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Major rewrite. Removed superfluous text and tables (someone let me know if I went too far!), added an analysis as a circle of 5ths and as a chain of mid 3rds.
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Expanding the "movable-do" solfege system for [[17edo]]: an aid for microtonal singing; a way of wrapping your 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"
|-
|-
![[17edo]]
! 0
! 0
! 1
! 1
Line 22: Line 24:
! 15
! 15
! 16
! 16
!17
|-
|-
!notes (fixed-do)
| C
| C
| Db
| Db
Line 40: Line 44:
| A#
| A#
| B
| 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
Note that syllables usually treated as enharmonic equivalents become distinct pitches in 17 (eg. "ra" & "di"). Spelling matters here.
 
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:
 
{| class="wikitable"
|-
! 0
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
! 10
! 11
! 12
! 13
! 14
! 15
! 16
|-
| C
| Db
| C#
| D
| Eb
| D#
| E
| F
| Gb
| F#
| G
| Ab
| G#
| A
| Bb
| A#
| B
|-
|-
| C
!solfege
| C-up
|Do
| D-down
|Ra
| D
|Di
| D-up
|Re
| E-down
|Me
| E
|Ri
| F
|Mi
| F-up
|Fa
| G-down
|Se
| G
|Fi
| G-up
|So
| A-down
|Le
| A
|Si
| A-up
|La
| B-down
|Te
| B
|Li
|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 circle of 5ths: Se Ra Le Me Te Fa '''Do''' So Re La Mi Ti Fi '''Di''' Si Ri Li (Se)


But what if we want solfege syllables for these respellings?
The intervals run from dim5 to aug6. Note the strangely-spelled 5th from Li to Se (a double-dim 7th) that completes the circle.


===ru, mu, lu & tu===
=== 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.


I offer the suffix "-u" to indicate neutral 2nds, 3rds, 6ths, & 7ths.
{| class="wikitable" style="text-align:center"
 
{| class="wikitable"
|-
|-
! 0
! 0
Line 148: Line 113:
! 15
! 15
! 16
! 16
!17
|-
|-
| C
| C
| Db
| ^C / Db
| '''D-down'''
| C# / vD
| D
| D
| Eb
| ^D / Eb
| '''E-down'''
| D# / vE
| E
| E
| F
| F
| Gb
| ^F / Gb
| F#
| F# / vG
| G
| G
| Ab
| ^G / Ab
| '''A-down'''
| G# / vA
| A
| A
| Bb
| ^A / Bb
| '''B-down'''
| A# / vB
| B
| B
|C
|-
|P1
|^1 / m2
|A1 / ~2
|M2
|^M2 / m3
|A2 / ~3
|M3
|P4
|~4 / d5
|A4 / ~5
|P5
|^5 / m6
|A5 / ~6
|M6
|^M6 / m7
|A6 / ~7
|M7
|P8
|-
|-
| do
|Do
| ra
|Da / Ra
| '''ru'''
|Di / Ru
| re
|Re
| me
|Ro / Me
| '''mu'''
|Ri / Mu
| mi
|Mi
| fa
|Fa
| se
|Fu / Se
| fi
|Fi / Su
| sol
|So
| le
|Sa / Le
| '''lu'''
|Si / Lu
| la
|La
| te
|Lo / Te
| '''tu'''
|Li / Tu
| ti
|Ti
|Do
|}
|}


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.
Listed as a chain of mid-3rds, with 6 gaps:


===fu & su===
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


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".
Listed by degree:
 
{| class="wikitable" style="text-align:center"
{| class="wikitable"
|+
![[17edo]]
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
!15
!16
!17
|-
|-
! 0
!1sns
! 1
|Do
! 2
|Da
! 3
|Di
! 4
|
! 5
|
! 6
|
! 7
|
! 8
|
! 9
|
! 10
|
! 11
|
! 12
|
! 13
|
! 14
|
! 15
|
! 16
|
|
|
|-
|-
| C
!2nds
| Db
|
| D-down
|Ra
| D
|Ru
| Eb
|Re
| E-down
|Ro
| E
|Ri
| F
|
| '''F-up'''
|
| '''G-down'''
|
| G
|
| Ab
|
| A-down
|
| A
|
| Bb
|
| B-down
|
| B
|
|
|
|-
|-
| do
!3rds
| ra
|
| ru
|
| re
|
| me
|
| mu
|Me
| mi
|Mu
| fa
|Mi
| '''fu'''
|
| '''su'''
|
| sol
|
| le
|
| lu
|
| la
|
| te
|
| tu
|
| ti
|
|}
|
 
|
===other enharmonics===
 
Some offers, to fill out the octave:
 
{| class="wikitable"
|-
|-
! 0
!4ths
! 1
|
! 2
|
! 3
|
! 4
|
! 5
|
! 6
|
! 7
|
! 8
|Fa
! 9
|Fu
! 10
|Fi
! 11
|
! 12
|
! 13
|
! 14
|
! 15
|
! 16
|
|
|
|-
|-
| C
!5ths
| '''C-up'''
|
| D-down
|
| D
|
| '''D-up'''
|
| E-down
|
| E
|
| F
|
| F-up
|
| G-down
|Se
| G
|Su
| '''G-up'''
|So
| A-down
|Sa
| A
|Si
| '''A-up'''
|
| B-down
|
| B
|
|
|
|-
|-
| do
!6ths
| '''da'''
|
| du
|
| re
|
| '''ro'''
|
| mu
|
| mi
|
| fa
|
| fu
|
| su
|
| sol
|
| '''sa'''
|
| lu
|Le
| la
|Lu
| '''lo'''
|La
| tu
|Lo
| do
|Li
|}
|
 
|
===side-by-side===
 
For comparison, the full system:
 
{| class="wikitable"
|-
|-
! 0
!7ths
! 1
|
! 2
|
! 3
|
! 4
|
! 5
|
! 6
|
! 7
|
! 8
|
! 9
|
! 10
|
! 11
|
! 12
|
! 13
|
! 14
|
! 15
|Te
! 16
|Tu
|Ti
|
|-
|-
| C
!8ves
| Db/C-up
|
| C#/D-down
|
| D
|
| Eb/D-up
|
| D#/E-down
|
| E
|
| F
|
| Gb/F-up
|
| F#/G-down
|
| G
|
| Ab/G-up
|
| G#/A-down
|
| A
|
| Bb/A-up
|
| A#/B-down
|
| B
|
|-
|
| do
|Do
| ra
| di
| re
| me
| ri
| mi
| fa
| se
| fi
| sol
| le
| si
| la
| te
| li
| do
|-
| do
| da
| du
| re
| ro
| mu
| mi
| fa
| fu
| su
| sol
| sa
| lu
| la
| lo
| tu
| do
|}
|}
See also [[22edo Solfege]]
See also [[22edo Solfege]]


[[Category:17edo]]
[[Category:17edo]]
[[Category:Solfege]]
[[Category:Solfege]]
Retrieved from "https://en.xen.wiki/w/17edo_solfege"