fro
!3
|Ru/No
!2
|'''Na'''
!1
|Fa
!0
|'''Sa'''
!-1
|Su/Flo
!-2
|Lu/Tho
!-3
|Tha
!-4
|Da
!-5
|-
!-6
!8th 5L4s
!sLsLsLLsL
|Da
|Du/Fro
|Ru/No
|Na
|Fa
|'''Fu/Sho'''
|Su/Flo
|'''Lu/Tho'''
|Tha
|Da
|-
|-
! rowspan="3" |Fa's
!9th 5L4s
!sLsLsLsLL
|Da
|Du/Fro
|Ru/No
|Na
|Fa
|Fu/Sho
|Su/Flo
|'''Fla'''
|Tha
|Da
|}
== #4 (P8, P5/2) half-5th (list alternate pergens) ==
* G = ^m3/vM3 = ~3 = 350¢ + c/2
* EU = vvA1 = 0¢
* ^ = 50¢ + 3.5c = 7G - 2P
 
MOS scales covered:


genchain
* 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)


perspan = 1
{| 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
!solfege
|No
|Sha
|Tho
|Tho
|Le
|Fra
|Fo
|Fla
|Fla
|Do
|Na
|So
|So
|Pe/Shu
Shu
|Tha
|Ro
Fru
|Fa
|Fa
|Lo
Flu
|'''Da'''
|Mo
|Mo
|Nu
Nu
|Sa
|To
Thu
|Ra
|Ra
|Fri
|Po
Fu
|La
|Du
|Du
|Ma
|Su
|Ta
|Ta
|Thi
|Ru
|Pa
|Lu
|-
|-
!intervals
!intervals
|vm3
|d5
|vm7
|vm7
|vvM6
|m2
|v4
|m6
|m6
|v5
|v8
|vvA4/^d5
|m3
|~5
|m7
|~2
|P4
|P4
|vM3
|~6
|^m3
|'''P1'''
|~3
|P5
|~7
|M2
|M2
|^^m2
|~4
|M6
|^1
|^1
|M3
|^5
|M7
|M7
|^^m7
|^M2
|A4
|^M6
|-
|-
!notes
!notes
|vEb
|Gb
|vBb
|vBb
|vvA
|Db
|vF
|Ab
|Ab
|vG
|vC
|vvF#/^Gb
|Eb
|^Gb
 
vG
|Bb
|^Db
 
vD
|F
|F
|vE
|^Ab
 
vA
|'''C'''
|^Eb
|^Eb
vE
|G
|^Bb
vB
|D
|D
|^^Db
|^F
 
vF#
|A
|^C
|^C
|E
|^G
|B
|B
|^^Bb
|^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
|-
|-
| colspan="15" |
!1st 3L4s
!LsLsLss
|Da
|Ra
|Mo
|Po
|Sa
|'''La'''
|To
|Da
|-
|-
! rowspan="3" |Da's
!2nd 3L4s
 
!LsLssLs
genchain
|Da
 
|Ra
perspan = 0
|Mo
!solfege
|'''Po'''
|Sha
|Sa
|Fo
|'''Lo'''
|Me
|Na
|Ro
|Fru
|'''Da'''
|To
|To
|Thu
|Da
|La
|Fli
|Su
|Pa
|-
|-
!intervals
!3rd 3L4s
|d5
!LssLsLs
|v4
|Da
|vvM3
|'''Ra'''
|m3
|Mo
|vM2
|'''Fa'''
|^m2
|Sa
|'''P1'''
|Lo
|vM7
|To
|^m7
|Da
|M6
|^^m6
|^5
|A4
|-
|-
!notes
!4th 3L4s
|Gb
!sLsLsLs
|vF
|Da
|vvE
|'''Ro'''
|Eb
|Mo
|vD
|Fa
|^Db
|Sa
|'''C'''
|Lo
|vB
|'''To'''
|^Bb
|Da
|A
|^^Ab
|^G
|F#
|-
|-
| colspan="15" |
!5th 3L4s
!sLsLssL
|Da
|Ro
|Mo
|Fa
|'''Sa'''
|Lo
|'''Tha'''
|Da
|-
|-
! rowspan="3" |Sa's
!6th 3L4s
 
!sLssLsL
genchain
|Da
 
|Ro
perspan = -1
|'''Mo'''
!solfege
|Fa
|Re
|'''So'''
|Fra
|Lo
|Do
|Te
|Tha
|Tha
|Da
|-
!7th 3L4s
!ssLsLsL
|Da
|Ro
|'''Na'''
|Fa
|So
|Lo
|Lo
|Flu
|Tha
|Sa
|Da
|Po/Shi
|}
|Fu
For 10-note scales, both up notes and down notes are needed.
|Ma
{| class="wikitable center-all"
|Ni
|+7L3s MOS scales (L = ^m2 = vM2 = different degree, s = ^1 = vA1 = same degree)
|Ru
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
|-
|-
!intervals
!1st 7L3s
|vvM2
!sLLsLLsLLL
|m2
|Da
|v1
|Du
|vvM7
|Ra
|m7
|Nu/Mo
|vM6
|Ma
|^m6
|Fu/Po
|P5
|Sa
|vA4/^^d5
|'''Su'''
|^4
|La
|M3
|Thu/To
|^^m3
|Da
|^M2
|-
|-
!notes
!2nd 7L3s
|vvD
!sLLsLLLsLL
|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
|Da
|'''Nu'''
|Du
|Mo
|Ra
|'''Sa'''
|Nu/Mo
|Flu
|'''Ma'''
|'''To'''
|Fu/Po
|Sa
|'''Flu/Lo'''
|La
|Thu/To
|Da
|Da
|-
|-
!2nd 3L3s
!3rd 7L3s
!sL-sL-sL
!sLLLsLLsLL
|Da
|Da
|'''Fru'''
|'''Du'''
|Mo
|Ra
|Nu/Mo
|'''Fa'''
|'''Fa'''
|Flu
|Fu/Po
|'''Lo'''
|Sa
|Flu/Lo
|La
|Thu/To
|Da
|Da
|}
|-
{| class="wikitable center-all"
!4th 7L3s
|+
!LsLLsLLsLL
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
|Da
|'''Ra'''
|'''Fru/Ro'''
|Nu
|Ra
|Mo
|Nu/Mo
|'''Po'''
|Fa
|Fu/Po
|Sa
|Sa
|Flu
|Flu/Lo
|'''Thu'''
|'''La'''
|To
|Thu/To
|Da
|Da
|-
|-
!2nd 3L6s
!5th 7L3s
!sLs-sLs-sLs
!LsLLsLLLsL
|Da
|Da
|'''Fru'''
|Fru/Ro
|'''Nu'''
|Ra
|Mo
|Nu/Mo
|'''Fa'''
|Fa
|'''Sa'''
|'''Fu/Po'''
|Flu
|Sa
|'''Lo'''
|Flu/Lo
|'''To'''
|'''Tha'''
|Thu/To
|Da
|Da
|-
|-
!3rd 3L6s
!6th 7L3s
!ssL-ssL-ssL
!LsLLLsLLsL
|Da
|Da
|Fru
|Fru/Ro
|'''Ro'''
|'''Ra'''
|Mo
|Nu/Mo
|Fa
|Fa
|'''Shu'''
|'''Shu/So'''
|Flu
|Sa
|Lo
|Flu/Lo
|'''Tha'''
|Tha
| Thu/To
|Da
|-
!7th 7L3s
! LLsLLsLLsL
|Da
|Da
|}
|Fru/Ro
 
|'''Na'''
{| class="wikitable center-all"
|Nu/Mo
|+
|Fa
3L9s MOS scales (L = vA1/^^m2, s = ^m2/vvA1)
| Shu/So
![[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
|Sa
|Flu
|Flu/Lo
|'''La'''
|Tha
|Thu
|'''Thu/To'''
|To
| Da
|Da
|-
|-
!2nd 3L9s
!8th 7L3s
!sLss-sLss-sLss
!LLsLLsLLLs
|Da
|Da
|'''Fru'''
|Fru/Ro
|'''Ra'''
|Na
|Nu
|Nu/Mo
|Mo
|'''Fa'''
|'''Po'''
|Sa
|Flu
|'''Lo'''
|'''Thu'''
|To
|Da
|-
!3rd 3L9s
!ssLs-ssLs-ssLs
|Da
|Fru
|'''Ro'''
|'''Nu'''
|Mo
|Fa
|Fa
|'''Shu'''
|Shu/So
|'''Sa'''
|'''Sa'''
|Flu
|Flu/Lo
|Lo
|Tha
|'''Tha'''
|'''Do'''
|'''To'''
|Da
|Da
|-
|-
!4th 3L9s
!9th 7L3s
!sssL-sssL-sssL
!LLsLLLsLLs
|Da
|Da
|Fru
|Fru/Ro
|Ro
|Na
|'''Na'''
|'''Nu/Mo'''
|Mo
|Fa
|Fa
|Pe/Shu
|Shu/So
|'''So'''
|'''Fla'''
|Flu
|Flu/Lo
|Lo
|Tha
|Tha
|'''Te'''
|Do
|Da
|-
!10th 7L3s
!LLLsLLsLLs
|Da
|Fru/Ro
|Na
|'''Fo'''
|Fa
|Shu/So
|Fla
|Flu/Lo
|Tha
|Do
|Da
|Da
|}
|}
Similar tables can be made for 15- and 18-note scales.
==#5 (P8/2, P4/2) half-everything (incomplete)==
* 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:
* 10 =


=== Solfege #2 (P5 < 700¢) ===
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
'''solfege #2 (-a = plain, -u = up, -o = down)'''
'''solfege (-a = plain, -u = up, -o = down, -i = lift, -e = drop, -uwi = uplift, -owe = downdrop)'''
|-
|-
! colspan="2" |genspan (gen = P5)
!genspan
!13
!12
!11
!10
!9
!8
!7
!6
!5
!4
!3
!2
!1
!0
!-1
!-2
!-2
!-1
!-3
!0
!-4
!1
!-5
!2
!-6
!-7
!-8
!-9
!-10
!-11
!-12
!-13
|-
|-
! rowspan="3" |up
! rowspan="3" |plain


genchain
genchain


perspan = 1
 
!solfege
perspan = 0
|Flu
|Sha
|Nu
|Fra
|Thu
|Fla
|Fu
 
Sho
|Na
|Du
 
Fro
|Tha
|Su
 
Flo
|Fa
|Ru
|Ru
No
|'''Da'''
|Lu
|Lu
Tho
|Sa
|Mu
|Mu
Fo
|Ra
|Tu
|Tu
Do
|La
|Pu
|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
|^M2
vm3
|'''P1'''
|^M6
|^M6
vm7
|P5
|^M3
|^M3
v4
|M2
|^M7
|^M7
v8
|M6
|^A4
|^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
|^D
vEb
|'''C'''
|^A
|^A
vBb
|G
|^E
|^E
vF
|D
|^B
|^B
vC
|A
|^F#
|^F#
vG
|E
|vD
|B
|vA
|F#
|vE
|-
|-
| colspan="7" |
| colspan="28" |
|-
|-
! rowspan="3" |plain
! rowspan="3" |lift/drop


genchain
genchain


perspan = 0
 
!solfege
perspan = ±1
|Tha
|Ne
|Fa
|Frowe
|'''Da'''
|The
|Sa
|Shuwi
|Ra
Flowe
|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
|Muwi
Powe
|Ri
|Tuwi
|Li
|-
|-
!intervals
|\m3
|m7
|v\m2
|P4
|\m7
|'''P1'''
|^/d5
|P5
v\m6
|M2
|\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
|^/M3
v\A4
|/M2
|^/M7
|/M6
|-
|-
!notes
|\Eb
|Bb
|vDb
|F
|\Bb
|'''C'''
|^/Gb
|G
v\Ab
|D
|\F
|-
|^/Db
| colspan="7" |
v\Eb
|-
|\C
! rowspan="3" |down
|^/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
|^/E
v\F#
|/D
|^/B
|/A
|}
10-note scale's 1st and last modes have only 1 name for an inbetween note and 2 mid notes. (Ro/Di/Si and Thu/De/Fe)
 
== #6 (P8/3, P5) third-8ve ==
There are two solfeges. Use solfege #1 if P5 > 700¢, and use solfege #2 if P5 < 700¢.
* P = vM3/^^d4 (solfege #1) '''<u>or</u>''' ^M3/vvd4 (solfege #2) = 400¢
* G = P5 = 700¢ + c '''<u>or</u>''' vvA1/^m2 (solfege #1) '''<u>or</u>''' ^^A1/vm2 (solfege #2) = 100¢ - c
* EU = ^<sup>3</sup>d2 = 0¢
* ^ = 4 '''⋅''' |c|


genchain
MOS scales covered:


perspan = -1
* 6 = 3L3s (either solfege)
!solfege
* 9 = 3L6s (either solfege) or 6L3s (solfege #2 only)
|Sho
* 12 = 3L9s (extended solfege #1 only) or 9L3s (extended solfege #2 only)
|Fro
* 15 = 12L3s (extended solfege #1 only) or 3L12s (extended solfege #1 only, P5 > 3\5 = 720¢)
|Flo
* 18 = 15L3s (extended solfege #1 only) (P5 > 3\5 = 720¢, if P5 > 11\18 = 733¢, you get 3L15s)
|No
* 21= 12L9s (extended solfege #2 only)
|Tho
* 21 = 18L3s (extended solfege #1 only) (P5 > 3\5 = 720¢, if P5 > 13\21 = 743¢, you get 3L18s)
|-
 
!intervals
=== Solfege #1 (P5 > 700¢) ===
|vd5
|vm2
|vm6
|vm3
|vm7
|-
!notes
|vGb
|vDb
|vAb
|vEb
|vBb
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
'''solfege #2 (-a = plain, -u = up, -o = down)'''
'''solfege #1 (-a = plain, -u = up, -o = down)'''
|-
|-
! colspan="2" |genspan (gen = ^^A1/vm2)
! colspan="2" |genspan (gen = P5)
!-2
!-1
!0
!1
!2
!2
!1
!0
!-1
!-2
|-
|-
! rowspan="3" |Fa's
! rowspan="3" |down


genchain
genchain
Line 13,099: Line 13,140:
perspan = 1
perspan = 1
!solfege
!solfege
|Sho
|Ro
|Fa
|Lo
|Mu
|Mo
|No
|To
|Ra
|Po
|-
|-
!intervals
!intervals
|vd5
|vM2
|P4
|vM6
|^M3
|vM3
|vm3
|vM7
|M2
|vA4
|-
|-
!notes
!notes
|vGb
|vD
|F
|vA
|^E
|vE
|vEb
|vB
|D
|vF#
|-
|-
| colspan="7" |
| colspan="7" |
|-
|-
! rowspan="3" |Da's
! rowspan="3" |plain


genchain
genchain
Line 13,127: Line 13,168:
perspan = 0
perspan = 0
!solfege
!solfege
|Ru
|Tha
|Fro
|Fa
|'''Da'''
|'''Da'''
|Tu
|Sa
|Tho
|Ra
|-
|-
!intervals
!intervals
|^M2
|m7
|vm2
|P4
|'''P1'''
|'''P1'''
|^M7
|P5
|vm7
|M2
|-
|-
!notes
!notes
|^D
|Bb
|vDb
|F
|'''C'''
|'''C'''
|^B
|G
|vBb
|D
|-
|-
| colspan="7" |
| colspan="7" |
|-
|-
! rowspan="3" |Sa's
! rowspan="3" |up


genchain
genchain
Line 13,155: Line 13,196:
perspan = -1
perspan = -1
!solfege
!solfege
|Tha
|Shu
|Lu
|Fru
|Flo
|Flu
|Sa
|Nu
|Pu
|Thu
|-
|-
!intervals
!intervals
|m7
|^d5
|^M6
|^m2
|vm6
|^m6
|P5
|^m3
|^A4
|^m7
|-
|-
!notes
!notes
|Bb
|^Gb
|^A
|^Db
|vAb
|^Ab
|G
|^Eb
|^F#
|^Bb
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
'''extended solfege #2 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
'''solfege #1 (-a = plain, -u = up, -o = down) [[mingen]] format'''
|-
|-
! colspan="2" |genspan (gen = P5)
! colspan="2" |genspan (gen = vvA1/^m2)
!-6
!2
!-5
!1
!-4
!0
!-3
!-1
!-2
!-2
!-1
!0
!1
!2
!3
!4
!5
!6
|-
|-
! rowspan="3" |up/dud
! rowspan="3" |Fa's


genchain
genchain
Line 13,200: Line 13,233:
perspan = 1
perspan = 1
!solfege
!solfege
|Thu
|Shu
|Fu
|Fa
|Du
|Mo
|Su
|Nu
|Ru
|Ra
|Lu
|Mu
|Tu
|Pu/She
|Fre
|Fle
|Ne
|The
|-
|-
!intervals
!intervals
|^m7
|^d5
|^4
|P4
|^1
|vM3
|^5
|^m3
|^M2
|M2
|^M6
|-
|^M3
!notes
|^M7
|^Gb
|^A4/vvd5
|F
|vvm2
|vE
|vvm6
|^Eb
|vvm3
|D
|vvm7
|-
|-
!notes
| colspan="7" |
|Bb
|^F
|^C
|^G
|^D
|^A
|^E
|^B
|^F#/vvGb
|vvDb
|vvAb
|vvEb
|vvBb
|-
|-
| colspan="15" |
! rowspan="3" |Da's
|-
! rowspan="3" |plain


genchain
genchain
Line 13,252: Line 13,261:
perspan = 0
perspan = 0
!solfege
!solfege
|Sha
|Ro
|Fra
|Fru
|Fla
|Na
|Tha
|Fa
|'''Da'''
|'''Da'''
|Sa
|To
|Ra
|Thu
|La
|Ma
|Ta
|Pa
|-
|-
!intervals
!intervals
|d5
|vM2
|m2
|^m2
|m6
|m3
|m7
|P4
|'''P1'''
|'''P1'''
|P5
|vM7
|M2
|^m7
|M6
|M3
|M7
|A4
|-
|-
!notes
!notes
|Gb
|vD
|Db
|^Db
|Ab
|Eb
|Bb
|F
|'''C'''
|'''C'''
|G
|vB
|D
|^Bb
|A
|E
|B
|F#
|-
|-
| colspan="15" |
| colspan="7" |
|-
|-
! rowspan="3" |down/dup
! rowspan="3" |Sa's


genchain
genchain
Line 13,304: Line 13,289:
perspan = -1
perspan = -1
!solfege
!solfege
|Ri
|Tha
|Li
|Lo
|Mi
|Flu
|Ti
|Sa
|Pi/Sho
|Po
|Fro
|-
|Flo
!intervals
|No
|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
|Tho
|Fo
|Fo
Line 13,317: Line 13,339:
|So
|So
|Ro
|Ro
|Lo
|Mo
|To
|Po/Shi
|Fri
|Fli
|Ni
|Thi
|-
|-
!intervals
!intervals
|^^M2
|^^M6
|^^M3
|^^M7
|^^A4/vd5
|vm2
|vm6
|vm3
|vm7
|vm7
|v4
|v4
Line 13,332: Line 13,354:
|v5
|v5
|vM2
|vM2
|vM6
|vM3
|vM7
|vA4/^^d5
|^^m2
|^^m6
|^^m3
|^^m7
|-
|-
!notes
!notes
|^^D
|^^A
|^^E
|^^B
|^^F#/vGb
|vDb
|vAb
|vEb
|vBb
|vBb
|vF
|vF
Line 13,347: Line 13,369:
|vG
|vG
|vD
|vD
|}
|vA
{| class="wikitable center-all"
|vE
|+
|vB
'''extended solfege #2 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|vF#/^^Gb
|-
|^^Db
! colspan="2" |genspan (gen = ^^A1/vm2)
|^^Ab
!6
|^^Eb
!5
|^^Bb
!4
|-
!3
| colspan="15" |
!2
!1
!0
!-1
!-2
!-3
!-4
!-5
!-6
|-
|-
! rowspan="3" |Fa's
! rowspan="3" |plain


genchain
genchain


perspan = 1
perspan = 0
!solfege
!solfege
|Thu
|Sha
|Li
|Fra
|Fla
|Fla
|Su
|Na
|Pi/Sho
|Tha
|Fa
|Fa
|Mu
|'''Da'''
|No
|Sa
|Ra
|Ra
|Fre
|La
|Do
|Ma
|Ta
|Ta
|The
|Pa
|-
|-
!intervals
!intervals
|^m7
|d5
|^^M6
|m2
|m6
|m6
|^5
|m3
|^^A4/vd5
|m7
|P4
|P4
|^M3
|'''P1'''
|vm3
|P5
|M2
|M2
|vvm2
|M6
|v1
|M3
|M7
|M7
|vvm7
|A4
|-
|-
!notes
!notes
|^Bb
|Gb
|^^A
|Db
|Ab
|Ab
|^G
|Eb
|^^F#/vGb
|Bb
|F
|F
|^E
|'''C'''
|vEb
|G
|D
|D
|vvDb
|A
|vC
|E
|B
|B
|vvBb
|F#
|-
|-
| colspan="15" |
| colspan="15" |
|-
|-
! rowspan="3" |Da's
! rowspan="3" |up


genchain
genchain


perspan = 0
perspan = -1
!solfege
!solfege
|Sha
|Re
|Fu
|Le
|Mi
|Me
|Na
|Te
|Pe/Shu
|Fru
|Flu
|Nu
|Thu
|Fu
|Du
|Su
|Ru
|Ru
|Fro
|'''Da'''
|Tu
|Tho
|La
|Fle
|So
|Pa
|-
|-
!intervals
!intervals
|d5
|vvM2
|vvM6
|vvM3
|vvM7
|vvA4/^d5
|^m2
|^m6
|^m3
|^m7
|^4
|^4
|^^M3
|^1
|m3
|^5
|^M2
|^M2
|vm2
|'''P1'''
|^M7
|vm7
|M6
|vvm6
|v5
|A4
|-
|-
!notes
!notes
|Gb
|vvD
|vvA
|vvE
|vvB
|vvF#/^Gb
|^Db
|^Ab
|^Eb
|^Bb
|^F
|^F
|^^E
|^C
|Eb
|^G
|^D
|^D
|vDb
|}
|'''C'''
{| class="wikitable center-all"
|^B
|+
|vBb
'''extended solfege #1 (-a = plain, -u = up, -o = down, -i = dup, -e = dud) [[mingen]] format'''
|A
|vvAb
|vG
|F#
|-
|-
| colspan="15" |
! colspan="2" |genspan (gen = vvA1/^m2)
!6
!5
!4
!3
!2
!1
!0
!-1
!-2
!-3
!-4
!-5
!-6
|-
|-
! rowspan="3" |Sa's
! rowspan="3" |Fa's


genchain
genchain


perspan = -1
perspan = 1
!solfege
!solfege
|Ri
|Tho
|Fra
|Le
|Du
|Fla
|Ti
|So
|Tha
|Pe/Shu
|Lu
|Fa
|Flo
|Mo
|Sa
|Nu
|Pu/She
|Ra
|Fo
|Fri
|Ma
|Du
|Ne
|Ta
|Ro
|Thi
|-
|-
!intervals
!intervals
|^^M2
|vm7
|m2
|vvM6
|m6
|v5
|vvA4/^d5
|P4
|vM3
|^m3
|M2
|^^m2
|^1
|^1
|^^M7
|M7
|m7
|^^m7
|^M6
|vm6
|P5
|^A4/vvd5
|v4
|M3
|vvm3
|vM2
|-
|-
!notes
!notes
|^^D
|vBb
|Db
|vvA
|Ab
|vG
|vvF#/^Gb
|F
|vE
|^Eb
|D
|^^Db
|^C
|^C
|^^B
|B
|Bb
|^^Bb
|^A
|-
|vAb
| colspan="15" |
|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
! rowspan="3" |Da's
!Ls-Ls-Ls
 
|Da
genchain
|'''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
perspan = 0
![[Genchain mode numbering|GMN]] name
!solfege
!scale
|Sha
!1sn
|Fo
!2nd
|Me
!
|Na
!3rd
|Ro
!4th
|Fru
!5th
|'''Da'''
!6th
|To
!
|Thu
!7th
|La
!8ve
|Fli
|Su
|Pa
|-
|-
!1st 3L6s
!intervals
!Lss-Lss-Lss
|d5
|Da
|v4
|'''Ra'''
|vvM3
|No
|m3
|Mu
|vM2
|'''Pu'''
|^m2
|Sa
|'''P1'''
|Flo
|vM7
|'''Tho'''
|^m7
|Tu
|M6
|Da
|^^m6
|^5
|A4
|-
|-
!2nd 3L6s
!notes
!sLs-sLs-sLs
|Gb
|Da
|vF
|'''Fro'''
|vvE
|'''No'''
|Eb
|Mu
|vD
|'''Fa'''
|^Db
|'''Sa'''
|'''C'''
|Flo
|vB
|'''Lu'''
|^Bb
|'''Tu'''
|A
|Da
|^^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
|-
|-
!3rd 3L6s
!notes
!ssL-ssL-ssL
|vvD
|Da
|Db
|Fro
|vC
|'''Ru'''
|vvB
|Mu
|Bb
|Fa
|vA
|'''Sho'''
|^Ab
|Flo
|G
|Lu
|vF#/^^Gb
|'''Tha'''
|^F
|Da
|E
|^^Eb
|^D
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
9L3s MOS scales (L = ^A1/vvm2, s = ^^A1/vm2)  
3L3s MOS scales (L = ^m3/vvA2, s = ^m2/vvA1)
![[Genchain mode numbering|GMN]] name
![[Genchain mode numbering|GMN]] name
!scale
!scale
!1sn
!1sn
! colspan="2" |2nds
!
! colspan="2" |3rds
!3rd
!4th
!
!tritone
!6th
!5th
!
! colspan="2" |6ths
! colspan="2" |7ths
!8ve
!8ve
|-
|-
!1st 9L3s
!1st 3L3s
!sLLL-sLLL-sLLL
!Ls-Ls-Ls
|Da
|Da
|'''Fre'''
|'''Nu'''
|Ra
|Mo
|No
|'''Sa'''
|Mu
|Flu
|'''Fo'''
|'''To'''
|Pu/She
|Sa
|Flo
|'''La'''
|Tho
|Tu
|Da
|Da
|-
|-
!2nd 9L3s
!2nd 3L3s
!LsLL-LsLL-LsLL
!sL-sL-sL
|Da
|Da
|'''Fro'''
|'''Fru'''
|'''Ra'''
|Mo
|No
|Mu
|'''Fa'''
|'''Fa'''
|'''Pu'''
|Flu
|Sa
|'''Lo'''
|Flo
|'''Lu'''
|'''Tho'''
|Tu
|Da
|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
|-
|-
!3rd 9L3s
!1st 3L6s
!LLsL-LLsL-LLsL
!Lss-Lss-Lss
|Da
|Da
|Fro
|'''Ra'''
|'''Ru'''
|Nu
|'''No'''
|Mo
|Mu
|'''Po'''
|Fa
|Sa
|'''Sho'''
|Flu
|'''Sa'''
|'''Thu'''
|Flo
|To
|Lu
|'''Tha'''
|'''Tu'''
|Da
|Da
|-
|-
!4th 9L3s
!2nd 3L6s
!LLLs-LLLs-LLLs
!sLs-sLs-sLs
|Da
|Da
|Fro
|'''Fru'''
|Ru
|'''Nu'''
|'''Na'''
|Mo
|Mu
|'''Fa'''
|'''Sa'''
|Flu
|'''Lo'''
|'''To'''
|Da
|-
!3rd 3L6s
!ssL-ssL-ssL
|Da
|Fru
|'''Ro'''
|Mo
|Fa
|Fa
|Pi/Sho
|'''Shu'''
|'''Su'''
|Flu
|Flo
|Lo
|Lu
|'''Tha'''
|Tha
|'''Ti'''
|Da
|Da
|}
|}
== #7 (P8, P4/3) third-4th ==
* G = vM2/^^m2 = ^~2 = 167¢ - c/3
* EI = 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"
{| class="wikitable center-all"
|+
|+
'''uniform solfege (-a = plain, -u = up, -o = down)'''
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
|-
|-
!genspan
!2nd 3L9s
!13
!sLss-sLss-sLss
!12
|Da
!11
|'''Fru'''
!10
|'''Ra'''
!9
|Nu
!8
|Mo
!7
|'''Fa'''
!6
|'''Po'''
!5
|Sa
!4
|Flu
!3
|'''Lo'''
!2
|'''Thu'''
!1
|To
!0
|Da
!-1
!-2
!-3
!-4
!-5
!-6
!-7
!-8
!-9
!-10
!-11
!-12
!-13
|-
|-
!solfege
!3rd 3L9s
|Tho
!ssLs-ssLs-ssLs
|Fla
|Da
|Shu
|Fo
|Na
|Fru
|Fru
|Do
|'''Ro'''
|Tha
|'''Nu'''
|Mo
|Fa
|'''Shu'''
|'''Sa'''
|Flu
|Flu
|So
|Lo
|'''Tha'''
|'''To'''
|Da
|-
!4th 3L9s
!sssL-sssL-sssL
|Da
|Fru
|Ro
|'''Na'''
|Mo
|Fa
|Fa
|Nu
|Pe/Shu
|Ro
|'''So'''
|'''Da'''
|Flu
|Thu
|Lo
|Lo
|Sa
|Tha
|Fu
|'''Te'''
|Mo
|Da
|Ra
|}
|Du
Similar tables can be made for 15- and 18-note scales.
|To
 
|La
=== Solfege #2 (P5 < 700¢) ===
|Su
{| class="wikitable center-all"
|Po
|+
|Ma
'''solfege #2 (-a = plain, -u = up, -o = down)'''
|Ru
|-
|-
!intervals
! colspan="2" |genspan (gen = P5)
|vm7
!-2
|m6
!-1
|^d5
!0
|v4
!1
|m3
!2
|^m2
|-
|v8
! 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
|m7
|^m6
|v5
|P4
|P4
|^m3
|vM2
|'''P1'''
|'''P1'''
|^m7
|vM6
|P5
|P5
|^4
|vM3
|M2
|M2
|^1
|vM7
|M6
|^5
|vA4
|M3
|^M2
|-
|-
!notes
!notes
|vBb
|Ab
|^Gb
|vF
|Eb
|^Db
|vC
|Bb
|Bb
|^Ab
|vG
|F
|F
|^Eb
|vD
|'''C'''
|'''C'''
|^Bb
|vA
|G
|G
|^F
|vE
|D
|D
|^C
|-
|vB
| colspan="7" |
|A
|-
|^G
! rowspan="3" |down
|vF#
 
|E
genchain
|^D
 
perspan = -1
!solfege
|Sho
|Fro
|Flo
|No
|Tho
|-
!intervals
|vd5
|vm2
|vm6
|vm3
|vm7
|-
!notes
|vGb
|vDb
|vAb
|vEb
|vBb
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
'''uniform solfege in melodic order (Po and Shu switch places when P5 > 13\22 = 709¢)'''
'''solfege #2 (-a = plain, -u = up, -o = down) [[mingen]] format'''
!index
|-
!0
! colspan="2" |genspan (gen = ^^A1/vm2)
!2
!1
!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
!0
!-7
!-1
!8
!1
!-6
!-13
!9
!2
!-5
!-12
!10
!3
!-4
!-11
!11
!4
!-3
!-10
!12
!5
!-2
!-2
!-9
!13
!6
!-1
!-8
!7
!0
|-
|-
! rowspan="3" |Fa's
genchain
perspan = 1
!solfege
!solfege
|Da
|Sho
|Du
|Fa
|Fru
|Mu
|Ro
|No
|Ra
|Ra
|-
!intervals
|vd5
|P4
|^M3
|vm3
|M2
|-
!notes
|vGb
|F
|^E
|vEb
|D
|-
| colspan="7" |
|-
! rowspan="3" |Da's
genchain
perspan = 0
!solfege
|Ru
|Ru
|Na
|Fro
|Nu
|'''Da'''
|Mo
|Tu
|Ma
|Fo
|Fa
|Fu
|Po
|Shu
|So
|Sa
|Su
|Fla
|Flu
|Lo
|La
|Tho
|Tho
|Tha
|Thu
|To
|Do
|Da
|-
|-
!intervals
!intervals
|P1
|^1
|^m2
|vM2
|M2
|^M2
|^M2
|m3
|vm2
|^m3
|'''P1'''
|vM3
|^M7
|M3
|v4
|P4
|^4
|vA4
|^d5
|v5
|P5
|^5
|m6
|^m6
|vM6
|M6
|vm7
|vm7
|m7
|^m7
|vM7
|v8
|P1
|-
|-
!notes
!notes
|C
|^C
|^Db
|vD
|D
|^D
|^D
|Eb
|vDb
|^Eb
|'''C'''
|vE
|^B
|E
|vF
|F
|^F
|vF#
|^Gb
|vG
|G
|^G
|Ab
|^Ab
|vA
|A
|vBb
|vBb
|-
| colspan="7" |
|-
! rowspan="3" |Sa's
genchain
perspan = -1
!solfege
|Tha
|Lu
|Flo
|Sa
|Pu
|-
!intervals
|m7
|^M6
|vm6
|P5
|^A4
|-
!notes
|Bb
|Bb
|^Bb
|^A
|vB
|vAb
|vC
|G
|C
|^F#
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
1L6s MOS scales (L = M2 = rhymes, s = vM2/^^m2 = no rhyme)
'''extended solfege #2 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
![[Genchain mode numbering|GMN]] name
!scale
!1sn
!2nd
!3rd
!4th
!5th
!6th
!7th
!8ve
|-
|-
!1st 1L6s
! colspan="2" |genspan (gen = P5)
!Lssssss
!-6
|Da
!-5
|'''Ra'''
!-4
|Mo
!-3
|Fu
!-2
|Sa
!-1
|Lo
!0
|Thu
!1
|Da
!2
!3
!4
!5
!6
|-
|-
!2nd 1L6s
! rowspan="3" |up/dud
!sLsssss
 
|Da
genchain
|'''Ro'''
 
|'''Mo'''
perspan = 1
!solfege
|Thu
|Fu
|Fu
|Sa
|Du
|Lo
|Su
|Thu
|Ru
|Da
|Lu
|Mu
|Tu
|Pu/She
|Fre
|Fle
|Ne
|The
|-
|-
!3rd 1L6s
!intervals
!ssLssss
|^m7
|Da
|^4
|Ro
|^1
|'''Nu'''
|^5
|'''Fu'''
|^M2
|Sa
|^M6
|Lo
|^M3
|Thu
|^M7
|Da
|^A4/vvd5
|vvm2
|vvm6
|vvm3
|vvm7
|-
|-
!4th 1L6s
!notes
!sssLsss
|Bb
|Da
|^F
|Ro
|^C
|Nu
|^G
|'''Fa'''
|^D
|'''Sa'''
|^A
|Lo
|^E
|Thu
|^B
|Da
|^F#/vvGb
|vvDb
|vvAb
|vvEb
|vvBb
|-
|-
!5th 1L6s
| colspan="15" |
!ssssLss
|Da
|Ro
|Nu
|Fa
|'''So'''
|'''Lo'''
|Thu
|Da
|-
|-
!6th 1L6s
! rowspan="3" |plain
!sssssLs
 
|Da
genchain
|Ro
 
|Nu
perspan = 0
!solfege
|Sha
|Fra
|Fla
|Na
|Tha
|Fa
|Fa
|So
|'''Da'''
|'''Flu'''
|Sa
|'''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
|Ra
|Mo
|La
|Fu
|Ma
|Sa
|Ta
|Lo
|Pa
|Thu
|Da
|-
|-
!2nd 7L1s
!intervals
!LsLLLLLL
|d5
|Da
|m2
|'''Ro'''
|m6
|'''Ra'''
|m3
|Mo
|m7
|Fu
|P4
|Sa
|'''P1'''
|Lo
|P5
|Thu
|M2
|Da
|M6
|M3
|M7
|A4
|-
|-
!3rd 7L1s
!notes
!LLsLLLLL
|Gb
|Da
|Db
|Ro
|Ab
|'''Nu'''
|Eb
|'''Mo'''
|Bb
|Fu
|F
|Sa
|'''C'''
|Lo
|G
|Thu
|D
|Da
|A
|E
|B
|F#
|-
|-
!4th 7L1s
| colspan="15" |
!LLLsLLLL
|Da
|Ro
|Nu
|'''Fa'''
|'''Fu'''
|Sa
|Lo
|Thu
|Da
|-
|-
!5th 7L1s
! rowspan="3" |down/dup
!LLLLsLLL
 
|Da
genchain
|Ro
 
|Nu
perspan = -1
|Fa
!solfege
|'''So'''
|Ri
|'''Sa'''
|Li
|Lo
|Mi
|Thu
|Ti
|Da
|Pi/Sho
|-
|Fro
!6th 7L1s
|Flo
!LLLLLsLL
|No
|Da
|Tho
|Ro
|Fo
|Nu
|Do
|Fa
|So
|So
|'''Flu'''
|'''Lo'''
|Thu
|Da
|-
!7th 7L1s
!LLLLLLsL
|Da
|Ro
|Ro
|Nu
|Fa
|So
|Flu
|'''Tha'''
|'''Thu'''
|Da
|-
|-
!8th 7L1s
!intervals
!LLLLLLLs
|^^M2
|Da
|^^M6
|Ro
|^^M3
|Nu
|^^M7
|Fa
|^^A4/vd5
|So
|vm2
|Flu
|vm6
|Tha
|vm3
|'''Do'''
|vm7
|Da
|v4
|v1
|v5
|vM2
|-
!notes
|^^D
|^^A
|^^E
|^^B
|^^F#/vGb
|vDb
|vAb
|vEb
|vBb
|vF
|vC
|vG
|vD
|}
|}
A similar table can be made for 7L8s, but it will lack the 1st and 15th modes.
== #8 (P8, P5/3) third-5th ==
* G = ^M2/vvm3 = 233¢ + c/3
* EI = 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"
{| class="wikitable center-all"
|+
|+
'''uniform solfege (-a = plain, -u = up, -o = down)'''
'''extended solfege #2 (-a = plain, -u = up, -o = down, -i = dup, -e = dud) [[mingen]] format'''
|-
|-
!-15
! colspan="2" |genspan (gen = ^^A1/vm2)
!-14
!6
!-13
!5
!-12
!4
!-11
!3
!-10
!2
!-9
!1
!-8
!0
!-7
!-1
!-2
!-3
!-4
!-5
!-6
!-6
!-5
|-
!-4
! rowspan="3" |Fa's
!-3
 
!-2
genchain
!-1
 
!0
perspan = 1
!1
!solfege
!2
|Thu
!3
|Li
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
!15
|-
|Fra
|Nu
|Sho
|Fla
|Fla
|Thu
|Su
|Fro
|Pi/Sho
|Na
|Fa
|Fu
|Mu
|Flo
|Tha
|Du
|No
|No
|Fa
|Ra
|Su
|Fre
|Tho
|'''Da'''
|Ru
|Fo
|Sa
|Lu
|Do
|Do
|Ra
|Mu
|So
|La
|Tu
|Ro
|Ma
|Pu
|Lo
|Ta
|Ta
|The
|-
|-
|m2
!intervals
|^m3
|^m7
|vd5
|^^M6
|m6
|m6
|^m7
|^5
|vm2
|^^A4/vd5
|m3
|P4
|^4
|^M3
|vm6
|m7
|^1
|vm3
|vm3
|P4
|^5
|vm7
|'''P1'''
|^M2
|v4
|P5
|^M6
|v8
|M2
|M2
|^M3
|vvm2
|v5
|v1
|M6
|^M7
|vM2
|M3
|^A4
|vM6
|M7
|M7
|vvm7
|-
|-
|Db
!notes
|^Eb
|^Bb
|vGb
|^^A
|Ab
|Ab
|^Bb
|^G
|vDb
|^^F#/vGb
|Eb
|F
|^F
|^E
|vAb
|Bb
|^C
|vEb
|vEb
|F
|D
|^G
|vvDb
|vBb
|'''C'''
|^D
|vF
|G
|^A
|vC
|vC
|D
|^E
|vG
|A
|^B
|vD
|E
|^F#
|vA
|B
|B
|}
|vvBb
{| 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
| colspan="15" |
!ssssL
|Da
|Ru
|Fo
|Sa
|'''Lu'''
|Da
|-
|-
!2nd 1L4s
! rowspan="3" |Da's
!sssLs
 
|Da
genchain
 
perspan = 0
!solfege
|Sha
|Fu
|Mi
|Na
|Ru
|Ru
|Fo
|Fro
|'''Sa'''
|'''Da'''
|'''Tho'''
|Tu
|Da
|-
!3rd 1L4s
!ssLss
|Da
|Ru
|'''Fo'''
|'''Su'''
|Tho
|Tho
|Da
|La
|Fle
|So
|Pa
|-
|-
!4th 1L4s
!intervals
!sLsss
|d5
|Da
|^4
|'''Ru'''
|^^M3
|'''Fa'''
|m3
|Su
|^M2
|Tho
|vm2
|Da
|'''P1'''
|^M7
|vm7
|M6
|vvm6
|v5
|A4
|-
!notes
|Gb
|^F
|^^E
|Eb
|^D
|vDb
|'''C'''
|^B
|vBb
|A
|vvAb
|vG
|F#
|-
|-
!5th 1L4s
| colspan="15" |
!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
! rowspan="3" |Sa's
!LLLLLs
 
|Da
genchain
|Ru
 
perspan = -1
!solfege
|Ri
|Fra
|Du
|Ti
|Tha
|Lu
|Flo
|Sa
|Pu/She
|Fo
|Fo
|Sa
|Ma
|Lu
|Ne
|'''Do'''
|Ro
|Da
|-
|-
!2nd 5L1s
!intervals
!LLLLsL
|^^M2
|Da
|m2
|Ru
|^1
|Fo
|^^M7
|Sa
|m7
|'''Lu'''
|^M6
|'''Tho'''
|vm6
|Da
|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
|-
|-
!3rd 5L1s
!1st 3L3s
!LLLsLL
!Ls-Ls-Ls
|Da
|Da
|Ru
|'''No'''
|Fo
|Mu
|'''Sa'''
|'''Sa'''
|'''Su'''
|Flo
|Tho
|'''Tu'''
|Da
|Da
|-
|-
!4th 5L1s
!2nd 3L3s
!LLsLLL
!sL-sL-sL
|Da
|Da
|Ru
|'''Fro'''
|'''Fo'''
|Mu
|'''Fa'''
|'''Fa'''
|Su
|Flo
|Tho
|'''Lu'''
|Da
|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
|-
|-
!5th 5L1s
!1st 3L6s
!LsLLLL
!Lss-Lss-Lss
|Da
|'''Ra'''
|No
|Mu
|'''Pu'''
|Sa
|Flo
|'''Tho'''
|Tu
|Da
|-
!2nd 3L6s
!sLs-sLs-sLs
|Da
|Da
|'''Ru'''
|'''Fro'''
|'''No'''
|'''No'''
|Fa
|Mu
|Su
|'''Fa'''
|Tho
|'''Sa'''
|Flo
|'''Lu'''
|'''Tu'''
|Da
|Da
|-
|-
!6th 5L1s
!3rd 3L6s
!sLLLLL
!ssL-ssL-ssL
|Da
|Da
|'''Du'''
|Fro
|No
|'''Ru'''
|Mu
|Fa
|Fa
|Su
|'''Sho'''
|Tho
|Flo
|Lu
|'''Tha'''
|Da
|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
* EI = v<sup>3</sup>M2 = 0¢
* ^ = (200¢ + 2c) / 3 (quite large, a literal third-tone)


MOS scales covered:
* 5 = 2L3s
* 7 = 2L5s
* 9 = 2L7s
* 11 = 2L9s
* etc. up to 19 = 17L2s
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
'''uniform solfege (-a = plain, -u = up, -o = down)'''
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
|-
|-
!18
!1st 9L3s
!...
!sLLL-sLLL-sLLL
!12
|Da
!11
|'''Fre'''
!10
|Ra
!9
|No
!8
|Mu
!7
|'''Fo'''
!6
|Pu/She
!5
|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
!4
!3
!3
Line 14,501: Line 14,571:
!-11
!-11
!-12
!-12
!...
!-13
!-18
|-
|-
|Sha
!solfege
|...
|Tho
|Fla
|Fla
|No
|Shu
|Flu
|Fo
|Na
|Na
|Tho
|Fru
|Nu
|Do
|Tha
|Tha
|Fo
|Flu
|Thu
|So
|Fa
|Fa
|Do
|Nu
|Fu
|Ro
|'''Da'''
|'''Da'''
|So
|Thu
|Du
|Lo
|Sa
|Sa
|Ro
|Fu
|Su
|Mo
|Ra
|Ra
|Lo
|Du
|Ru
|To
|La
|La
|Mo
|Su
|Lu
|Po
|Ma
|Ma
|...
|Ru
|Pa
|-
|-
|d5
!intervals
|...
|vm7
|m6
|m6
|vm3
|^d5
|^m6
|v4
|m3
|m3
|vm7
|^m2
|^m3
|v8
|m7
|m7
|v4
|^m6
|^m7
|v5
|P4
|P4
|v8
|^m3
|^4
|vM2
|'''P1'''
|'''P1'''
|v5
|^m7
|^1
|vM6
|P5
|P5
|vM2
|^4
|^5
|vM3
|M2
|M2
|vM6
|^1
|^M2
|vM7
|M6
|M6
|vM3
|^5
|^M6
|vA4
|M3
|M3
|...
|^M2
|A4
|-
|-
|Gb
!notes
|...
|vBb
|Ab
|Ab
|vEb
|^Gb
|^Ab
|vF
|Eb
|Eb
|vBb
|^Db
|^Eb
|vC
|Bb
|Bb
|vF
|^Ab
|^Bb
|vG
|F
|F
|vC
|^Eb
|^F
|vD
|'''C'''
|'''C'''
|vG
|^Bb
|^C
|vA
|G
|G
|vD
|^F
|^G
|vE
|D
|D
|vA
|^C
|^D
|vB
|A
|A
|vE
|^G
|^A
|vF#
|E
|E
|...
|^D
|F#
|}
|}
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"
{| class="wikitable center-all"
|+
|+
2L7s MOS scales (L = ^m3/vv4, s = vvM2/^1)
'''solfege in melodic order (Po and Shu switch places when P5 > 13\22 = 709¢)'''
![[Genchain mode numbering|GMN]] name
!index
!scale
!0
!0
!1
!1
Line 14,609: Line 14,675:
!8
!8
!9
!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
|-
|-
!1st 2L7s
!solfege
!ssssLsssL
|Da
|Da
|Du
|Du
|Fru
|Ro
|Ro
|Ra
|Ra
|'''Ru'''
|Ru
|So
|Na
|Sa
|Nu
|Su
|Mo
|Lo
|Ma
|Da
|Fo
|-
|Fa
!2nd 2L7s
!sssLssssL
|Da
|Du
|Ro
|Ra
|'''Fu'''
|So
|Sa
|Su
|'''Lo'''
|Da
|-
!3rd 2L7s
!sssLsssLs
|Da
|Du
|Ro
|'''Ra'''
|Fu
|Fu
|Po
|Shu
|So
|So
|Sa
|Sa
|Su
|Su
|'''Do'''
|Fla
|Da
|Flu
|-
|Lo
!4th 2L7s
|La
!ssLssssLs
|Tho
|Da
|Tha
|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
|Thu
|To
|Do
|Do
|Da
|Da
|-
|-
!7th 2L7s
!intervals
!sLsssLsss
|P1
|Da
|^1
|'''Du'''
|^m2
|Fo
|vM2
|Fa
|M2
|Fu
|^M2
|So
|m3
|'''Tha'''
|^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
|Thu
|Do
|Da
|Da
|-
|-
!8th 2L7s
!2nd 1L6s
!LssssLsss
!sLsssss
|Da
|Da
|'''Nu'''
|'''Ro'''
|Fo
|'''Mo'''
|Fa
|Fu
|Fu
|'''So'''
|Sa
|Tha
|Lo
|Thu
|Thu
|Do
|Da
|Da
|-
|-
!9th 2L7s
!3rd 1L6s
!LsssLssss
!ssLssss
|Da
|Ro
|'''Nu'''
|'''Fu'''
|Sa
|Lo
|Thu
|Da
|-
!4th 1L6s
!sssLsss
|Da
|Ro
|Nu
|'''Fa'''
|'''Sa'''
|Lo
|Thu
|Da
|-
!5th 1L6s
!ssssLss
|Da
|Da
|Ro
|Nu
|Nu
|Fo
|Fa
|Fa
|Fu
|'''So'''
|'''Tho'''
|'''Lo'''
|Tha
|Thu
|Thu
|Do
|Da
|-
!6th 1L6s
!sssssLs
|Da
|Ro
|Nu
|Fa
|So
|'''Flu'''
|'''Thu'''
|Da
|-
!7th 1L6s
!ssssssL
|Da
|Ro
|Nu
|Fa
|So
|Flu
|'''Tha'''
|Da
|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.
== <nowiki>#</nowiki>16 (P8/4, P5) quarter-8ve ==
There are two solfeges. Use solfege #1 if P5 > 700¢, and use solfege #2 if P5 < 700¢.
* P = ^m3/v<sup>3</sup>A2 (solfege #1) '''<u>or</u>''' vm3/^<sup>3</sup>A2 (solfege #2) = 300¢
* G = P5 = 700¢ + c '''<u>or</u>''' vvA1/^^m2 (solfege #1) '''<u>or</u>''' ^^A1/vvm2 (solfege #2) = 100¢ + c
* EI = ^<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"
{| class="wikitable center-all"
|+
|+
'''solfege #1 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
7L1s MOS scales (L = vM2/^^m2, s = ^1/vvA1 = same degree)
|-
![[Genchain mode numbering|GMN]] name
! colspan="2" |genspan (gen = P5)
!scale
!-3
!-2
!-1
!0
!0
!1
!1
!2
!2
!3
!3
!4
!5
!6
!7
!8
|-
|-
! rowspan="3" |up
!1st 7L1s
 
!sLLLLLLL
genchain
|Da
 
|'''Du'''
perspan = 1
|Ra
!solfege
|Mo
|Shu
|Fu
|Fru
|Sa
|Flu
|Lo
|Nu
|Thu
|Thu
|Da
|-
!2nd 7L1s
!LsLLLLLL
|Da
|'''Ro'''
|'''Ra'''
|Mo
|Fu
|Fu
|Du
|Sa
|Lo
|Thu
|Da
|-
|-
!intervals
!3rd 7L1s
|^d5
!LLsLLLLL
|^m2
|Da
|^m6
|Ro
|^m3
|'''Nu'''
|^m7
|'''Mo'''
|^4
|Fu
|^1
|Sa
|Lo
|Thu
|Da
|-
|-
!notes
!4th 7L1s
|^Gb
!LLLsLLLL
|^Db
|Da
|^Ab
|Ro
|^Eb
|Nu
|^Bb
|'''Fa'''
|^F
|'''Fu'''
|^C
|Sa
|Lo
|Thu
|Da
|-
|-
| colspan="9" |
!5th 7L1s
|-
!LLLLsLLL
! rowspan="3" |plain
|Da
 
|Ro
genchain
|Nu
 
perspan = 0
!solfege
|Na
|Tha
|Fa
|Fa
|'''Da'''
|'''So'''
|Sa
|'''Sa'''
|Ra
|Lo
|La
|Thu
|Da
|-
|-
!intervals
!6th 7L1s
|m3
!LLLLLsLL
|m7
|Da
|P4
|Ro
|'''P1'''
|Nu
|P5
|Fa
|M2
|So
|M6
|'''Flu'''
|'''Lo'''
|Thu
|Da
|-
|-
!notes
!7th 7L1s
|Eb
!LLLLLLsL
|Bb
|Da
|F
|Ro
|'''C'''
|Nu
|G
|Fa
|D
|So
|A
|Flu
|'''Tha'''
|'''Thu'''
|Da
|-
|-
| colspan="9" |
!8th 7L1s
|-
!LLLLLLLs
! rowspan="3" |down
|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:


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


perspan = -1
{| class="wikitable center-all"
!solfege
|+
|Do
'''solfege (-a = plain, -u = up, -o = down)'''
|So
|Ro
|Lo
|Mo
|To
|Po
|-
|-
!intervals
!-15
|v8
!-14
|v5
!-13
|vM2
!-12
|vM6
!-11
|vM3
!-10
|vM7
!-9
|vA4
!-8
|-
!-7
!notes
!-6
|vC
!-5
|vG
!-4
|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)'''
|-
! colspan="2" |genspan (gen = vvA1/^^m2)
!-3
!-3
!-2
!-2
Line 14,902: Line 15,052:
!2
!2
!3
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
!15
|-
|-
! rowspan="3" |Nu's
|Fra
 
genchain
 
perspan = 1
!solfege
|Do
|Fru
|Ro
|Nu
|Nu
|Mo
|Sho
|Fla
|Thu
|Fro
|Na
|Fu
|Fu
|Po
|Flo
|-
!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
|Tha
|Te
|Du
|No
|Fa
|Su
|Tho
|'''Da'''
|'''Da'''
|Fri
|Ru
|Fo
|Sa
|Lu
|Do
|Ra
|Ra
|Ni
|Mu
|So
|La
|Tu
|Ro
|Ma
|Pu
|Lo
|Ta
|-
|-
!intervals
|m2
|vvM6
|^m3
|vd5
|m6
|^m7
|vm2
|m3
|^4
|vm6
|m7
|m7
|vvM7
|^1
|vm3
|P4
|^5
|vm7
|'''P1'''
|'''P1'''
|^^m2
|^M2
|v4
|P5
|^M6
|v8
|M2
|M2
|^^m3
|^M3
|v5
|M6
|^M7
|vM2
|M3
|^A4
|vM6
|M7
|-
|-
!notes
|Db
|vvA
|^Eb
|vGb
|Ab
|^Bb
|vDb
|Eb
|^F
|vAb
|Bb
|Bb
|vvB
|^C
|vEb
|F
|^G
|vBb
|'''C'''
|'''C'''
|^^Db
|^D
|vF
|G
|^A
|vC
|D
|D
|^^Eb
|^E
|-
| 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
|vG
|^Ab
|A
|^B
|vD
|E
|^F#
|vA
|vA
|^Bb
|B
|vB
|}
|^C
{| 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
|-
|-
| colspan="9" |
!1st 1L4s
!ssssL
|Da
|Ru
|Fo
|Sa
|'''Lu'''
|Da
|-
|-
! rowspan="3" |Sa's
!2nd 1L4s
 
!sssLs
genchain
|Da
 
|Ru
perspan = ±2
|Fo
!solfege
|'''Sa'''
|Na
|'''Tho'''
|Me
|Da
|Fa
|Pe/Shi
|Sa
|Fli
|La
|-
|-
!intervals
!3rd 1L4s
|m3
!ssLss
|vvM3
|Da
|P4
|Ru
|vvA4/^^d5
|'''Fo'''
|P5
|'''Su'''
|^^m6
|Tho
|M6
|Da
|-
|-
!notes
!4th 1L4s
|Eb
!sLsss
|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
|Da
|'''Fri'''
|'''Ru'''
|Nu
|'''Fa'''
|'''Mo'''
|Su
|Pe/Shi
|Tho
|'''Sa'''
|Lo
|'''Thu'''
|Da
|Da
|-
|-
!2nd 4L4s
!5th 1L4s
!Ls-Ls-Ls-Ls
!Lssss
|Da
|Da
|'''Ro'''
|'''No'''
|Nu
|Fa
|'''Fa'''
|Su
|Pe/Shi
|Tho
|'''Flu'''
|Lo
|'''Te'''
|Da
|Da
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
8L4s MOS scales (L = vvA1/^^m2, s = vvvA1/^m2) using solfege #1
5L1s MOS scales (L = ^M2/vvm3, s = ^1/vvM2)
![[Genchain mode numbering|GMN]] name
![[Genchain mode numbering|GMN]] name
!scale
!scale
!1sn
!0
! colspan="2" |2nds
!1
! colspan="2" |3rds
!2
!4th
!3
!tritone
!4
!5th
!5
! colspan="2" |6ths
!6
! colspan="2" |7ths
|-
!8ve
!1st 5L1s
!LLLLLs
|Da
|Ru
|Fo
|Sa
|Lu
|'''Do'''
|Da
|-
|-
!1st 8L4s
!2nd 5L1s
!LLs-LLs-LLs-LLs
!LLLLsL
|Da
|Da
|Fri
|Ru
|'''Ra'''
|Fo
|Nu
|Mo
|'''Fu'''
|Pe/Shi
|Sa
|Sa
|'''Fli'''
|'''Lu'''
|Lo
|'''Tho'''
|Thu
|'''To'''
|Da
|Da
|-
|-
!2nd 8L4s
!3rd 5L1s
!LsL-LsL-LsL-LsL
!LLLsLL
|Da
|Da
|'''Fri'''
|Ru
|'''Ro'''
|Fo
|Nu
|'''Mo'''
|'''Fa'''
|Pe/Shi
|'''Sa'''
|'''Sa'''
|'''Flu'''
|'''Su'''
|Lo
|Tho
|'''Thu'''
|'''Te'''
|Da
|Da
|-
|-
!3rd 8L4s
!4th 5L1s
!sLL-sLL-sLL-sLL
!LLsLLL
|Da
|Da
|'''Fru'''
|Ru
|Ro
|'''Fo'''
|Nu
|'''Fa'''
|'''Me'''
|Su
|Fa
|Tho
|Pe/Shi
|'''So'''
|Flu
|Lo
|'''Tha'''
|Te
|Da
|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)
!5th 5L1s
!-3
!LsLLLL
!-2
|Da
!-1
|'''Ru'''
!0
|'''No'''
!1
|Fa
!2
|Su
!3
|Tho
|Da
|-
|-
! rowspan="3" |down
!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¢
* ^ = (200¢ + 2c) / 3 (quite large, a literal third-tone)


genchain
MOS scales covered:


perspan = 1
* 5 = 2L3s
!solfege
* 7 = 2L5s
|Sho
* 9 = 2L7s
|Fro
* 11 = 2L9s
|Flo
* 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
|No
|Flu
|Na
|Tho
|Tho
|Nu
|Tha
|Fo
|Fo
|Thu
|Fa
|Do
|Do
|-
|Fu
!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'''
|'''Da'''
|So
|Du
|Sa
|Sa
|Ro
|Su
|Ra
|Ra
|Lo
|Ru
|La
|La
|Mo
|Lu
|Ma
|...
|Pa
|-
|-
!intervals
|d5
|...
|m6
|vm3
|^m6
|m3
|m3
|vm7
|^m3
|m7
|m7
|v4
|^m7
|P4
|P4
|v8
|^4
|'''P1'''
|'''P1'''
|v5
|^1
|P5
|P5
|vM2
|^5
|M2
|M2
|vM6
|^M2
|M6
|M6
|vM3
|^M6
|M3
|...
|A4
|-
|-
!notes
|Gb
|...
|Ab
|vEb
|^Ab
|Eb
|Eb
|vBb
|^Eb
|Bb
|Bb
|vF
|^Bb
|F
|F
|vC
|^F
|'''C'''
|'''C'''
|vG
|^C
|G
|G
|vD
|^G
|D
|D
|vA
|^D
|A
|A
|-
|vE
| colspan="9" |
|^A
|-
|E
! rowspan="3" |up
|...
 
|F#
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"
{| class="wikitable center-all"
|+
|+
'''solfege #2 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
2L7s MOS scales (L = ^m3/vv4, s = vvM2/^1)
|-
![[Genchain mode numbering|GMN]] name
! colspan="2" |genspan (gen = ^^A1/vvm2)
!scale
!-3
!-2
!-1
!0
!0
!1
!1
!2
!2
!3
!3
!4
!5
!6
!7
!8
!9
|-
|-
! rowspan="3" |No's
!1st 2L7s
 
!ssssLsssL
genchain
|Da
 
perspan = 1
!solfege
|Du
|Du
|Fro
|Ro
|Ru
|Ra
|No
|'''Ru'''
|Mu
|So
|Fo
|Sa
|Pu
|Su
|Lo
|Da
|-
|-
!intervals
!2nd 2L7s
|^8
!sssLssssL
|vm2
|Da
|^M2
|Du
|vm3
|Ro
|^M3
|Ra
|v4
|'''Fu'''
|^A4
|So
|Sa
|Su
|'''Lo'''
|Da
|-
|-
!notes
!3rd 2L7s
|^C
!sssLsssLs
|vDb
|Da
|^D
|Du
|vEb
|Ro
|^E
|'''Ra'''
|vF
|Fu
|^F#
|So
|Sa
|Su
|'''Do'''
|Da
|-
|-
| colspan="9" |
!4th 2L7s
!ssLssssLs
|Da
|Du
|Ro
|'''Fa'''
|Fu
|So
|Sa
|'''Su'''
|Do
|Da
|-
|-
! rowspan="3" |Da's
!5th 2L7s
 
!ssLsssLss
genchain
|Da
 
|Du
perspan = 0
|'''Ro'''
!solfege
|Fa
|Li
|Fu
|Tha
|So
|Ti
|Sa
|'''Da'''
|'''Thu'''
|Fre
|Do
|Ra
|Da
|Ne
|-
|-
!intervals
!6th 2L7s
|^^M6
!sLssssLss
|m7
|Da
|^^M7
|Du
|'''P1'''
|'''Fo'''
|vvm2
|Fa
|M2
|Fu
|vvm3
|So
|'''Sa'''
|Thu
|Do
|Da
|-
|-
!notes
!7th 2L7s
|^^A
!sLsssLsss
|Bb
|Da
|^^B
|'''Du'''
|'''C'''
|Fo
|vvDb
|Fa
|D
|Fu
|vvEb
|So
|'''Tha'''
|Thu
|Do
|Da
|-
|-
| colspan="9" |
!8th 2L7s
!LssssLsss
|Da
|'''Nu'''
|Fo
|Fa
|Fu
|'''So'''
|Tha
|Thu
|Do
|Da
|-
|-
! rowspan="3" |Lu's
!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.


genchain
== #10 (P8/3, P4/2) third-8ve half-4th (incomplete) ==
* P = ^\M3 = v\4 = 400¢
* G = ^M2 = vm3 = 250¢ - c/2  '''<u>or</u>'''  \M2 = 150¢ + c/2
* EU = vvm2, \<sup>6</sup>A2, ^\<sup>3</sup>A1 = 0¢
* ^ = 50¢ - 2.5c
* / = 50¢ + 1.5c


perspan = -1
MOS scales covered:
!solfege
{| class="wikitable center-all"
|Sho
|+
|Su
'''solfege (-a = plain, -u = up, -o = down, i = lift, -e = drop)'''
|Flo
|-
|Lu
! colspan="2" |genspan (gen = ^M2 = vm3)
|Tho
!5
|Tu
!4
|Do
!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
!intervals
|vd5
|\4
|^5
|^\M2
|vm6
|\1
|^M6
|^\M6
|vm7
|\5
|^M7
|^\M3
|v1
|\M2
|^\M7
|\M6
|^\A4
|\M3
|-
|-
!notes
!notes
|vGb
|\F
|^G
|^\D
|vAb
|\C
|^A
|^\A
|vBb
|\G
|^B
|^\E
|vC
|\D
|^\B
|\A
|^\F#
|\E
|-
|-
| colspan="9" |
| colspan="13" |
|-
|-
! rowspan="3" |Sa's
! rowspan="3" |plain


genchain
genchain


perspan = ±2
perspan = 0
!solfege
!solfege
|Na
|Du / Fro
|Mi
|Tha
|Su / Flo
|Fa
|Fa
|Pi/She
|Ru / No
|'''Da'''
|Lu / Tho
|Sa
|Sa
|Fle
|Mu / Fo
|La
|Ra
|Tu / Do
|-
|-
!intervals
!intervals
|m3
|^1 = vm2
|^^M3
|m7
|^5 = vm6
|P4
|P4
|^^A4/vvd5
|^M2 = vm3
|'''P1'''
|^M6 = vm7
|P5
|P5
|vvm6
|^M3 = v4
|M6
|M2
|^M7 = v8
|-
|-
!notes
!notes
|Eb
|^C = vDb
|^^E
|Bb
|^G = vAb
|F
|F
|^^F#/vvGb
|^D = vEb
|'''C'''
|^A = vBb
|G
|G
|vvAb
|^E = vF
|A
|D
|}
|^B = vC
{| class="wikitable center-all"
|-
|+
| colspan="13" |
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
! rowspan="3" |lift
!sL-sL-sL-sL
 
|Da
genchain
|'''Fre'''
 
|No
perspan = -1
|'''Mu'''
!solfege
|Pi/She
|Fli
|'''Sa'''
|Showi
|Lu
|Ni
|'''Tho'''
|Frowi
|Da
|Thi
|Flowi
|Fi
|Nowi
|Di
|Thowi
|Si
|-
!intervals
|/m6
|v/d5
|/m3
|v/m2
|/m7
|v/m6
|/4
|v/m3
|/1
|v/m7
|/5
|-
|-
!2nd 4L4s
!notes
!Ls-Ls-Ls-Ls
|/Ab
|Da
|v/Gb
|'''Ru'''
|/Eb
|No
|v/Db
|'''Fa'''
|/Bb
|Pi/She
|v/Ab
|'''Flo'''
|/F
|Lu
|v/Eb
|'''Ti'''
|/C
|Da
|v/Bb
|/G
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
4L8s MOS scales (L = ^<sup>3</sup>A1/vm2, s = ^^A1/vvm2) using solfege #2
'''solfege (-a = plain, -u = up, -o = down, i = lift, -e = drop''' mingen format''')'''
![[Genchain mode numbering|GMN]] name
|-
!scale
! colspan="2" |genspan (gen = \M2 = v//A1)
!1sn
!-5
! colspan="2" |2nds
!-4
! colspan="2" |3rds
!-3
!4th
!-2
!tritone
!-1
!5th
!0
! colspan="2" |6ths
!1
! colspan="2" |7ths
!2
!8ve
!3
!4
!5
|-
|-
!1st 8L4s
! rowspan="3" |Sa's
!ssL-ssL-ssL-ssL
 
|Da
genchain
|Fre
 
|'''Ra'''
perspan = 1
|No
!solfege
|Mu
|Fli
|'''Fo'''
|Tha
|Pi/She
|De
|Frowi
|Ru / No
|Muwe
|Fi
|Sa
|Sa
|'''Fle'''
|Le
|Lu
|Thowi
|Tho
|Tu / Do
|'''Tu'''
|Da
|-
|-
!2nd 8L4s
!intervals
!sLs-sLs-sLs-sLs
|/m6
|Da
|m7
|'''Fre'''
|\1
|'''Ru'''
|v/m2
|No
|^M2 = vm3
|'''Mu'''
|^\M3
|'''Fa'''
|/4
|Pi/She
|P5
|'''Sa'''
|\M6
|'''Flo'''
|v/m7
|Lu
|^M7 = v8
|'''Tho'''
|-
|'''Ti'''
!notes
|Da
|/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" |
|-
|-
!3rd 8L4s
! rowspan="3" |Fa's
!Lss-Lss-Lss-Lss
 
|Da
genchain
|'''Fro'''
 
|Ru
perspan = -1
|No
!solfege
|'''Mi'''
|Du / Fro
|Ruwe
|Ni
|Fa
|Fa
|Pi/She
|Se
|'''Su'''
|Flowi
|Flo
|Lu / Tho
|Lu
|Tuwe
|'''Tha'''
|Di
|Ti
|Ra
|Da
|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
|}
|}
{| 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
== <nowiki>#</nowiki>16 (P8/4, P5) quarter-8ve ==
![[Genchain mode numbering|GMN]] name
There are two solfeges. Use solfege #1 if P5 > 700¢, and use solfege #2 if P5 < 700¢.
!scale
* P = ^m3/v<sup>3</sup>A2 (solfege #1) '''<u>or</u>''' vm3/^<sup>3</sup>A2 (solfege #2) = 300¢
!1sn
* G = P5 = 700¢ + c '''<u>or</u>''' vvA1/^^m2 (solfege #1) '''<u>or</u>''' ^^A1/vvm2 (solfege #2) = 100¢ + c
!
* EU = ^<sup>4</sup>d2 = 0¢
!2nd
* ^ = 3 '''⋅''' |c|
!
 
! colspan="2" |3rds
MOS scales covered:
!
 
!4th
* 8 = 4L4s (either solfege)
!tritone
* 12 = 8L4s (solfege #1 only) or 4L8s (solfege #2 only)
!5th
* 16 = 12L4s (solfege #2 only) or 4L12s (solfege #2 only)
!
 
! colspan="2" |6ths
=== Solfege #1 (P5 > 700¢) ===
!
{| class="wikitable center-all"
!7th
|+
!
'''solfege #1 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
!8ve
|-
! colspan="2" |genspan (gen = P5)
!-3
!-2
!-1
!0
!1
!2
!3
|-
|-
!1st 12L4s
! rowspan="3" |up
!LLLs-LLLs-LLLs-LLLs
 
|Da
genchain
|Fre
 
|Ra
perspan = 1
|'''Ne'''
!solfege
|No
|Shu
|Mu
|Fru
|Fo
|Flu
|'''Pu'''
|Nu
|Pi/She
|Thu
|Sa
|Fu
|Fle
|Du
|'''La'''
|Lu
|Tho
|Tu
|'''Do'''
|Da
|-
|-
!2nd 12L4s
!intervals
!LLsL-LLsL-LLsL-LLsL
|^d5
|Da
|^m2
|Fre
|^m6
|'''Ra'''
|^m3
|'''Ru'''
|^m7
|No
|^4
|Mu
|^1
|'''Fo'''
|-
|'''Fa'''
!notes
|Pi/She
|^Gb
|Sa
|^Db
|'''Fle'''
|^Ab
|'''Flo'''
|^Eb
|Lu
|^Bb
|Tho
|^F
|'''Tu'''
|^C
|'''Ti'''
|Da
|-
|-
!3rd 12L4s
| colspan="9" |
!LsLL-LsLL-LsLL-LsLL
|Da
|'''Fre'''
|'''Fro'''
|Ru
|No
|'''Mu'''
|'''Mi'''
|Fa
|Pi/She
|'''Sa'''
|'''Su'''
|Flo
|Lu
|'''Tho'''
|'''Tha'''
|Ti
|Da
|-
|-
!4th 12L4s
! rowspan="3" |plain
!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 ==
genchain
* G = ^m2 = v<sup>3</sup>AA1 = v\M2 = v/A1 = 125¢ - c/4
* EI's = ^<sup>4</sup>dd2, \\m2, ^^\d2, vv\A1, etc.
* ^ = 25¢ + 4.75c
* / = 50¢ - 2.5c


MOS scales covered:
perspan = 0
 
!solfege
* 8 = 1L7s
|Na
* 9 = 1L8s
|Tha
* 10 = 9L1s (all but 2 modes)
|Fa
* 11 = 10L1s (all but 4 modes) Sa must be > 3\5 = 720¢
|'''Da'''
* etc.
|Sa
 
|Ra
{| class="wikitable center-all"
|La
|+
'''uniform solfege (-a = plain, -u = up, -o = down, -i = lift, -e = drop)'''
|-
|-
!genspan
!intervals
!8
|m3
!7
|m7
!6
|P4
!5
|'''P1'''
!4
|P5
!3
|M2
!2
|M6
!1
|-
!0
!notes
!-1
|Eb
!-2
|Bb
!-3
|F
!-4
|'''C'''
!-5
|G
!-6
|D
!-7
|A
!-8
|-
| colspan="9" |
|-
|-
! rowspan="3" |down
genchain
perspan = -1
!solfege
!solfege
|Tha
|Do
|So
|Ro
|Lo
|Lo
|Si
Fle
|Shu
|Fa
|Mo
|Mo
|Ri
Ne
|Fru
|'''Da'''
|To
|To
|Li
The
|Flu
|Sa
|Po
|Po
|Mi
Fe
|Nu
|Ra
|-
|-
!intervals
!intervals
|m7
|v8
|v5
|vM2
|vM6
|vM6
|/5
\m6
|^d5
|P4
|vM3
|vM3
|/M2
\m3
|^m2
|'''P1'''
|vM7
|vM7
|/M6
\m7
|^m6
|P5
|vA4
|vA4
|/M3
\4
|^m3
|M2
|-
|-
!notes
!notes
|Bb
|vC
|vG
|vD
|vA
|vA
|/G
\Ab
|^Gb
|F
|vE
|vE
|/D
|vB
\Eb
|^Db
|'''C'''
|vB
|/A
\Bb
|^Ab
|G
|vF#
|vF#
|/E
|-
\F
| colspan="9" |
|^Eb
|-
|D
! 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"
{| class="wikitable center-all"
|+
|+
1L7s MOS scales (L = ^m3 = v/A2, s = ^m2 = v/A1)
'''solfege #1 (-a = plain, -u = up, -o = down, -i = dup, -e = dud) [[mingen]] format'''
![[Genchain mode numbering|GMN]] name
|-
!scale
! colspan="2" |genspan (gen = vvA1/^^m2)
!-3
!-2
!-1
!0
!0
!1
!1
!2
!2
!3
!3
!4
!5
!6
!7
!8
|-
|-
!1st 1L7s
! rowspan="3" |Nu's
!Lsssssss
 
|Da
genchain
|'''Nu'''
 
|Mi/Fe
perspan = 1
!solfege
|Do
|Fru
|Ro
|Nu
|Mo
|Fu
|Po
|Po
|Sa
|Flu
|Li/The
|To
|Da
|-
|-
!2nd 1L7s
!intervals
!sLssssss
|v8
|Da
|^m2
|'''Fru'''
|vM2
|'''Mi/Fe'''
|^m3
|Po
|vM3
|Sa
|^4
|Flu
|vA4
|Li/The
|To
|Da
|-
|-
!3rd 1L7s
!notes
!ssLsssss
|vC
|Da
|^Db
|Fru
|vD
|'''Ri/Ne'''
|^Eb
|'''Po'''
|vE
|Sa
|^F
|Flu
|vF#
|Li/The
|To
|Da
|-
|-
!4th 1L7s
| colspan="9" |
!sssLssss
|Da
|Fru
|Ri/Ne
|'''Mo'''
|'''Sa'''
|Flu
|Li/The
|To
|Da
|-
|-
!5th 1L7s
! rowspan="3" |Da's
!ssssLsss
 
|Da
genchain
|Fru
 
|Ri/Ne
perspan = 0
|Mo
!solfege
|'''Fa'''
|Le
|'''Flu'''
|Tha
|Li/The
|Te
|To
|'''Da'''
|Da
|Fri
|Ra
|Ni
|-
|-
!6th 1L7s
!intervals
!sssssLss
|vvM6
|Da
|m7
|Fru
|vvM7
|Ri/Ne
|'''P1'''
|Mo
|^^m2
|Fa
|M2
|'''Shu'''
|^^m3
|'''Li/The'''
|To
|Da
|-
|-
!7th 1L7s
!notes
!ssssssLs
|vvA
|Da
|Bb
|Fru
|vvB
|Ri/Ne
|'''C'''
|Mo
|^^Db
|Fa
|D
|Shu
|^^Eb
|'''Si/Fle'''
|-
|'''To'''
| colspan="9" |
|Da
|-
|-
!8th 1L7s
! rowspan="3" |Lo's
!sssssssL
 
|Da
genchain
|Fru
 
|Ri/Ne
perspan = -1
|Mo
!solfege
|Fa
|Shu
|Shu
|Si/Fle
|So
|'''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
|Flu
|Li/The
|Lo
|Thu
|To
|To
|Da
|Du
|-
|-
!2nd 1L8s
!intervals
!sLsssssss
|^d5
|Da
|v5
|'''Fru'''
|^m6
|'''Nu'''
|vM6
|Mi/Fe
|^m7
|Po
|vM7
|Sa
|^1
|Flu
|Li/The
|To
|Da
|-
|-
!3rd 1L8s
!notes
!ssLssssss
|^Gb
|Da
|vG
|Fru
|^Ab
|'''Ri/Ne'''
|vA
|'''Mi/Fe'''
|^Bb
|Po
|vB
|^C
|-
| colspan="9" |
|-
! rowspan="3" |Sa's
 
genchain
 
perspan = ±2
!solfege
|Na
|Me
|Fa
|Pe/Shi
|Sa
|Sa
|Flu
|Fli
|Li/The
|La
|To
|-
|Da
!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
|-
|-
!4th 1L8s
!1st 4L4s
!sssLsssss
!sL-sL-sL-sL
|Da
|Da
|Fru
|'''Fri'''
|Ri/Ne
|Nu
|'''Mo'''
|'''Mo'''
|'''Po'''
|Pe/Shi
|Sa
|'''Sa'''
|Flu
|Lo
|Li/The
|'''Thu'''
|To
|Da
|Da
|-
|-
!5th 1L8s
!2nd 4L4s
!ssssLssss
!Ls-Ls-Ls-Ls
|Da
|Da
|Fru
|'''Ro'''
|Ri/Ne
|Nu
|Mo
|'''Fa'''
|'''Fa'''
|'''Sa'''
|Pe/Shi
|Flu
|Li/The
|To
|Da
|-
!6th 1L8s
!sssssLsss
|Da
|Fru
|Ri/Ne
|Mo
|Fa
|'''Shu'''
|'''Flu'''
|'''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
|Lo
|'''Tha'''
|'''Te'''
|Da
|Da
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
9L1s MOS scales (L = ^m2 = v/A1, s = vA1 = ^\m2) Sa must be > 5\9 = 667¢
8L4s MOS scales (L = vvA1/^^m2, s = vvvA1/^m2) using solfege #1
![[Genchain mode numbering|GMN]] name
![[Genchain mode numbering|GMN]] name
!scale
!scale
!1sn
!1sn
!2nd
! colspan="2" |2nds
!
! colspan="2" |3rds
!3rd
!4th
!4th
!tritone
!tritone
!5th
!5th
!6th
! colspan="2" |6ths
!
! colspan="2" |7ths
!7th
!8ve
!8ve
|-
|-
!1st 9L1s
!1st 8L4s
!sLLLLLLLLL
!LLs-LLs-LLs-LLs
|Da
|Da
|'''???'''
|Fri
|Ra
|'''Ra'''
|Nu
|Nu
|Mi/Fe
|Mo
|Po
|'''Fu'''
|Pe/Shi
|Sa
|Sa
|Flu
|'''Fli'''
|Li/The
|Lo
|To
|Thu
|'''To'''
|Da
|Da
|-
|-
!2nd 9L1s
!2nd 8L4s
!LsLLLLLLLL
!LsL-LsL-LsL-LsL
|Da
|Da
|'''Fru'''
|'''Fri'''
|'''Ra'''
|'''Ro'''
|Nu
|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'''
|'''Mo'''
|'''Mi/Fe'''
|Po
|Sa
|Flu
|Li/The
|To
|Da
|-
!5th 9L1s
!LLLLsLLLLL
|Da
|Fru
|Ri/Ne
|Mo
|'''Fa'''
|'''Fa'''
|'''Po'''
|Pe/Shi
|Sa
|'''Sa'''
|Flu
|'''Flu'''
|Li/The
|Lo
|To
|'''Thu'''
|'''Te'''
|Da
|Da
|-
|-
!6th 9L1s
!3rd 8L4s
!LLLLLsLLLL
!sLL-sLL-sLL-sLL
|Da
|Da
|Fru
|'''Fru'''
|Ri/Ne
|Ro
|Mo
|Nu
|'''Me'''
|Fa
|Fa
|'''Shu'''
|Pe/Shi
|'''Sa'''
|'''So'''
|Flu
|Flu
|Li/The
|Lo
|To
|'''Tha'''
|Te
|Da
|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
* EI = v<sup>4</sup>A1 = 0¢
* ^ = 25¢ + 1.75c
 
MOS scales covered:
 
* 7 = 6L1s
* 13 = 7L6s


=== Solfege #2 (P5 < 700¢) ===
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
'''uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
'''solfege #2 (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
|-
!genspan
! colspan="2" |genspan (gen = P5)
!-20
!...
!-12
!-11
!-10
!-9
!-8
!-7
!-6
!-5
!-4
!-3
!-3
!-2
!-2
Line 16,186: Line 16,307:
!2
!2
!3
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!...
!20
|-
|-
! 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
!solfege
|Fra
|...
|Na
|Na
|Fo
|Shi
Se
|Flu
|Tha
|Tha
|Do
|Fri
Re
|Nu
|Fa
|Fa
|So
|Fli
Le
|Thu
|'''Da'''
|'''Da'''
|Ro
|Ni
Me
|Fu
|Sa
|Sa
|Lo
|Thi
Te
|Du
|Ra
|Ra
|Mo
|Fi
Pe
|Su
|La
|La
|...
|Ta
|-
|-
!intervals
!intervals
|m2
|...
|m3
|m3
|v4
|~5
|^m6
|m7
|m7
|v8
|~2
|^m3
|P4
|P4
|v5
|~6
|^m7
|'''P1'''
|'''P1'''
|vM2
|~3
|^4
|P5
|P5
|vM6
|~7
|^1
|M2
|M2
|vM3
|~4
|^5
|M6
|M6
|...
|M7
|-
|-
!notes
!notes
|Db
|...
|Eb
|Eb
|vF
|^^Gb
vvG
|^Ab
|Bb
|Bb
|vC
|^^Db
vvD
|^Eb
|F
|F
|vG
|^^Ab
vvA
|^Bb
|'''C'''
|'''C'''
|vD
|^^Eb
vvE
|^F
|G
|G
|vA
|^^Bb
vvB
|^C
|D
|D
|vE
|^^F
vvF#
|^G
|A
|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
| colspan="9" |
!LLLLLLs
|Da
|Ro
|Ni/Me
|Fu
|Sa
|Lo
|'''Thi/Te'''
|Da
|-
|-
!2nd 6L1s
! rowspan="3" |up
!LLLLLsL
 
|Da
genchain
|Ro
 
|Ni/Me
perspan = -1
|Fu
!solfege
|Sa
|Du
|'''Lo'''
|Su
|'''Thu'''
|Ru
|Da
|Lu
|Mu
|Tu
|Pu
|-
|-
!3rd 6L1s
!intervals
!LLLLsLL
|^8
|Da
|^5
|Ro
|^M2
|Ni/Me
|^M6
|Fu
|^M3
|'''Sa'''
|^M7
|'''Fli/Le'''
|^A4
|Thu
|Da
|-
|-
!4th 6L1s
!notes
!LLLsLLL
|^C
|Da
|^G
|Ro
|^D
|Ni/Me
|^A
|'''Fu'''
|^E
|'''So'''
|^B
|Fli/Le
|^F#
|Thu
|Da
|-
|-
!5th 6L1s
| colspan="9" |
!LLsLLLL
|Da
|Ro
|'''Ni/Me'''
|'''Fa'''
|So
|Fli/Le
|Thu
|Da
|-
|-
!6th 6L1s
! rowspan="3" |dup/dud
!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 ==
genchain
* G = ^M3 = v<sup>3</sup>4 = v\4 = v/d4 = ^//m3 = 425¢ - c/4
* EI's = v<sup>4</sup>dd3, \\A1, vv\m2, vv/d2, etc.
* ^ = 25¢ - 4.25c
* / = 50¢ + 3.5c
MOS scales covered:


* 5 = 3L2s
perspan = ±2
* 8 = 3L5s
!solfege
* 11 = 3L8s
|Li
 
|Mi
{| class="wikitable center-all"
|Ti
|+
|Pi/She
'''uniform solfege (-a = plain, -u = up, -o = down, -i = lift, -e = drop)'''
|Fre
|Fle
|Ne
|-
|-
!genspan
!intervals
!10
|^^M6
!9
|^^M3
!8
|^^M7
!7
|^^A4/vvd5
!6
|vvm2
!5
|vvm6
!4
|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
!3
!2
!1
!0
!-1
!-2
!-3
!-4
!-5
!-6
!-7
!-8
!-9
!-10
|-
|-
! rowspan="3" |No's
genchain
perspan = 1
!solfege
!solfege
|Shi
|Du
Se
|Fro
|Ru
|Ru
|Tha
|No
|Sho
|Fri
Re
|Lu
|Fa
|Fro
|Fli
Le
|Mu
|Mu
|'''Da'''
|Fo
|Flo
|Ni
Me
|Tu
|Sa
|No
|Thi
Te
|Pu
|Pu
|Ra
|Tho
|Fi
Pe
|-
|-
!intervals
!intervals
|~5
|^8
|vm2
|^M2
|^M2
|m7
|vm3
|vd5
|^M3
|~2
|v4
|^M6
|P4
|vm2
|~6
|^M3
|'''P1'''
|vm6
|~3
|^M7
|P5
|vm3
|~7
|^A4
|^A4
|M2
|vm7
|~4
|-
|-
!notes
!notes
|/Gb
|^C
\G
|vDb
|^D
|^D
|Bb
|vEb
|vGb
|/Db
\D
|^A
|F
|vDb
|/Ab
\A
|^E
|^E
|'''C'''
|vF
|vAb
|/Eb
\E
|^B
|G
|vEb
|/Bb
\B
|^F#
|^F#
|D
|-
|vBb
| colspan="9" |
|/F
|-
\F#
! rowspan="3" |Da's
|}
 
genchain


{| class="wikitable center-all"
perspan = 0
|+
!solfege
3L2s MOS scales (L = ~3 = ^^A2 = vvd4, s = vm2 = ^/1)
|Li
![[Genchain mode numbering|GMN]] name
|Tha
!scale
|Ti
!0
|'''Da'''
!1
|Fre
!2
|Ra
!3
|Ne
!4
!5
|-
|-
!1st 3L2s
!intervals
!LLsLs
|^^M6
|Da
|m7
|Ni/Me
|^^M7
|'''Sa'''
|'''P1'''
|Flo
|vvm2
|Tu
|M2
|Da
|vvm3
|-
|-
!2nd 3L2s
!notes
!LsLLs
|^^A
|Da
|Bb
|Ni/Me
|^^B
|'''Mu'''
|'''C'''
|Flo
|vvDb
|'''Tu'''
|D
|Da
|vvEb
|-
|-
!3rd 3L2s
| colspan="9" |
!LsLsL
|Da
|'''Ni/Me'''
|Mu
|Flo
|'''Fli/Le'''
|Da
|-
|-
!4th 3L2s
! rowspan="3" |Lu's
!sLLsL
 
|Da
genchain
|'''Fro'''
 
|Mu
perspan = -1
|'''Flo'''
!solfege
|Fli/Le
|Sho
|Da
|Su
|-
!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
|Flo
|Thi/Te
|Lu
|Tho
|Tu
|Tu
|Da
|Do
|-
!intervals
|vd5
|^5
|vm6
|^M6
|vm7
|^M7
|v1
|-
|-
!2nd 3L5s
!notes
!LssLsLss
|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
|Da
|'''Fre'''
|No
|No
|Ni/Me
|'''Mu'''
|'''Mu'''
|Sa
|Pi/She
|Flo
|'''Sa'''
|'''Thi/Te'''
|Lu
|Tu
|'''Tho'''
|Da
|Da
|-
|-
!3rd 3L5s
!2nd 4L4s
!LssLssLs
!Ls-Ls-Ls-Ls
|Da
|Da
|'''No'''
|'''Ru'''
|Ni/Me
|No
|Mu
|'''Fa'''
|Sa
|Pi/She
|Flo
|'''Flo'''
|'''Fli/Le'''
|Lu
|Tu
|'''Ti'''
|Da
|Da
|-
|}
!4th 3L5s
{| class="wikitable center-all"
!sLsLssLs
|+
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
|Da
|'''Fro'''
|Fre
|Ni/Me
|'''Ra'''
|No
|Mu
|Mu
|'''Sa'''
|'''Fo'''
|Flo
|Pi/She
|Fli/Le
|Sa
|Tu
|'''Fle'''
|Lu
|Tho
|'''Tu'''
|Da
|Da
|-
|-
!5th 3L5s
!2nd 8L4s
!sLssLsLs
!sLs-sLs-sLs-sLs
|Da
|Da
|Fro
|'''Fre'''
|Ni/Me
|'''Ru'''
|Mu
|No
|'''Mu'''
|'''Fa'''
|'''Fa'''
|Flo
|Pi/She
|Fli/Le
|'''Sa'''
|'''Tu'''
|'''Flo'''
|Lu
|'''Tho'''
|'''Ti'''
|Da
|Da
|-
|-
!6th 3L5s
!3rd 8L4s
!sLssLssL
!Lss-Lss-Lss-Lss
|Da
|Da
|Fro
|'''Fro'''
|'''Ni/Me'''
|Ru
|Mu
|No
|'''Mi'''
|Fa
|Fa
|Pi/She
|'''Su'''
|Flo
|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
|Lu
|'''Tha'''
|Ti
|Da
|Da
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
3L8s MOS scales (L = M2 = rhymes, s = vm2 = ^/1 = ^\A1 = no rhyme)
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
![[Genchain mode numbering|GMN]] name
!scale
!scale
!1sn
!1sn
!
!2nd
!2nd
!
!
!
! colspan="2" |3rds
!
!
!4th
!4th
!tritone
!5th
!5th
!
!
! colspan="2" |6ths
!
!
!7th
!
!
!7th
!8ve
!8ve
|-
|-
!1st 3L8s
!1st 12L4s
!LssLsssLsss
!LLLs-LLLs-LLLs-LLLs
|Da
|Da
|Fre
|Ra
|Ra
|'''Ne'''
|No
|No
|Ni/Me
|Mu
|'''Fi/Pe'''
|Fo
|Pu
|'''Pu'''
|Pi/She
|Sa
|Sa
|Flo
|Fle
|'''La'''
|Lu
|Tho
|Tho
|Thi/Te
|Tu
|Tu
|'''Do'''
|Da
|Da
|-
|-
!2nd 3L8s
!2nd 12L4s
!LsssLssLsss
!LLsL-LLsL-LLsL-LLsL
|Da
|Ra
|No
|Ni/Me
|'''Mu'''
|Pu
|Sa
|Flo
|'''Tho'''
|Thi/Te
|Tu
|Da
|-
!3rd 3L8s
!LsssLsssLss
|Da
|Da
|Fre
|'''Ra'''
|'''Ra'''
|'''Ru'''
|No
|No
|Ni/Me
|Mu
|Mu
|Pu
|'''Fo'''
|'''Fa'''
|Pi/She
|Sa
|Sa
|Flo
|'''Fle'''
|'''Fli/Le'''
|'''Flo'''
|Thi/Te
|Lu
|Tu
|Tho
|'''Tu'''
|'''Ti'''
|Da
|Da
|-
|-
!4th 3L8s
!3rd 12L4s
!sLssLsssLss
!LsLL-LsLL-LsLL-LsLL
|Da
|Da
|'''Fre'''
|'''Fro'''
|'''Fro'''
|Ru
|No
|No
|Ni/Me
|'''Mu'''
|Mu
|'''Mi'''
|'''Pu'''
|Fa
|Sa
|Pi/She
|'''Sa'''
|'''Su'''
|Flo
|Flo
|Fli/Le
|Lu
|Thi/Te
|'''Tho'''
|Tu
|'''Tha'''
|Ti
|Da
|Da
|-
|-
!5th 3L8s
!4th 12L4s
!sLsssLssLss
!sLLL-sLLL-sLLL-sLLL
|Da
|Da
|'''Du'''
|Fro
|Fro
|Ru
|No
|No
|Ni/Me
|'''Na'''
|Mu
|Mi
|'''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
|Fa
|Pi/She
|'''Sho'''
|'''Sho'''
|Su
|Flo
|Flo
|Fli/Le
|Lu
|Lu
|'''Tu'''
|'''Li'''
|Tha
|Ti
|Da
|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)'''
|-
|-
!9th 3L8s
!genspan
!ssLsssLsssL
!8
|Da
!7
|Fro
!6
|Fri/Re
!5
|'''Ni/Me'''
!4
|Mu
!3
|Fa
!2
|Sho
!1
|Flo
!0
|Fli/Le
!-1
|Lu
!-2
|'''Tha'''
!-3
|Da
!-4
!-5
!-6
!-7
!-8
|-
|-
!10th 3L8s
!solfege
!sssLssLsssL
|Tha
|Da
|Lo
|Fro
|Si
|Fri/Re
Fle
|'''Ru'''
|Shu
|Mu
|Fa
|Fa
|Sho
|Mo
|'''Flo'''
|Ri
|Fli/Le
Ne
|Lu
|Fru
|Tha
|'''Da'''
|Da
|To
|Li
The
|Flu
|Sa
|Po
|Mi
Fe
|Nu
|Ra
|-
|-
!11th 3L8s
!intervals
!sssLsssLssL
|m7
|Da
|vM6
|Fro
|/5
|Fri/Re
\m6
|Ru
|^d5
|Mu
|P4
|Fa
|vM3
|Sho
|/M2
|'''Shi/Se'''
\m3
|Fli/Le
|^m2
|Lu
|'''P1'''
|Tha
|vM7
|Da
|/M6
|}
\m7
== <nowiki>#</nowiki>20 (P8, P12/4) quarter-12th (incomplete) ==
|^m6
 
|P5
* G = v4 = ^<sup>3</sup>M3 = 475¢ + c/4
|vA4
* EI = v<sup>4</sup>m2 = 0¢
|/M3
* ^ = 25¢ - 1.25c
\4
 
|^m3
MOS scales covered:
|M2
 
|-
* 5 = 3L2s
!notes
* 7 = 5L2s (if P5 > 3\5 = 720¢)
|Bb
* 8 = 5L3s
|vA
* 13 = 5L8s
|/G
* 18 = 5L13s
\Ab
 
|^Gb
|F
|vE
|/D
\Eb
|^Db
|'''C'''
|vB
|/A
\Bb
|^Ab
|G
|vF#
|/E
\F
|^Eb
|D
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
'''uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
1L7s MOS scales (L = ^m3 = v/A2, s = ^m2 = v/A1)
|-
![[Genchain mode numbering|GMN]] name
!-17
!scale
!...
!-12
!-11
!-10
!-9
!-8
!-7
!-6
!-5
!-4
!-3
!-2
!-1
!0
!0
!1
!1
Line 16,907: Line 16,915:
!7
!7
!8
!8
!9
!10
!11
!12
!...
!17
|-
|-
|Nu
!1st 1L7s
|...
!Lsssssss
|Na
|Da
|Flo
|'''Nu'''
|Di
|Mi/Fe
Fre
|Po
|Fu
|Sa
|Tha
|Flu
|No
|Li/The
|Si
|To
Fle
|Da
|Du
|-
|Fa
!2nd 1L7s
|Tho
!sLssssss
|Ri
|Da
Ne
|'''Fru'''
|Su
|'''Mi/Fe'''
|'''Da'''
|Po
|Fo
|Li
The
|Ru
|Sa
|Sa
|Do
|Flu
|Mi
|Li/The
Fe
|To
|Lu
|Da
|Ra
|So
|Ti
De
|Mu
|La
|...
|Lo
|-
|-
|^m3
!3rd 1L7s
|...
!ssLsssss
|m3
|Da
|vm6
|Fru
|^^1
|'''Ri/Ne'''
vvm2
|'''Po'''
|^4
|Sa
|m7
|Flu
|vm3
|Li/The
|^^5
|To
vvm6
|Da
|^1
|P4
|vm7
|^^M2
vvm3
|^5
|'''P1'''
|v4
|^^M6
vvm7
|^M2
|P5
|v8
|^^M3
vv4
|^M6
|M2
|v5
|^^M7
vv8
|^M3
|M6
|...
|vM6
|-
|-
|^Eb
!4th 1L7s
|...
!sssLssss
|Eb
|Da
|vAb
|Fru
|^^C
|Ri/Ne
vvDb
|'''Mo'''
|^F
|'''Sa'''
|Bb
|Flu
|vEb
|Li/The
|^^G
|To
vvAb
|Da
|^C
|-
|F
!5th 1L7s
|vBb
!ssssLsss
|^^D
|Da
vvEb
|Fru
|^G
|Ri/Ne
|'''C'''
|Mo
|vF
|'''Fa'''
|^^A
|'''Flu'''
vvBb
|Li/The
|^D
|To
|G
|Da
|vC
|^^E
vvF
|^A
|D
|vG
|^^B
vvC
|^E
|A
|...
|vA
|}
 
 
== <nowiki>#</nowiki>22 (P8/2, M2/4) half-8ve quarter-tone ==
* P = ^^4 = vv5 = 600¢
* G = ^1 = v<sup>3</sup>M2 = 50¢ + c/2
* EI = 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"
|+
'''uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
|-
|
!6th 1L7s
!-11
!sssssLss
!-10
|Da
!-9
|Fru
!-8
|Ri/Ne
!-7
|Mo
!-6
|Fa
!-5
|'''Shu'''
!-4
|'''Li/The'''
!-3
|To
!-2
|Da
!-1
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
|-
|-
! rowspan="3" |Da's
!7th 1L7s
 
!ssssssLs
gen-
|Da
 
|Fru
chain
|Ri/Ne
 
|Mo
per-span = 0
|Fa
|Shu
|Shu
|Shi
|'''Si/Fle'''
Fle
|'''To'''
|Flo
|Da
|Fla
|-
|Flu
!8th 1L7s
|Fli
!sssssssL
The
|Da
|Tho
|Fru
|Tha
|Ri/Ne
|Thu
|Thi
De
|Do
|'''Da'''
|Du
|Di
Re
|Ro
|Ra
|Ru
|Ri
Me
|Mo
|Mo
|Ma
|Fa
|Mu
|Shu
|Mi
|Si/Fle
Pe
|'''Lo'''
|Po
|Da
|-
|}
|^d5
{| class="wikitable center-all"
|^^d5
|+
vvm6
1L8s MOS scales (L = M2 = rhymes, s = ^m2 = v/A1)
|vm6
![[Genchain mode numbering|GMN]] name
|m6
!scale
|^m6
!1sn
|^^m6
!2nd
vvm7
!
|vm7
!3rd
|m7
!4th
|^m7
!5th
|^^m7
!6th
vv8
!
|v8
!7th
|'''P1'''
!8ve
|^1
|^^1
vvM2
|vM2
|M2
|^M2
|^^M2
vvM3
|vM3
|M3
|^M3
|^^M3
vvA4
|vA4
|-
|-
|^Gb
!1st 1L8s
|^^Gb
!Lssssssss
vvAb
|Da
|vAb
|'''Ra'''
|Ab
|Nu
|^Ab
|Mi/Fe
|^^Ab
|Po
vvBb
|Sa
|vBb
|Flu
|Bb
|Li/The
|^Bb
|To
|^^Bb
|Da
vvC
|vC
|'''C'''
|^C
|^^C
vvD
|vD
|D
|^D
|^^D
vvE
|vE
|E
|^E
|^^E
vvF#
|vF#
|-
|-
| colspan="24" |
!2nd 1L8s
!sLsssssss
|Da
|'''Fru'''
|'''Nu'''
|Mi/Fe
|Po
|Sa
|Flu
|Li/The
|To
|Da
|-
|-
! rowspan="3" |Sa's
!3rd 1L8s
 
!ssLssssss
gen-
|Da
 
chain
 
per-span = ±1
|Fro
|Fra
|Fru
|Fru
|Fri
|'''Ri/Ne'''
Ne
|'''Mi/Fe'''
|No
|Po
|Na
|Nu
|Ni
Fe
|Fo
|Fa
|Fu
|Fi
Se
|So
|Sa
|Sa
|Su
|Flu
|Si
|Li/The
Le
|Lo
|La
|Lu
|Li
Te
|To
|To
|Ta
|Da
|Tu
|-
|-
|vm2
!4th 1L8s
|m2
!sssLsssss
|^m2
|Da
|^^m2
|Fru
vvm3
|Ri/Ne
|vm3
|'''Mo'''
|m3
|'''Po'''
|^m3
|Sa
|^^m3
|Flu
vv4
|Li/The
|v4
|To
|P4
|Da
|^4
|^^4
vv5
|v5
|P5
|^5
|^^5
vvM6
|vM6
|M6
|^M6
|^^M6
vvM7
|vM7
|M7
|^M7
|-
|-
|vDb
!5th 1L8s
|Db
!ssssLssss
|^Db
|Da
|^^Db
|Fru
vvEb
|Ri/Ne
|vEb
|Mo
|Eb
|'''Fa'''
|^Eb
|'''Sa'''
|^^Eb
|Flu
vvF
|Li/The
|vF
|To
|F
|Da
|^F
|-
|^^F
!6th 1L8s
vvG
!sssssLsss
|vG
|Da
|G
|Fru
|^G
|Ri/Ne
|^^G
|Mo
vvA
|Fa
|vA
|'''Shu'''
|A
|'''Flu'''
|^A
|Li/The
|^^A
|To
vvB
|Da
|vB
|-
|B
!7th 1L8s
|^B
!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"
{| class="wikitable center-all"
|+
|+
2L20s MOS scales (L = m2 = rhymes, s = ^1/v<sup>3</sup>M2 = no rhyme)
9L1s MOS scales (L = ^m2 = v/A1, s = vA1 = ^\m2) Sa must be > 5\9 = 667¢
![[Genchain mode numbering|GMN]] name
![[Genchain mode numbering|GMN]] name
!scale
!scale
!0
!1sn
!1
!2nd
!2
!
!3
!3rd
!4
!4th
!5
!tritone
!6
!5th
!7
!6th
!8
!
!9
!7th
!10
!8ve
!11
!12
!13
!14
!15
!16
!17
!18
!19
!20
!21
!22
|-
|-
!1st 2L20s
!1st 9L1s
!ssssssssssL x2
!sLLLLLLLLL
|Da
|Da
|Du
|'''???'''
|Di
Re
|Ro
|Ra
|Ra
|Ru
|Nu
|Ri
|Mi/Fe
Me
|Po
|Mo
|Ma
|Mu
|'''Mi'''
'''Pe'''
|Fi
Se
|So
|Sa
|Sa
|Su
|Flu
|Si
|Li/The
Le
|Lo
|La
|Lu
|Li
Te
|To
|To
|'''Ta'''
|Da
|Da
|-
|-
!2nd 2L20s
!2nd 9L1s
!sssssssssLs x2
!LsLLLLLLLL
|Da
|'''Fru'''
|'''Ra'''
|Nu
|Mi/Fe
|Po
|Sa
|Flu
|Li/The
|To
|Da
|Da
|Du
|-
|Di
!3rd 9L1s
Re
!LLsLLLLLLL
|Ro
|Da
|Ra
|Fru
|Ru
|'''Ri/Ne'''
|Ri
|'''Nu'''
Me
|Mi/Fe
|Mo
|Po
|Ma
|Sa
|'''Mu'''
|Flu
|'''Fu'''
|Li/The
|Fi
|To
Se
|Da
|So
|-
!4th 9L1s
!LLLsLLLLLL
|Da
|Fru
|Ri/Ne
|'''Mo'''
|'''Mi/Fe'''
|Po
|Sa
|Sa
|Su
|Flu
|Si
|Li/The
Le
|To
|Lo
|La
|Lu
|Li
Te
|'''To'''
|'''Do'''
|Da
|Da
|-
|-
!3rd 2L20s
!5th 9L1s
!ssssssssLss x2
!LLLLsLLLLL
|Da
|Da
|Du
|Fru
|Di
|Ri/Ne
Re
|Ro
|Ra
|Ru
|Ri
Me
|Mo
|Mo
|'''Ma'''
|'''Fa'''
|'''Fa'''
|Fu
|'''Po'''
|Fi
Se
|So
|Sa
|Sa
|Su
|Flu
|Si
|Li/The
Le
|To
|Lo
|La
|Lu
|'''Li'''
'''Te'''
|'''Thi'''
'''De'''
|Do
|Da
|Da
|-
|-
!4th 2L20s
!6th 9L1s
!sssssssLsss x2
!LLLLLsLLLL
|Da
|Da
|Du
|Fru
|Di
|Ri/Ne
Re
|Mo
|Ro
|Fa
|Ra
|'''Shu'''
|Ru
|'''Sa'''
|Ri
|Flu
Me
|Li/The
|'''Mo'''
|To
|'''Fo'''
|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
|Fa
|Fu
|Shu
|Fi
|Si/Fle
Se
|'''Lo'''
|So
|'''Li/The'''
|Sa
|To
|Su
|Si
Le
|Lo
|La
|'''Lu'''
|'''Thu'''
|Thi
De
|Do
|Da
|Da
|-
|-
!5th 2L20s
!9th 9L1s
!ssssssLssss x2
!LLLLLLLLsL
|Da
|Da
|Du
|Fru
|Di
|Ri/Ne
Re
|Mo
|Ro
|Ra
|Ru
|'''Ri'''
'''Me'''
|'''Ni'''
'''Fe'''
|Fo
|Fa
|Fa
|Fu
|Shu
|Fi
|Si/Fle
Se
|So
|Sa
|Su
|Si
Le
|Lo
|Lo
|'''La'''
|'''Tha'''
|'''Tha'''
|Thu
|'''To'''
|Thi
De
|Do
|Da
|Da
|-
|-
!6th 2L20s
!10th 9L1s
!sssssLsssss x2
!LLLLLLLLLs
|Da
|Da
|Du
|Fru
|Di
|Ri/Ne
Re
|Mo
|Ro
|Ra
|'''Ru'''
|'''Nu'''
|Ni
Fe
|Fo
|Fa
|Fa
|Fu
|Shu
|Fi
|Si/Fle
Se
|Lo
|So
|Sa
|Su
|Si
Le
|'''Lo'''
|'''Tho'''
|Tha
|Tha
|Thu
|'''???'''
|Thi
De
|Do
|Da
|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
{| class="wikitable center-all"
|+
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
|-
!7th 2L20s
!genspan
!ssssLssssss x2
!-20
|Da
!...
|Du
!-12
|Di
!-11
Re
!-10
|Ro
!-9
|'''Ra'''
!-8
|'''Na'''
!-7
|Nu
!-6
|Ni
!-5
Fe
!-4
|Fo
!-3
|Fa
!-2
|Fu
!-1
|Fi
!0
Se
!1
|So
!2
|Sa
!3
|Su
!4
|'''Si'''
!5
'''Le'''
!6
|'''Fli'''
!7
'''The'''
!8
|Tho
!9
|Tha
!10
|Thu
!11
|Thi
!12
De
!...
|Do
!20
|Da
|-
|-
!8th 2L20s
!solfege
!sssLsssssss x2
|Fra
|Da
|...
|Du
|Di
Re
|'''Ro'''
|'''No'''
|Na
|Na
|Nu
|Ni
Fe
|Fo
|Fo
|Fa
|Shi
|Fu
|Fi
Se
Se
|So
|Flu
|Sa
|'''Su'''
|'''Flu'''
|Fli
The
|Tho
|Tha
|Tha
|Thu
|Thi
De
|Do
|Do
|Da
|Fri
|-
Re
!9th 2L20s
!ssLssssssss x2
|Da
|Du
|'''Di'''
'''Re'''
|'''Fri'''
'''Ne'''
|No
|Na
|Nu
|Nu
|Ni
Fe
|Fo
|Fa
|Fa
|Fu
|Fi
Se
|So
|So
|'''Sa'''
|'''Fla'''
|Flu
|Fli
|Fli
The
Le
|Tho
|Tha
|Thu
|Thu
|'''Da'''
|Ro
|Ni
Me
|Fu
|Sa
|Lo
|Thi
|Thi
De
Te
|Do
|Du
|Da
|Ra
|-
|Mo
!10th 2L20s
!sLsssssssss x2
|Da
|'''Du'''
|'''Fru'''
|Fri
Ne
|No
|Na
|Nu
|Ni
Fe
|Fo
|Fa
|Fu
|Fi
|Fi
Se
Pe
|'''So'''
|Su
|'''Flo'''
|La
|Fla
|...
|Flu
|Ta
|Fli
The
|Tho
|Tha
|Thu
|Thi
De
|Do
|Da
|-
|-
!11th 2L20s
!intervals
!Lssssssssss x2
|m2
|Da
|...
|'''Fra'''
|m3
|Fru
|v4
|Fri
|~5
Ne
|^m6
|No
|m7
|Na
|v8
|Nu
|~2
|Ni
|^m3
Fe
|P4
|Fo
|v5
|Fa
|~6
|Fu
|^m7
|Fi
|'''P1'''
Se
|vM2
|'''Shi'''
|~3
'''Fle'''
|^4
|Flo
|P5
|Fla
|vM6
|Flu
|~7
|Fli
|^1
The
|M2
|Tho
|vM3
|Tha
|~4
|Thu
|^5
|Thi
|M6
De
|...
|Do
|M7
|Da
|}
 
== <nowiki>#</nowiki>33 (P8/5, P5) fifth-8ve ==
If P5 > 3\5 = 720¢, swap up with down, and dup with dud, to get solfege #2.
* P = ^^M2 = v<sup>3</sup>m3 = 240¢
* G = P5 = 700¢ + c '''<u>or</u>''' ^1 = v<sup>4</sup>m2 = 20¢ - c
* EI = 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
!notes
|vDb
|Db
|vAb
|...
|vEb
|Eb
|vBb
|vF
|vF
|^^Gb
vvG
|^Ab
|Bb
|vC
|vC
|^^Db
vvD
|^Eb
|F
|vG
|vG
|^^Ab
vvA
|^Bb
|'''C'''
|vD
|vD
|^^Eb
vvE
|^F
|G
|vA
|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
|^^Bb
vvB
|^C
|D
|vE
|^^F
|^^F
|^^C
vvF#
|^^G
|^G
|^^D
|A
|^^A
|...
|^^E
|B
|^^B
|}
|^^F#
{| 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
|-
|-
| colspan="10" |
!1st 6L1s
|
!LLLLLLs
|Da
|Ro
|Ni/Me
|Fu
|Sa
|Lo
|'''Thi/Te'''
|Da
|-
|-
! rowspan="3" |plain
!2nd 6L1s
 
!LLLLLsL
genchain
|Da
 
|Ro
perspan = 0
|Ni/Me
!solfege
|Fu
|Fla
|Na
|Tha
|Fa
|'''Da'''
|Sa
|Sa
|Ra
|'''Lo'''
|La
|'''Thu'''
|Ma
|Da
|-
!3rd 6L1s
!LLLLsLL
|Da
|Ro
|Ni/Me
|Fu
|'''Sa'''
|'''Fli/Le'''
|Thu
|Da
|-
|-
!intervals
!4th 6L1s
|m6
!LLLsLLL
|m3
|Da
|m7
|Ro
|P4
|Ni/Me
|'''P1'''
|'''Fu'''
|P5
|'''So'''
|M2
|Fli/Le
|M6
|Thu
|M3
|Da
|-
|-
!notes
!5th 6L1s
|Ab
!LLsLLLL
|Eb
|Da
|Bb
|Ro
|F
|'''Ni/Me'''
|'''C'''
|'''Fa'''
|G
|So
|D
|Fli/Le
|A
|Thu
|E
|Da
|-
|-
| colspan="10" |
!6th 6L1s
|
!LsLLLLL
|Da
|'''Ro'''
|'''Nu'''
|Fa
|So
|Fli/Le
|Thu
|Da
|-
|-
! rowspan="3" |dud
!7th 6L1s
!sLLLLLL
|Da
|'''Fri/Re'''
|Nu
|Fa
|So
|Fli/Le
|Thu
|Da
|}


genchain
== <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


perspan = -1
{| class="wikitable center-all"
!solfege
|+
|She
'''solfege (-a = plain, -u = up, -o = down, -i = lift, -e = drop)'''
|Fre
|Fle
|Ne
|The
|Fe
|De
|Se
|Re
|-
|-
!intervals
!genspan
|vvd5
!10
|vvm2
!9
|vvm6
!8
|vvm3
!7
|vvm7
!6
|vv4
!5
|vv8
!4
|vv5
!3
|vvM2
!2
|-
!1
!notes
!0
|vvGb
!-1
|vvDb
!-2
|vvAb
!-3
|vvEb
!-4
|vvBb
!-5
|vvF
!-6
|vvC
!-7
|vvG
!-8
|vvD
!-9
|-
!-10
| colspan="10" |
|
|-
|-
! rowspan="3" |up
genchain
perspan = -2
!solfege
!solfege
|Nu
|Shi
|Thu
Se
|Fu
|Du
|Su
|Ru
|Ru
|Tha
|Sho
|Fri
Re
|Lu
|Lu
|Fa
|Fro
|Fli
Le
|Mu
|Mu
|'''Da'''
|Flo
|Ni
Me
|Tu
|Tu
|Sa
|No
|Thi
Te
|Pu
|Ra
|Tho
|Fi
Pe
|-
|-
!intervals
!intervals
|^m3
|~5
|^m7
|^4
|^1
|^5
|^M2
|^M2
|m7
|vd5
|~2
|^M6
|^M6
|P4
|vm2
|~6
|^M3
|^M3
|'''P1'''
|vm6
|~3
|^M7
|^M7
|P5
|vm3
|~7
|^A4
|M2
|vm7
|~4
|-
|-
!notes
!notes
|^Eb
|/Gb
|^Bb
\G
|^F
|^C
|^G
|^D
|^D
|Bb
|vGb
|/Db
\D
|^A
|^A
|F
|vDb
|/Ab
\A
|^E
|^E
|'''C'''
|vAb
|/Eb
\E
|^B
|^B
|G
|vEb
|/Bb
\B
|^F#
|D
|vBb
|/F
\F#
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
3L2s MOS scales (L = ~3 = ^^A2 = vvd4, s = vm2 = ^/1)
|-
![[Genchain mode numbering|GMN]] name
! colspan="2" |genspan (gen = ^1)
!scale
!0
!1
!2
!3
!4
!4
!3
!5
!2
!1
!0
!-1
!-2
!-3
!-4
|-
|-
! rowspan="3" |Fa's
!1st 3L2s
 
!LLsLs
genchain
|Da
 
|Ni/Me
perspan = 2
|'''Sa'''
!solfege
|Flo
|She
|Tu
|Fi
|Da
|Fu
|Fa
|Fo
|Fe
|Mi
|Mu
|Ma
|-
|-
!intervals
!2nd 3L2s
|vvd5
!LsLLs
|^^4
|Da
|^4
|Ni/Me
|P4
|'''Mu'''
|v4
|Flo
|vv4
|'''Tu'''
|^^M3
|Da
|^M3
|M3
|-
|-
!notes
!3rd 3L2s
|vvGb
!LsLsL
|^^F
|Da
|^F
|'''Ni/Me'''
|F
|Mu
|vF
|Flo
|vvF
|'''Fli/Le'''
|^^E
|Da
|^E
|E
|-
|-
| colspan="11" |
!4th 3L2s
!sLLsL
|Da
|'''Fro'''
|Mu
|'''Flo'''
|Fli/Le
|Da
|-
|-
! rowspan="3" |Ra's
!5th 3L2s
 
!sLsLL
genchain
|Da
 
|Fro
perspan = 1
|Mu
!solfege
|'''Fa'''
|Nu
|Fli/Le
|Na
|Da
|No
|}
|Ne
{| class="wikitable center-all"
|Ri
|+
|Ru
3L5s MOS scales (L = vm3 = ^/M2, s = vm2 = ^/1)
|Ra
![[Genchain mode numbering|GMN]] name
|Ro
!scale
|Re
!plain
!down
!mid
!up
!plain
!down
!mid
!up
!plain
|-
|-
!intervals
!1st 3L5s
|^m3
!LsLssLss
|m3
|Da
|vm3
|No
|vvm3
|Ni/Me
|^^M2
|'''Pu'''
|^M2
|Sa
|M2
|Flo
|vM2
|Thi/Te
|vvM2
|Tu
|Da
|-
|-
!notes
!2nd 3L5s
|^Eb
!LssLsLss
|Eb
|Da
|vEb
|No
|vvEb
|Ni/Me
|^^D
|'''Mu'''
|^D
|Sa
|D
|Flo
|vD
|'''Thi/Te'''
|vvD
|Tu
|Da
|-
|-
| colspan="11" |
!3rd 3L5s
|-
!LssLssLs
! rowspan="3" |Da's
|Da
 
|'''No'''
genchain
|Ni/Me
 
|Mu
perspan = 0
|Sa
!solfege
|Flo
|Fro
|'''Fli/Le'''
|Fre
|Di
|Du
|'''Da'''
|Do
|De
|Ti
|Tu
|Tu
|Da
|-
|-
!intervals
!4th 3L5s
|vm2
!sLsLssLs
|vvm2
|Da
|^^1
|'''Fro'''
|^1
|Ni/Me
|'''P1'''
|Mu
|v8
|'''Sa'''
|vv8
|Flo
|^^M7
|Fli/Le
|^M7
|Tu
|Da
|-
|-
!notes
!5th 3L5s
|vDb
!sLssLsLs
|vvDb
|Da
|^^C
|Fro
|^C
|Ni/Me
|'''C'''
|Mu
|vC
|'''Fa'''
|vvC
|Flo
|^^B
|Fli/Le
|^B
|'''Tu'''
|Da
|-
|-
| colspan="11" |
!6th 3L5s
!sLssLssL
|Da
|Fro
|'''Ni/Me'''
|Mu
|Fa
|Flo
|Fli/Le
|'''Lu'''
|Da
|-
|-
! rowspan="3" |Tha's
!7th 3L5s
 
!ssLsLssL
genchain
|Da
 
|Fro
perspan = -1
|'''Fri/Re'''
!solfege
|Mu
|Thi
|Fa
|Thu
|'''Flo'''
|Tha
|Fli/Le
|Tho
|The
|Li
|Lu
|Lu
|La
|Da
|Lo
|-
|-
!intervals
!8th 3L5s
|^^m7
!ssLssLsL
|^m7
|Da
|m7
|Fro
|vm7
|Fri/Re
|vvm7
|Mu
|^^M6
|Fa
|^M6
|'''Sho'''
|M6
|Fli/Le
|vM6
|Lu
|-
|Da
!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"
{| class="wikitable center-all"
|+
|+
5L5s MOS scales (L = ^M2/v<sup>4</sup>m3, s = ^1)
3L8s MOS scales (L = M2 = rhymes, s = vm2 = ^/1 = ^\A1 = no rhyme)
![[Genchain mode numbering|GMN]] name
![[Genchain mode numbering|GMN]] name
!scale
!scale
!1sn
!1sn
!2nd
!
!
!
!2nd
!
!
!4th
!4th
!5th
!
!
!
!5th
!
!
!7th
!7th
!
!8ve
!8ve
|-
|-
!1st 5L5s
!1st 3L8s
!Ls-Ls-Ls-Ls-Ls
!LssLsssLsss
|Da
|Da
|'''Ru'''
|Ra
|Ri
|No
|'''Fe'''
|Ni/Me
|Fo
|'''Fi/Pe'''
|'''Sa'''
|Pu
|Su
|Sa
|'''Li'''
|Flo
|The
|Tho
|'''Do'''
|Thi/Te
|Tu
|Da
|Da
|-
|-
!2nd 5L5s
!2nd 3L8s
!sL-sL-sL-sL-sL
!LsssLssLsss
|Da
|Da
|'''Du'''
|Ra
|Ri
|No
|'''Ne'''
|Ni/Me
|Fo
|'''Mu'''
|'''Fa'''
|Pu
|Su
|Sa
|'''Si'''
|Flo
|The
|'''Tho'''
|'''Tho'''
|Thi/Te
|Tu
|Da
|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
!3rd 3L8s
!Lss-Lss-Lss-Lss-Lss
!LsssLsssLss
|Da
|Da
|'''Ra'''
|'''Ra'''
|Ru
|No
|Ri
|Ni/Me
|'''Mi'''
|Mu
|Fe
|Pu
|Fo
|'''So'''
|Sa
|Sa
|Su
|Flo
|'''Lu'''
|'''Fli/Le'''
|Li
|Thi/Te
|The
|Tu
|'''De'''
|Do
|Da
|Da
|-
|-
!2nd 5L10s
!4th 3L8s
!sLs-sLs-sLs-sLs-sLs
!sLssLsssLss
|Da
|Da
|'''Du'''
|'''Fro'''
|'''Ru'''
|No
|Ri
|Ni/Me
|'''Ne'''
|Mu
|'''Fe'''
|'''Pu'''
|Fo
|Sa
|'''Fa'''
|Flo
|'''Sa'''
|Fli/Le
|Su
|Thi/Te
|'''Si'''
|Tu
|'''Li'''
|Da
|The
|-
|'''Tho'''
!5th 3L8s
|'''Do'''
!sLsssLssLss
|Da
|Fro
|No
|Ni/Me
|Mu
|'''Fa'''
|Sa
|Flo
|Fli/Le
|'''Thi/Te'''
|Tu
|Da
|Da
|-
|-
!3rd 5L10s
!6th 3L8s
!ssL-ssL-ssL-ssL-ssL
!sLsssLsssLs
|Da
|Da
|Du
|Fro
|'''Di'''
|Ri
|Ne
|'''No'''
|'''No'''
|Fo
|Ni/Me
|Mu
|Fa
|Fa
|'''Fu'''
|Sa
|Su
|Flo
|Si
|Fli/Le
|'''Fle'''
|'''Lu'''
|The
|Tu
|Tho
|'''Tha'''
|Da
|Da
|}
== <nowiki>#</nowiki>34 (P8, P4/5) fifth-4th ==
* G = ^^m2 = v<sup>3</sup>A1 = 100¢ - c/5
* EI = ^<sup>5</sup>d2 = 0¢
* ^ = 2.4c
MOS scales covered:
* 10 = 1L9s
* 11 = 1L10s
* 12 = 1L11s (all but 2 modes)
{| class="wikitable center-all"
|+
'''uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
|-
!genspan
!7th 3L8s
!10
!ssLssLsssLs
!9
|Da
!8
|Fro
!7
|'''Fri/Re'''
!6
|Ni/Me
!5
|Mu
!4
|Fa
!3
|'''Sa'''
!2
|Flo
!1
|Fli/Le
!0
|Lu
!-1
|Tu
!-2
|Da
!-3
!-4
!-5
!-6
!-7
!-8
!-9
!-10
|-
|-
!solfege
!8th 3L8s
|Tha
!ssLsssLssLs
|Le
|Da
|Flu
|Fro
|So
|Fri/Re
|Shi
|Ni/Me
|Mu
|Fa
|Fa
|Me
|'''Sho'''
|Nu
|Flo
|Ro
|Fli/Le
|Fri
|Lu
|'''Da'''
|'''Tu'''
|Te
|Da
|Thu
|Lo
|Fli
|Sa
|Pe
|Fu
|Mo
|Ni
|Ra
|-
|-
!intervals
!9th 3L8s
|m7
!ssLsssLsssL
|vvM6
|Da
|^m6
|Fro
|v5
|Fri/Re
|^^d5
|'''Ni/Me'''
|P4
|Mu
|vvM3
|Fa
|^m3
|Sho
|vM2
|Flo
|^^m2
|Fli/Le
|'''P1'''
|Lu
|vvM7
|'''Tha'''
|^m7
|Da
|vM6
|^^m6
|P5
|vvA4
|^4
|vM3
|^^m3
|M2
|-
|-
!notes
!10th 3L8s
|Bb
!sssLssLsssL
|vvA
|Da
|^Ab
|Fro
|vG
|Fri/Re
|^^Gb
|'''Ru'''
|F
|Mu
|vvE
|Fa
|^Eb
|Sho
|vD
|'''Flo'''
|^^Db
|Fli/Le
|'''C'''
|Lu
|vvB
|Tha
|^Bb
|Da
|vA
|-
|^^Ab
!11th 3L8s
|G
!sssLsssLssL
|vvF#
|Da
|^F
|Fro
|vE
|Fri/Re
|^^Eb
|Ru
|D
|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"
{| class="wikitable center-all"
|+
|+
1L9s MOS scales (L = ^^m3/v<sup>3</sup>A2, s = ^^m2/v<sup>3</sup>A1)
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
![[Genchain mode numbering|GMN]] name
|-
!scale
!-17
!...
!-12
!-11
!-10
!-9
!-8
!-7
!-6
!-5
!-4
!-3
!-2
!-1
!0
!0
!1
!1
Line 18,333: Line 18,061:
!9
!9
!10
!10
!11
!12
!...
!17
|-
|-
!1st 1L9s
|Nu
!Lsssssssss
|...
|Da
|Na
|'''Ni'''
|Flo
|Mo
|Di
Fre
|Fu
|Fu
|Pe
|Tha
|Sa
|No
|Fli
|Si
|Lo
Fle
|Thu
|Du
|Te
|Fa
|Da
|Tho
|-
|Ri
!2nd 1L9s
Ne
!sLssssssss
|Su
|Da
|'''Da'''
|'''Fri'''
|Fo
|'''Mo'''
|Li
|Fu
The
|Pe
|Ru
|Sa
|Sa
|Fli
|Do
|Mi
Fe
|Lu
|Ra
|So
|Ti
De
|Mu
|La
|...
|Lo
|Lo
|Thu
|Te
|Da
|-
|-
!3rd 1L9s
|^m3
!ssLsssssss
|...
|Da
|m3
|Fri
|vm6
|'''Ro'''
|^^1
|'''Fu'''
vvm2
|Pe
|^4
|Sa
|m7
|Fli
|vm3
|Lo
|^^5
|Thu
vvm6
|Te
|^1
|Da
|P4
|-
|vm7
!4th 1L9s
|^^M2
!sssLssssss
vvm3
|Da
|^5
|Fri
|'''P1'''
|Ro
|v4
|'''Nu'''
|^^M6
|'''Pe'''
vvm7
|Sa
|^M2
|Fli
|P5
|Lo
|v8
|Thu
|^^M3
|Te
vv4
|Da
|^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
|-
|-
!5th 1L9s
!1st 3L2s
!ssssLsssss
!sLsLL
|Da
|Da
|Fri
|Ru
|Ro
|Fo
|Nu
|'''Me'''
|'''Sa'''
|'''Sa'''
|Fli
|Li/The
|Lo
|Thu
|Te
|Da
|Da
|-
|-
!6th 1L9s
!2nd 3L2s
!sssssLssss
!sLLsL
|Da
|Da
|Fri
|'''Ru'''
|Ro
|Fo
|Nu
|'''Su'''
|Me
|Li/The
|'''Fa'''
|'''Fli'''
|Lo
|Thu
|Te
|Da
|Da
|-
|-
!7th 1L9s
!3rd 3L2s
!ssssssLsss
!LsLsL
|Da
|Da
|Fri
|'''Ri/Ne'''
|Ro
|Fo
|Nu
|Su
|Me
|'''Li/The'''
|Fa
|'''Shi'''
|'''Lo'''
|Thu
|Te
|Da
|Da
|-
|-
!8th 1L9s
!4th 3L2s
!sssssssLss
!LsLLs
|Da
|Da
|Fri
|Ri/Ne
|Ro
|'''Fo'''
|Nu
|Su
|Me
|'''Tho'''
|Fa
|Shi
|'''So'''
|'''Thu'''
|Te
|Da
|Da
|-
|-
!9th 1L9s
!5th 3L2s
!ssssssssLs
!LLsLs
|Da
|Da
|Fri
|Ri/Ne
|Ro
|'''Fa'''
|Nu
|Su
|Me
|Tho
|Fa
|Shi
|So
|'''Flu'''
|'''Te'''
|Da
|-
!10th 1L9s
!sssssssssL
|Da
|Fri
|Ro
|Nu
|Me
|Fa
|Shi
|So
|Flu
|'''Le'''
|Da
|Da
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
1L10s MOS scales (L = M2 = rhymes, s = ^^m2/v<sup>3</sup>A1 = no rhyme)
5L3s MOS scales (L = ^M2 = v<sup>3</sup>m3, s = ^1 = v<sup>3</sup>m2)
![[Genchain mode numbering|GMN]] name
![[Genchain mode numbering|GMN]] name
!scale
!scale
!1sn
!plain
!2nd
!up
!
!dup/dud
!3rd
!down
!
!plain
!4th
!up
!5th
!dup/dud
!
!down
!6th
!plain
!
|-
!7th
!1st 5L3s
!8ve
!LLsLLsLs
|-
!1st 1L10s
!Lssssssssss
|Da
|Da
|'''Ra'''
|Ru
|Ni
|Mi/Fe
|Mo
|Fo
|Fu
|Pe
|Sa
|Sa
|Fli
|'''Lu'''
|Lo
|Li/The
|Thu
|Do
|Te
|Da
|Da
|-
|-
!2nd 1L10s
!2nd 5L3s
!sLsssssssss
!LLsLsLLs
|Da
|Da
|'''Fri'''
|Ru
|'''Ni'''
|'''Mi/Fe'''
|Mo
|Fo
|Fu
|Pe
|Sa
|Sa
|Fli
|'''Su'''
|Lo
|Li/The
|Thu
|Do
|Te
|Da
|Da
|-
|-
!3rd 1L10s
!3rd 5L3s
!ssLssssssss
!LsLLsLLs
|Da
|Da
|Fri
|Ru
|'''Ro'''
|'''Ri/Ne'''
|'''Mo'''
|Fo
|Fu
|Pe
|Sa
|Sa
|Fli
|Su
|Lo
|Li/The
|Thu
|'''Do'''
|Te
|Da
|Da
|-
|-
!4th 1L10s
!4th 5L3s
!sssLsssssss
!LsLLsLsL
|Da
|Da
|Fri
|Ru
|Ro
|Ri/Ne
|'''Nu'''
|Fo
|'''Fu'''
|'''Sa'''
|Pe
|Su
|Sa
|Li/The
|Fli
|'''Tho'''
|Lo
|Thu
|Te
|Da
|Da
|-
|-
!5th 1L10s
!5th 5L3s
!ssssLssssss
!LsLsLLsL
|Da
|Da
|Fri
|'''Ru'''
|Ro
|Ri/Ne
|Nu
|Fo
|'''Me'''
|'''Fa'''
|'''Pe'''
|Su
|Sa
|Li/The
|Fli
|Tho
|Lo
|Thu
|Te
|Da
|Da
|-
|-
!6th 1L10s
!6th 5L3s
!sssssLsssss
!sLLsLLsL
|Da
|Da
|Fri
|'''Du'''
|Ro
|Ri/Ne
|Nu
|Fo
|Me
|'''Fa'''
|'''Sa'''
|Fli
|Lo
|Thu
|Te
|Da
|-
!7th 1L10s
!ssssssLssss
|Da
|Fri
|Ro
|Nu
|Me
|Fa
|Fa
|'''Shi'''
|Su
|'''Fli'''
|'''Li/The'''
|Lo
|Tho
|Thu
|Te
|Da
|Da
|-
|-
!8th 1L10s
!7th 5L3s
!sssssssLsss
!sLLsLsLL
|Da
|Da
|Fri
|Du
|Ro
|Ri/Ne
|Nu
|'''Fo'''
|Me
|Fa
|Fa
|Shi
|Su
|'''So'''
|'''Si/Fle'''
|'''Lo'''
|Tho
|Thu
|Te
|Da
|Da
|-
|-
!9th 1L10s
!8th 5L3s
!ssssssssLss
!sLsLLsLL
|Da
|Da
|Fri
|Du
|Ro
|Ri/Ne
|Nu
|'''No'''
|Me
|Fa
|Fa
|Shi
|Su
|So
|Si/Fle
|'''Flu'''
|Tho
|'''Thu'''
|Te
|Da
|Da
|}
== <nowiki>#</nowiki>22 (P8/2, M2/4) half-8ve 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)'''
|-
|-
!10th 1L10s
|
!sssssssssLs
!-11
|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
* EI = 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"
|+
'''uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
!genspan
!-16
!...
!-10
!-10
!-9
!-9
Line 18,698: Line 18,386:
!9
!9
!10
!10
!...
!11
!16
|-
|-
!solfege
! rowspan="3" |Da's
|Fru
 
|...
gen-
 
chain
 
per-span = 0
|Shu
|Shi
Fle
|Flo
|Fla
|Flu
|Fli
The
|Tho
|Tha
|Tha
|Thu
|Thi
De
|Do
|Do
|Re
|Fri
|Nu
|Fa
|So
|Le
|Fli
|Thu
|'''Da'''
|'''Da'''
|Du
|Di
Re
|Ro
|Ro
|Me
|Ra
|Ni
|Ru
|Fu
|Ri
|Sa
Me
|Lo
|Mo
|Te
|Ma
|Thi
|Mu
|Du
|Mi
|Ra
Pe
|...
|Po
|To
|-
|-
!intervals
|^d5
|^m2
|^^d5
|...
vvm6
|vm6
|m6
|^m6
|^^m6
vvm7
|vm7
|m7
|m7
|^m7
|^^m7
vv8
|v8
|v8
|vvM2
|^^m2
|^m3
|P4
|v5
|vvM6
|^^m6
|^m7
|'''P1'''
|'''P1'''
|^1
|^^1
vvM2
|vM2
|vM2
|vvM3
|^^m3
|^4
|P5
|vM6
|vvM7
|^^m7
|^1
|M2
|M2
|...
|^M2
|vM7
|^^M2
vvM3
|vM3
|M3
|^M3
|^^M3
vvA4
|vA4
|-
|-
!notes
|^Gb
|^Db
|^^Gb
|...
vvAb
|vAb
|Ab
|^Ab
|^^Ab
vvBb
|vBb
|Bb
|Bb
|^Bb
|^^Bb
vvC
|vC
|vC
|vvD
|^^Db
|^Eb
|F
|vG
|vvA
|^^Ab
|^Bb
|'''C'''
|'''C'''
|^C
|^^C
vvD
|vD
|vD
|vvE
|^^Eb
|^F
|G
|vA
|vvB
|^^Bb
|^C
|D
|D
|...
|^D
|vB
|^^D
|}
vvE
{| class="wikitable center-all"
|vE
|+
|E
1L7s MOS scales (L = ^^m2/v<sup>3</sup>M3, s = vM2/^<sup>4</sup>d1)
|^E
![[Genchain mode numbering|GMN]] name
|^^E
!scale
vvF#
!1sn
|vF#
!2nd
|-
!3rd
| colspan="24" |
!
!tritone
!
!6th
!7th
!8ve
|-
|-
!1st 1L7s
! rowspan="3" |Sa's
!sssssssL
 
|Da
gen-
|Ro
 
|Me
chain
 
per-span = ±1
|Fro
|Fra
|Fru
|Fri
Ne
|No
|Na
|Nu
|Ni
|Ni
Fe
|Fo
|Fa
|Fu
|Fu
|Fi
Se
|So
|Sa
|Sa
|Su
|Si
Le
|Lo
|Lo
|'''Te'''
|La
|Da
|Lu
|Li
Te
|To
|Ta
|Tu
|-
|-
!2nd 1L7s
|vm2
!ssssssLs
|m2
|Da
|^m2
|Ro
|^^m2
|Me
vvm3
|Ni
|vm3
|Fu
|m3
|Sa
|^m3
|'''Lo'''
|^^m3
|'''Thu'''
vv4
|Da
|v4
|P4
|^4
|^^4
vv5
|v5
|P5
|^5
|^^5
vvM6
|vM6
|M6
|^M6
|^^M6
vvM7
|vM7
|M7
|^M7
|-
|-
!3rd 1L7s
|vDb
!sssssLss
|Db
|Da
|^Db
|Ro
|^^Db
|Me
vvEb
|Ni
|vEb
|Fu
|Eb
|'''Sa'''
|^Eb
|'''Fli'''
|^^Eb
|Thu
vvF
|Da
|vF
|-
|F
!4th 1L7s
|^F
!ssssLsss
|^^F
|Da
vvG
|Ro
|vG
|Me
|G
|Ni
|^G
|'''Fu'''
|^^G
|'''Le'''
vvA
|Fli
|vA
|Thu
|A
|Da
|^A
|-
|^^A
!5th 1L7s
vvB
!sssLssss
|vB
|Da
|B
|Ro
|^B
|Me
|}
|'''Ni'''
 
|'''So'''
{| class="wikitable center-all"
|Le
|+
|Fli
2L20s MOS scales (L = m2 =  rhymes, s = ^1/v<sup>3</sup>M2 = no rhyme)
|Thu
![[Genchain mode numbering|GMN]] name
|Da
!scale
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
!15
!16
!17
!18
!19
!20
!21
!22
|-
|-
!6th 1L7s
!1st 2L20s
!ssLsssss
!ssssssssssL x2
|Da
|Da
|Du
|Di
Re
|Ro
|Ro
|'''Me'''
|Ra
|'''Fa'''
|Ru
|Ri
Me
|Mo
|Ma
|Mu
|'''Mi'''
'''Pe'''
|Fi
Se
|So
|So
|Le
|Sa
|Fli
|Su
|Thu
|Si
Le
|Lo
|La
|Lu
|Li
Te
|To
|'''Ta'''
|Da
|Da
|-
|-
!7th 1L7s
!2nd 2L20s
!sLssssss
!sssssssssLs x2
|Da
|Da
|'''Ro'''
|Du
|'''Nu'''
|Di
|Fa
Re
|Ro
|Ra
|Ru
|Ri
Me
|Mo
|Ma
|'''Mu'''
|'''Fu'''
|Fi
Se
|So
|So
|Le
|Sa
|Fli
|Su
|Thu
|Si
Le
|Lo
|La
|Lu
|Li
Te
|'''To'''
|'''Do'''
|Da
|Da
|-
|-
!8th 1L7s
!3rd 2L20s
!Lsssssss
!ssssssssLss x2
|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
|Da
|Du
|Di
Re
|Ro
|Ro
|Me
|Ra
|Ni
|Ru
|Ri
Me
|Mo
|'''Ma'''
|'''Fa'''
|Fu
|Fu
|Fi
Se
|So
|Sa
|Sa
|Su
|Si
Le
|Lo
|Lo
|Te
|La
|Lu
|'''Li'''
'''Te'''
|'''Thi'''
|'''Thi'''
'''De'''
|Do
|Da
|Da
|-
|-
!2nd 8L1s
!4th 2L20s
!LLLLLLLsL
!sssssssLsss x2
|Da
|Da
|Du
|Di
Re
|Ro
|Ro
|Me
|Ra
|Ni
|Ru
|Ri
Me
|'''Mo'''
|'''Fo'''
|Fa
|Fu
|Fu
|Sa
|Fi
Se
|So
|Sa
|Su
|Si
Le
|Lo
|Lo
|'''Te'''
|La
|'''Lu'''
|'''Thu'''
|'''Thu'''
|Thi
De
|Do
|Da
|Da
|-
|-
!3rd 8L1s
!5th 2L20s
!LLLLLLsLL
!ssssssLssss x2
|Da
|Da
|Du
|Di
Re
|Ro
|Ro
|Me
|Ra
|Ni
|Ru
|'''Ri'''
'''Me'''
|'''Ni'''
'''Fe'''
|Fo
|Fa
|Fu
|Fu
|Fi
Se
|So
|Sa
|Sa
|'''Lo'''
|Su
|'''Fli'''
|Si
Le
|Lo
|'''La'''
|'''Tha'''
|Thu
|Thu
|Thi
De
|Do
|Da
|Da
|-
|-
!4th 8L1s
!6th 2L20s
!LLLLLsLLL
!sssssLsssss x2
|Da
|Da
|Du
|Di
Re
|Ro
|Ro
|Me
|Ra
|'''Ru'''
|'''Nu'''
|Ni
|Ni
Fe
|Fo
|Fa
|Fu
|Fu
|'''Sa'''
|Fi
|'''Le'''
Se
|Fli
|So
|Sa
|Su
|Si
Le
|'''Lo'''
|'''Tho'''
|Tha
|Thu
|Thu
|Thi
De
|Do
|Da
|Da
|-
|-
!5th 8L1s
!7th 2L20s
!LLLLsLLLL
!ssssLssssss x2
|Da
|Da
|Du
|Di
Re
|Ro
|Ro
|Me
|'''Ra'''
|'''Na'''
|Nu
|Ni
|Ni
|'''Fu'''
Fe
|'''So'''
|Fo
|Le
|Fa
|Fli
|Fu
|Thu
|Fi
|Da
Se
|-
!6th 8L1s
!LLLsLLLLL
|Da
|Ro
|Me
|'''Ni'''
|'''Fa'''
|So
|So
|Le
|Sa
|Fli
|Su
|'''Si'''
'''Le'''
|'''Fli'''
'''The'''
|Tho
|Tha
|Thu
|Thu
|Thi
De
|Do
|Da
|Da
|-
|-
!7th 8L1s
!8th 2L20s
!LLsLLLLLL
!sssLsssssss x2
|Da
|Da
|Ro
|Du
|'''Me'''
|Di
|'''Nu'''
Re
|'''Ro'''
|'''No'''
|Na
|Nu
|Ni
Fe
|Fo
|Fa
|Fa
|Fu
|Fi
Se
|So
|So
|Le
|Sa
|'''Su'''
|'''Flu'''
|Fli
|Fli
The
|Tho
|Tha
|Thu
|Thu
|Thi
De
|Do
|Da
|Da
|-
|-
!8th 8L1s
!9th 2L20s
!LsLLLLLLL
!ssLssssssss x2
|Da
|Da
|'''Ro'''
|Du
|'''Di'''
'''Re'''
|'''Fri'''
|'''Fri'''
'''Ne'''
|No
|Na
|Nu
|Nu
|Ni
Fe
|Fo
|Fa
|Fa
|Fu
|Fi
Se
|So
|So
|Le
|'''Sa'''
|'''Fla'''
|Flu
|Fli
|Fli
The
|Tho
|Tha
|Thu
|Thu
|Thi
De
|Do
|Da
|Da
|-
|-
!9th 8L1s
!10th 2L20s
!sLLLLLLLL
!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
|Da
|'''Re'''
|'''Fra'''
|Fru
|Fri
|Fri
Ne
|No
|Na
|Nu
|Nu
|Ni
Fe
|Fo
|Fa
|Fa
|So
|Fu
|Le
|Fi
Se
|'''Shi'''
'''Fle'''
|Flo
|Fla
|Flu
|Fli
|Fli
The
|Tho
|Tha
|Thu
|Thu
|Thi
De
|Do
|Da
|Da
|}
|}


== <nowiki>#</nowiki>36 (P8, P11/5) fifth-11th ==
== <nowiki>#</nowiki>33 (P8/5, P5) fifth-8ve ==
This pergen can be thought of as "half-down5th".
For the pergen that equates P5 with 3\5, see (P8/5, ^1) below.


* G = ^^m3 = v<sup>3</sup>M3 = 340¢ - c/5
If P5 > 3\5 = 720¢, swap up with down, and dup with dud, to get solfege #2.
* EI = v<sup>5</sup>A1 = 0¢
* P = ^^M2 = v<sup>3</sup>m3 = 240¢
* ^ = 20¢ + 1.4c
* G = P5 = 700¢ + c '''<u>or</u>''' ^1 = v<sup>4</sup>m2 = 20¢ - c
* EU = v<sup>5</sup>m2 = 0¢
* ^ = 20¢ - c


MOS scales covered:
MOS scales covered:
* 7 = 4L3s if P5 > 4\7 = 686¢ (for 3L4s use half-5th solfege)
 
* 11 = 7L4s
* 10 = 5L5s
* 18 = 7L11s and 11L7s
* 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"
{| class="wikitable center-all"
|+
|+
'''uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
|-
!genspan
! colspan="2" |genspan (gen = P5)
!-20
!-4
!...
!-3
!10
!-2
!9
!-1
!8
!0
!7
!1
!6
!2
!5
!3
!4
!4
!3
!2
!1
!0
!-1
!-2
!-3
!-4
!-5
!-6
!-7
!-8
!-9
!-10
!...
!-20
|-
|-
! rowspan="3" |down
genchain
perspan = 2
!solfege
!solfege
|Fla
|Fro
|...
|Flo
|Tha
|No
|Se
|Tho
|Nu
|Fo
|Do
|Do
|Fli
|Fa
|Re
|Thu
|So
|So
|Ni
|'''Da'''
|Le
|Fu
|Ro
|Ro
|Thi
|Sa
|Me
|Du
|Lo
|Lo
|Fi
|Ra
|...
|Ma
|-
|-
!intervals
!intervals
|m6
|vm2
|...
|vm6
|m7
|vm3
|^~5
|vm7
|^m3
|v4
|v8
|v8
|v~6
|P4
|^~2
|^m7
|v5
|v5
|v~3
|'''P1'''
|^~6
|^4
|vM2
|vM2
|v~7
|P5
|^~2
|^1
|vM6
|vM6
|v~4
|M2
|...
|M3
|-
|-
!notes
!notes
|Ab
|vDb
|...
|vAb
|Bb
|vEb
|vvG
|vBb
|^Eb
|vF
|vC
|vC
|^^Ab
|F
|vvD
|^Bb
|vG
|vG
|^^Eb
|'''C'''
|vvA
|^F
|vD
|vD
|^^Bb
|G
|vvE
|^C
|vA
|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
| colspan="10" |
!LLsLsLs
|
|Da
|Ro
|'''Me'''
|Fu
|Sa
|Le
|Thi
|Da
|-
|-
!2nd 4L3s
! rowspan="3" |dup
!LsLLsLs
 
|Da
genchain
|Ro
 
|'''Ni'''
perspan = 1
|Fu
!solfege
|'''Sa'''
|Le
|Thi
|Thi
|Da
|Fi
|Di
|Si
|Ri
|Li
|Mi
|Ti
|Pi
|-
|-
!3rd 4L3s
!intervals
!LsLsLLs
|^^m7
|Da
|^^4
|Ro
|^^1
|Ni
|^^5
|Fu
|^^M2
|'''So'''
|^^M6
|Le
|^^M3
|'''Thi'''
|^^M7
|Da
|^^A4
|-
|-
!4th 4L3s
!notes
!LsLsLsL
|^^Bb
|Da
|^^F
|'''Ro'''
|^^C
|Ni
|^^G
|Fu
|^^D
|So
|^^A
|Le
|^^E
|'''Thu'''
|^^B
|Da
|^^F#
|-
|-
!5th 4L3s
| colspan="10" |
!sLLsLsL
|
|Da
|'''Re'''
|Ni
|'''Fu'''
|So
|Le
|Thu
|Da
|-
|-
!6th 4L3s
! rowspan="3" |plain
!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
* EI'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:
genchain


* 7 = 3L4s (P5 is 515-800¢), but better to use half-5th solfege
perspan = 0
* 10 = 3L7s (P5 is 600-800¢)
!solfege
* 13 = 3L10s (and 10L3s if P5 < 7\13)
|Fla
 
|Na
{| class="wikitable center-all"
|Tha
|+
|Fa
'''uniform solfege (-a = plain, -u = up, -o = down, -i = lift, -e = drop)'''
|'''Da'''
|Sa
|Ra
|La
|Ma
|-
|-
!genspan
!intervals
!-12
|m6
!-11
|m3
!-10
|m7
!-9
|P4
!-8
|'''P1'''
!-7
|P5
!-6
|M2
!-5
|M6
!-4
|M3
!-3
|-
!-2
!notes
!-1
|Ab
!0
|Eb
!1
|Bb
!2
|F
!3
|'''C'''
!4
|G
!5
|D
!6
|A
!7
|E
!8
|-
!9
| colspan="10" |
!10
|
!11
!12
|-
|-
! rowspan="3" |dud
genchain
perspan = -1
!solfege
!solfege
|Ri
|Shu
|Tha
|Ro
|She
|She
|Li
|Fru
|Fa
|Lo
|Fre
|Fre
|Mi
|Flu
|'''Da'''
|Mo
|Fle
|Fle
|Ti
|Nu
|Sa
|To
|Ne
|Ne
|Pi
|Thu
|Ra
|Po
|The
|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
!intervals
|/M2
|^d5
|m7
|vM2
|\d5
|/M6
|^m2
|P4
|vM6
|\m2
|/M3
|^m6
|'''P1'''
|vM3
|\m6
|/M7
|^m3
|^m3
|P5
|vM7
|\m3
|/A4
|^m7
|^m7
|M2
|^4
|vA4
|^1
|\m7
|^5
|^M2
|^M6
|^M3
|^M7
|-
|-
!notes
!notes
|/D
|^Gb
|Bb
|vD
|\Gb
|/A
|^Db
|F
|vA
|\Db
|/E
|^Ab
|'''C'''
|vE
|\Ab
|/B
|^Eb
|^Eb
|G
|vB
|\Eb
|/F#
|^Bb
|^Bb
|D
|^F
|vF#
|^C
|\Bb
|^G
|^D
|^A
|^E
|^B
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
3L4s MOS scales (L = ^m3 = v/A2 = \\d4, s = ^/1 = vvA1 = \m2)
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud) [[mingen]] format'''
![[Genchain mode numbering|GMN]] name
|-
!scale
! colspan="2" |genspan (gen = ^1)
!4
!3
!2
!1
!0
!0
!1
!-1
!2
!-2
!3
!-3
!4
!-4
!5
|-
!6
! rowspan="3" |Fa's
!7
 
genchain
 
perspan = 2
!solfege
|She
|Fi
|Fu
|Fa
|Fo
|Fe
|Mi
|Mu
|Ma
|-
|-
!1st 3L4s
!intervals
!LsLsLss
|vvd5
|Da
|^^4
|Nu
|^4
|Mo
|P4
|Sa
|v4
|Fle
|vv4
|'''To'''
|^^M3
|Ti
|^M3
|Da
|M3
|-
|-
!2nd 3L4s
!notes
!LsLssLs
|vvGb
|Da
|^^F
|Nu
|^F
|Mo
|F
|'''Sa'''
|vF
|Fle
|vvF
|'''Flu'''
|^^E
|Ti
|^E
|Da
|E
|-
|-
!3rd 3L4s
| colspan="11" |
!LssLsLs
|Da
|'''Nu'''
|Mo
|'''Mi'''
|Fle
|Flu
|Ti
|Da
|-
|-
!4th 3L4s
! rowspan="3" |Ra's
!sLsLsLs
 
|Da
genchain
|'''Fre'''
 
|Mo
perspan = 1
|Mi
!solfege
|Fle
|Nu
|Flu
|Na
|'''Ti'''
|No
|Da
|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
|-
|-
!5th 3L4s
| colspan="11" |
!sLsLssL
|Da
|Fre
|Mo
|Mi
|'''Fle'''
|Flu
|'''Lo'''
|Da
|-
|-
!6th 3L4s
! rowspan="3" |Da's
!sLssLsL
 
|Da
genchain
 
perspan = 0
!solfege
|Fro
|Fre
|Fre
|'''Mo'''
|Di
|Mi
|Du
|'''Fa'''
|'''Da'''
|Flu
|Do
|Lo
|De
|Da
|Ti
|Tu
|-
|-
!7th 3L4s
!intervals
!ssLsLsL
|vm2
|Da
|vvm2
|Fre
|^^1
|'''Fru'''
|^1
|Mi
|'''P1'''
|Fa
|v8
|Flu
|vv8
|Lo
|^^M7
|Da
|^M7
|}
{| 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
!notes
!LssLssLsss
|vDb
|Da
|vvDb
|Ne
|^^C
|Nu
|^C
|Mo
|'''C'''
|Pi
|vC
|Sa
|vvC
|Fle
|^^B
|'''Thu'''
|^B
|To
|Ti
|Da
|-
|-
!2nd 3L7s
| colspan="11" |
!LssLsssLss
|Da
|Ne
|Nu
|Mo
|'''Pi'''
|Sa
|Fle
|'''Flu'''
|To
|Ti
|Da
|-
|-
!3rd 3L7s
! rowspan="3" |Tha's
!LsssLssLss
 
|Da
genchain
|'''Ne'''
 
|Nu
perspan = -1
|Mo
!solfege
|'''Mi'''
|Thi
|Sa
|Thu
|Fle
|Tha
|Flu
|Tho
|To
|The
|Ti
|Li
|Da
|Lu
|La
|Lo
|-
|-
!4th 3L7s
!intervals
!sLssLssLss
|^^m7
|Da
|^m7
|'''Fre'''
|m7
|Nu
|vm7
|Mo
|vvm7
|Mi
|^^M6
|Sa
|^M6
|Fle
|M6
|Flu
|vM6
|'''To'''
|Ti
|Da
|-
|-
!5th 3L7s
!notes
!sLssLsssLs
|^^Bb
|Da
|^Bb
|Fre
|Bb
|Nu
|vBb
|Mo
|vvBb
|Mi
|^^A
|'''Sa'''
|^A
|Fle
|A
|Flu
|vA
|'''Lo'''
|Ti
|Da
|-
|-
!6th 3L7s
| colspan="11" |
!sLsssLssLs
|Da
|Fre
|'''Nu'''
|Mo
|Mi
|'''Fa'''
|Fle
|Flu
|Lo
|Ti
|Da
|-
|-
!7th 3L7s
! rowspan="3" |Sa's
!ssLssLssLs
 
|Da
genchain
|Fre
 
|'''Fru'''
perspan = -2
|Mo
!solfege
|Mi
|Fla
|Fa
|Flo
|Fle
|Fle
|Flu
|Si
|Lo
|Su
|'''Ti'''
|Sa
|Da
|So
|Se
|Pi
|-
|-
!8th 3L7s
!intervals
!ssLssLsssL
|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
|Da
|Fre
|'''Ru'''
|Fru
|Ri
|Mo
|'''Fe'''
|Mi
|Fo
|Fa
|'''Sa'''
|'''Fle'''
|Su
|Flu
|Lo
|'''Li'''
|'''Li'''
|The
|'''Do'''
|Da
|Da
|-
|-
!9th 3L7s
!2nd 5L5s
!ssLsssLssL
!sL-sL-sL-sL-sL
|Da
|Da
|Fre
|'''Du'''
|Fru
|Ri
|'''Mo'''
|'''Ne'''
|Mi
|Fo
|Fa
|'''Fa'''
|'''She'''
|Su
|Flu
|'''Si'''
|Lo
|The
|Li
|'''Tho'''
|Da
|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
* EI = v<sup>5</sup>M2 = 0¢
* ^ = 40¢ + 0.4c
 
MOS scales covered:
* 5 = 2L3s
* 7 = 2L5s
* 9 = 2L7s
* 11 = 2L9s
* etc.


{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
'''uniform solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
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
|-
|-
!genspan
!1st 5L10s
!30
!Lss-Lss-Lss-Lss-Lss
!...
|Da
!10
|'''Ra'''
!9
|Ru
!8
|Ri
!7
|'''Mi'''
!6
!5
!4
!3
!2
!1
!0
!-1
!-2
!-3
!-4
!-5
!-6
!-7
!-8
!-9
!-10
!...
!-30
|-
!solfege
|Sha
|...
|Tha
|Fe
|Fe
|Thu
|Fo
|Fo
|Thi
|'''So'''
|Fa
|Sa
|De
|Su
|Fu
|'''Lu'''
|Li
|The
|'''De'''
|Do
|Do
|Fi
|Da
|'''Da'''
|-
|Se
!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
|Du
|So
|'''Di'''
|Di
|Ri
|Sa
|Ne
|Re
|'''No'''
|Fo
|Fa
|'''Fu'''
|Su
|Su
|Ro
|Si
|Si
|Ra
|'''Fle'''
|...
|The
|Pa
|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)'''
|-
|-
!intervals
!genspan
|d5
!10
|...
!9
|m7
!8
|vv4
!7
|^m7
!6
|v4
!5
|^^m7
!4
|P4
!3
|vv8
!2
|^4
!1
|v8
!0
|^^4
!-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'''
|'''P1'''
|vv5
|vvM7
|^1
|^m7
|v5
|vM6
|^^1
|^^m6
|P5
|P5
|vvM2
|vvA4
|^5
|^4
|vM2
|vM3
|^^5
|^^m3
|M2
|M2
|...
|A4
|-
|-
!notes
!notes
|Gb
|...
|Bb
|Bb
|vvF
|vvA
|^Bb
|^Ab
|vF
|vG
|^^Bb
|^^Gb
|F
|F
|vvC
|vvE
|^F
|^Eb
|vC
|vD
|^^F
|^^Db
|'''C'''
|'''C'''
|vvG
|vvB
|^C
|^Bb
|vG
|vA
|^^C
|^^Ab
|G
|G
|vvD
|vvF#
|^G
|^F
|vD
|vE
|^^G
|^^Eb
|D
|D
|...
|F#
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
2L7s MOS scales (L = v4 = ^<sup>4</sup>m3, s = ^1 = v<sup>4</sup>M2)
1L9s MOS scales (L = ^^m3/v<sup>3</sup>A2, s = ^^m2/v<sup>3</sup>A1)
![[Genchain mode numbering|GMN]] name
![[Genchain mode numbering|GMN]] name
!scale
!scale
Line 19,755: Line 19,656:
!8
!8
!9
!9
!10
|-
|-
!1st 2L7s
!1st 1L9s
!ssssLsssL
!Lsssssssss
|Da
|Da
|Du
|'''Ni'''
|Di
|Mo
|Re
|Fu
|'''Ro'''
|Pe
|Se
|So
|Sa
|Sa
|Su
|Fli
|Lo
|Thu
|Te
|Da
|Da
|-
|-
!2nd 2L7s
!2nd 1L9s
!sssLssssL
!sLssssssss
|Da
|Da
|Du
|'''Fri'''
|Di
|'''Mo'''
|Re
|Fu
|'''Fi'''
|Pe
|Se
|So
|Sa
|Sa
|'''Su'''
|Fli
|Lo
|Thu
|Te
|Da
|Da
|-
|-
!3rd 2L7s
!3rd 1L9s
!sssLsssLs
!ssLsssssss
|Da
|Da
|Du
|Fri
|Di
|'''Ro'''
|'''Re'''
|'''Fu'''
|Fi
|Pe
|Se
|So
|Sa
|Sa
|'''Do'''
|Fli
|Lo
|Thu
|Te
|Da
|Da
|-
|-
!4th 2L7s
!4th 1L9s
!ssLssssLs
!sssLssssss
|Da
|Da
|Du
|Fri
|Di
|Ro
|'''Fu'''
|'''Nu'''
|Fi
|'''Pe'''
|Se
|Sa
|So
|Fli
|'''Sa'''
|Lo
|Do
|Thu
|Te
|Da
|Da
|-
|-
!5th 2L7s
!5th 1L9s
!ssLsssLss
!ssssLsssss
|Da
|Da
|Du
|Fri
|'''Di'''
|Ro
|Fu
|Nu
|Fi
|'''Me'''
|Se
|'''Sa'''
|So
|Fli
|'''De'''
|Lo
|Do
|Thu
|Te
|Da
|Da
|-
|-
!6th 2L7s
!6th 1L9s
!sLssssLss
!sssssLssss
|Da
|Da
|Du
|Fri
|Ro
|Nu
|Me
|'''Fa'''
|'''Fa'''
|Fu
|'''Fli'''
|Fi
|Lo
|Se
|Thu
|'''So'''
|Te
|De
|Do
|Da
|Da
|-
|-
!7th 2L7s
!7th 1L9s
!sLsssLsss
!ssssssLsss
|Da
|Da
|'''Du'''
|Fri
|Ro
|Nu
|Me
|Fa
|Fa
|Fu
|'''Shi'''
|Fi
|'''Lo'''
|Se
|Thu
|'''Thi'''
|Te
|De
|Do
|Da
|Da
|-
|-
!8th 2L7s
!8th 1L9s
!LssssLsss
!sssssssLss
|Da
|Da
|'''Fo'''
|Fri
|Ro
|Nu
|Me
|Fa
|Fa
|Fu
|Shi
|Fi
|'''So'''
|'''Se'''
|'''Thu'''
|Thi
|Te
|De
|Do
|Da
|Da
|-
|-
!9th 2L7s
!9th 1L9s
!LsssLssss
!ssssssssLs
|Da
|Da
|Fo
|Fri
|Ro
|Nu
|Me
|Fa
|Shi
|So
|'''Flu'''
|'''Te'''
|Da
|-
!10th 1L9s
!sssssssssL
|Da
|Fri
|Ro
|Nu
|Me
|Fa
|Fa
|Fu
|Shi
|Fi
|So
|'''Thu'''
|Flu
|Thi
|'''Le'''
|De
|Do
|Da
|Da
|}
|}
== Multi-edo pergens of the form (P8/m, ^1) ==
These pergens map the 5th to an edo, and other primes to other rings (offset copies of the edo). They only make sense musically if the edo's approximation of the 5th has a relative error < 25%. Otherwise there will be a better Sa on another ring. For example, 4-edo with 34% error has 3/2 = 600¢, but additional rings will add a note between 600¢ and 850¢ that will be a much 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¢.
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
rank-2 edos with Sa mapped to a good spot
1L10s MOS scales (L = M2 = rhymes, s = ^^m2/v<sup>3</sup>A1 = no rhyme)
!edo
![[Genchain mode numbering|GMN]] name
!rel. error
!scale
!generator range
!1sn
!mapping
!2nd
!notes
!
!3rd
!
!4th
!5th
!
!6th
!
!7th
!8ve
|-
|-
!2-edo
!1st 1L10s
|17%
!Lssssssssss
|204-300¢
|Da
|(2 3...) (0 0...)
|'''Ra'''
|maximum of 4 notes
|Ni
|Mo
|Fu
|Pe
|Sa
|Fli
|Lo
|Thu
|Te
|Da
|-
|-
!3-edo
!2nd 1L10s
|24.5%
!sLsssssssss
|196-200¢
|Da
|(3 5...) (0 0...)
|'''Fri'''
|maximum of 6 notes, within 4¢ of 6-edo
|'''Ni'''
|Mo
|Fu
|Pe
|Sa
|Fli
|Lo
|Thu
|Te
|Da
|-
|-
!4-edo
!3rd 1L10s
|34%
!ssLssssssss
|none
|Da
|
|Fri
|
|'''Ro'''
|'''Mo'''
|Fu
|Pe
|Sa
|Fli
|Lo
|Thu
|Te
|Da
|-
|-
!5-edo
!4th 1L10s
|7.5%
!sssLsssssss
|36-120¢
|Da
|(5 8...) (0 0...)
|Fri
|Sawa aka Blackwood
|Ro
|'''Nu'''
|'''Fu'''
|Pe
|Sa
|Fli
|Lo
|Thu
|Te
|Da
|-
|-
!6-edo
!5th 1L10s
|49%
!ssssLssssss
|none
|Da
|
|Fri
|
|Ro
|Nu
|'''Me'''
|'''Pe'''
|Sa
|Fli
|Lo
|Thu
|Te
|Da
|-
|-
!7-edo
!6th 1L10s
|9.5%
!sssssLsssss
|32-85¢
|Da
|(7 11...) (0 0...)
|Fri
|Lawa aka Whitewood
|Ro
|Nu
|Me
|'''Fa'''
|'''Sa'''
|Fli
|Lo
|Thu
|Te
|Da
|-
|-
!8-edo
!7th 1L10s
|32%
!ssssssLssss
|none
|Da
|
|Fri
|
|Ro
|-
|Nu
!9-edo
|Me
|26.5%
|Fa
|none
|'''Shi'''
|
|'''Fli'''
|
|Lo
|Thu
|Te
|Da
|-
|-
!10-edo
!8th 1L10s
|15%
!sssssssLsss
|36-60¢
|Da
|(10 16...) (0 0...)
|Fri
|needs 2 more primes to be a valid mapping
|Ro
|Nu
|Me
|Fa
|Shi
|'''So'''
|'''Lo'''
|Thu
|Te
|Da
|-
|-
!11-edo
!9th 1L10s
|47.5%
!ssssssssLss
|none
|Da
|
|Fri
|
|Ro
|Nu
|Me
|Fa
|Shi
|So
|'''Flu'''
|'''Thu'''
|Te
|Da
|-
|-
!12-edo
!10th 1L10s
|2%
!sssssssssLs
|4-50¢
|Da
|(12 19...) (0 0...)
|Fri
|Lalawa aka Compton
|Ro
|Nu
|Me
|Fa
|Shi
|So
|Flu
|'''Le'''
|'''Te'''
|Da
|-
|-
!13-edo
!11th 1L10s
|40%
!ssssssssssL
|none
|Da
|
|Fri
|
|Ro
|-
|Nu
!14-edo
|Me
|19%
|Fa
|32-43¢
|Shi
|(14 22...) (0 0...)
|So
|needs 2 more primes to be a valid mapping
|Flu
|-
|Le
!15-edo
|'''Tha'''
|
|Da
|
|
|
|}
|}


===(P8/5, ^1)===
== <nowiki>#</nowiki>35 (P8, P5/5) fifth-5th ==
*P = M2/m3 = 200¢
 
*G = ^1 = c (stands for 81/80 in Blackwood)
* G = vM2 = ^<sup>4</sup>d1 = 140¢ + c/5
*EI = d2 = 0¢
* EU = v<sup>5</sup>A2 = 0¢
*^ = c
* ^ = 60¢ + 1.8c


MOS scales covered:
MOS scales covered:
*10 = 5L5s
* 8 = 1L7s
*15 = 5L10s or 10L5s
* 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"
{| class="wikitable center-all"
|+
|+
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
|-
! colspan="2" |genspan (gen = ^1)
!genspan
!-16
!...
!-10
!-9
!-8
!-7
!-6
!-5
!-4
!-3
!-2
!-2
!-1
!-1
Line 19,989: Line 20,014:
!1
!1
!2
!2
!3
!4
!5
!6
!7
!8
!9
!10
!...
!16
|-
|-
! rowspan="3" |Fa's
genchain
perspan = 2
!solfege
!solfege
|Me/Fe
|Fru
|Mo/Fo
|...
|Tha
|Do
|Re
|Fri
|Nu
|Fa
|Fa
|So
|Le
|Fli
|Thu
|'''Da'''
|Ro
|Me
|Ni
|Fu
|Fu
|Fi
|Sa
|Lo
|Te
|Thi
|Du
|Ra
|...
|To
|-
|-
!intervals
!intervals
|vvM3/vv4
|^m2
|vM3/v4
|...
|P4
|m7
|v8
|vvM2
|^^m2
|^m3
|P4
|v5
|vvM6
|^^m6
|^m7
|'''P1'''
|vM2
|vvM3
|^^m3
|^4
|^4
|^^4
|P5
|vM6
|vvM7
|^^m7
|^1
|M2
|...
|vM7
|-
|-
!notes
!notes
|vvE/vvF
|^Db
|vE/vF
|...
|Bb
|vC
|vvD
|^^Db
|^Eb
|F
|F
|vG
|vvA
|^^Ab
|^Bb
|'''C'''
|vD
|vvE
|^^Eb
|^F
|^F
|^^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
|-
|-
| colspan="7" |
!1st 1L7s
!sssssssL
|Da
|Ro
|Me
|Ni
|Fu
|Sa
|Lo
|'''Te'''
|Da
|-
|-
! rowspan="3" |Ra's
!2nd 1L7s
 
!ssssssLs
genchain
|Da
 
perspan = 1
!solfege
|Re
|Ro
|Ro
|Ra/Na
|Me
|Ru/Nu
|Ni
|Ri/Ni
|Fu
|-
|Sa
!intervals
|'''Lo'''
|vvM2
|'''Thu'''
|vM2
|Da
|M2/m3
|^M2/^m3
|^^M2/^^m3
|-
|-
!notes
!3rd 1L7s
|vvD
!sssssLss
|vD
|Da
|D/Eb
|Ro
|^D/^Eb
|Me
|^^D/^^Eb
|Ni
|Fu
|'''Sa'''
|'''Fli'''
|Thu
|Da
|-
|-
| colspan="7" |
!4th 1L7s
!ssssLsss
|Da
|Ro
|Me
|Ni
|'''Fu'''
|'''Le'''
|Fli
|Thu
|Da
|-
|-
! rowspan="3" |Da's
!5th 1L7s
 
!sssLssss
genchain
|Da
 
|Ro
perspan = 0
|Me
!solfege
|'''Ni'''
|De
|'''So'''
|Do
|Le
|'''Da'''
|Fli
|Du
|Thu
|Di
|Da
|-
|-
!intervals
!6th 1L7s
|vv8
!ssLsssss
|v8
|Da
|'''P1'''
|Ro
|^1
|'''Me'''
|^^1
|'''Fa'''
|So
|Le
|Fli
|Thu
|Da
|-
|-
!notes
!7th 1L7s
|vvC
!sLssssss
|vC
|Da
|'''C'''
|'''Ro'''
|^C
|'''Nu'''
|^^C
|Fa
|-
|So
| colspan="7" |
|Le
|-
|Fli
! rowspan="3" |Tha's
 
genchain
 
perspan = -1
!solfege
|Le/The
|Lo/Tho
|La/Tha
|Thu
|Thu
|Thi
|Da
|-
|-
!intervals
!8th 1L7s
|vvM6/vvm7
!Lsssssss
|vM6/vm7
|Da
|M6/m7
|'''Fri'''
|^m7
|Nu
|^^m7
|Fa
|-
!notes
|vvA/vvBb
|vA/vBb
|A/Bb
|^Bb
|^^Bb
|-
| colspan="7" |
|-
! rowspan="3" |Sa's
 
genchain
 
perspan = -2
!solfege
|Se
|So
|So
|Sa
|Le
|Su/Flu
|Fli
|Si/Fli
|Thu
|-
|Da
!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"
{| class="wikitable center-all"
|+
|+
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
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
|-
|-
! colspan="2" |genspan (gen = vM3)
!1st 8L1s
!2
!LLLLLLLLs
!1
|Da
!0
|Ro
!-1
|Me
!-2
|Ni
|Fu
|Sa
|Lo
|Te
|'''Thi'''
|Da
|-
|-
! rowspan="3" |Fa's
!2nd 8L1s
 
!LLLLLLLsL
genchain
|Da
 
|Ro
perspan = 2
|Me
!solfege
|Ni
|Re
|Fu
|Sa
|Lo
|Lo
|Ma/Fa
|'''Te'''
|Du
|'''Thu'''
|Fli
|Da
|-
|-
!intervals
!3rd 8L1s
|vvM2
!LLLLLLsLL
|vM6
|Da
|M3/P4
|Ro
|^1
|Me
|^^m6
|Ni
|Fu
|Sa
|'''Lo'''
|'''Fli'''
|Thu
|Da
|-
|-
!notes
!4th 8L1s
|vvD
!LLLLLsLLL
|vA
|Da
|E/F
|Ro
|^C
|Me
|^^Ab
|Ni
|Fu
|'''Sa'''
|'''Le'''
|Fli
|Thu
|Da
|-
|-
|
!5th 8L1s
|
!LLLLsLLLL
|
|Da
|
|Ro
|
|Me
|
|Ni
|
|'''Fu'''
|'''So'''
|Le
|Fli
|Thu
|Da
|-
|-
! rowspan="3" |Ra's
!6th 8L1s
 
!LLLsLLLLL
genchain
|Da
 
|Ro
perspan = 1
|Me
!solfege
|'''Ni'''
|De
|'''Fa'''
|So
|So
|Ra/Na
|Le
|Fli
|Thu
|Thu
|Fi
|Da
|-
|-
!intervals
!7th 8L1s
|vv8
!LLsLLLLLL
|v5
|Da
|M2/m3
|Ro
|^m7
|'''Me'''
|^^4
|'''Nu'''
|Fa
|So
|Le
|Fli
|Thu
|Da
|-
|-
!notes
!8th 8L1s
|vvC
!LsLLLLLLL
|vG
|Da
|D/Eb
|'''Ro'''
|^Bb
|'''Fri'''
|^^F
|Nu
|Fa
|So
|Le
|Fli
|Thu
|Da
|-
|-
|
!9th 8L1s
|
!sLLLLLLLL
|
|Da
|
|'''Re'''
|
|Fri
|
|Nu
|
|Fa
|-
|So
! rowspan="3" |Da's
|Le
|Fli
|Thu
|Da
|}


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


perspan = 0
* 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
!solfege
|Fla
|...
|Tha
|Se
|Nu
|Do
|Fli
|Fa
|Re
|Thu
|So
|Ni
|'''Da'''
|Le
|Le
|Mo
|Fu
|'''Da'''
|Ro
|Flu
|Thi
|Ri/Ni
|Sa
|Me
|Du
|Lo
|Fi
|Ra
|...
|Ma
|-
|-
!intervals
!intervals
|vvM6
|m6
|vM3
|...
|m7
|^~5
|^m3
|v8
|v~6
|P4
|^~2
|^m7
|v5
|v~3
|'''P1'''
|'''P1'''
|^m6
|^~6
|^^M2/^^m3
|^4
|-
!notes
|vvA
|vE
|'''C'''
|^Ab
|^^D/^^Eb
|-
|
|
|
|
|
|
|
|-
! rowspan="3" |Tha's
 
genchain
 
perspan = -1
!solfege
|Se
|Ro
|La/Tha
|Fu
|Di
|-
!intervals
|vv5
|vM2
|vM2
|M6/m7
|v~7
|^4
|P5
|^^1
|^~2
|^1
|vM6
|v~4
|M2
|...
|M3
|-
|-
!notes
!notes
|Ab
|...
|Bb
|vvG
|vvG
|^Eb
|vC
|^^Ab
|F
|vvD
|^Bb
|vG
|^^Eb
|'''C'''
|vvA
|^F
|vD
|vD
|A/Bb
|^^Bb
|^F
|G
|^^C
|vvE
|-
|^C
|
|vA
|
|^^F
|
|D
|
|...
|
|E
|
|}
|
|-
! rowspan="3" |Sa's


genchain
{| class="wikitable center-all"
 
|+
perspan = -2
4L3s MOS scales (L = vM2 = ^<sup>4</sup>m2, s = vvM2 = ^<sup>3</sup>m2)
!solfege
![[Genchain mode numbering|GMN]] name
|Me
!scale
|Do
!1sn
|Sa/Fla
!2nd
|Ru/Nu
!3rd
|Thi
!4th
|-
!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
!5th
!6th
!6th
!7th
!7th
!
!8ve
!8ve
|-
|-
!1st 5L5s
!1st 4L3s
!LsLsLsLsLs
!LLsLsLs
|Da
|Ro
|'''Me'''
|Fu
|Sa
|Le
|Thi
|Da
|-
!2nd 4L3s
!LsLLsLs
|Da
|Ro
|'''Ni'''
|Fu
|'''Sa'''
|Le
|Thi
|Da
|-
!3rd 4L3s
!LsLsLLs
|Da
|Da
|'''Ro'''
|Ro
|Ra
|Ni
|'''Mo'''
|Fu
|Fa
|'''So'''
|'''So'''
|Sa
|Le
|Lo
|'''Thi'''
|Tha
|'''Do'''
|Da
|Da
|-
|-
!2nd 5L5s
!4th 4L3s
!sLsLsLsLsL
!LsLsLsL
|Da
|Da
|'''Du'''
|'''Ro'''
|Ra
|Ni
|'''Nu'''
|Fu
|Fa
|So
|'''Fu'''
|Le
|Sa
|Flu
|Tha
|'''Thu'''
|'''Thu'''
|Da
|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
!5th 4L3s
!Lss x5
!sLLsLsL
|Da
|Da
|'''Re'''
|'''Re'''
|Ro
|Ni
|Ra
|'''Fu'''
|'''Me'''
|Mo
|Fa
|'''Se'''
|So
|So
|Sa
|Le
|'''Le'''
|Thu
|Lo
|Tha
|'''De'''
|Do
|Da
|Da
|-
|-
!2nd 5L10s
!6th 4L3s
!sLs x5
!sLsLLsL
|Da
|Da
|'''Du'''
|Re
|'''Ro'''
|Ni
|Ra
|'''Fa'''
|'''Nu'''
|So
|'''Mo'''
|'''Le'''
|Fa
|Thu
|'''Fu'''
|'''So'''
|Sa
|'''Flu'''
|'''Lo'''
|Tha
|'''Thu'''
|'''Do'''
|Da
|Da
|-
|-
!3rd 5L10s
!7th 4L3s
!ssL x5
!sLsLsLL
|Da
|Da
|Du
|Re
|'''Di'''
|Ni
|Ra
|Nu
|'''Ni'''
|Fa
|Fa
|Fu
|So
|'''Fi'''
|Sa
|Flu
|'''Fli'''
|'''Fli'''
|Tha
|Thu
|Thu
|'''Thi'''
|Da
|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


===(P8/7, ^1) ===
MOS scales covered:
*P = M2/m2 = 171¢
 
*G = ^1 = c (stands for 135/128 in Whitewood)
* 7 = 3L4s (P5 is 515-800¢), but better to use half-5th solfege
*EI = A1 = 0¢
* 10 = 3L7s (P5 is 600-800¢)
*^ = c
* 13 = 3L10s (and 10L3s if P5 < 7\13)


MOS scales covered:
*14 = 7L7s
*21 = 7L14s and 14L7s
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
'''solfege (-a = plain, -u = up, -o = down, -i = lift, -e = drop)'''
|-
|-
! colspan="2" |genspan (gen = ^1)
!genspan
!-12
!-11
!-10
!-9
!-8
!-7
!-6
!-5
!-4
!-3
!-2
!-2
!-1
!-1
Line 20,444: Line 20,600:
!1
!1
!2
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
|-
|-
! rowspan="3" |Fa's
genchain
perspan = 3
!solfege
!solfege
|Fe
|Ri
|Fo
|Shu
|Tha
|Ro
|She
|Li
|Fru
|Fa
|Fa
|Fu
|Lo
|Fi
|Fre
|Mi
|Flu
|'''Da'''
|Mo
|Fle
|Ti
|Nu
|Sa
|To
|Ne
|Pi
|Thu
|Ra
|Po
|The
|-
|-
!intervals
!intervals
|vv4
|/M2
|v4
|^d5
|m7
|vM2
|\d5
|/M6
|^m2
|P4
|P4
|^4
|vM6
|^^4
|\m2
|-
|/M3
!notes
|^m6
|vvF
|'''P1'''
|vF
|vM3
|F
|\m6
|^F
|/M7
|^^F
|^m3
|-
|P5
| colspan="7" |
|vM7
|-
|\m3
! rowspan="3" |Ma's
|/A4
 
|^m7
genchain
|M2
 
|vA4
perspan = 2
|\m7
!solfege
|Me
|Mo
|Ma
|Mu
|Mi
|-
!intervals
|vvM3
|vM3
|M3
|^M3
|^^M3
|-
|-
!notes
!notes
|vvE
|/D
|^Gb
|Bb
|vD
|\Gb
|/A
|^Db
|F
|vA
|\Db
|/E
|^Ab
|'''C'''
|vE
|vE
|E
|\Ab
|^E
|/B
|^^E
|^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
|-
|-
| colspan="7" |
!1st 3L4s
!LsLsLss
|Da
|Nu
|Mo
|Sa
|Fle
|'''To'''
|Ti
|Da
|-
|-
! rowspan="3" |Ra's
!2nd 3L4s
 
!LsLssLs
genchain
|Da
 
|Nu
perspan = 1
|Mo
!solfege
|'''Sa'''
|Re
|Fle
|Ro
|'''Flu'''
|Ra
|Ti
|Ru
|Da
|Ri
|-
|-
!intervals
!3rd 3L4s
|vvM2
!LssLsLs
|vM2
|Da
|M2
|'''Nu'''
|^M2
|Mo
|^^M2
|'''Mi'''
|Fle
|Flu
|Ti
|Da
|-
|-
!notes
!4th 3L4s
|vvD
!sLsLsLs
|vD
|Da
|D
|'''Fre'''
|^D
|Mo
|^^D
|Mi
|Fle
|Flu
|'''Ti'''
|Da
|-
|-
| colspan="7" |
!5th 3L4s
!sLsLssL
|Da
|Fre
|Mo
|Mi
|'''Fle'''
|Flu
|'''Lo'''
|Da
|-
|-
! rowspan="3" |Da's
!6th 3L4s
 
!sLssLsL
genchain
|Da
 
|Fre
perspan = 0
|'''Mo'''
!solfege
|Mi
|De
|'''Fa'''
|Do
|Flu
|'''Da'''
|Lo
|Du
|Da
|Di
|-
|-
!intervals
!7th 3L4s
|vv8
!ssLsLsL
|v8
|Da
|'''P1'''
|Fre
|^1
|'''Fru'''
|^^1
|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
|-
|-
!notes
!1st 3L7s
|vvC
!LssLssLsss
|vC
|Da
|'''C'''
|Ne
|^C
|Nu
|^^C
|Mo
|Pi
|Sa
|Fle
|'''Thu'''
|To
|Ti
|Da
|-
|-
| colspan="7" |
!2nd 3L7s
!LssLsssLss
|Da
|Ne
|Nu
|Mo
|'''Pi'''
|Sa
|Fle
|'''Flu'''
|To
|Ti
|Da
|-
|-
! rowspan="3" |Ta's
!3rd 3L7s
 
!LsssLssLss
genchain
|Da
 
|'''Ne'''
perspan = -1
|Nu
!solfege
|Mo
|Te
|'''Mi'''
|Sa
|Fle
|Flu
|To
|To
|Ta
|Tu
|Ti
|Ti
|Da
|-
|-
!intervals
!4th 3L7s
|vvM7
!sLssLssLss
|vM7
|Da
|M7
|'''Fre'''
|^M7
|Nu
|^^M7
|Mo
|Mi
|Sa
|Fle
|Flu
|'''To'''
|Ti
|Da
|-
|-
!notes
!5th 3L7s
|vvB
!sLssLsssLs
|vB
|Da
|B
|Fre
|^B
|Nu
|^^B
|Mo
|Mi
|'''Sa'''
|Fle
|Flu
|'''Lo'''
|Ti
|Da
|-
|-
| colspan="7" |
!6th 3L7s
!sLsssLssLs
|Da
|Fre
|'''Nu'''
|Mo
|Mi
|'''Fa'''
|Fle
|Flu
|Lo
|Ti
|Da
|-
|-
! rowspan="3" |La's
!7th 3L7s
 
!ssLssLssLs
genchain
|Da
 
|Fre
perspan = -2
|'''Fru'''
!solfege
|Mo
|Le
|Mi
|Fa
|Fle
|Flu
|Lo
|Lo
|La
|'''Ti'''
|Lu
|Da
|Li
|-
|-
!intervals
!8th 3L7s
|vvM6
!ssLssLsssL
|vM6
|Da
|M6
|Fre
|^M6
|Fru
|^^M6
|Mo
|Mi
|Fa
|'''Fle'''
|Flu
|Lo
|'''Li'''
|Da
|-
|-
!notes
!9th 3L7s
|vvA
!ssLsssLssL
|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
|Da
|'''Ro'''
|Fre
|Ra
|Fru
|'''Mo'''
|'''Mo'''
|Ma
|Mi
|'''Fo'''
|Fa
|Fa
|'''So'''
|'''She'''
|Sa
|Flu
|'''Lo'''
|Lo
|La
|Li
|'''To'''
|Ta
|'''Do'''
|Da
|Da
|-
|-
!2nd 7L7s
!10th 3L7s
!sL x7
!sssLssLssL
|Da
|Da
|'''Du'''
|Fre
|Ra
|Fru
|'''Ru'''
|'''Ro'''
|Ma
|Mi
|'''Mu'''
|Fa
|Fa
|She
|'''Fu'''
|Flu
|Sa
|Lo
|'''Su'''
|Li
|La
|'''Lu'''
|Ta
|'''Thu'''
|Da
|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"
{| class="wikitable center-all"
|+
|+
7L14s MOS scales (L = vvM2/vvm2, s = ^1)
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
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
!genspan
!Lss x7
!30
|Da
!...
|'''Re'''
!10
|Ro
!9
|Ra
!8
|'''Me'''
!7
|Mo
!6
|Ma
!5
|'''Fe'''
!4
|Fo
!3
|Fa
!2
|'''Se'''
!1
|So
!0
|Sa
!-1
|'''Le'''
!-2
|Lo
!-3
|La
!-4
|'''Te'''
!-5
|To
!-6
|Ta
!-7
|'''De'''
!-8
|Do
!-9
|Da
!-10
!...
!-30
|-
|-
!2nd 7L14s
!solfege
!sLs x7
|Sha
|Da
|...
|'''Du'''
|Tha
|'''Ro'''
|Fe
|Ra
|Thu
|'''Ru'''
|Fo
|'''Mo'''
|Thi
|Ma
|'''Mu'''
|'''Fo'''
|Fa
|Fa
|'''Fu'''
|De
|'''So'''
|Fu
|Sa
|Do
|'''Su'''
|Fi
|'''Lo'''
|'''Da'''
|La
|Se
|'''Lu'''
|'''To'''
|Ta
|'''Tu'''
|'''Do'''
|Da
|-
!3rd 7L14s
!ssL x7
|Da
|Du
|Du
|'''Di'''
|So
|Ra
|Di
|Ru
|'''Ri'''
|Ma
|Mu
|'''Mi'''
|Fa
|Fu
|'''Fi'''
|Sa
|Sa
|Re
|Su
|Su
|'''Si'''
|Ro
|La
|Si
|Lu
|Ra
|'''Li'''
|...
|Ta
|Pa
|Tu
|-
|'''Ti'''
!intervals
|Da
|d5
|}
|...
 
|m7
== Pergens Summary ==
|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"
{| class="wikitable center-all"
|+
|+
bolded entries are tippy, meaning that ^ and v can easiiy swap
2L7s MOS scales (L = v4 = ^<sup>4</sup>m3, s = ^1 = v<sup>4</sup>M2)
!
![[Genchain mode numbering|GMN]] name
!pergen
!scale
!EI
!0
! colspan="2" |vowels
!perchain and/or genchain
!mapping
!notes
|-
!1
!1
|(P8, P5)
|vA1
| -a -u -o
|aug / dim
| Da - Sa
|(1 1...) (0 1...)
| -i = AA, -e = dd
|-
!2
!2
|(P8/2, P5)
|'''^^d2'''
| -a -u -o
|
|'''Da - Po/Shu- Da'''
|(2 2...) (0 1...)
|tips if P5 < 700¢
|-
!3
!3
|(P8, P4/2)
|vvm2
| -a -u -o
|
|Da - Ru/No - Fa
|(1 2...) (0 -2...)
|
|-
!4
!4
| (P8, P5/2)
!5
|vvA1
!6
| -a -u -o
!7
|
!8
|Da - Nu/Mo - Sa
!9
|(1 1...) (0 2...)
|
|-
|-
!6
!1st 2L7s
|(P8/3, P5)
!ssssLsssL
|'''^<sup>3</sup>d2'''
|Da
| -a -u -o
|Du
|
|Di
|'''Da - Mo - Flu - Da'''
|Re
|(3 3...) (0 1...)
|'''Ro'''
|tips if P5 < 700¢
|Se
|So
|Sa
|Su
|Da
|-
|-
!7
!2nd 2L7s
|(P8, P4/3)
!sssLssssL
|v<sup>3</sup>A1
|Da
| -a -u -o
|Du
|
|Di
|Da - Ro - Nu - Fa
|Re
|(1 2...) (0 -3...)
|'''Fi'''
|
|Se
|So
|Sa
|'''Su'''
|Da
|-
|-
!8
!3rd 2L7s
|(P8, P5/3)
!sssLsssLs
|v<sup>3</sup>m2
|Da
| -a -u -o
|Du
|
|Di
|Da - Ru - Fo - Sa
|'''Re'''
|(1 1...) (0 3...)
|Fi
|
|Se
|So
|Sa
|'''Do'''
|Da
|-
|-
!9
!4th 2L7s
|(P8, P11/3)
!ssLssssLs
|v<sup>3</sup>M2
|Da
| -a -u -o
|Du
|
|Di
|Da - Fu - Do - Fa
|'''Fu'''
|(1 3...) (0 -3...)
|Fi
|
|Se
|So
|'''Sa'''
|Do
|Da
|-
|-
!16
!5th 2L7s
|(P8/4, P5)
!ssLsssLss
|'''^<sup>4</sup>d2'''
|Da
| -a -u -o -i -e
|Du
|
|'''Di'''
|'''Da - Nu - Pe/Shi - Lo - Da'''
|Fu
|(4 4...) (0 1...)
|Fi
|tips if P5 < 700¢
|Se
|So
|'''De'''
|Do
|Da
|-
!6th 2L7s
!sLssssLss
|Da
|Du
|'''Fa'''
|Fu
|Fi
|Se
|'''So'''
|De
|Do
|Da
|-
|-
!17
!7th 2L7s
|(P8, P4/4)
!sLsssLsss
|\\m2, ^^\d2, vv\A1
|Da
| -a -u -o -i -e
|'''Du'''
|lift / drop
|Fa
|Da - Fru - Ri/Ne - Mo - Fa
|Fu
|(1 2...) (0 -4...)
|Fi
|
|Se
|'''Thi'''
|De
|Do
|Da
|-
|-
!18
!8th 2L7s
|(P8, P5/4)
!LssssLsss
|v<sup>4</sup>A1
|Da
|<nowiki>-a -u -o -i -e</nowiki>
|'''Fo'''
|
|Fa
|Da - Ro - Ni/Me - Fu - Sa
|Fu
|(1 1...) (0 4...)
|Fi
|
|'''Se'''
|Thi
|De
|Do
|Da
|-
|-
!19
!9th 2L7s
|(P8, P11/4)
!LsssLssss
|\\A1, vv\m2, vv/d2
|Da
| -a -u -o -i -e
|Fo
|lift / drop
|Fa
|Da - Mu - Fli/Le - Fro - Fa
|Fu
|Fi
|'''Thu'''
|Thi
|De
|Do
|Da
|}
 
== Multi-edo pergens of the form (P8/m, ^1) ==
These pergens map the 5th to an edo, and other primes to other rings (offset copies of the edo). They only make sense musically if the edo's approximation of the 5th has a relative error < 25%. Otherwise there will be a better Sa on another ring. For example, 4-edo with 34% error has 3/2 = 600¢, but additional rings will add a note between 600¢ and 850¢ that will be a much 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¢.
{| class="wikitable center-all"
|+
rank-2 edos with Sa mapped to a good spot
!edo
!rel. error
!generator range
!mapping
!notes
|-
!2-edo
|17%
|204-300¢
|(2 3...) (0 0...)
|maximum of 4 notes
|-
!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...)
|needs 2 more primes to be a valid mapping
|-
!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...)
|needs 2 more primes to be a valid mapping
|-
!15-edo
|
|
|
|
|}
 
===(P8/5, ^1)===
*P = M2/m3 = 200¢
*G = ^1 = c (stands for 81/80 in Blackwood)
*EU = d2 = 0¢
*^ = c
 
MOS scales covered:
*10 = 5L5s
*15 = 5L10s or 10L5s
{| 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) ===
*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
|'''Thu'''
|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
|}
 
== Pergens Summary ==
{| class="wikitable center-all"
|+
bolded entries are tippy, meaning that ^ and v can easiiy swap
 
-uwi = uplift, -owe = downdrop
!
! colspan="2" |pergen
!EU
!vowels
!perchain and/or genchain
!mapping
!tipping points
|-
!1
|(P8, P5)
|unsplit
|vA1
|  -a -u -o (-i -e)
| Da - Sa
|(1 1...) (0 1...)
|
|-
!2
|(P8/2, P5)
|half-8ve
|'''^^d2'''
| -a -u -o
|'''Da - Po/Shu- Da'''
|(2 2...) (0 1...)
|7\12 = 700¢
|-
!3
|(P8, P4/2)
|half-4th
|vvm2
| -a -u -o
|Da - Ru/No - Fa
|(1 2...) (0 -2...)
|
|-
!4
| (P8, P5/2)
|half-5th
|vvA1
| -a -u -o
|Da - Nu/Mo - Sa
|(1 1...) (0 2...)
|
|-
!5
|(P8/2, P4/2)
true double
|half-everything
|vvm2, \\A1, vv\\M2
|  -a -u -o -i -e<br>-uwi -owe
|Da - Ru/No - Fa<br>Fuwi/Sowe - Fli/Le - Duwi/Rowe<br>Da - Ni/Me - Sa
|(2 4...) (0 -2...)
|
|-
!6
|(P8/3, P5)
|third-8ve
|'''^<sup>3</sup>d2'''
| -a -u -o
|'''Da - Mo - Flu - Da'''
|(3 3...) (0 1...)
|7\12 = 700¢
|-
!7
|(P8, P4/3)
|third-4th
|v<sup>3</sup>A1
| -a -u -o
|Da - Ro - Nu - Fa
|(1 2...) (0 -3...)
|
|-
!8
|(P8, P5/3)
|third-5th
|v<sup>3</sup>m2
| -a -u -o
|Da - Ru - Fo - Sa
|(1 1...) (0 3...)
|
|-
!9
|(P8, P11/3)
|third-11th
|v<sup>3</sup>M2
| -a -u -o
|Da - Fu - Do - Fa
|(1 3...) (0 -3...)
|
|-
!10
|(P8/3, P4/2)
|third-8ve<br>half-4th
|vvm2, \<sup>6</sup>A2
|  -a -u -o -i -e<br>-owi -uwe
|Muwe - Se - Luwe<br>Da - Ru/No - Fa<br>Flowi - Thi - Frowi
|(3 6...) (0 -2...)
|
|-
!12
|(P8/2, P4/3)
|half-8ve
third-4th
|'''^^d2''', \<sup>3</sup>A1
| -a -u -o -i -e<br>-uwi -uwe -owi -owe
|Da - Re - Ni - Fa<br>'''Po/Shu - Fluwe - Lowi - To'''
|(2 4...) (0 -3...)
|7\12 = 700¢
|-
!16
|(P8/4, P5)
|quarter-8ve
|'''^<sup>4</sup>d2'''
|  -a -u -o -i -e
|'''Da - Nu - Pe/Shi - Lo - Da'''
|(4 4...) (0 1...)
|7\12 = 700¢
|-
!17
|(P8, P4/4)
|quarter-4th
|'''^<sup>4</sup>dd2''', \\m2, ^^\d2, vv\A1
|  -a -u -o -i -e
|'''Da - Fru - Ri/Ne - Mo - Fa'''
|(1 2...) (0 -4...)
|11\19 = 695¢
|-
!18
|(P8, P5/4)
|quarter-5th
|v<sup>4</sup>A1
|<nowiki>-a -u -o -i -e</nowiki>
|Da - Ro - Ni/Me - Fu - Sa
|(1 1...) (0 4...)
|
|-
!19
|(P8, P11/4)
|quarter-11th
|'''v<sup>4</sup>dd3''', \\A1, vv\m2, vv/d2
|  -a -u -o -i -e
|'''Da - Mu - Fli/Le - Fro - Fa'''
|(1 3...) (0 -4...)
|(1 3...) (0 -4...)
|
|10\17 = 706¢
|-
|-
!20
!20
|(P8, P12/4)
|(P8, P12/4)
|v<sup>4</sup>m2
|quarter-12th
| -a -u -o -i -e
|v<sup>4</sup>m2
|
| -a -u -o -i -e
|Da - Fo - Li/The - Ru - Sa
|Da - Fo - Li/The - Ru - Sa
|(1 0...) (0 4...)
|(1 0...) (0 4...)
|
|
|-
|-
!22
!22
|(P8/2, M2/4)
|(P8/2, M2/4)
|v<sup>4</sup>M2
|half-8ve<br>quarter-tone
| -a -u -o -i -e
|v<sup>4</sup>M2
|
| -a -u -o -i -e
|Da - Fi/Se - Da
|Da - Fi/Se - Da<br>Da - Du - Di/Re - Ro - Ra
Da - Du - Di/Re - Ro - Ra
|(2 3...) (0 2...)
|(2 3...) (0 2...)
|
|(1/2 0)
|-
 
!33
(-3/4 1/2)
|(P8/5, P5)
|-
|fifth-8ve
!33
|v<sup>5</sup>m2
|(P8/5, P5)
| -a -u -o -i -e
|v<sup>5</sup>m2
|Da - Ri - Fo - Su - The - Da
| -a -u -o -i -e
|(5 5...) (0 1...)
|
|
|Da - Ri - Fo - Su - The - Da
|-
|(5 5...) (0 1...)
!34
|(1/5 0) (-1 1)
|(P8, P4/5)
|-
|fifth-4th
!34
|'''^<sup>5</sup>d2'''
|(P8, P4/5)
| -a -u -o -i -e
|^<sup>5</sup>d2
|'''Da - Fri - Ro - Nu - Me - Fa'''
| -a -u -o -i -e
|(1 2...) (0 5...)
|
|7\12 = 700¢
|Da - Fri - Ro - Nu - Me - Fa
|-
|(1 2...) (0 5...)
!35
|
|(P8, P5/5)
|-
|fifth-5th
!35
|v<sup>5</sup>A2
|(P8, P5/5)
| -a -u -o -i -e
|v<sup>5</sup>A2
|Da - Ro - Me - Ni - Fu - Sa
| -a -u -o -i -e
|(1 1...) (0 5...)
|
|
|Da - Ro - Me - Ni - Fu - Sa
|-
|(1 1...) (0 5...)
!36
|
|(P8, P11/5)
|-
|fifth-11th
!36
|v<sup>5</sup>A1
|(P8, P11/5)
| -a -u -o -i -e
|v<sup>5</sup>A1
|Da - Ni - So - Thu - Re - Fa
| -a -u -o -i -e
|(1 3...) (0 -5...)
|
|
|Da - Ni - So - Thu - Re - Fa
|-
|(1 3...) (0 -5...)
!37
|
|(P8, P12/5)
|-
|fifth-12th
!37
|'''^<sup>5</sup>dd2, \<sup>5</sup>d<sup>3</sup>4,''' ^^\d2, v\\m2
|(P8, P12/5)
| -a -u -o -i -e
|^^\d2, v\\m2
|'''Da - Mo - Fle - Ti - Nu - Sa'''
| -a -u -o -i -e
|(1 0...) (0 5...)
|lift / drop
|11\19 = 695¢,<br>13\22 = 709¢
|Da - Mo - Fle - Ti - Nu - Sa
|-
|(1 0...) (0 5...)
!38
|
|(P8, ccP4/5)
|-
|fifth-coco4th
!38
|v<sup>5</sup>M2
|(P8, ccP4/5)
| -a -u -o -i -e
|v<sup>5</sup>M2
|Da - Fi - Do - Fu - De - Fa
| -a -u -o -i -e
|(1 4...) (0 -5...)
|
|
|Da - Fi - Do - Fu - De - Fa
|-
|(1 4...) (0 -5...)
!65
|
|(P8, P4/6)
|}
|sixth-4th
{| class="wikitable center-all"
|v<sup>3</sup>A1, \\m2
|+
| -a -u -o -i -e<br>-uwi -uwe -owi -owe
Multi-edo pergens -- genchain is De Do Da Du Di
|Da - Duwi/Fruwe - Ro - Ri/Ne -<br>- Nu - Mowi/Fowe - Fa
!pergen
|(1 2...) (0 -6...)
!period
|
!5-limit generator
|-
!EI
!66
!perchain
|(P8, P5/6)
!mapping
|sixth-5th
!notes
|vvvm2, \\A1
|-
| -a -u -o -i -e<br>-uwe -owi
| (P8/5, ^1)
|Da - Frowi - Ru - Ni/Me -<br>- Fo - Puwe - Sa
|M2 / m3
|(1 1...) (0 6...)
|16/15 or 81/80
|
|m2
|-
|Da - Ra/Na - Ma/Fa - Sa/Fla - La/Tha- Da
!67
|(5 8...)
|(P8, P11/6)
 
|sitxh-11th
(0 0...)
|vvA1, \<sup>3</sup>M2
|Sawa/Blackwood
| -a -u -o -i -e<br>-uwe -owi
|-
|Da - Nuwe - Fi - Flu/Lo -<br>- Do - Rowi - Fa
|(P8/7, ^1)
|(1 3...) (0 -6...)
|M2 / m2
|
|135/128 or 80/81
|-
|A1
!68
|Da - Ra - Ma - Fa - Sa - La - Ta - Da
|(P8, P12/6)
|(7 11...)
|sixth-12th
(0 0...)
|vvm2, \<sup>3</sup>M2
|Lawa/Whitewood
| -a -u -o -i -e<br>-uwe -owi
|-
|Da - Nowi - Se - Lu/Tho -<br>- Di - Muwe - Sa
|(P8/10, ^1)
|(1 0...) (0 6...)
|???
|
|
|-
|???
!70
|Da - Fra - Ra/Na - Ma - Fa - Pa/Sha - Sa - Fla - La/Tha - Ta - Da
|(P8, ccP5/6)
|(10 16...)
|sixth-coco-5th
(0 0...)
|v<sup>6</sup>A1
|
| -a -u -o -i -e<br>-iyu -eyo
|-
|Da - Fu - Thi - Niyu/Meyo -<br>- Le - Ro - Sa
|(P8/12, ^1)
|(1 -1...) (0 -6...)
|
|-
!100
|(P8, P12/7)
|seventh-12th
|v<sup>7</sup>A2
| -a -u -o -i -e<br>-iyu -eyo
|Da - Meyo - Fu - Le -<br>- Thi - Ro - Niyu - Sa
|(1 0...) (0 7...)
|
|}
{| class="wikitable center-all"
|+
Multi-edo pergens -- genchain is always De Do Da Du Di
! colspan="2" |pergen
!EU
!period
!perchain
!mapping
!notes
|-
|(P8/2, ^1)
|rank-2 2-edo
|M2
|P4 / P5
|Da - Fa/Sa - Da
|(2 3...) (0 0...)
|silly, 9/8 vanishes
|-
|(P8/3, ^1)
|rank-2 3-edo
|m3
|M2 / P4
|Da - Fa - Sa - Da
|(3 5...) (0 0...)
|silly, 32/27 vanishes
|-
|(P8/4, ^1)
|rank-2 4-edo
|M2
|??
|Da - ?? - Fa/Sa - ?? - Da
|(4 6...) (0 0...)
|silly, 9/8 vanishes<br>multi-ring
|-
| (P8/5, ^1)
|rank-2 5-edo
|m2
|M2 / m3
|Da - Ra/Na - Ma/Fa - Sa/Fla - La/Tha- Da
|(5 8...) (0 0...)
|if Blackwood,<br>generator = 16/15
|-
|(P8/7, ^1)
|rank-2 7-edo
|A1
|M2 / m2
|Da - Ra - Ma - Fa - Sa - La - Ta - Da
|(7 11...) (0 0...)
|if Whitewood,<br>generator = 135/128
|-
|(P8/10, ^1)
|rank-2 10-edo
|???
|???
|Da - Fra - Ra/Na - Ma - Fa - Pa/Sha - Sa - Fla - La/Tha - Ta - Da
|(10 16...) (0 0...)
|'''solfege names'''<br>'''may be wrong'''
|-
|(P8/12, ^1)
|rank-2 12-edo
|d2
|A1 / m2
|A1 / m2
|
|d2
|Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da
|Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da
|(12 19...) (0 0...)
|(12 19 28...) (0 0 -1...)
|Lalawa/Compton
|if Compton,<br>generator = 81/80
|}
|}
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