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==Kite Giedraitis's diatonic solfege==
==Uniform solfege==


[[Kite Giedraitis|Kite's]] diatonic solfege uses the conventional 7 consonants D, R, M, F, S, L and T. It uses unconventional vowels. For each degree, the sequence runs [[wikipedia:Front_vowel|front]] to [[wikipedia:Back_vowel|back]] (i.e. bright to dim) -i -e -a -o -u for upmajor-major-mid-minor-downminor. It uses the exact same 33 note names as Kite's [[31edo solfege]].
See [[Uniform Solfege]] for a full explanation.
{| class="wikitable" style="text-align:center"
{| class="wikitable"
|+Kite's diatonic solfege (-i -e -a -o -u = ^M M ~ m vm), see 31edo
|+
![[24edo]]
![[24edo]]
!0
!0
Line 33: Line 33:
!notes
!notes
|C
|C
|^C<br>vDb
|^C
vDb
|Db
|Db
|vD
|^Db
vD
|D
|D
|^D<br>vEb
|^D
vEb
|Eb
|Eb
|vE
|^Eb
vE
|E
|E
|^E<br>vF
|^E
vF
|F
|F
|^F<br>vGb
|^F
|F#<br>Gb
vF# vGb
|^F#<br>vG
|F#
Gb
|^F#
^Gb vG
|G
|G
|^G<br>vAb
|^G
vAb
|Ab
|Ab
|vA
|^Ab
vA
|A
|A
|^A<br>vBb
|^A
vBb
|Bb
|Bb
|vB
|^Bb
vB
|B
|B
|^B<br>vC
|^B
vC
|C
|C
|-
|-
!intervals
!intervals
|P1
|P1
|^1<br>vm2
|^1
vm2
|m2
|m2
|~2
|~2
|M2
|M2
|^M2<br>vm3
|^M2
vm3
|m3
|m3
|~3
|~3
|M3
|M3
|^M3<br>v4
|^M3
v4
|P4
|P4
|^4<br>vd5
|~4
|A4<br>d5
vd5
|^A4<br>v5
|A4
d5
|~5
v5
|P5
|P5
|^5<br>vm6
|^5
vm6
|m6
|m6
|~6
|~6
|M6
|M6
|^M6<br>vm7
|^M6
vm7
|m7
|m7
|~7
|~7
|M7
|M7
|^M7<br>v8
|^M7
v8
|P8
|P8
|-
|-
!solfege
!solfege
|Do
|Da
|Da<br>Ru
|Du
|Ro
Fro
|Fra
|Fru
Ro
|Ra
|Ra
|Re
|Ru
|Ri<br>Mu
No
|Mo
|Na
|Nu
Mo
|Ma
|Ma
|Me
|Mu
|Mi<br>Fu
Fo
|Fo
|Fa
|Fa<br>Su
|Fu
|Fe<br>So
Po Sho
|Fi<br>Sa
|Pa
|Se
Sha
|Si<br>Lu
|Pu
|Lo
Shu So
|Sa
|Su
Flo
|Fla
|Flu
Lo
|La
|La
|Le
|Lu
|Li<br>Tu
Tho
|To
|Tha
|Thu
To
|Ta
|Ta
|Te
|Tu
|Ti<br>Du
Do
|Do
|Da
|}
|}
Beware: Mi, Fa, So, La and Ti all have new meanings.
Fru, Nu, Flu and Thu are included to complete the -u circle, so that one can do interval arithmetic within it.
{| class="wikitable" style="text-align:center"
{| class="wikitable"
|+
|+'''circles of fifths'''
Example scales
! rowspan="3" |plain
circle
!
!0
!14
!4
!18
!8
!22
!12
!2
!16
!6
!20
!10
!24
|-
|-
!Upmajor scale
!-a
|Do
|Da
|Re
|Sa
|Mi
|Ra
|Fo
|La
|Se
|Ma
|Li
|Ta
|Ti
|Pa
|Do
|
|
|
|
|
|
|-
|-
!Major scale
!-a
|Do
|
|Re
|
|Me
|
|Fo
|
|Se
|
|Le
|
|Te
|Sha
|Do
|Fra
|Fla
|Na
|Tha
|Fa
|Da
|-
|-
!Mid scale
| colspan="15" |
|Do
|Re
|Ma
|Fo
|Se
|La
|Ta
|Do
|-
|-
!Minor scale
!
|Do
!
|Re
!1
|Mo
!15
|Fo
!5
|Se
!19
|Lo
!9
|To
!23
|Do
!13
!3
!17
!7
!21
!11
!1
|-
|-
!Downminor scale
! rowspan="2" |up
|Do
circle
|Re
!-u
|Du
|Su
|Ru
|Lu
|Mu
|Mu
|Fo
|Se
|Lu
|Tu
|Tu
|Do
|Pu
|}
|
To find the [[octave complement]] of any interval:
|
 
|
*change the '''degree''' as usual: 2nd <--> 7th, 3rd <--> 6th, and 4th <--> 5th
|
*change the '''vowel''' as expected: -i <--> -u and -e <--> -o (-a is unchanged)
|
 
|
===The two circles of fifths===
|-
The plain circle lacks ups and downs, hence the name.
!-u
{| class="wikitable" style="text-align:center"
|
|+The plain circle of 5ths
|
!P1
|
!P5
|
!M2
|
!M6
|
!M3
|Shu
!M7
|Fru
!A4/d5
|Flu
!m2
|Nu
!m6
|Thu
!m3
|Fu
!m7
|Du
!P4
!P1
|-
|-
! rowspan="2" |down
circle
!-o
|Fro
|Flo
|No
|Tho
|Fo
|Do
|Do
|Se
|So
|Re
| Le
| Me
|Te
|Fe/So
|Ro
|Ro
|Lo
|Lo
| Mo
|Mo
|To
|To
|Fo
|Po
|Do
|
|}
The "off" circle contains the 6 offperfect intervals (^1 ^4 v4 ^5 v5 v8). The other 6 notes could be thought of as offmajor or offminor. Most of the notes in this circle have two names.
{| class="wikitable" style="text-align:center"
|+The "off" circle of 5ths
!vm2<br>^1
!vm6<br>^5
!vm3<br>^M2
!vm7<br>^M6
!v4<br>^M3
!v8<br>^M7
!v5<br>^A4
!~2
!~6
!~3
!~7
!vd5<br>^4
!vm2<br>^1
|-
|-
!-o
|
|
|
|
Line 232: Line 276:
|
|
|
|
|Su
|Sho
|Ru
|Fro
|}
{| class="wikitable" style="text-align:center"
|+
Example scales
|-
|-
| Ru
!Upmajor scale
|Da
|Ra
|Mu
|Fa
|Sa
|Lu
|Lu
|Mu
|Tu
|Tu
|Fu
|Da
|Du
|-
!Major scale
|Da
|Ra
|Ma
|Fa
|Sa
|La
|Ta
|Da
|-
!Mid scale
|Da
|Ra
|Mo
|Fa
|Sa
|Sa
|Lo
|To
|Da
|-
!Minor scale
|Da
|Ra
|Ra
| La
|Na
|Ma
| Ta
|Fa
|Fa
|Sa
|Fla
|Tha
|Da
|Da
|-
|-
| Da
!Downminor scale
|Si
|Da
|Ri
|Ra
|Li
|No
|Mi
|Fa
|Ti
|Sa
|Fi
|Flo
|
|Tho
|
|Da
|
|
|
|
|}
|}
Viewed as chains instead of circles:
===Other circles===
 
*plain chain: So Ro Lo Mo To Fo '''Do''' Se Re Le Me Te Fe
*off chain: Su Ru Lu Mu Tu Fu '''Du''' Sa Ra La Ma Ta Fa '''Da''' Si Ri Li Mi Ti Fi
 
It's fairly easy to find the note a 4th or 5th above any note. The consonant is as would be expected from conventional interval arithmetic. There are only 3 fifths that don't rhyme:
 
*Do - Se (P1 to P5)
*Da - Si (^1 to ^5)
*Du - Sa (v1 to v5)
Thus Re plus a 4th is Se, Ro plus a 5th is Lo, etc. And in the example scales above, the 3rd, 6th and 7th always rhyme, as do the tonic and 4th, as do the 2nd and 5th.
 
However going a 5th up from an aug or upaug 4th would go to an aug or upaug 8ve, which doesn't exist in this solfege. Therefore one must rename the 4th as a dim 5th, then go up a 5th to a minor 2nd. Thus Fe + 5th = So + 5th = Ro. Likewise when adding a 4th, dim 5ths need renaming: So + 4th = Fe + 4th = Te.
 
=== Other circles===
The two circles of 5ths can be interwoven to make a circle of mid 3rds.
The two circles of 5ths can be interwoven to make a circle of mid 3rds.
{| class="wikitable" style="text-align:center"
{| class="wikitable" style="text-align:center"
|+
|+
! P1
!P1
!~3
!~3
!P5
!P5
Line 288: Line 344:
!^4<br>vd5
!^4<br>vd5
!M6
!M6
! ^1<br>vm2
!^1<br>vm2
!M3
!M3
!^5<br>vm6
!^5<br>vm6
!M7
!M7
!^M2<br>vm3
!^M2<br>vm3
!A4<br>d5
!A4
d5
!^M6<br>vm7
!^M6<br>vm7
!m2
!m2
! ^M3<br>v4
!^M3<br>v4
!m6
!m6
! ^M7<br>v8
!^M7<br>v8
!m3
!m3
!^A4<br>v5
!^d5<br>v5
!m7
!m7
!~2
!~2
Line 307: Line 364:
!P1
!P1
|-
|-
|Do
|Da
|Mo
|Sa
|To
|Ra
|Fu<br>Sho
|La
|Du<br>Fro
|Ma
|Ma
|Se
|Su<br>Flo
|Ta
|Ta
|Re
|Ru<br>No
|Fa<br>Shu
|Pa<br>Sha
|Le
|Lu<br>Tho
|Da<br>Ru
|Fra
|Me
|Mu<br>Fo
|Si<br>Lu
|Fla
| Te
|Tu<br>Do
|Ri<br>Mu
|Na
|Fe<br>So
|Shu<br>So
|Li<br>Tu
|Tha
|Ro
|Ro
|Mi<br>Fu
|Fa
|Lo
|Lo
| Ti<br>Du
|Da
|Mo
|Fi<br>Sa
|To
|Ra
|Fo
|La
|Do
|}
|}
The two circles of 4ths can be interwoven to make a circle of half-4ths.
The two circles of 4ths can be interwoven to make a circle of half-4ths.
Line 348: Line 405:
!m2
!m2
!~3
!~3
!A4<br>d5
!A4
d5
!~6
!~6
!M7
!M7
!~2
!~2
!M3
!M3
!^A4<br>v5
!^d5<br>v5
!M6
!M6
!^M7<br>v8
!^M7<br>v8
Line 362: Line 420:
!P1
!P1
|-
|-
|Do
|Da
|Ri<br>Mu
|Ru
|Fo
No
|Si<br>Lu
|Fa
|Su<br>Flo
|Tha
|Du
Fro
|Na
|Fu<br>Sho
|Fla
|To
|To
|Da<br>Ru
|Fra
|Mo
|Mo
|Fa<br>Su
|Pa
Sha
|Lo
|Lo
| Ta
|Ta
|Ro
|Ro
|Ma
|Ma
|Fe<br>So
|Shu
So
|La
|La
|Te
|Tu<br>Do
|Ra
|Ra
|Me
|Mu<br>Fo
|Fi<br>Sa
|Sa
|Le
|Lu<br>Tho
|Ti<br>Du
|Da
|Re
|Mi<br>Fu
|Se
|Li<br>Tu
|Do
|}
|}
There is also a circle of down 5ths.
There is also a circle of down 5ths.
==Kite Giedraitis's chromatic solfege==
==Kite Giedraitis's solfege==


[[Kite Giedraitis|Kite's]] chromatic solfege uses the 7 conventional consonants D, R, M, F, S, L and T, plus 5 altered consonants that indicate flattening. It uses unconventional vowels: "oo" = u = '''u'''p, "oh" = o = d'''o'''wn, and "ah" = a = pl'''a'''in. It's a subset of Kite's [[41edo solfege]].
[[Kite Giedraitis|Kite's]] solfege uses the conventional 7 consonants D, R, M, F, S, L and T. It uses unconventional vowels. For each degree, the sequence runs [[wikipedia:Front_vowel|front]] to [[wikipedia:Back_vowel|back]] (i.e. bright to dim) -i -e -a -o -u for upmajor-major-mid-minor-downminor. It uses the exact same 33 note names as Kite's [[31edo solfege]].
 
*Fr- = '''f'''lat Re
*Fl- = '''f'''lat La
*Sh- = flat So = sharp Fa
*Th = flat Ti
*N- = flat Mi
{| class="wikitable" style="text-align:center"
{| class="wikitable" style="text-align:center"
!24edo
|+Kite's diatonic solfege (-i -e -a -o -u = ^M M ~ m vm), see 31edo
![[24edo]]
!0
!0
!1
!1
Line 481: Line 538:
|-
|-
!solfege
!solfege
|Da
|Do
|Du<br>Fro
|Da<br>Ru
|Fra
|Ro
|Ro
|Ra
|Ra
|Ru<br>No
|Re
|Na
|Ri<br>Mu
|Mo
|Mo
|Ma
|Ma
|Mu<br>Fo
|Me
|Fa
|Mi<br>Fu
|Fu<br>Sho
|Fo
|Sha
|Fa<br>Su
|Shu<br>So
|Fe<br>So
|Sa
|Fi<br>Sa
|Su<br>Flo
|Se
|Fla
|Si<br>Lu
|Lo
|Lo
|La
|La
|Lu<br>Tho
|Le
|Tha
|Li<br>Tu
|To
|To
|Ta
|Ta
|Tu<br>Do
|Te
|Da
|Ti<br>Du
|Do
|}
|}
Beware, Do and So have new meanings.
Beware: Mi, Fa, So, La and Ti all have new meanings.
{| class="wikitable" style="text-align:center"
{| class="wikitable" style="text-align:center"
|+
|+
Line 513: Line 570:
|-
|-
!Upmajor scale
!Upmajor scale
|Da
|Do
|Ra
|Re
|Mu
|Mi
|Fa
|Fo
|Sa
|Se
|Lu
|Li
|Tu
|Ti
|Da
|Do
|-
|-
!Major scale
!Major scale
|Da
|Do
|Ra
|Re
|Me
|Fo
|Se
|Le
|Te
|Do
|-
!Mid scale
|Do
|Re
|Ma
|Ma
|Fa
|Fo
|Sa
|Se
|La
|La
|Ta
|Ta
|Da
|Do
|-
|-
!Mid scale
!Minor scale
|Da
|Do
|Ra
|Re
|Mo
|Mo
|Fa
|Fo
|Sa
|Se
|Lo
|Lo
|To
|To
|Da
|Do
|-
!Minor scale
|Da
|Ra
|Na
|Fa
|Sa
|Fla
|Tha
|Da
|-
|-
!Downminor scale
!Downminor scale
|Da
|Do
|Ra
|Re
|No
|Mu
|Fa
|Fo
|Sa
|Se
|Flo
|Lu
|Tho
|Tu
|Da
|Do
|}
|}
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, aug <--> dim, but perfect and mid are unchanged
*change the '''vowel''' as expected: -i <--> -u and -e <--> -o (-a is unchanged)
*change the '''vowel''' as expected: -i <--> -u and -e <--> -o (-a is unchanged)
*if you get an aug 4th, change it to a dim 5th with the same vowel
*if you get an upminor interval Fru, Nu, Flu or Thu, change it to downmajor: Ro, Mo, Lo or To


===The two circles of fifths===
===The two circles of fifths===
Line 588: Line 642:
!P1
!P1
|-
|-
|Da
|Do
|Sa
|Se
|Ra
|Re
|La
| Le
|Ma
| Me
|Ta
|Te
|Sha
|Fe/So
|Fra
|Ro
|Fla
|Lo
|Na
| Mo
|Tha
|To
|Fa
|Fo
|Da
|Do
|}
|}
The "off" circle contains the 6 offperfect intervals (^1 ^4 v4 ^5 v5 v8). The other 6 notes could be thought of as offmajor or offminor. Most of the notes in this circle have two names.
The "off" circle contains the 6 offperfect intervals (^1 ^4 v4 ^5 v5 v8). The other 6 notes could be thought of as offmajor or offminor. Most of the notes in this circle have two names.
Line 611: Line 665:
!v4<br>^M3
!v4<br>^M3
!v8<br>^M7
!v8<br>^M7
!v5<br>^d5
!v5<br>^A4
!~2
!~2
!~6
!~6
Line 619: Line 673:
!vm2<br>^1
!vm2<br>^1
|-
|-
|Fro
|
|Flo
|
|No
|
|Tho
|
|Fo
|
|Do
|
|So
|
|Ro
|
|Lo
|
|Mo
|
|To
|
|Sho
|Fro
|-
|Du
|Su
|Su
|Ru
|Ru
|-
| Ru
|Lu
|Lu
|Mu
|Mu
|Tu
|Tu
|Shu
|Fu
|Du
|Sa
|Ra
| La
|Ma
| Ta
|Fa
|Da
|-
| Da
|Si
|Ri
|Li
|Mi
|Ti
|Fi
|
|
|
|
|
|
|
|
|
|
|Fu
|Du
|}
|}
Viewed as chains instead of circles:
Viewed as chains instead of circles:


*plain chain: Sha Fra Fla Na Tha Fa '''Da''' Sa Ra La Ma Ta
*plain chain: So Ro Lo Mo To Fo '''Do''' Se Re Le Me Te Fe
*off chain: Sho Fro Flo No Tho Fo '''Do''' So Ro Lo Mo To and Fu '''Du''' Su Ru Lu Mu Tu Shu
*off chain: Su Ru Lu Mu Tu Fu '''Du''' Sa Ra La Ma Ta Fa '''Da''' Si Ri Li Mi Ti Fi


It's fairly easy to find the note a 4th or 5th above any note. The vowels match, i.e. the syllables rhyme. The consonant is as would be expected from conventional interval arithmetic. However, remember that an aug 4th is named as a dim 5th:
It's fairly easy to find the note a 4th or 5th above any note. The consonant is as would be expected from conventional interval arithmetic. There are only 3 fifths that don't rhyme:
 
*Do - Se (P1 to P5)
*Da - Si (^1 to ^5)
*Du - Sa (v1 to v5)
Thus Re plus a 4th is Se, Ro plus a 5th is Lo, etc. And in the example scales above, the 3rd, 6th and 7th always rhyme, as do the tonic and 4th, as do the 2nd and 5th.


*To + P5 = Sho
However going a 5th up from an aug or upaug 4th would go to an aug or upaug 8ve, which doesn't exist in this solfege. Therefore one must rename the 4th as a dim 5th, then go up a 5th to a minor 2nd. Thus Fe + 5th = So + 5th = Ro. Likewise when adding a 4th, dim 5ths need renaming: So + 4th = Fe + 4th = Te.
*Ta + P5 = Sha
*Tu + P5 = Shu
Thus Ra plus a 4th is Sa, Ro plus a 5th is Lo, etc. And in the example scales above, the 3rd, 6th and 7th always rhyme, as do the tonic, 2nd, 4th and 5th.


===Other circles===
=== Other circles===
The two circles of 5ths can be interwoven to make a circle of mid 3rds.
The two circles of 5ths can be interwoven to make a circle of mid 3rds.
{| class="wikitable" style="text-align:center"
{| class="wikitable" style="text-align:center"
|+
|+
!P1
! P1
!~3
!~3
!P5
!P5
Line 670: Line 740:
!^4<br>vd5
!^4<br>vd5
!M6
!M6
!^1<br>vm2
! ^1<br>vm2
!M3
!M3
!^5<br>vm6
!^5<br>vm6
!M7
!M7
!^M2<br>vm3
!^M2<br>vm3
!d5
!A4<br>d5
!^M6<br>vm7
!^M6<br>vm7
!m2
!m2
!^M3<br>v4
! ^M3<br>v4
!m6
!m6
!^M7<br>v8
! ^M7<br>v8
!m3
!m3
!^d5<br>v5
!^A4<br>v5
!m7
!m7
!~2
!~2
Line 689: Line 759:
!P1
!P1
|-
|-
|Da
|Do
|Ma
|Se
|Ta
|Re
|Fa<br>Shu
|Le
|Da<br>Ru
|Me
|Si<br>Lu
| Te
|Ri<br>Mu
|Fe<br>So
|Li<br>Tu
|Ro
|Mi<br>Fu
|Lo
| Ti<br>Du
|Mo
|Mo
|Sa
|Fi<br>Sa
|To
|To
|Ra
|Ra
|Fu<br>Sho
|Fo
|La
|La
|Du<br>Fro
|Do
|Ma
|Su<br>Flo
|Ta
|Ru<br>No
|Sha
|Lu<br>Tho
|Fra
|Mu<br>Fo
|Fla
|Tu<br>Do
|Na
|Shu<br>So
|Tha
|Ro
|Fa
|Lo
|Da
|}
|}
The two circles of 4ths can be interwoven to make a circle of half-4ths.
The two circles of 4ths can be interwoven to make a circle of half-4ths.
Line 730: Line 800:
!m2
!m2
!~3
!~3
!d5
!A4<br>d5
!~6
!~6
!M7
!M7
!~2
!~2
!M3
!M3
!^d5<br>v5
!^A4<br>v5
!M6
!M6
!^M7<br>v8
!^M7<br>v8
Line 744: Line 814:
!P1
!P1
|-
|-
|Da
|Do
|Ru
|Ri<br>Mu
No
|Fo
|Fa
|Si<br>Lu
|Su<br>Flo
|Tha
|Du
Fro
|Na
|Fu<br>Sho
|Fla
|To
|To
|Fra
|Da<br>Ru
|Mo
|Mo
|Sha
|Fa<br>Su
|Lo
|Lo
|Ta
| Ta
|Ro
|Ro
|Ma
|Ma
|Shu
|Fe<br>So
So
|La
|La
|Tu<br>Do
|Te
|Ra
|Ra
|Mu<br>Fo
|Me
|Sa
|Fi<br>Sa
|Lu<br>Tho
|Le
|Da
|Ti<br>Du
|Re
|Mi<br>Fu
|Se
|Li<br>Tu
|Do
|}
|}
There is also a circle of down 5ths.
There is also a circle of down 5ths.
[[Category:24edo]]
[[Category:24edo]]
[[Category:Solfege]]
[[Category:Solfege]]
Retrieved from "https://en.xen.wiki/w/24edo_solfege"