User:TallKite/Solfeges: Difference between revisions

maybe break up into 2 pages?

'''Numeric''' solfeges are for small edos that aren't heptatonic-friendly, like 5, 6, and 8-11. All other edos use the conventional consonants D R M F S L T.

'''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 a type of solfege developed by [[Kite Giedraitis]]. They are closely related to his [[ups and downs notation]]. A uniform solfege lets one perform basic interval arithmetic directly within the solfege, without having to translate to note names or interval names and back. They use a uniform vowel sequence for each degree, hence the name. They use the conventional consonants D R M F S L T. But all consonants except D have an alternate form that indicates flattening or sharpening:

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).

!3 vowels

!14-22, etc,

|

|

|-

!4 vowels

!31, 41

|-

!5 vowels

!53, 60

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?

Edos 5, 7 and 12 have only -a. 10edo has -a and -o but no -u.

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".

(The prime limits assumes a larger edo in which both 81/80 and 64/63 = 1 edostep)

|+

! rowspan="2" |3-limit

|Da

|}

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:

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

Next add in the 6 altered consonants, making a 12-edo-like solfege:

Once this is fully internalized, add in the other vowels, and learn how to respell the various tritones.

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

For example, Fru = minor-Re-up becomes major-Ti-down = To.

The 13 -a notes form a chain of 5ths running from the dim 5th to the aug 4th:

Thus as long as one spells the tritone correctly, all 5ths rhyme. This makes interval arithmetic very easy.

The note a 4th or 5th above any note always rhymes, and the consonant is as would be expected from conventional interval arithmetic. Ra plus a 4th is Sa, Fro plus a 5th is Flo, etc. Thus in the example scales above, the 3rd, 6th and 7th always rhyme, as do the tonic, 2nd, 4th and 5th.

However, consider the aug 4th, a P- note. The note a 5th above it would be an augmented 8ve, which doesn't exist in a uniform solfege. Therefore one must rename the tritone as a dim or mid 5th. Thus in 31edo Pa + 5th = Sho + 5th = Fro. Likewise, Sho and Sha need renaming when adding a 4th: Sha + 4th = Pu + 4th = Tu.

The same rule for 4ths and 5ths mostly holds for plain major 2nds. Keep the vowel, and change the consonant as expected. Ra + M2 = Ma. But an aug 4th must be renamed as a 5th. Beware, this rule breaks down entirely for major and mid 7ths (the T- notes), due to the lack of aug and mid 8ves.

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.

|+

colorspeak correlations for all 25 diatonic edos that have uniform solfeges with 5 vowels or less

!34

!36

!39

!40

|

|}

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.

|+

!

| rowspan="4" |5 7 12

| rowspan="4" |5 6

8 9

|

|10 15 16 17 19 22 24

26 29 31 36

|-

|}

![[5edo]]

!0

|Da

|}

!

!0

|Da

|}

![[6edo]]

!0

|Wa

|}

|+

BC & uniform solfeges

|Da

|}

!

!0

|Da

|}

![[8edo]]

!0

|Wa

|}

![[9edo]]

!0

|Wa

|}

![[9edo]]

!0

Of qustionable merit. Circle of 5ths: Da Sa Ra La/Sha Ma/Fra Ta/Fla Pa/Na Tha Fa Da

![[10edo]]

!0

|Wa

|}

![[10edo]]

!0

|

|}

! colspan="7" |plain circle

| rowspan="4" |

|Ro

|}

![[11edo]]

!0

|Wa

|}

![[11edo]]

!0

|}

Of qustionable merit. Circle of 5ths: Da Sa/Fu Ra/Du La/Su Ma/Ri Ta/Li Mi/Fra Ti/Fla Na/Fo Tha/Do Fa/So Da

![[11edo]]

!0

|Do

|}

![[12edo]]

!0

|Do

|}

!0

!7

! colspan="2" |perfect

|}

![[12edo]]

!0

|Tu

|}

!

!0

|Da

|}

![[12edo]]

!0

|

|}

!

!0

|Da

|}

![[13edo]]

!0

|Da

|}

!

!0

|Da

|}

![[14edo]]

!0

|Da

|}

! colspan="9" |plain circle

| rowspan="4" |

|So

|}

![[15edo]]

!0

|

|}

! colspan="6" |plain circle

| rowspan="4" |

|Ro

|}

![[15edo]]

!0

|To

|Da

![[15edo]]

!0

|Do

|}

![[16edo]]

!0

|

|}

!

!0

! colspan="2" |perfect

|}

![[16edo]]

!0

|Do

|}

![[17edo]]

!0

|

|}

!

!0

! colspan="2" |perfect

|}

![[17edo]]

!0

|Do

|}

![[18edo]]

!0

|C

|^C

vD

|D

|^D

vDb

|Db

E

|^E

vEb

|Eb

|^Eb / ^F#

vF

|F

|^F

vG

|G

|^G

^Gb / vA

|A

|^A

vAb

|Ab

B

|^B

vBb

|Bb

|^Bb

vC

|C

|P1

|^1

vM2

|M2

|~2

|m2

M3

|~3

|m3

|^m3 / ^A4

v4

|P4

|^4

v5

|P5

|^5

vd5 / vM6

|M6

|~6

|m6

M7

|~7

|m7

|^m7

v8

|P8

|Da

|Du

Ro

|Ra

|Ru

Fro

|Fra

Ma

|Mu

No

|Na

|Nu / Pu

Fo

|Fa

|Fu

So

|Sa

|Su

Sho / Lo

|La

|Lu

Flo

|Fla

Ta

|Tu

Tho

|Tha

|Thu

Do

|Da

|

|}

! colspan="11" |plain circle

| rowspan="4" |

|So

|}

![[19edo]]

!0

|Do

|}

![[19edo]]

!0

|

|}

!

!0

! colspan="2" |perfect

|}

![[19edo]]

!0

|

|

![[20edo]]

!0

|

|}

! colspan="6" |plain circle

| rowspan="4" |

|Ro

|}

![[20edo]]

!0

|Ta/Da

|}

![[21edo]]

!0

|Da

|}

! colspan="8" |plain circle

| rowspan="3" |

|Do

|}

![[22edo]]

!0

|Da

|Du

Fra

|Fru

|Fa

|Fu

Sha

|Po

Shu

|Pa

So

|Sa

|To

|Ta

Do

|Da

|Fo

|Mu

Sho

|

|

|Pu

Flo

|Su

|Tu

|}

!

!0

! colspan="2" |perfect

|}

![[22edo]]

!0

|Da

|}

!

!0

|Da

|}

![[22edo]]

!0

|Do

|}

![[23edo]]

!0

|Db

|Dbb

E#

|E

|Ab

|Abb

B#

|B

|m2

|d2

A3

|M3

|m6

|d6

A7

|M7

|Fra

|Fru

Mo

|Ma

|Nu

|Fo

Pa

|Fa

|Sa

|Su

Sha

|Lo

|Fla

|Flu

To

|Ta

|

|}

!

!0

|Da

|}

![[24edo]]

!0

|C

|^C

vDb

|Db

|^Db

vD

|D

|^D

vEb

|Eb

|^Eb

vE

|E

|^E

vF

|F

|^F

vF# vGb

|F#

Gb

|^F#

^Gb vG

|G

|^G

vAb

|Ab

|^Ab

vA

|A

|^A

vBb

|Bb

|^Bb

vB

|B

|^B

vC

|C

|P1

|^1

vm2

|m2

|M2

|^M2

vm3

|m3

|M3

|^M3

v4

|P4

|~4

vd5

|A4

d5

|~5

v5

|P5

|^5

vm6

|m6

|M6

|^M6

vm7

|m7

|M7

|^M7

v8

|P8

|Da

|Du

Fro

|Fra

|Fru

Ro

|Ra

|Ru

No

|Na

|Nu

Mo

|Ma

|Mu

Fo

|Fa

|Fu

Po

Sho

|Pa

Sha

|Pu

Shu So

|Sa

|Su

Flo

|Fla

|Flu

Lo

|La

|Lu

Tho

|Tha

|Thu

To

|Ta

|Tu

Do

|Da

|}

Fru, Nu, Flu andThu are included to complete the -u circle, so you can do interval arithmetic within it.

! rowspan="3" |plain

circle

!

|-

! rowspan="2" |up

circle

!-u

|-

! rowspan="2" |down

circle

!-o

|Fro

|}

![[24edo]]

!0

|Di

|Da

Da Sa Ra La Ma Ta Pa/Sha Fra Fla Na Tha Fa Da

''Simpler, but you can't name the in-between notes (50¢, 250¢, 450¢) as up notes, which is nice.''

![[24edo]]

!0

|C

|^C

vDb

|Db

|D

|^D

vEb

|Eb

|E

|^E

vF

|F

|^F

vGb

|F#

Gb

|^F#

vG

|G

|^G

vAb

|Ab

|A

|^A

vBb

|Bb

|B

|^B

vC

|C

|P1

|^1

vm2

|m2

|M2

|^M2

vm3

|m3

|M3

|^M3

v4

|P4

|^4

vd5

|A4

d5

|^A4

v5

|P5

|^5

vm6

|m6

|M6

|^M6

vm7

|m7

|M7

|^M7

v8

|P8

|Do

|Da

Ru

|Ro

|Re

|Ri

Mu

|Mo

|Me

|Mi

Fu

|Fo

|Fa

Su

|Fe

So

|Fi

Sa

|Se

|Si

Lu

|Lo

|Le

|Li

Tu

|To

|Te

|Ti

Du

|Do

|}

![[25edo]]

!edosteps

| colspan="2" |vB/vC C (^C)

|}

![[25edo]]

!edosteps

| colspan="2" |'''v8''' P8 (^8)

| colspan="2" |'''vC''' C (^C)

up ring: Fu/Shu Du/Fru Flu Nu Thu Fu/Shu

down ring: Po/So Ro Lo Mo To/Do Po/So

!

! colspan="6" |plain circle

|-

! rowspan="3" |up

circle

!1

|-

! rowspan="3" |downmid

circle

!2

|-

! rowspan="3" |upmid

circle

!3

|-

! rowspan="3" |down

circle

!4

|Ro

|}

![[26edo]]

!edosteps

| colspan="2" |d8 P8 (A8)

| colspan="2" |Cb C (C#)

![[26edo]]

!edosteps

|d8 P8 (A8)

|Cb C (C#)