17edo solfege: Difference between revisions

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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]]

Revision as of 06:56, 22 August 2022

Andrew Heathwaite's solfege

Basic solfege

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).

17edo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
notes (fixed-do) C Db C# D Eb D# E F Gb F# G Ab G# A Bb A# B C
intervals (movable-do) P1 m2 A1 M2 m3 A2 M3 P4 d5 A4 P5 m6 A5 M6 m7 A6 M7 P8
solfege Do Ra Di Re Me Ri Mi Fa Se Fi So Le Si La Te Li Ti Do

Listed as a circle of 5ths: Se Ra Le Me Te Fa Do So Re La Mi Ti Fi Di Si Ri Li (Se)

The intervals run from dim5 to aug6. Note the strangely-spelled 5th from Li to Se (a double-dim 7th) that completes the circle.

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.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
C ^C / Db C# / vD D ^D / Eb D# / vE E F ^F / Gb F# / vG G ^G / Ab G# / vA A ^A / Bb A# / vB 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 Da / Ra Di / Ru Re Ro / Me Ri / Mu Mi Fa Fu / Se Fi / Su So Sa / Le Si / Lu La Lo / Te Li / Tu Ti Do

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

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

Listed by degree:

17edo 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
3rds Me Mu Mi
4ths Fa Fu Fi
5ths Se Su So Sa Si
6ths Le Lu La Lo Li
7ths Te Tu Ti
8ves Do

See also 22edo Solfege

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