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==Quarter tone system==
==Uniform Solfege==
 
See [[Uniform solfege]] for a full explanation.
While [[31edo]] is a system with fifth of tones, the quarter tone notations is handy and allow to name all the notes in a logical way. Because one tone is 5 degrees, between C and D (do and re) for example, we have the following notes:
{| class="wikitable center-all"
 
|+
{| class="wikitable"
![[31edo]]
!edosteps
! colspan="2" |solfege names
! colspan="4" |[[Ups and downs notation|ups and downs]] names
|-
!unisons
|0-1
| colspan="2" |Da Du
| colspan="2" |P1 ^1
| colspan="2" |C ^C
|-
!2nds
|2-6
|Fro Fra
|Ro Ra Ru
|vm2 m2
| ~2 M2 ^M2
|vDb Db
|vD D ^D
|-
|-
| | '''Degree'''
!3rds
| | '''Letter'''
|7-11
| | '''Name'''
|No Na
| | '''English full name'''
|Mo Ma Mu
|vm3 m3
|~3 M3 ^M3
| vEb Eb
| vE E ^E
|-
|-
| | 0
! 4ths
| | C
|12-14
| | do
| colspan="2" |Fo Fa Fu/Po
| | C
| colspan="2" |v4 P4 ^4
| colspan="2" |vF F ^F/vF#
|-
|-
| | 1
!tritones
| | C+
|15-16
| | do+
| colspan="2" |Pa/Sho Pu/Sha
| | C half-sharp
| colspan="2" | A4/vd5 ^A4/d5
| colspan="2" |F#/vGb ^F#/Gb
|-
|-
| | 2
! 5ths
| | C#
|17-19
| | do#
| colspan="2" |So Sa Su
| | C sharp
| colspan="2" |v5 P5 ^5
| colspan="2" |vG G ^G
|-
|-
| | 3
!6ths
| | Db
|20-24
| | re b
|Flo Fla
| | D flat
|Lo La Lu
|vm6 m6
|~6 M6 ^M6
|vAb Ab
|vA A ^A
|-
|-
| | 4
!7ths
| | Dd
|25-29
| | re d
|Tho Tha
| | D half-flat
|To Ta Tu
|vm7 m7
| ~7 M7 ^M7
| vBb Bb
|vB B ^B
|-
|-
| | 5
!8ves
| | D
|30-31
| | re
| colspan="2" |Do Da
| | D
| colspan="2" |v8 P8
| colspan="2" |vC C
|}
|}
Otherwise we can use double sharp and double flat:
Extra names: Fru=Ro, Nu=Mo, Shu=So, Flu=Lo, Thu=To


circle of 5ths: '''Da''' Sa Ra La Ma Ta Pa/Sho Fro Flo No Tho Fo '''Do''' So Ro Lo Mo To Po/Fu '''Du''' Su Ru Lu Mu Tu Pu/Sha Fra Fla Na Tha Fa '''Da'''
== Consistent Solfege ==
{| class="wikitable"
{| class="wikitable"
![[31edo]]
!solfege names
![[Ups and downs notation|ups and downs]] names
!edosteps
|-
|-
| | '''Degree'''
!1sns
| | '''Letter'''
|Do Du
| | '''Name'''
|P1 ^1
| | '''English full name'''
|0-1
|-
|-
| | 0
!2nds
| | C
|Ruh Re Ru Ra Ri
| | do
|vm2 m2 ~2 M2 ^M2
| | C
|2-6
|-
|-
| | 1
!3rds
| | Dbb
|Muh Me Mu Ma Mi
| | do bb
|vm3 m3 ~3 M3 ^M3
| | D double flat
|7-11
|-
|-
| | 2
!4ths
| | C#
|Fuh Fo/Fe Fu
| | do#
|v4 P4 ^4
| | C sharp
|12-14
|-
|-
| | 3
!tritones
| | Db
|Fa/Suh Fi/Se
| | re b
|A4/vd5 ^A4/d5
| | D flat
|15-16
|-
|-
| | 4
!5ths
| | Cx
|Su So/Sa Si
| | re x
|v5 P5 ^5
| | C double sharp
|17-19
|-
|-
| | 5
!6ths
| | D
|Luh Le Lu La Li
| | re
|vm6 m6 ~6 M6 ^M6
| | D
|20-24
|-
!7ths
|Tuh Te Tu Ta Ti
|vm7 m7 ~7 M7 ^M7
|25-29
|-
!8ves
|Duh Do (Du)
|v8 P8 (^8)
|30-31 (32)
|}
|}
While using double sharp and double flat seem a bit confusing because it then alternates between C and D, it makes sense from a musical point of view. Indeed, as far as harmonics and chords are concerned, using double sharp and double flat allow to have a way of writing chord that is consistent with traditional solfege.


Indeed, if we consider the subminor chord, and write it with D# for the second note and A# for the seventh harmonic, we get the following chords:
=== Example scales ===
 
{| class="wikitable"
*C / D# / G / A#
|+
*C# / Dx / G# / Ax
!Major scale
*Db / E / Ab / B
|Do
*D / E# / A / B#</li></ul>
|Ra
|Ma
|Fo
|So
|La
|Ta
|Do
|-
!Minor scale
|Do
|Ra
|Me
|Fo
|So
|Le
|Te
|Do
|-
!Upmajor scale
|Do
|Ra
|Mi
|Fo
|So
|Li
|Ti
|Do
|-
!Downminor scale
|Do
|Ra
|Muh
|Fo
|So
|Luh
|Tuh
|Do
|-
!Mid scale
|Do
|Ra
|Mu
|Fo
|So
|Lu
|Tu
|Do
|}
The system shown preserved vowels in perfect fifths in any scale that only uses notes from [[meantone]][7] modes, [[mohajira]][7] modes, and substitutions of meantone intervals with corresponding [[7-limit|septimal]] (7-limit) [[subminor]] or [[supermajor]] intervals, allowing for any diatonic type scale to be simple as easy to learn, as the inconsistencies of So-Ra and Te-Fo can be smoothed out by the fact that Ra can also be called Ro, for perfect second, or [[9/8]], and Fo is also Fe, as it's the "minor fourth", as [[4/3]] is tempered together with [[27/20]]. These [[comma]]s being [[tempered]] allows the system to preserve a surprising amount of consistency, being extremely easy to learn. Du is used for the up unison because it helps consistency, is generally used as a [[quartertone]] in scales like [[Centaurus]], and because it allows the also common augmented and upaugmented unisons to be named, with Da and Di.


So, as in 12-ET, we have the equation C# ~ Db and E# ~ F, in 31-ET, we have C# ≠ Db and E# ≠ F but we have:
The system is built on this consistency, and preserves the standard minor intervals names, as well as -a as the standard major from La, and Ti as the strongest leading tone, here being the upmajor seventh. The remaining vowels of -uh for sub and -u for neutral are used because they correspond to the vowel sounds from their respective words.


*Cx = Dd
=== Expanding the System ===
*C+ = Dbb
To expand into intervals that surpass these, such as the ^A5, we will extend to Augmented, Diminished, Upaugmented, and Downdiminished intervals. The vowels for these are -ah (short a sound), -ih (for the short i in diminished), oy, and ow (for down) respectively. They work similarly to the others, and are first used in the second set of unisons, allowing the M7-A4 and d5-m2 perfect fifths and others of the sort to still use consistent vowels, as they show up in diatonic scales.
*E# = Fd
*E+ = Fb
*Ex = F+
*Ed = Fbb


It is not necessary to learn all by heart. Simply that there are 5 degrees in a tone, and 3 degrees in a diatonic semitone. So going from one note name to another name is always an odd difference of degrees. If the change is even, it can be written as sharp and flat.
If intervals are used solely for their 3-limit role, such as the M2 or in some cases the M6, the names Ro and Lo may be used, for perfect second or perfect sixth, as Ra can be thought of to imply 10/9, while Ro would imply 9/8, similarly to Lo and 27/16. In other cases, Mo would be 32/27 and To would be 16/9. A situation where this naming scheme may be used would be in Harrison Major, P1 M2 ^M3 P4 P5 M6 ^M7 P8, where the M6 is used so that the ii chord has a perfect fifth, while the vi chord has a [[Wolf interval|wolf fifth]] in order to be used as a "wolf tonic" to prevent tonicization.


An exception to using flat and sharp is the rast scale, where there is Ed and Bd, which are defined as such and not derived from other intervals.
==Kite Giedraitis's solfege==


==Andrew Heathwaite system==
[[Kite Giedraitis|Kite's]] solfege (not to be confused with the above-mentioned uniform solfege for 31edo, also by Kite) uses the conventional 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. Kite's [[24edo solfege]] is a subset of this solfege.
 
{| class="wikitable" style="text-align:center"
[[Andrew Heathwaite]] proposes the following solfege system for singing the intervals of [[31edo]]. Note that this is a subset of the syllables used for singing [[41edo]].
|+
 
![[31edo]]
{| class="wikitable"
!solfege names
![[Ups and downs notation|ups and downs]] names
!edosteps
|-
|-
| | degrees of 31edo
!unisons
| | syllable
|Do Da
|P1 ^1
|0-1
|-
|-
| | 0
! 2nds
| | do
|Ru Ro Ra Re Ri
| vm2 m2 ~2 M2 ^M2
| 2-6
|-
|-
| | 1
!3rds
| | di
|Mu Mo Ma Me Mi
|vm3 m3 ~3 M3 ^M3
| 7-11
|-
|-
| | 2
!4ths
| | ro
|Fu Fo Fa
| v4 P4 ^4
|12-14
|-
|-
| | 3
!tritones
| | ra
|Fe/Su Fi/So
|A4/vd5 ^A4/d5
|15-16
|-
|-
| | 4
! 5ths
| | ru
|Sa Se Si
|v5 P5 ^5
| 17-19
|-
|-
| | 5
!6ths
| | re
| Lu Lo La Le Li
|vm6 m6 ~6 M6 ^M6
|20-24
|-
|-
| | 6
!7ths
| | ri
|Tu To Ta Te Ti
|vm7 m7 ~7 M7 ^M7
| 25-29
|-
|-
| | 7
! 8ves
| | ma
|Du Do
|v8 P8
|30-31
|}
Beware: Mi, Fa, So, La and Ti all have new meanings!
 
===Example scales===
{| class="wikitable" style="text-align:center"
|+
!Major scale
|Do
|Re
|Me
|Fo
|Se
|Le
|Te
|Do
|-
|-
| | 8
!Minor scale
| | me
|Do
|Re
|Mo
|Fo
|Se
|Lo
|To
|Do
|-
|-
| | 9
!Upmajor scale
| | mu
|Do
|Re
|Mi
|Fo
|Se
|Li
|Ti
|Do
|-
|-
| | 10
!Downminor scale
| | mi
|Do
|Re
|Mu
|Fo
|Se
|Lu
|Tu
|Do
|-
|-
| | 11
!Mid scale
| | mo
|Do
|Re
|Ma
|Fo
|Se
|La
|Ta
|Do
|}
 
===Learning suggestion===
Even with many familiar consonants and a consistent vowel sequence, it can take a while to master 35 syllables. One might want to divide-and-conquer. Start with using this simple solfege:
 
Da - Ra - Ma - Fa - Sa - La - Ta - Da
 
Each syllable is a catch-all term. For example, Ra covers Ri, Re, Ra, Ro and Ru. Using this solfege helps with <u>un</u>learning the syllables Mi, Fa, So, La and Ti, which are still present but have a changed meaning.
 
Once this is fully internalized, add in the other 4 vowels.
 
===The circle of fifths===
The 5 vowels create 5 [[chain of fifths|chains of fifths]]. The 2 [[tritone]]s with duplicate names each connect 2 pairs of chains. Thus there are only 3 fifths that don't rhyme:
 
*Do - Se (P1 to P5)
*Da - Si (^1 to ^5)
*Du - Sa (v1 to v5)
 
{| class="wikitable" style="text-align:center"
|+The 33 note names in circle-of-5ths order
(read left-to-right, top-row-to-bottom-row)
!1sn
! 5th
! 2nd
!6th
!3rd
!7th
!4th
!1sn
|-
|-
| | 12
|Do
| | fe
|Se
|Re
|Le
|Me
|Te
|Fe (Su)
|
|-
|-
| | 13
| rowspan="4" |
| | fa
|Su
|Ru
|Lu
|Mu
|Tu
|Fu
|Du
|-
|-
| | 14
|Sa
| | fu
|Ra
|La
|Ma
|Ta
|Fa
|Da
|-
|-
| | 15
|Si
| | fi
|Ri
|Li
|Mi
|Ti
|Fi (So)
|
|-
|-
| | 16
|So
| | se
| Ro
|Lo
|Mo
|To
|Fo
|Do
|}Because the chains mostly connect up, it's fairly easy to find the note a 4th or 5th above any note. It always rhymes (except the three 5ths from D- to S-), and the consonant is as would be expected from conventional interval arithmetic. 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 to a minor 2nd. Thus Fe + 5th = Su + 5th = Ru. Dim 5ths may also need renaming: So + 4th = Fi + 4th = Ti.
 
==Andrew Heathwaite's solfege==
[[Andrew Heathwaite]]'s solfege is a subset of his [[41edo]] solfege. It expands on the conventional Do - Di/Ra - Re - Ri/Me - Mi - Fa - Fi/Se - So - Si/Le - La - Li/Te - Ti - Do. As a result there are 6 different vowel sequences.
{| class="wikitable" style="text-align:center"
|+
![[31edo]]
!solfege names
![[Ups and downs notation|ups and downs]] names
!edosteps
|-
|-
| | 17
!unisons
| | su
|Do Di
|P1 ^1
| 0-1
|-
|-
| | 18
!2nds
| | so or sol
|Ro Ra Ru Re Ri
|vm2 m2 ~2 M2 ^M2
|2-6
|-
|-
| | 19
! 3rds
| | si
|Ma Me Mu Mi Mo
|vm3 m3 ~3 M3 ^M3
|7-11
|-
|-
| | 20
!4ths
| | lo
|Fe Fa Fu Fi
|v4 P4 ^4 A4
|12-15
|-
|-
| | 21
!5ths
| | le
|Se Su So (or Sol) Si
| d5 v5 P5 ^5
|16-19
|-
|-
| | 22
!6ths
| | lu
|Lo Le Lu La Li
|vm6 m6 ~6 M6 ^M6
|20-24
|-
|-
| | 23
!7ths
| | la
|Ta Te Tu Ti To
|vm7 m7 ~7 M7 ^M7
|25-29
|-
|-
| | 24
!8ves
| | li
|Da Do
|-
|v8 P8
| | 25
|30-31
| | ta
|-
| | 26
| | te
|-
| | 27
| | tu
|-
| | 28
| | ti
|-
| | 29
| | to
|-
| | 30
| | da
|-
| | 31
| | do
|}
|}
See also: [[17edo Solfege]], [[22edo Solfege]], [[29edo solfege|29edo Solfege]] and [[41edo solfege|41edo Solfege]].


See also: [[17edo Solfege]], [[22edo Solfege]], [[29edo solfege|29edo Solfege]]
For intervals that appear in the [[diatonic scale]], the traditional solfege names are grandfathered in. While this makes it easier to learn the new syllables as extensions of the old ones — if you are trained with the old ones to begin with — it also makes for many irregularities.
 
=Comments=
For intervals that appear in the diatonic scale, the traditional solfege names are grandfathered in. While this makes it easier to learn the new syllables as extensions of the old ones — if you are trained with the old ones to begin with — it also makes for many irregularities.


The syllables '''do, re, mi, fa, so[l], la, ti''' have the same meaning as traditional major and perfect intervals. The names for minor intervals are also retained: '''ra, me, le, te''', as well as the augmented fourth, '''fi''', and diminished fifth, '''se'''. Some traditional names for chromatically-altered intervals appear here, but altered by a semisharp or semiflat, rather than a full sharp or flat: '''di''' for a semiaugmented unison, '''da''' for a semidiminished unison, '''ri''' for a semiaugmented second, '''fe''' for a semidiminished fourth, '''si''' for a semiaugmented fifth, and '''li''' for a semiaugmented sixth. The remaining syllables flesh out the septimal and undecimal intervals which are not represented in 12edo.
The syllables '''do, re, mi, fa, so[l], la, ti''' have the same meaning as traditional major and perfect intervals. The names for minor intervals are also retained: '''ra, me, le, te''', as well as the augmented fourth, '''fi''', and diminished fifth, '''se'''. Some traditional names for chromatically-altered intervals appear here, but altered by a semisharp or semiflat, rather than a full sharp or flat: '''di''' for a semiaugmented unison, '''da''' for a semidiminished unison, '''ri''' for a semiaugmented second, '''fe''' for a semidiminished fourth, '''si''' for a semiaugmented fifth, and '''li''' for a semiaugmented sixth. The remaining syllables flesh out the septimal and undecimal intervals which are not represented in 12edo.
Line 278: Line 496:
'''to''' =&gt; '''se'''
'''to''' =&gt; '''se'''


'''da''' =&gt; '''su'''     [[Category:31edo]]
'''da''' =&gt; '''su'''
===Example scales===
{| class="wikitable" style="text-align:center"
|+
!Major scale
|Do
|Re
|Mi
|Fa
|Sol
|La
|Ti
|Do
|-
!Minor scale
|Do
|Re
|Me
|Fa
|Sol
|Le
|Te
|Do
|-
!Upmajor scale
|Do
|Re
|Mo
|Fa
|Sol
|Li
|To
|Do
|-
!Downminor scale
|Do
|Re
|Ma
|Fa
|Sol
|Lo
|Ta
|Do
|-
!Mid scale
|Do
|Re
|Mu
|Fa
|Sol
|Lu
|Tu
|Do
|}
The major and minor scales are the same as conventional solfege.
[[Category:31edo]]
[[Category:Solfege]]
[[Category:Solfege]]
Retrieved from "https://en.xen.wiki/w/31edo_solfege"