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Line 7: Line 7:
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: 12-edo numeric solfege, the ultimate performer solfege
discuss performerr 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 33: Line 33:
Sharpening and flattening refers to adding/subtracting the [[2187/2048|lawa unison]] Lw1. In edos 7, 14, 21, 28 and 35, there is no need for the altered consonants, since Lw1 is tempered out. Some other edos (12, ??) also omit them.
Sharpening and flattening refers to adding/subtracting the [[2187/2048|lawa unison]] Lw1. In edos 7, 14, 21, 28 and 35, there is no need for the altered consonants, since Lw1 is tempered out. Some other edos (12, ??) also omit them.


The vowel sequence varies depending on the edo or pergen. There is always -a for pl'''a'''in, and almost always -u for '''u'''p and -o for d'''o'''wn. Larger edos also have either -i for m'''i'''d, or -i for dup (double-up) and -e for dud (double-down).
The vowel sequence varies depending on the edo or pergen. There is always -a for pl'''a'''in, and almost always -u for '''u'''p and -o for d'''o'''wn. Larger edos also have either -i for m'''i'''d, or -i for dup (double-up) and -e for dud (double-down). Pergens are similar, except occasionally -i/-e means lift/drop.
{| class="wikitable center-all"
{| class="wikitable center-all"
|+ the three vowel sequences
|+ the three vowel sequences
Line 54: Line 54:
!5 vowels
!5 vowels
!53, 60
!53, 60
|<nowiki>-e = dud</nowiki>
| -e = dud (or drop)
|<nowiki>-o = down</nowiki>
|<nowiki>-o = down</nowiki>
|<nowiki>-a = plain</nowiki>
|<nowiki>-a = plain</nowiki>
|<nowiki>-u = up</nowiki>
|<nowiki>-u = up</nowiki>
|<nowiki>-i = dup</nowiki>
| -i = dup (or lift)
|}
|}
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.
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Superflat edos have a very flat 5th. A uniform solfege can still be used, but the size of the interval won't match what its name implies very well.
Superflat edos have a very flat 5th. A uniform solfege can still be used, but the size of the interval won't match what its name implies very well.


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


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


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


In edos with an even [[Sharpness|penta-sharpness]], there are "in-between" notes with two names. For example, 4\19 (Ru/No) is named as both a 2nd and a 3rd, a "serd".
In edos with an even [[Sharpness|penta-sharpness]], there are "in-between" notes with two names. For example, 4\19 (Ru/No) is named as both a 2nd and a 3rd.
 
* 1sn/2nd = unisecond (secison)
* 2nd/3rd = serd (thecond)
* 3rd/4th = ford (thorth)
* 4th/5th = tritone
* 5th/6th = sifth (sexth)
* 6th/7th =  sexth? siventh?
* 7th/8ve = setave? octenth?


=== Example Scales ===
=== Example Scales ===
(The prime limits assumes a larger edo in which both 81/80 and 64/63 = 1 edostep)
(The prime limits assumes a larger edo in which both 81/80 and 64/63 are 1 edostep.)
{| class="wikitable  center-all"
{| class="wikitable  center-all"
|+
|+
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=== Suggestion for learning ===
=== Suggestion for learning ===
Even with many familiar consonants and a consistent vowel sequence, it can take a while to master a large solfege. One might want to divide-and-conquer. Start with using this simple solfege:
Even with many familiar consonants and a consistent vowel sequence, it can take a while to master a large solfege. One might want to take a divide-and-conquer approach. Start with using this simple solfege:


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


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


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:
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To find the [[octave complement]] of any interval:
To find the [[octave complement]] of any interval:


* change the '''degree''' as usual: 2nd <--> 7th, 3rd <--> 6th, and 4th <--> 5th
* change the '''degree''' as usual: 2nd <--> 7th, 3rd <--> 6th, and 4th <--> 5th.
* change the '''quality''' as usual: major <--> minor and aug <--> dim, but perfect and mid are unchanged
* change the '''quality''' as usual: major <--> minor and aug <--> dim, but perfect and mid are unchanged.
* find the '''consonant''' via the quality and degree
* get the new '''consonant''' from the quality and degree.
* change the '''vowel''' as expected: -u <--> -o, but -a is unchanged. If -e is used, -i <--> -e, otherwise -i is unchanged.
* change the '''vowel''' as expected: -u <--> -o, but -a is unchanged. If -e is used, -i <--> -e, otherwise -i is unchanged.


Line 185: Line 177:
Sha - Fra - Fla - Na - Tha - Fa - Da - Sa - Ra - La - Ma - Ta - Pa
Sha - Fra - Fla - Na - Tha - Fa - Da - Sa - Ra - La - Ma - Ta - Pa


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


For example, 31edo uses 3 vowels. Since Pa = Sho, the end of the -a chain connects to the start of the -o chain. Since Po = Fu, the -o chain connects to the -u chain. Since Pu = Sha, the -u chain connects back to the -a chain, making a circle of 31 5ths:
For example, 31edo uses 3 vowels. Since Pa = Sho, the end of the -a chain connects to the start of the -o chain. Since Po = Fu, the -o chain connects to the -u chain. Since Pu = Sha, the -u chain connects back to the -a chain, making a circle of 31 5ths:
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* ya (5-limit): yo/gu = 5-over/5-under = subtract/add 81/80
* ya (5-limit): yo/gu = 5-over/5-under = subtract/add 81/80
* za (2.3.7): zo/ru = 7-over/7-under = subtract/add 64/63
* za (2.3.7): zo/ru = 7-over/7-under = subtract/add 64/63
* ila (2.3.11): ilo/lu = 11-over/11-under = subtract/add 729/704
* ila (2.3.11): ilo/lu = 11-over/11-under = subtract/add [[729/704]]
* tha (2.3.13): tho/thu = 13-over/13-under = subtract/add 27/26
* tha (2.3.13): tho/thu = 13-over/13-under = subtract/add 27/26


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


If 81/80 maps to 1 edostep, then gu/yo = up/down. Likewise with the other commas. The table below shows that almost every edo has at least one such correlation. Parentheses are used when the prime's relative error is high, e.g. 12edo's prime 11.
If 81/80 maps to 1 edostep, then yo/gu = down/up = -o/-u. Likewise with the other commas. The table below shows that almost every edo has at least one such correlation. Parentheses are used when the prime's relative error is high, e.g. 12edo's prime 11.
{| class="wikitable  center-all"
{| class="wikitable  center-all"
|+
|+
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|-
|-
! rowspan="2" |ya
! rowspan="2" |ya
|
|(yo)
|
|yo
|
|
|yo
|yo
|
|
|
|yo
|
|
|(yo)
|
|yo
|
|
|yo
|(yo)
|
|yo
|
|yo
|-
|
|
|(gu)
|(gu)
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|gu
|gu
|-
|-
! rowspan="2" |za
|
|
|(yo)
|
|
|yo
|zo
|
|
|zo
|zo
|
|
|yo
|zo
|yo
|zo
|
|
|zo
|zo
|zo
|zo
|(zo)
|
|
|zo
|zo
|
|
|yo
|zo
|zo
|
|
|zo
|
|
|(yo)
|
|yo
|
|
|yo
|(yo)
|
|yo
|
|
|yo
|-
|-
! rowspan="2" |za
|
|
|
|
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|
|
|-
|-
! rowspan="2" |ila
|(ilo)
|ilo
|
|
|
|
|zo
|ilo
|
|
|zo
|zo
|
|
|zo
|zo
|
|
|zo
|ilo
|zo
|zo
|zo
|(zo)
|
|zo
|zo
|
|zo
|zo
|
|zo
|
|
|-
! rowspan="2" |ila
|(ilo)
|ilo
|
|
|ilo
|
|
|
|ilo
|
|
|
|
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== About the edo list ==
== About the edo list ==
This list only includes edos that have uniform solfeges, which are edos with both sharpness and penta-sharpness of 5 or less. Smaller edos are included with numeric solfeges. Excluded edos: 30, 37, 42, 44, 47, 49, 51-52, 54, 56-59, and everything under 5 or over 60. A total of 43 edos, and 41 uniform solfeges.
This list only includes edos that have uniform solfeges, which are edos with both sharpness and penta-sharpness of 5 or less. However, smaller edos are included with numeric solfeges. Excluded edos: 1-4, 30, 37, 42, 44, 47, 49, 51-52, 54, 56-59, and everything under 5 or over 60. A total of 43 edos, and 41 uniform solfeges.
{| class="wikitable  center-all"
{| class="wikitable  center-all"
|+
|+
Line 5,197: Line 5,189:
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
uniform solfege #2 (-a = plain, -i = mid/down)
Kite's diatonic solfege (-i -e -a -o -u = ^M M ~ m vm), see 31edo
![[24edo]]
![[24edo]]
!0
!0
Line 5,227: Line 5,219:
!notes
!notes
|C
|C
|vDb
|^C
 
vDb
|Db
|Db
|vD
|vD
|D
|D
|vEb
|^D
 
vEb
|Eb
|Eb
|vE
|vE
|E
|E
|vF
|^E
 
vF
|F
|F
|vF#/vGb
|^F
|F#/Gb
 
|vG
vGb
|F#
 
Gb
|^F#
 
vG
|G
|G
|vAb
|^G
 
vAb
|Ab
|Ab
|vA
|vA
|A
|A
|vBb
|^A
 
vBb
|Bb
|Bb
|vB
|vB
|B
|B
|vC
|^B
 
vC
|C
|C
|-
|-
!intervals
!intervals
|P1
|P1
|vm2
|^1
 
vm2
|m2
|m2
|~2
|~2
|M2
|M2
|vm3
|^M2
 
vm3
|m3
|m3
|~3
|~3
|M3
|M3
|v4
|^M3
 
v4
|P4
|P4
|vA4/vd5
|^4
|A4/d5
 
|v5
vd5
|A4
 
d5
|^A4
 
v5
|P5
|P5
|vm6
|^5
 
vm6
|m6
|m6
|~6
|~6
|M6
|M6
|vm7
|^M6
 
vm7
|m7
|m7
|~7
|~7
|M7
|M7
|v8
|^M7
 
v8
|P8
|P8
|-
|-
!solfege
!solfege
|Do
|Da
|Da
|Fri
 
|Fra
Ru
|Ro
|Ra
|Re
|Ri
|Ri
|Ra
 
|Ni
Mu
|Na
|Mo
|Ma
|Me
|Mi
|Mi
|Ma
 
Fu
|Fo
|Fa
 
Su
|Fe
 
So
|Fi
|Fi
|Fa
 
|Pi/Shi
Sa
|Pa/Sha
|Se
|Si
|Si
|Sa
 
|Fli
Lu
|Fla
|Lo
|La
|Le
|Li
|Li
|La
 
|Thi
Tu
|Tha
|To
|Ta
|Te
|Ti
|Ti
|Ta
 
|Di
Du
|Da
|Do
|}
|}
plain/mid rings:


Da Sa Ra La Ma Ta Pa/Sha Fra Fla Na Tha Fa Da
* plain circle: <u>Do Se</u> Re Le Me Te Fe/So Ro Lo Mo To Fo Do
* mid/inbetween circle: Da/Ru Si/Lu Ri/Mu Li/Tu Mi/Fu Ti/Du Fi/Sa Ra La Ma Ta Fa/Su Da/Ru


Di Si Ri Li Mi Ti Pi/Shi Fri Fli Ni Thi Fi Di
== 25edo ==
 
''Simpler, but you can't name the in-between notes (50¢, 250¢, 450¢) as up notes, which is nice.''
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
Kite's diatonic solfege (-i -e -a -o -u = ^M M ~ m vm), see 31edo
uniform solfege (-a = plain, -u = up, -o = down, -i = dup/dud = downmid/upmid)
![[24edo]]
![[25edo]]
!0
!edosteps
!1
! colspan="2" |solfege names
!2
! colspan="4" |[[Ups and downs notation|ups and downs]] names
!3
|-
!4
!unisons
!5
|0-1
!6
| colspan="2" |Da Du/Fru
!7
| colspan="2" |P1 ^1/^m2
!8
| colspan="2" |C ^C/^Db
!9
!10
!11
!12
!13
!14
!15
!16
!17
!18
!19
!20
!21
!22
!23
!24
|-
|-
!notes
!2nds
|C
|1-5
|^C
|Du/Fru Fri
 
|Ri Ro Ra/Na
vDb
|^1/^m2 v~2
|Db
|^~2 vM2 M2/m3
|vD
|^C/^Db ^^Db
|D
|vvD vD D/Eb
|^D
 
vEb
|Eb
|vE
|E
|^E
 
vF
|F
|^F
 
vGb
|F#
 
Gb
|^F#
 
vG
|G
|^G
 
vAb
|Ab
|vA
|A
|^A
 
vBb
|Bb
|vB
|B
|^B
 
vC
|C
|-
|-
!intervals
!3rds
|P1
|5-9
|^1
|Ra/Na Nu Ni
 
|Mi Mo
vm2
|M2/m3 ^m3 v~3
|m2
|^~3 vM3
|~2
|D/Eb ^Eb ^^Eb
|M2
|vvE vE
|^M2
|-
 
!4ths
vm3
|10
|m3
| colspan="2" |Fa
|~3
| colspan="2" |P4
|M3
| colspan="2" |F
|^M3
|-
 
!tritones
v4
|11-14
|P4
| colspan="2" |Fu/Shu Fi/Shi Pi/Si Po/So
|^4
| colspan="2" |^4/^d5 v~4/v~5 ^~4/^~5 vA4/v5
 
| colspan="2" |^F/^Gb ^^F/^^Gb vvF#/vvG vF#/vG
vd5
|-
|A4
!5ths
 
|15
d5
| colspan="2" |Sa
|^A4
| colspan="2" |P5
 
| colspan="2" |G
v5
|P5
|^5
 
vm6
|m6
|~6
|M6
|^M6
 
vm7
|m7
|~7
|M7
|^M7
 
v8
|P8
|-
|-
!solfege
!6ths
|Do
|16-20
|Da
 
Ru
|Ro
|Ra
|Re
|Ri
 
Mu
|Mo
|Ma
|Me
|Mi
 
Fu
|Fo
|Fa
 
Su
|Fe
 
So
|Fi
 
Sa
|Se
|Si
 
Lu
|Lo
|La
|Le
|Li
 
Tu
|To
|Ta
|Te
|Ti
 
Du
|Do
|}
 
== 25edo ==
{| class="wikitable center-all"
|+
uniform solfege (-a = plain, -u = up, -o = down, -i = dup/dud = downmid/upmid)
![[25edo]]
!edosteps
! colspan="2" |solfege names
! colspan="4" |[[Ups and downs notation|ups and downs]] names
|-
!unisons
|0-1
| colspan="2" |Da Du/Fru
| colspan="2" |P1 ^1/^m2
| colspan="2" |C ^C/^Db
|-
!2nds
|1-5
|Du/Fru Fri
|Ri Ro Ra/Na
|^1/^m2 v~2
|^~2 vM2 M2/m3
|^C/^Db ^^Db
|vvD vD D/Eb
|-
!3rds
|5-9
|Ra/Na Nu Ni
|Mi Mo
|M2/m3 ^m3 v~3
|^~3 vM3
|D/Eb ^Eb ^^Eb
|vvE vE
|-
!4ths
|10
| colspan="2" |Fa
| colspan="2" |P4
| colspan="2" |F
|-
!tritones
|11-14
| colspan="2" |Fu/Shu Fi/Shi Pi/Si Po/So
| colspan="2" |^4/^d5 v~4/v~5 ^~4/^~5 vA4/v5
| colspan="2" |^F/^Gb ^^F/^^Gb vvF#/vvG vF#/vG
|-
!5ths
|15
| colspan="2" |Sa
| colspan="2" |P5
| colspan="2" |G
|-
!6ths
|16-20
|Flu Fli
|Flu Fli
|Li Lo La/Tha
|Li Lo La/Tha
Line 5,628: Line 5,505:
| colspan="2" |'''vC''' C (^C)
| colspan="2" |'''vC''' C (^C)
|}
|}
plain ring: Da Sa Ra/Na La/Tha Fa Da


up ring: Fu/Shu Du/Fru Flu Nu Thu Fu/Shu
* plain ring: Da Sa Ra/Na La/Tha Fa Da
 
* up ring: Fu/Shu Du/Fru Flu Nu Thu Fu/Shu
downmid ring: Fi/Shi Fri Fli Ni Thi Fi/Shi
* downmid ring: Fi/Shi Fri Fli Ni Thi Fi/Shi
 
* upmid ring: Pi/Si Ri Li Mi Ti Pi/Si
upmid ring: Pi/Si Ri Li Mi Ti Pi/Si
* down ring: Po/So Ro Lo Mo To/Do Po/So
 
{| class="wikitable center-all"
down ring: Po/So Ro Lo Mo To/Do Po/So
{| class="wikitable center-all"
|+
|+
'''circles of fifths'''
'''circles of fifths'''
Line 6,364: Line 6,238:
{| class="wikitable center-all"
{| class="wikitable center-all"
|+
|+
Kite's bright-dim solfege (-i -e -a -o -u = ^M M ~ m vm), see 24edo
Kite's bright-to-dim solfege (-i -e -a -o -u = ^M M ~ m vm), see 24edo
![[31edo]]
![[31edo]]
!solfege names
!solfege names
Line 9,553: Line 9,427:
|-
|-
!genspan
!genspan
!...
!-13
!-12
!-11
!-11
!-10
!-10
Line 9,577: Line 9,452:
!10
!10
!11
!11
!...
!12
!13
|-
|-
!solfege
!solfege
| rowspan="3" |...
|Sho
|Fro
|Flo
|Flo
|No
|No
Line 9,604: Line 9,481:
|Lu
|Lu
|Mu
|Mu
| rowspan="3" |...
|Tu
|Pu
|-
|-
!intervals
!intervals
|dd5
|d2
|d6
|d6
|d3
|d3
Line 9,630: Line 9,510:
|A6
|A6
|A3
|A3
|A7
|AA4
|-
|-
!notes
!notes
|Gbb
|Dbb
|Abb
|Abb
|Ebb
|Ebb
Line 9,655: Line 9,539:
|A#
|A#
|E#
|E#
|B#
|Fx
|}
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
Line 11,816: Line 11,702:
Similar tables can be made for every mode of 7L3s, 10L3s or 3L10s
Similar tables can be made for every mode of 7L3s, 10L3s or 3L10s


== #5 (P8/2, P4/2) half-all (incomplete) ==
== #5 (P8/2, P4/2) half-everything (incomplete) ==
It has only 4 fifthchains, but two of them are at the half-octave, and require double names. Hmm must think about this...
It has only 4 fifthchains, but two of them are at the half-octave, and require double names. Hmm must think about this...


Line 16,603: Line 16,489:
|Ni
|Ni
Fe
Fe
|Fo
|Fo
|Fa
|Fa
|Fu
|Fu
|Fi
|Fi
Se
Se
|So
|So
|'''Sa'''
|'''Sa'''
|'''Fla'''
|'''Fla'''
|Flu
|Flu
|Fli
|Fli
The
The
|Tho
|Tho
|Tha
|Tha
|Thu
|Thu
|Thi
|Thi
De
De
|Do
|Do
|Da
|Da
|-
|-
!10th 2L20s
!10th 2L20s
!sLsssssssss x2
!sLsssssssss x2
|Da
|Da
|'''Du'''
|'''Du'''
|'''Fru'''
|'''Fru'''
|Fri
|Fri
Ne
Ne
|No
|No
|Na
|Na
|Nu
|Nu
|Ni
|Ni
Fe
Fe
|Fo
|Fo
|Fa
|Fa
|Fu
|Fu
|Fi
|Fi
Se
Se
|'''So'''
|'''So'''
|'''Flo'''
|'''Flo'''
|Fla
|Fla
|Flu
|Flu
|Fli
|Fli
The
The
|Tho
|Tho
|Tha
|Tha
|Thu
|Thu
|Thi
|Thi
De
De
|Do
|Do
|Da
|Da
|-
|-
!11th 2L20s
!11th 2L20s
!Lssssssssss x2
!Lssssssssss x2
|Da
|Da
|'''Fra'''
|'''Fra'''
|Fru
|Fru
|Fri
|Fri
Ne
Ne
|No
|No
|Na
|Na
|Nu
|Nu
|Ni
|Ni
Fe
Fe
|Fo
|Fo
|Fa
|Fa
|Fu
|Fu
|Fi
|Fi
Se
Se
|'''Shi'''
|'''Shi'''
'''Fle'''
'''Fle'''
|Flo
|Flo
|Fla
|Fla
|Flu
|Flu
|Fli
The
|Tho
|Tha
|Thu
|Thi
De
|Do
|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
* G = P5 '''<u>or</u>''' ^1/v<sup>4</sup>m2
* 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
!solfege
|Fro
|Flo
|No
|Tho
|Fo
|Do
|So
|Ro
|Lo
|-
!intervals
|vm2
|vm6
|vm3
|vm7
|v4
|v8
|v5
|vM2
|vM6
|-
!notes
|vDb
|vAb
|vEb
|vBb
|vF
|vC
|vG
|vD
|vA
|-
| colspan="10" |
|
|-
! rowspan="3" |dup
 
genchain
!solfege
|Thi
|Fi
|Di
|Si
|Ri
|Li
|Mi
|Ti
|Pi
|-
!intervals
|^^m7
|^^4
|^^1
|^^5
|^^M2
|^^M6
|^^M3
|^^M7
|^^A4
|-
!notes
|^^Bb
|^^F
|^^C
|^^G
|^^D
|^^A
|^^E
|^^B
|^^F#
|-
| colspan="10" |
|
|-
! rowspan="3" |plain
 
genchain
!solfege
|Fla
|Na
|Tha
|Fa
|'''Da'''
|Sa
|Ra
|La
|Ma
|-
!intervals
|m6
|m3
|m7
|P4
|'''P1'''
|P5
|M2
|M6
|M3
|-
!notes
|Ab
|Eb
|Bb
|F
|'''C'''
|G
|D
|A
|E
|-
| colspan="10" |
|
|-
! rowspan="3" |dud
 
genchain
!solfege
|She
|Fre
|Fle
|Ne
|The
|Fe
|De
|Se
|Re
|-
!intervals
|vvd5
|vvm2
|vvm6
|vvm3
|vvm7
|vv4
|vv8
|vv5
|vvM2
|-
!notes
|vvGb
|vvDb
|vvAb
|vvEb
|vvBb
|vvF
|vvC
|vvG
|vvD
|-
| colspan="10" |
|
|-
! rowspan="3" |up
 
genchain
!solfege
|Nu
|Thu
|Fu
|Du
|Su
|Ru
|Lu
|Mu
|Tu
|-
!intervals
|^m3
|^m7
|^4
|^1
|^5
|^M2
|^M6
|^M3
|^M7
|-
!notes
|^Eb
|^Bb
|^F
|^C
|^G
|^D
|^A
|^E
|^B
|}
{| class="wikitable center-all"
|+
'''solfege (-a = plain, -u = up, -o = down, -i = dup, -e = dud)'''
|-
! colspan="2" |genspan (gen = ^1)
!4
!3
!2
!1
!0
!-1
!-2
!-3
!-4
|-
! rowspan="3" |Fa's
 
genchain
!solfege
|She
|Fi
|Fu
|Fa
|Fo
|Fe
|Mi
|Mu
|Ma
|-
!intervals
|vvd5
|^^4
|^4
|P4
|v4
|vv4
|^^M3
|^M3
|M3
|-
!notes
|vvGb
|^^F
|^F
|F
|vF
|vvF
|^^E
|^E
|E
|-
| colspan="11" |
|-
! rowspan="3" |Ra's
 
genchain
!solfege
|Nu
|Na
|No
|Ne
|Ri
|Ru
|Ra
|Ro
|Re
|-
!intervals
|^m3
|m3
|vm3
|vvm3
|^^M2
|^M2
|M2
|vM2
|vvM2
|-
!notes
|^Eb
|Eb
|vEb
|vvEb
|^^D
|^D
|D
|vD
|vvD
|-
| colspan="11" |
|-
! rowspan="3" |Da's
 
genchain
!solfege
|Fro
|Fre
|Di
|Du
|'''Da'''
|Do
|De
|Ti
|Tu
|-
!intervals
|vm2
|vvm2
|^^1
|^1
|'''P1'''
|v8
|vv8
|^^M7
|^M7
|-
!notes
|vDb
|vvDb
|^^C
|^C
|'''C'''
|vC
|vvC
|^^B
|^B
|-
| colspan="11" |
|-
! rowspan="3" |Tha's
 
genchain
!solfege
|Thi
|Thu
|Tha
|Tho
|The
|Li
|Lu
|La
|Lo
|-
!intervals
|^^m7
|^m7
|m7
|vm7
|vvm7
|^^M6
|^M6
|M6
|vM6
|-
!notes
|^^Bb
|^Bb
|Bb
|vBb
|vvBb
|^^A
|^A
|A
|vA
|-
| colspan="11" |
|-
! rowspan="3" |Sa's
 
genchain
!solfege
|Fla
|Flo
|Fle
|Si
|Su
|Sa
|So
|Se
|Pi
|-
!intervals
|m6
|vm6
|vvm6
|^^5
|^5
|P5
|v5
|vv5
|^^A4
|-
!notes
|Ab
|vAb
|vvAb
|^^G
|^G
|G
|vG
|vvG
|^^F#
|}
 
{| class="wikitable center-all"
|+
5L5s MOS scales (L = ^M2/v<sup>4</sup>m3, s = ^1)
![[Genchain mode numbering|GMN]] name
!scale
!1sn
!
!2nd
!
!4th
!
!5th
!
!7th
!
!8ve
|-
!1st 5L5s
!Ls-Ls-Ls-Ls-Ls
|Da
|'''Ru'''
|Ri
|'''Fe'''
|Fo
|'''Sa'''
|Su
|'''Li'''
|The
|'''Do'''
|Da
|-
!2nd 5L5s
!sL-sL-sL-sL-sL
|Da
|'''Du'''
|Ri
|'''Ne'''
|Fo
|'''Fa'''
|Su
|'''Si'''
|The
|'''Tho'''
|Da
|}
 
{| class="wikitable center-all"
|+
5L10s MOS scales (L = M2 = rhymes, s = ^1/v<sup>4</sup>m2 = no rhyme)
 
if P5 < 8\15 = 640¢, swap L and s to get 10L5s
![[Genchain mode numbering|GMN]] name
!scale
!1sn
!
!
!2nd
!3rd
!
!4th
!
!
!5th
!
!6th
!7th
!
!
!8ve
|-
!1st 5L10s
!Lss-Lss-Lss-Lss-Lss
|Da
|'''Ra'''
|Ru
|Ri
|'''Mi'''
|Fe
|Fo
|'''So'''
|Sa
|Su
|'''Lu'''
|Li
|The
|'''De'''
|Do
|Da
|-
!2nd 5L10s
!sLs-sLs-sLs-sLs-sLs
|Da
|'''Du'''
|'''Ru'''
|Ri
|'''Ne'''
|'''Fe'''
|Fo
|'''Fa'''
|'''Sa'''
|Su
|'''Si'''
|'''Li'''
|The
|'''Tho'''
|'''Do'''
|Da
|-
!3rd 5L10s
!ssL-ssL-ssL-ssL-ssL
|Da
|Du
|'''Di'''
|Ri
|Ne
|'''No'''
|Fo
|Fa
|'''Fu'''
|Su
|Si
|'''Fle'''
|The
|Tho
|'''Tha'''
|Da
|}
 
== <nowiki>#</nowiki>34 (P8, P4/5) fifth-4th ==
 
* G = ^^m2/v<sup>3</sup>A1
* EI = ^<sup>5</sup>d2
* ^ = 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
!10
!9
!8
!7
!6
!5
!4
!3
!2
!1
!0
!-1
!-2
!-3
!-4
!-5
!-6
!-7
!-8
!-9
!-10
|-
!solfege
|Tha
|Le
|Flu
|So
|Shi
|Fa
|Me
|Nu
|Ro
|Fri
|'''Da'''
|Te
|Thu
|Lo
|Fli
|Sa
|Pe
|Fu
|Mo
|Ni
|Ra
|-
!intervals
|m7
|vvM6
|^m6
|v5
|^^d5
|P4
|vvM3
|^m3
|vM2
|^^m2
|'''P1'''
|vvM7
|^m7
|vM6
|^^m6
|P5
|vvA4
|^4
|vM3
|^^m3
|M2
|-
!notes
|Bb
|vvA
|^Ab
|vG
|^^Gb
|F
|vvE
|^Eb
|vD
|^^Db
|'''C'''
|vvB
|^Bb
|vA
|^^Ab
|G
|vvF#
|^F
|vE
|^^Eb
|D
|}
{| class="wikitable center-all"
|+
1L9s MOS scales (L = ^^m3/v<sup>3</sup>A2, s = ^^m2/v<sup>3</sup>A1)
![[Genchain mode numbering|GMN]] name
!scale
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
|-
!1st 1L9s
!Lsssssssss
|Da
|'''Ni'''
|Mo
|Fu
|Pe
|Sa
|Fli
|Lo
|Thu
|Te
|Da
|-
!2nd 1L9s
!sLssssssss
|Da
|'''Fri'''
|'''Mo'''
|Fu
|Pe
|Sa
|Fli
|Lo
|Thu
|Te
|Da
|-
!3rd 1L9s
!ssLsssssss
|Da
|Fri
|'''Ro'''
|'''Fu'''
|Pe
|Sa
|Fli
|Lo
|Thu
|Te
|Da
|-
!4th 1L9s
!sssLssssss
|Da
|Fri
|Ro
|'''Nu'''
|'''Pe'''
|Sa
|Fli
|Lo
|Thu
|Te
|Da
|-
!5th 1L9s
!ssssLsssss
|Da
|Fri
|Ro
|Nu
|'''Me'''
|'''Sa'''
|Fli
|Lo
|Thu
|Te
|Da
|-
!6th 1L9s
!sssssLssss
|Da
|Fri
|Ro
|Nu
|Me
|'''Fa'''
|'''Fli'''
|Lo
|Thu
|Te
|Da
|-
!7th 1L9s
!ssssssLsss
|Da
|Fri
|Ro
|Nu
|Me
|Fa
|'''Shi'''
|'''Lo'''
|Thu
|Te
|Da
|-
!8th 1L9s
!sssssssLss
|Da
|Fri
|Ro
|Nu
|Me
|Fa
|Shi
|'''So'''
|'''Thu'''
|Te
|Da
|-
!9th 1L9s
!ssssssssLs
|Da
|Fri
|Ro
|Nu
|Me
|Fa
|Shi
|So
|'''Flu'''
|'''Te'''
|Da
|-
!10th 1L9s
!sssssssssL
|Da
|Fri
|Ro
|Nu
|Me
|Fa
|Shi
|So
|Flu
|'''Le'''
|Da
|}
{| class="wikitable center-all"
|+
1L10s MOS scales (L = M2 = rhymes, s = ^^m2/v<sup>3</sup>A1 = no rhyme)
![[Genchain mode numbering|GMN]] name
!scale
!1sn
!2nd
!
!3rd
!
!4th
!5th
!
!6th
!
!7th
!8ve
|-
!1st 1L10s
!Lssssssssss
|Da
|'''Ra'''
|Ni
|Mo
|Fu
|Pe
|Sa
|Fli
|Lo
|Thu
|Te
|Da
|-
!2nd 1L10s
!sLsssssssss
|Da
|'''Fri'''
|'''Ni'''
|Mo
|Fu
|Pe
|Sa
|Fli
|Lo
|Thu
|Te
|Da
|-
!3rd 1L10s
!ssLssssssss
|Da
|Fri
|'''Ro'''
|'''Mo'''
|Fu
|Pe
|Sa
|Fli
|Lo
|Thu
|Te
|Da
|-
!4th 1L10s
!sssLsssssss
|Da
|Fri
|Ro
|'''Nu'''
|'''Fu'''
|Pe
|Sa
|Fli
|Lo
|Thu
|Te
|Da
|-
!5th 1L10s
!ssssLssssss
|Da
|Fri
|Ro
|Nu
|'''Me'''
|'''Pe'''
|Sa
|Fli
|Lo
|Thu
|Te
|Da
|-
!6th 1L10s
!sssssLsssss
|Da
|Fri
|Ro
|Nu
|Me
|'''Fa'''
|'''Sa'''
|Fli
|Lo
|Thu
|Te
|Da
|-
!7th 1L10s
!ssssssLssss
|Da
|Fri
|Ro
|Nu
|Me
|Fa
|'''Shi'''
|'''Fli'''
|Lo
|Thu
|Te
|Da
|-
!8th 1L10s
!sssssssLsss
|Da
|Fri
|Ro
|Nu
|Me
|Fa
|Shi
|'''So'''
|'''Lo'''
|Thu
|Te
|Da
|-
!9th 1L10s
!ssssssssLss
|Da
|Fri
|Ro
|Nu
|Me
|Fa
|Shi
|So
|'''Flu'''
|'''Thu'''
|Te
|Da
|-
!10th 1L10s
!sssssssssLs
|Da
|Fri
|Ro
|Nu
|Me
|Fa
|Shi
|So
|Flu
|'''Le'''
|'''Te'''
|Da
|-
!11th 1L10s
!ssssssssssL
|Da
|Fri
|Ro
|Nu
|Me
|Fa
|Shi
|So
|Flu
|Le
|'''Tha'''
|Da
|}
 
== <nowiki>#</nowiki>35 (P8, P5/5) fifth-5th ==
 
* G = vM2 / ^<sup>4</sup>d1
* EI = v<sup>5</sup>A2
* ^ = 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
!-9
!-8
!-7
!-6
!-5
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!...
!16
|-
!solfege
|Fru
|...
|Tha
|Do
|Re
|Fri
|Nu
|Fa
|So
|Le
|Fli
|Thu
|'''Da'''
|Ro
|Me
|Ni
|Fu
|Sa
|Lo
|Te
|Thi
|Du
|Ra
|...
|To
|-
!intervals
|^m2
|...
|m7
|v8
|vvM2
|^^m2
|^m3
|P4
|v5
|vvM6
|^^m6
|^m7
|'''P1'''
|vM2
|vvM3
|^^m3
|^4
|P5
|vM6
|vvM7
|^^m7
|^1
|M2
|...
|vM7
|-
!notes
|^Db
|...
|Bb
|vC
|vvD
|^^Db
|^Eb
|F
|vG
|vvA
|^^Ab
|^Bb
|'''C'''
|vD
|vvE
|^^Eb
|^F
|G
|vA
|vvB
|^^Bb
|^C
|D
|...
|vB
|}
{| class="wikitable center-all"
|+
1L7s MOS scales (L = ^^m2/v<sup>3</sup>M3, s = vM2/^<sup>4</sup>d1)
![[Genchain mode numbering|GMN]] name
!scale
!1sn
!2nd
!3rd
!
!tritone
!
!6th
!7th
!8ve
|-
!1st 1L7s
!sssssssL
|Da
|Ro
|Me
|Ni
|Fu
|Sa
|Lo
|'''Te'''
|Da
|-
!2nd 1L7s
!ssssssLs
|Da
|Ro
|Me
|Ni
|Fu
|Sa
|'''Lo'''
|'''Thu'''
|Da
|-
!3rd 1L7s
!sssssLss
|Da
|Ro
|Me
|Ni
|Fu
|'''Sa'''
|'''Fli'''
|Thu
|Da
|-
!4th 1L7s
!ssssLsss
|Da
|Ro
|Me
|Ni
|'''Fu'''
|'''Le'''
|Fli
|Thu
|Da
|-
!5th 1L7s
!sssLssss
|Da
|Ro
|Me
|'''Ni'''
|'''So'''
|Le
|Fli
|Thu
|Da
|-
!6th 1L7s
!ssLsssss
|Da
|Ro
|'''Me'''
|'''Fa'''
|So
|Le
|Fli
|Thu
|Da
|-
!7th 1L7s
!sLssssss
|Da
|'''Ro'''
|'''Nu'''
|Fa
|So
|Le
|Fli
|Thu
|Da
|-
!8th 1L7s
!Lsssssss
|Da
|'''Fri'''
|Nu
|Fa
|So
|Le
|Fli
|Thu
|Da
|}
{| class="wikitable center-all"
|+
8L1s MOS scales (L = vM2/^<sup>4</sup>d1, s = vvM2/^<sup>3</sup>d1)
![[Genchain mode numbering|GMN]] name
!scale
!1sn
!2nd
!
!3rd
!4th
!5th
!6th
!
!7th
!8ve
|-
!1st 8L1s
!LLLLLLLLs
|Da
|Ro
|Me
|Ni
|Fu
|Sa
|Lo
|Te
|'''Thi'''
|Da
|-
!2nd 8L1s
!LLLLLLLsL
|Da
|Ro
|Me
|Ni
|Fu
|Sa
|Lo
|'''Te'''
|'''Thu'''
|Da
|-
!3rd 8L1s
!LLLLLLsLL
|Da
|Ro
|Me
|Ni
|Fu
|Sa
|'''Lo'''
|'''Fli'''
|Thu
|Da
|-
!4th 8L1s
!LLLLLsLLL
|Da
|Ro
|Me
|Ni
|Fu
|'''Sa'''
|'''Le'''
|Fli
|Thu
|Da
|-
!5th 8L1s
!LLLLsLLLL
|Da
|Ro
|Me
|Ni
|'''Fu'''
|'''So'''
|Le
|Fli
|Thu
|Da
|-
!6th 8L1s
!LLLsLLLLL
|Da
|Ro
|Me
|'''Ni'''
|'''Fa'''
|So
|Le
|Fli
|Thu
|Da
|-
!7th 8L1s
!LLsLLLLLL
|Da
|Ro
|'''Me'''
|'''Nu'''
|Fa
|So
|Le
|Fli
|Thu
|Da
|-
!8th 8L1s
!LsLLLLLLL
|Da
|'''Ro'''
|'''Fri'''
|Nu
|Fa
|So
|Le
|Fli
|Thu
|Da
|-
!9th 8L1s
!sLLLLLLLL
|Da
|'''Re'''
|Fri
|Nu
|Fa
|So
|Le
|Fli
|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 (Incomplete) ==
<nowiki>#</nowiki>37 (P8, P12/5) fifth-12th (incomplete)
If P5 > 720¢, swap up with down and dup with dud to get solfege #2.
 
 


<nowiki>#</nowiki>34 (P8, P4/5) fifth-of-a-4th
+2 genspan requires an aug 5th :(


<nowiki>#</nowiki>35 (P8, P5/5) fifth-of-a-5th
P1 -- vM3 -- vvA5=\m6 -- /M7=^^d8 -- ^m10 -- P12


<nowiki>#</nowiki>36 (P8, P11/5) fifth-of-an-11th
Da -- Mo -- Fle -- Ti -- Nu -- Sa


<nowiki>#</nowiki>37 (P8, P12/5) fifth-of-a-12th


<nowiki>#</nowiki>38 (P8, ccP4/5) fifth-of-a-coco-4th
<nowiki>#</nowiki>38 (P8, ccP4/5) fifth-coco-4th
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