Kite's uniform solfege: Difference between revisions

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 *-e = dud (double-down)
-However for certain edos such as 31 and 41, -i instead means m'''<u>i</u>'''d.
+However for certain edos such as 34 and 41, -i means m'''<u>i</u>'''d and -e is not used.
 (2) Whenever ups and downs are not used ([[Sharpness|sharp-1]] edos and the unsplit pergen):
@@ Line 167: / Line 167: @@
 |+the four vowel sequences, with example edos
 !1 vowel
-!5, 7, 12
+!5, 7, 9, 12
 |
 |
@@ Line 175: / Line 175: @@
 |-
 !3 vowels
-!10, 14-22, etc,
+!10, 13b-19, 22
 |
 |<nowiki>-o = down</nowiki>
@@ Line 183: / Line 183: @@
 |-
 !4 vowels
-!31, 41
+!25, 27, 34, 41
 |<nowiki>-i = mid</nowiki>
 |<nowiki>-o = down</nowiki>
@@ Line 191: / Line 191: @@
 |-
 !5 vowels
-!53, 60
+!43, 46, 53, 60
 | -e = dud
 |<nowiki>-o = down</nowiki>
@@ Line 559: / Line 559: @@
 |  -iyu
 |}
+== Application to fifthspan mappings ==
+In any single-ring edo, a prime can be mapped not only to a specific number of edosteps, but also to a specific number of fifths. This is called the [[fifthspan]]. The fifthspan of prime 2 is always zero and the fifthspan of prime 3 is always one. The fifthspans of all the primes of interest above 3 is called the fifthspan mapping. The mapping can be expressed very concisely as a string of uniform solfege syllables in which -u/-o means aug/dim. Note that this often differs from the EDO solfeges listed above, where -u/-o often refers to up/down.
+{| class="wikitable"
+|+[[Fifthspan|Fifthspans]] of various primes in various single-ring edos
+!
+!prime 2
+!prime 3
+!prime 5
+!prime 7
+!prime 11
+!prime 13
+!solfege string
+|-
+![[19-edo]]
+|0
+|1
+|4
+| -9
+|6
+| -4
+|MaThoPaFla
+|-
+![[22-edo]]
+|0
+|1
+|9
+| -2
+| -6
+| -9
+|RuThaShaTho
+|-
+![[31-edo]]
+|0
+|1
+|4
+|10
+| -13
+|15
+|MaLuShoSi
+|-
+![[41-edo]]
+|0
+|1
+| -8
+| -14
+| -18
+|20
+|FoDeFlePi
+|-
+![[53edo|53-edo]]
+|0
+|1
+| -8
+| -14
+|23
+|20
+|FoDeRiyuPi
+|}
+Two edos can have the same mapping. For example both 19edo and 26edo are MaThoPaFla.
+Each prime has a second, larger fifthspan which is found by adding/subtracting the edo itself. For example, 31edo's prime 13 fifthspan is 15 but also 15 - 31 = -16. Thus 31edo's solfege string is also MaLuShoThe.
+In a multi-ring edo such as 72, the vowels must be repurposed to mean up/down. Note that this system fails if a ring has more than 13 notes, since there are only 13 consonants and one vowel for each ring.
+{| class="wikitable"
+|+Solfege strings for various multi-ring edos
+!
+!prime 5
+!prime 7
+!prime 11
+!prime 13
+!solfege string
+|-
+![[15-edo]]
+|vM3
+|m7
+|^4
+|(N/A)
+|MoThaFu
+|-
+![[24-edo]]
+|M3
+|vm7
+|^4 or vA4
+|^m6 or vM6
+|MaThoFuFlu or
+MaThoPoLo
+|-
+![[34-edo]]
+|vM3
+|m7
+|~4
+|~6
+|MoThaFiLi
+|-
+![[72-edo]]
+|vM3
+|vvm7
+|^^^P4 or vvvA4
+|^^^m6 or vvvM6
+|MoTheFiyuFliyu or
+MoThePeyoLeyo
+|}
+The solfege string for all meantone edos starts with Ma, all [[schismatic]] edos start with Fo, all [[archy]] edos have Tha as the 2nd syllable, etc.
 == Application to Bosanquet keyboards ==
-Using fixed-solfege, each physical key on the Lumatone can be named. Since the meaning of ups and downs changes in different edos, better to use -u/-o to mean aug/dim. This picture shows the names if C is named Da.
+Using fixed-solfege, each physical key on the Lumatone can be named. It's best to let -u/-o mean aug/dim not up/down, since the meaning of ups and downs changes in different edos. This picture shows the names if Da corresponds to the note C.
 [[File:Lumatone 41edo with solfege.jpg|none|thumb]]
-The uppermost few keys use -iyi ("ee-yee"), meaning quadruple-aug. One could instead set Da to D, in order to get a more symmetrical layout, and thus change two -iyi's to -eyo's.
+The uppermost few keys use -iyi ("ee-yee"), meaning quadruple-aug. One could set Da to D not C, in order to get a more symmetrical layout, and thus change two of the three -iyi's to -eyo's.
-One could also name all the lumatone keys using only 7 consonants, using -eye ("ay-yay") for triple-diminished:
+Using movable-solfege, one can name the notes of a scale independently of the key. One can also name any physical interval on the lumatone. For example, one step in the 1:00 direction is always Du, two steps in the 2:30 direction is always Ma, etc.
-[[File:Lumatone 41edo with solfege 2.jpg|none|thumb]]
-Using movable-solfege, one can name the notes of a scale independent of key. One can also name any physical interval on the lumatone. For example, one step in the 1:00 direction is always Du, two steps in the 2:30 direction is always Ma, etc.
-See also: [[Fifthspan]]
+The placement of various primes on a Bosanquet keyboard is determined by the fifthspan mapping (see the previous section). Thus the solfege string tells a lumatone player the physical placement of all the primes of interest.
 [[Category:Solfege]]