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Expanding the "movable-do" solfege system for [[17edo|17edo]]: an aid for microtonal singing; a way of wrapping yr brain around a new sound system.
== Andrew Heathwaite's solfege ==


Ordinary solfege syllables work very well in 17:
=== Basic solfege ===
[[Andrew Heathwaite|Andrew]]'s solfege expands on the conventional Do - Di/Ra - Re - Ri/Me - Mi - Fa - Fi/Se - So - Si/Le - La - Li/Te - Ti - Do. Note that syllables usually treated as enharmonic equivalents become distinct pitches in 17edo. Note that Di (the A1) is wider than Ra (the m2).


{| class="wikitable"
{| class="wikitable" style="text-align:center"
|-
|-
| | 0
![[17edo]]
| | 1
! 0
| | 2
! 1
| | 3
! 2
| | 4
! 3
| | 5
! 4
| | 6
! 5
| | 7
! 6
| | 8
! 7
| | 9
! 8
| | 10
! 9
| | 11
! 10
| | 12
! 11
| | 13
! 12
| | 14
! 13
| | 15
! 14
| | 16
! 15
! 16
!17
|-
|-
| | C
!notes (fixed-do)
| | Db
| C
| | C#
| Db
| | D
| C#
| | Eb
| D
| | D#
| Eb
| | E
| D#
| | F
| E
| | Gb
| F
| | F#
| Gb
| | G
| F#
| | Ab
| G
| | G#
| Ab
| | A
| G#
| | Bb
| A
| | A#
| Bb
| | B
| A#
| B
|C
|-
|-
| | do
!intervals (movable-do)
| | ra
|P1
| | di
|m2
| | re
|A1
| | me
|M2
| | ri
|m3
| | mi
|A2
| | fa
|M3
| | se
|P4
| | fi
|d5
| | sol
|A4
| | le
|P5
| | si
|m6
| | la
|A5
| | te
|M6
| | li
|m7
| | do
|A6
|M7
|P8
|-
!solfege
|Do
|Ra
|Di
|Re
|Me
|Ri
|Mi
|Fa
|Se
|Fi
|So
|Le
|Si
|La
|Te
|Li
|Ti
|Do
|}
|}


Note that syllables usually treated as enharmonic equivalents become distinct pitches in 17 (eg. "ra" & "di"). Spelling matters here.
Listed as a circle of 5ths: Se Ra Le Me Te Fa '''Do''' So Re La Mi Ti Fi '''Di''' Si Ri Li (Se)


This system could work just fine on its own, but what if I want to respell the pitches to put them into another pitch class? For example, what if I want to treat D# as a kind of third (a neutral third) instead of a kind of second (an augmented second)? For pitches, we have up-down arrows (thank you Sagittal) that can allow us to respell like this:
The intervals run from dim5 to aug6. Note the strangely-spelled 5th from Li to Se (a double-dim 7th) that completes the circle.


{| class="wikitable"
=== Expanded solfege ===
To avoid naming ascending intervals as descending (e.g. Ra-Di or Me-Ri), 10 enharmonic equivalents are added, so that the 10 black keys each have two names. The 6 mid intervals use -u. The 4 half-aug intervals ^1, ^M2, ^5 and ^M6 use either -a or -o, whichever one doesn't conflict with a pre-existing syllable.
 
{| class="wikitable" style="text-align:center"
|-
! 0
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
! 10
! 11
! 12
! 13
! 14
! 15
! 16
!17
|-
|-
| | 0
| C
| | 1
| ^C / Db
| | 2
| C# / vD
| | 3
| D
| | 4
| ^D / Eb
| | 5
| D# / vE
| | 6
| E
| | 7
| F
| | 8
| ^F / Gb
| | 9
| F# / vG
| | 10
| G
| | 11
| ^G / Ab
| | 12
| G# / vA
| | 13
| A
| | 14
| ^A / Bb
| | 15
| A# / vB
| | 16
| B
|C
|-
|-
| | C
|P1
| | Db
|^1 / m2
| | C#
|A1 / ~2
| | D
|M2
| | Eb
|^M2 / m3
| | D#
|A2 / ~3
| | E
|M3
| | F
|P4
| | Gb
|~4 / d5
| | F#
|A4 / ~5
| | G
|P5
| | Ab
|^5 / m6
| | G#
|A5 / ~6
| | A
|M6
| | Bb
|^M6 / m7
| | A#
|A6 / ~7
| | B
|M7
|P8
|-
|-
| | C
|Do
| | C-up
|Da / Ra
| | D-down
|Di / Ru
| | D
|Re
| | D-up
|Ro / Me
| | E-down
|Ri / Mu
| | E
|Mi
| | F
|Fa
| | F-up
|Fu / Se
| | G-down
|Fi / Su
| | G
|So
| | G-up
|Sa / Le
| | A-down
|Si / Lu
| | A
|La
| | A-up
|Lo / Te
| | B-down
|Li / Tu
| | B
|Ti
|Do
|}
|}


So, for example, we can respell our augmented second, D#, as a neutral third, E-down, & get something more intuitive & useful for certain purposes.
Listed as a chain of mid-3rds, with 6 gaps:


But what if we want solfege syllables for these respellings?
Se (no vm7) Ra (no v4) Le (no '''v1''') Me Su Te Ru Fa Lu '''Do''' Mu So Tu Re Fu La '''Da''' Mi Sa Ti Ro Fi Lo '''Di''' (no ^M3) Si (no ^M7) Ri (no ^A4) Li


===ru, mu, lu & tu===
Listed by degree:
 
{| class="wikitable" style="text-align:center"
I offer the suffix "-u" to indicate neutral 2nds, 3rds, 6ths, & 7ths.
|+
 
![[17edo]]
{| class="wikitable"
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
!15
!16
!17
|-
!1sns
|Do
|Da
|Di
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
!2nds
|
|Ra
|Ru
|Re
|Ro
|Ri
|
|
|
|
|
|
|
|
|
|
|
|
|-
|-
| | 0
!3rds
| | 1
|
| | 2
|
| | 3
|
| | 4
|
| | 5
|Me
| | 6
|Mu
| | 7
|Mi
| | 8
|
| | 9
|
| | 10
|
| | 11
|
| | 12
|
| | 13
|
| | 14
|
| | 15
|
| | 16
|
|
|
|-
|-
| | C
!4ths
| | Db
|
| | '''D-down'''
|
| | D
|
| | Eb
|
| | '''E-down'''
|
| | E
|
| | F
|
| | Gb
|Fa
| | F#
|Fu
| | G
|Fi
| | Ab
|
| | '''A-down'''
|
| | A
|
| | Bb
|
| | '''B-down'''
|
| | B
|
|
|
|-
|-
| | do
!5ths
| | ra
|
| | '''ru'''
|
| | re
|
| | me
|
| | '''mu'''
|
| | mi
|
| | fa
|
| | se
|
| | fi
|Se
| | sol
|Su
| | le
|So
| | '''lu'''
|Sa
| | la
|Si
| | te
|
| | '''tu'''
|
| | ti
|
|}
|
 
|
So if we encounter a "ru," we know to take it as a neutral second (not an augmented unison); if we encounter "lu," we know to take it as a neutral sixth (not an augmented fifth) & so on.
 
===fu & su===
 
What about the two tritones? Perhaps you want to respell G-flat as F-up. For this, I offer "fu"; likewise, if you want G-down in place of F-up, I offer "su".
 
{| class="wikitable"
|-
|-
| | 0
!6ths
| | 1
|
| | 2
|
| | 3
|
| | 4
|
| | 5
|
| | 6
|
| | 7
|
| | 8
|
| | 9
|
| | 10
|
| | 11
|
| | 12
|Le
| | 13
|Lu
| | 14
|La
| | 15
|Lo
| | 16
|Li
|
|
|-
|-
| | C
!7ths
| | Db
|
| | D-down
|
| | D
|
| | Eb
|
| | E-down
|
| | E
|
| | F
|
| | '''F-up'''
|
| | '''G-down'''
|
| | G
|
| | Ab
|
| | A-down
|
| | A
|
| | Bb
|
| | B-down
|Te
| | B
|Tu
|Ti
|
|-
|-
| | do
!8ves
| | ra
|
| | ru
|
| | re
|
| | me
|
| | mu
|
| | mi
|
| | fa
|
| | '''fu'''
|
| | '''su'''
|
| | sol
|
| | le
|
| | lu
|
| | la
|
| | te
|
| | tu
|
| | ti
|
|
|Do
|}
|}
See also [[22edo Solfege]]


===other enharmonics===
== Uniform Solfege ==
 
See [[Uniform solfege]] for a full explanation.
Some offers, to fill out the octave:
{| class="wikitable center-all"
 
|+
{| class="wikitable"
![[17edo]]
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
!15
!16
!17
|-
!notes
|C
|^C / Db
|vD
|D
|^D / Eb
|vE
|E
|F
|^F / Gb
|F# / vG
|G
|Ab
|vA
|A
|^A / Bb
|vB
|B / vC
|C
|-
|-
| | 0
!intervals
| | 1
|P1
| | 2
|^1 / m2
| | 3
|~2
| | 4
|M2
| | 5
|^M2 / m3
| | 6
|~3
| | 7
|M3
| | 8
|P4
| | 9
|~4 / d5
| | 10
|A4 / ~5
| | 11
|P5
| | 12
|m6
| | 13
|~6
| | 14
|M6
| | 15
|^M6 / m7
| | 16
|~7
|M7 / v8
|P8
|-
|-
| | C
!solfege
| | '''C-up'''
|Da
| | D-down
|Du / Fra
| | D
|Ro
| | '''D-up'''
|Ra
| | E-down
|Na
| | E
|Mo
| | F
|Ma
| | F-up
|Fa
| | G-down
|Fu / Sha
| | G
|Pa / So
| | '''G-up'''
|Sa
| | A-down
|Fla
| | A
|Lo
| | '''A-up'''
|La
| | B-down
|Tha
| | B
|To
|Ta / Do
|Da
|-
|-
| | do
!extras
| | '''da'''
|
| | du
|
| | re
|Fru
| | '''ro'''
|No
| | mu
|Ru
| | mi
|Nu
| | fa
|Fo
| | fu
|
| | su
|
| | sol
|
| | '''sa'''
|
| | lu
|Su
| | la
|Flu
| | '''lo'''
|Tho
| | tu
|Lu
| | do
|Thu
|
|
|}
|}
 
{| class="wikitable center-all"
=== ===
|+circle of fifths
 
!
===side-by-side===
!0
 
!10
For comparison, the full system:
!3
 
!13
{| class="wikitable"
!6
!16
!9
!2
!12
!5
!15
!8
!1
!11
!4
!14
!7
!17
|-
!-a
|Da
|Sa
|Ra
|La
|Ma
|Ta
|Pa
|
|
|
|
|
|
|
|
|
|
|
|-
|-
| | 0
!-o
| | 1
|
| | 2
|
| | 3
|
| | 4
|
| | 5
|
| | 6
|Do
| | 7
|So
| | 8
|Ro
| | 9
|Lo
| | 10
|Mo
| | 11
|To
| | 12
|
| | 13
|
| | 14
|
| | 15
|
| | 16
|
|
|
|-
|-
| | C
!-u
| | Db/C-up
|
| | C#/D-down
|
| | D
|
| | Eb/D-up
|
| | D#/E-down
|
| | E
|
| | F
|
| | Gb/F-up
|(Fru)
| | F#/G-down
|(Flu)
| | G
|(Nu)
| | Ab/G-up
|(Thu)
| | G#/A-down
|Fu
| | A
|Du
| | Bb/A-up
|
| | A#/B-down
|
| | B
|
|
|
|-
|-
| | do
!-a
| | ra
|
| | di
|
| | re
|
| | me
|
| | ri
|
| | mi
|
| | fa
|
| | se
|
| | fi
|
| | sol
|
| | le
|
| | si
|Sha
| | la
|Fra
| | te
|Fla
| | li
|Na
| | do
|Tha
|Fa
|Da
|-
|-
| | do
!
| | da
! colspan="2" |perfect
| | du
! colspan="4" |major
| | re
! colspan="6" |mid
| | ro
! colspan="4" |minor
| | mu
! colspan="2" |perfect
| | mi
| | fa
| | fu
| | su
| | sol
| | sa
| | lu
| | la
| | lo
| | tu
| | do
|}
|}
 
[[Category:17edo]]
See also [[22edo_Solfege|22edo Solfege]]
[[Category:Solfege]]
Retrieved from "https://en.xen.wiki/w/17edo_solfege"