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== Rank-2 Uniform Solfeges by Pergen ==
== 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 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 can only be 5 fifthchains.
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.


Genchains are distinct from fifthchains. Each pergen has one or more genchains, 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 20 or 21 pergens.
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 go so far with only 13 consonants. But in general, it's enough to cover all the modes of any reasonably-sized MOS scale.


The EI (enharmonic interval) can be added to or subtracted from any note or interval to get an equivalent note or interval.
The EI (enharmonic interval) can be added to or subtracted from any note or interval to get an equivalent note or interval.
to do: discuss using numeric solfeges with non-diatonic-friendly MOSes


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.
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.
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|Da
|Da
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↵____________________________________________________________________________________
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{| class="wikitable center-all"
{| class="wikitable center-all"
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== #5 (P8/2, P4/2) ==
== #5 (P8/2, P4/2) ==
It has only 4 fifthchains, but it uses lifts and drops, 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...


== #6 (P8/3, P5) ==
== #6 (P8/3, P5) ==
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== <nowiki>#</nowiki>22 (P8/2, M2/4) ==
* P = ^^4 = vv5, G = ^1 = v<sup>3</sup>M2
* EI = v<sup>4</sup>M2
* ^ = 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)'''
| rowspan="2" |
! colspan="23" |genspan
|-
!-11
!-10
!-9
!-8
!-7
!-6
!-5
!-4
!-3
!-2
!-1
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
|-
! rowspan="3" |Da's


gen-


<nowiki>#</nowiki>22 (P8/2, M2/4)
chain
|Shu
|Shi
Fle
|Flo
|Fla
|Flu
|Fli
The
|Tho
|Tha
|Thu
|Thi
De
|Do
|'''Da'''
|Du
|Di
Re
|Ro
|Ra
|Ru
|Ri
Me
|Mo
|Ma
|Mu
|Mi
Pe
|Po
|-
|^d5
|^^d5
vvm6
|vm6
|m6
|^m6
|^^m6
vvm7
|vm7
|m7
|^m7
|^^m7
vv8
|v8
|'''P1'''
|^1
|^^1
vvM2
|vM2
|M2
|^M2
|^^M2
vvM3
|vM3
|M3
|^M3
|^^M3
vvA4
|vA4
|-
|^Gb
|^^Gb
vvAb
|vAb
|Ab
|^Ab
|^^Ab
vvBb
|vBb
|Bb
|^Bb
|^^Bb
vvC
|vC
|'''C'''
|^C
|^^C
vvD
|vD
|D
|^D
|^^D
vvE
|vE
|E
|^E
|^^E
vvF#
|vF#
|-
| colspan="24" |
|-
! rowspan="3" |Sa's
 
gen-
 
chain
|Fro
|Fra
|Fru
|Fri
Ne
|No
|Na
|Nu
|Ni
Fe
|Fo
|Fa
|Fu
|FI
Se
|So
|Sa
|Su
|Si
Le
|Lo
|La
|Lu
|Li
Te
|To
|Ta
|Tu
|-
|vm2
|m2
|^m2
|^^m2
vvm3
|vm3
|m3
|^m3
|^^m3
vv4
|v4
|P4
|^4
|^^4
vv5
|v5
|P5
|^5
|^^5
vvM6
|vM6
|M6
|^M6
|^^M6
vvM7
|vM7
|M7
|^M7
|-
|vDb
|Db
|^Db
|^^Db
vvEb
|vEb
|Eb
|^Eb
|^^Eb
vvF
|vF
|F
|^F
|^^F
vvG
|vG
|G
|^G
|^^G
vvA
|vA
|A
|^A
|^^A
vvB
|vB
|B
|^B
|}
 
{| class="wikitable center-all"
|+
2L20s MOS scales (L = m2 =  rhymes, s = ^1/v<sup>3</sup>M2 = no rhyme)
![[Genchain mode numbering|GMN]] name
!scale
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
!15
!16
!17
!18
!19
!20
!21
!22
|-
!1st 2L20s
!ssssssssssL x2
|Da
|Du
|Di
Re
|Ro
|Ra
|Ru
|Ri
Me
|Mo
|Ma
|Mu
|'''Mi'''
'''Pe'''
|Fi
Se
|So
|Sa
|Su
|Si
Le
|Lo
|La
|Lu
|Li
Te
|To
|'''Ta'''
|Da
|-
!2nd 2L20s
!sssssssssLs x2
|Da
|Du
|Di
Re
|Ro
|Ra
|Ru
|Ri
Me
|Mo
|Ma
|'''Mu'''
|'''Fu'''
|Fi
Se
|So
|Sa
|Su
|Si
Le
|Lo
|La
|Lu
|Li
Te
|'''To'''
|'''Do'''
|Da
|-
!3rd 2L20s
!ssssssssLss x2
|Da
|Du
|Di
Re
|Ro
|Ra
|Ru
|Ri
Me
|Mo
|'''Ma'''
|'''Fa'''
|Fu
|Fi
Se
|So
|Sa
|Su
|Si
Le
|Lo
|La
|Lu
|'''Li'''
'''Te'''
|'''Thi'''
'''De'''
|Do
|Da
|-
!4th 2L20s
!sssssssLsss x2
|Da
|Du
|Di
Re
|Ro
|Ra
|Ru
|Ri
Me
|'''Mo'''
|'''Fo'''
|Fa
|Fu
|Fi
Se
|So
|Sa
|Su
|Si
Le
|Lo
|La
|'''Lu'''
|'''Thu'''
|Thi
De
|Do
|Da
|-
!5th 2L20s
!ssssssLssss x2
|Da
|Du
|Di
Re
|Ro
|Ra
|Ru
|'''Ri'''
'''Me'''
|'''Ni'''
'''Fe'''
|Fo
|Fa
|Fu
|Fi
Se
|So
|Sa
|Su
|Si
Le
|Lo
|'''La'''
|'''Tha'''
|Thu
|Thi
De
|Do
|Da
|-
!6th 2L20s
!sssssLsssss x2
|Da
|Du
|Di
Re
|Ro
|Ra
|'''Ru'''
|'''Nu'''
|Ni
Fe
|Fo
|Fa
|Fu
|Fi
Se
|So
|Sa
|Su
|Si
Le
|'''Lo'''
|'''Tho'''
|Tha
|Thu
|Thi
De
|Do
|Da
|-
!7th 2L20s
!ssssLssssss x2
|Da
|Du
|Di
Re
|Ro
|'''Ra'''
|'''Na'''
|Nu
|Ni
Fe
|Fo
|Fa
|Fu
|Fi
Se
|So
|Sa
|Su
|'''Si'''
'''Le'''
|'''Fli'''
'''The'''
|Tho
|Tha
|Thu
|Thi
De
|Do
|Da
|-
!8th 2L20s
!sssLsssssss x2
|Da
|Du
|Di
Re
|'''Ro'''
|'''No'''
|Na
|Nu
|Ni
Fe
|Fo
|Fa
|Fu
|Fi
Se
|So
|Sa
|'''Su'''
|'''Flu'''
|Fli
The
|Tho
|Tha
|Thu
|Thi
De
|Do
|Da
|-
!9th 2L20s
!ssLssssssss x2
|Da
|Du
|'''Di'''
'''Re'''
|'''Fri'''
'''Ne'''
|No
|Na
|Nu
|Ni
Fe
|Fo
|Fa
|Fu
|Fi
Se
|So
|'''Sa'''
|'''Fla'''
|Flu
|Fli
The
|Tho
|Tha
|Thu
|Thi
De
|Do
|Da
|-
!10th 2L20s
!sLsssssssss x2
|Da
|'''Du'''
|'''Fru'''
|Fri
Ne
|No
|Na
|Nu
|Ni
Fe
|Fo
|Fa
|Fu
|Fi
Se
|'''So'''
|'''Flo'''
|Fla
|Flu
|Fli
The
|Tho
|Tha
|Thu
|Thi
De
|Do
|Da
|-
!11th 2L20s
!Lssssssssss x2
|Da
|'''Fra'''
|Fru
|Fri
Ne
|No
|Na
|Nu
|Ni
Fe
|Fo
|Fa
|Fu
|Fi
Se
|'''Shi'''
'''Fle'''
|Flo
|Fla
|Flu
|Fli
The
|Tho
|Tha
|Thu
|Thi
De
|Do
|Da
|}




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