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31edo solfege: Difference between revisions

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[[Kite Giedraitis|Kite's]] solfege 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.
[[Kite Giedraitis|Kite's]] solfege 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"
{| class="wikitable" style="text-align:center"
|+
|+
![[31edo]]
![[31edo]]
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!tritones
!tritones
|Fe/Su Fi/So
|Fe/Su Fi/So
|A4/vd5 ^A4/d5
| A4/vd5 ^A4/d5
|-
|-
!5ths
!5ths
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|v8 P8 (^8)
|v8 P8 (^8)
|}
|}
Beware: M,i Fa, So, La and Ti all have new meanings!
Beware: Mi, Fa, So, La and Ti all have new meanings!


=== Example scales ===
===Example scales===
{| class="wikitable"
{| class="wikitable" style="text-align:center"
|+
|+
!Major scale
!Major scale
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|-
|-
!Mid scale
!Mid scale
|Do
| Do
|Re
|Re
|Ma
|Ma
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|Se
|Se
|La
|La
|Ta
| Ta
|Do
|Do
|}
|}


=== The circle of fifths ===
===The circle of fifths===
The 5 vowels create 5 chains of fifths. The 2 tritones with duplicate names each connect 2 pairs of chains. Thus there are only 3 fifths that don't rhyme:  
The 5 vowels create 5 chains of fifths. The 2 tritones with duplicate names each connect 2 pairs of chains. Thus there are only 3 fifths that don't rhyme:  


* Do - Se (P1 to P5)
*Do - Se (P1 to P5)
* Da - Si (^1 to ^5)
*Da - Si (^1 to ^5)
* Du - Sa (v1 to v5)
*Du - Sa (v1 to v5)


{| class="wikitable"
{| class="wikitable" style="text-align:center"
|+The 33 note names in circle-of-5ths order  
|+The 33 note names in circle-of-5ths order  
(read left-to-right, top-row-to-bottom-row)
(read left-to-right, top-row-to-bottom-row)
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!5th
!5th
!2nd
!2nd
!6th
! 6th
!3rd
!3rd
!7th
!7th
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|So
|So
|Ro
|Ro
|Lo
| Lo
|Mo
| Mo
|To
|To
|Fo
|Fo
|Do
|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.
 
=== Adding/subtracting 4ths and 5ths ===
As a result of the aforementioned chains connecting up, it's fairly easy to find the note a 4th or 5th above any note. It always rhymes, 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, 2nd, 4th 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.
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.
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[[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.
[[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"
{| class="wikitable" style="text-align:center"
|+
|+
![[31edo]]
![[31edo]]
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![[Ups and downs notation|ups and downs]] names
![[Ups and downs notation|ups and downs]] names
|-
|-
!unisons
! unisons
|Do Di
| Do Di
|P1 ^1
|P1 ^1
|-
|-
!2nds
! 2nds
|Ro Ra Ru Re Ri
|Ro Ra Ru Re Ri
|vm2 m2 ~2 M2 ^M2
|vm2 m2 ~2 M2 ^M2
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|vm3 m3 ~3 M3 ^M3
|vm3 m3 ~3 M3 ^M3
|-
|-
!4ths
! 4ths
|Fe Fa Fu
|Fe Fa Fu Fi
|v4 P4 ^4
| v4 P4 ^4 A4
|-
!tritones
|Fi Se
|A4/vd5 ^A4/d5
|-
|-
!5ths
!5ths
|Su So (or Sol) Si
|Se Su So (or Sol) Si
|v5 P5 ^5
|d5 v5 P5 ^5
|-
|-
!6ths
! 6ths
|Lo Le Lu La Li
|Lo Le Lu La Li
|vm6 m6 ~6 M6 ^M6
|vm6 m6 ~6 M6 ^M6
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'''da''' => '''su'''
'''da''' => '''su'''
===Example scales===
===Example scales===
{| class="wikitable"
{| class="wikitable" style="text-align:center"
|+
|+
!Major scale
!Major scale
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|Sol
|Sol
|La
|La
|Ti
| Ti
|Do
|Do
|-
|-
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!Downminor scale
!Downminor scale
|Do
|Do
|Re
| Re
|Ma
|Ma
|Fa
|Fa
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