View source for User:Unque/On Solfege

In standard musical practice, the seven syllables ''do, re, mi, fa, so, la,'' and ''ti'' are used as a basis for representing relative pitch<sup>†</sup> in a way which is clear and unambiguous to learners, and can continue to be applied by musicians of all experience levels.  This practice of solfège syllables can be applied to xenharmonic tuning systems as well, though one must be careful as these syllables have implications concerning the scaleforms and qualities of the notes they describe.  On this page, I will attempt to document logical extensions as I see fit, in hopes that they may be useful as systematic extensions for others to utilize.

<small><sup>†</sup>"fixed-do" solfège is additionally used in some places to represent absolute pitch; on this page, however, only movable-do solfège will be applied.</small>

== Standard Solfège ==
In common-practice tradition, movable-do solfège features nineteen distinct syllables, centered on the diatonic scale, which are continuous across the circle of fifths; they may be most accurately analyzed representing as the 8|10 mode of meantone[19], or simply mapped to a non-MOS segment of the untempered circle of fifths.
{| class="wikitable sortable"
|+Diatonic Solfège Syllables
!Syllable
!Interval
!Notation (on C)
!3-limit
!Meantone
!Schismic
|-
|Do
|1
|C
|1/1
|1/1
|1/1
|-
|Di
|♯1
|C♯
|2187/2048
|25/24
|16/15
|-
|Ra
|♭2
|D♭
|256/243
|16/15
|25/24
|-
|Re
|2
|D
|9/8
|10/9
|9/8
|-
|Ri
|♯2
|D♯
|19683/16384
|7/6
|6/5
|-
|Me
|♭3
|E♭
|32/27
|6/5
|32/26
|-
|Mi
|3
|E
|81/64
|5/4
|81/64
|-
|Fe
|♭4
|F♭
|8192/6561
|9/7
|5/4
|-
|Fa
|4
|F
|4/3
|4/3
|4/3
|-
|Fi
|♯4
|F♯
|729/512
|7/5
|64/45
|-
|Se
|♭5
|G♭
|1024/729
|10/7
|45/32
|-
|So(l)
|5
|G
|3/2
|3/2
|3/2
|-
|Si
|♯5
|G♯
|6561/4096
|14/9
|8/5
|-
|Le
|♭6
|A♭
|128/81
|8/5
|128/81
|-
|La
|6
|A
|27/16
|5/3
|27/16
|-
|Li
|♯6
|A♯
|59049/32768
|7/4
|9/5
|-
|Te
|♭7
|B♭
|16/9
|9/5
|16/9
|-
|Ti
|7
|B
|243/128
|15/8
|48/25
|-
|De
|♭8
|C♭
|4096/2187
|48/25
|15/8
|-
|Do
|8
|C
|2/1
|2/1
|2/1
|}
These syllables will be the basis for all other solfège systems discussed on this page.

== Neutral Solfège ==
By splitting the perfect fifth into two neutral thirds, one may generate a continuous chain whereby every other interval is a member of the familiar circle of fifths, while those that fall in between are exact neutral intervals.  Because each new interval falls perfectly between two existing intervals of the same diatonic ordinal (and thus the same consonant), it can be represented by that consonant with the "u" vowel, which is not present in other solfège syllables.

Below are examples of where these neutral intervals fall in context; the neutrals themselves are shown in '''bold'''.
{| class="wikitable"
|+Solfège with neutrals
!Syllable
!Interval
!Notation (on C)
|-
|Ra
|♭2
|D♭
|-
|'''Ru'''
|'''d2'''
|'''Dd'''
|-
|Re
|2
|D
|-
|Me
|♭3
|E♭
|-
|'''Mu'''
|'''d3'''
|'''Ed'''
|-
|Mi
|3
|E
|-
|Fa
|4
|F
|-
|'''Fu'''
|'''‡4'''
|'''F‡'''
|-
|Fi
|♯4
|F♯
|-
|Se
|♭5
|G♭
|-
|'''Su'''
|'''d5'''
|'''Gd'''
|-
|So(l)
|5
|G
|-
|Le
|♭6
|A♭
|-
|'''Lu'''
|'''d6'''
|'''Ad'''
|-
|La
|6
|A
|-
|Te
|♭7
|B♭
|-
|'''Tu'''
|'''d7'''
|'''Bd'''
|-
|Ti
|7
|B
|}

== Interordinal Solfège ==
Syllables for describing certain [[Interordinal|interordinals]] have been proposed by [[User:Vector|Vector]], though these syllables neglect utility for describing the qualities of the ordinals.

The specific syllables that Vector suggests are as follows:

* "Na" for the [[Chthonic harmony|chthonic]] (semifourth)
** From the latter half of ''resonare'', origin also of the syllable ''re'', to reference that the chthonic is an [[interizer]] above ''re''.
** Because this syllable is suggested for Pajara, it may be taken as the minor chthonic, and "ni" used for major.
* "Zi" for the perfect tritone (semioctave)
** From an alteration of ''diabolus'', a reference to the infamous phrase ''diabolus in musica'' to describe the tritone.
** In scales that distinguish quality of the tritone, we may use "zi" for the major and "ze" for the minor.
* "Bi" or "be" for the perfect ouranic (semitwelfth)
** From the latter half of ''labii'', origin also of the syllable ''la'', to reference that the ouranic is an interizer above ''la''.
** This can be easily split into "be" for the minor and "bi" for the major ouranic.

By extension from these, we may derive syllables for the other interordinals:

* "Que" or "Ke" (pronounced variably as ''qu'' as in ''quail'', or ''k'' as in ''kale'') for the interizer (quartertone)
** From ''queant'' as in ''ut queant laxis'', the titular first line of the hymn which begat the solfège syllables.
** If we take "ke" as minor, then "ki" may be major.
* "Ge" (pronounced as "hard" ''g'' as in ''get'') for the naiadic (semisixth)
** From ''gestorum'' as in ''mira gestorum'', the phrase which begat the syllable ''mi''.
** If we take "ge" as minor, then "gi" may be major.
* "Ve" or "We" (pronounced variably as ''v'' as in ''vet'', or ''w'' as in ''wet'') for the cocytic (semitenth)
** From the latter half of ''solve'', origin also of the syllable ''sol.''
** If we take "ve" as minor, then "vi" may be major.
* "Jo" or "Yo" (pronounced variably as ''j'' as in ''join'', or ''y'' as in ''yawn'') for the anti-interizer (semifourteenth)
** From ''Ioannes'', the Latin name of St. John, an homage to ''si''<nowiki/>'s origin as a contraction of ''Sanctus Ioannes''.
** Because "ji" may be difficult to pronounce, and is illegal in many languages, "jo" will be taken as the major, with "ja" as the minor.

Just like the diatonic ordinals, the interordinals may be made neutral by usage of the vowel ''u''.

== Commatic Inflections ==
So far, all syllables discussed have been formed from the chain of fifths, or by splitting intervals therein.  But what of intervals that fall outside this chain completely?  In just intonation, and systems which approximate it, it may not be desirable to treat all intervals as detempers of meantone.  To distinguish comma-separated pairs, we might use diphthongs as a means of extending the syllable while remaining audibly similar to the ordinal form.

Specifically, the vowel ''i'' may be inserted between the consonant and main vowel to inflect upwards by 81/80 or 64/63; and ''u'' may be inserted to inflect downwards.  Below are examples of how these inflections may be used, with the commatic syllables shown in '''bold'''.
{| class="wikitable"
|+Commatic Solfège
!Syllable
!Interval
!JI
!Notation (on C)
|-
|'''Rua'''
|'''vm2'''
|'''28/27'''
|'''vD♭'''
|-
|Ra
|m2
|256/243
|D♭
|-
|'''Ria'''
|'''^m2'''
|'''16/15'''
|'''^D♭'''
|-
|'''Rue'''
|'''vM2'''
|'''10/9'''
|'''vD'''
|-
|Re
|M2
|9/8
|D
|-
|'''Rie'''
|'''^M2'''
|'''8/7'''
|'''^D'''
|-
|'''Mue'''
|'''vm3'''
|'''7/6'''
|'''vE♭'''
|-
|Me
|m3
|32/27
|E♭
|-
|'''Mie'''
|'''^m3'''
|'''6/5'''
|'''^E♭'''
|-
|'''Mui'''
|'''vM3'''
|'''5/4'''
|'''vE'''
|-
|Mi
|M3
|81/64
|E
|-
|'''Mii'''
|'''^M3'''
|'''9/7'''
|'''^E'''
|}
As can be seen above, complications arise with the usage of two ''i'' vowels in a single syllable.  The best fix I can think of is substituting the second one with a more open vowel sound; Germanic languages like English or German might use the "short" ''i'' sound of ''bit'', while speakers of Slavic languages like Russian or Polish might use the ''y''/''ы'' sound; however, many languages do not have a sound to substitute for this one without conflicting with other syllables, so this solution is not reliable.