Kite's uniform solfege: Difference between revisions

Line 561:

== 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.

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 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

Line 572:

!prime 13

!solfege string

!alternates

|-

![[19-edo]]

Line 581:

Line 582:

| -4

|MaThoPaFla

|Tho=Lu

|-

![[22-edo]]

Line 590:

Line 592:

| -9

|RuThaShaTho

|Ru=Sho, Tho=Pu

|-

![[31-edo]]

Line 599:

Line 602:

|15

|MaLuShoSi

|Sho=Mi, Si=The

|-

![[41-edo]]

Line 608:

Line 612:

|20

|FoDeFlePi

|Fle=Riyu, Pi=Deyo

|-

![[53edo|53-edo]]

Line 617:

Line 622:

|20

|FoDeRiyuPi

|Riyu=Theye

|}

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~~.

The solfege string for all meantone edos starts with Ma, all [[archy]] edos have Tha as the 2nd syllable, etc.

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~~.

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 alternate solfege string is MaLuShoThe. The alternate fifthspan is usually only of interest if the smaller fifthspan approaches half the edo, and the alternate fifthspan is only slightly more remote.

In a multi-ring edo such as 72, -u/-o must be repurposed to mean up/down. The alternates in the table below are exactly as remote as the primary names.

{| class="wikitable"

|+Solfege strings for various multi-ring edos

Line 631:

Line 639:

!prime 13

!solfege string

!alternates

|-

![[15-edo]]

Line 638:

Line 647:

|(N/A)

|MoThaFu

|

|-

![[24-edo]]

Line 644:

Line 654:

|^4 or vA4

|^m6 or vM6

|~~MaThoFuFlu or~~

|MaThoPoLo

~~MaThoPoLo~~

|Po=Fu, Lo=Flu

|-

![[34-edo]]

|vM3

|m7

|(N/A)

|~4

|^^4

|~6

|^^m6

|~~MoThaFiLi~~

|MeAPoLo

|Po=Fu, Lo=Flu

|-

![[72-edo]]

Line 659:

Line 670:

|^^^P4 or vvvA4

|^^^m6 or vvvM6

|~~MoTheFiyuFliyu or~~

|MoThePeyoLeyo

~~MoThePeyoLeyo~~

|Peyo=Fiyu, Leyo=Fliyu

|}

~~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~~.

34edo is an unusual case. Each ring has 17 notes, which is more than 13 consonants and 1 vowel can cover. So -u/-o means up/down within the ring, and -i/-e means lift/drop by an edostep from one ring to the next. Note the use of -A- to exclude prime 7, which in 34edo has a huge relative error of 45%.

== Application to Bosanquet keyboards ==

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.

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. For example, in 31edo an up equals a step in the 5:00 direction, but in 41edo it's the opposite, a step in the 11:00 direction.

This picture shows the solfege 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 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.

Line 671:

Line 684:

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.

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~~.

<u>Solfege strings</u>: The placement of various primes on a Bosanquet keyboard is determined by the fifthspan mapping (see the previous section). Thus an edo's solfege string tells a lumatone player the physical placement of various primes. Notes ending in -u/-i lie on the top half of the keyboard and those ending-o/-e lie on the bottom half. The alternate fifthspan is sometimes useful to bring one prime nearer the others. For example, 41edo's solfege string is FoDeFlePi, with prime 13 being an outlier. It's alternate string is FoDeFleDeyo, which makes for more compact chord shapes.

The solfege string can be used to compare edos. For example 41edo is FoDeFlePi (or FoDeFleDeyo) and 53edo is FoDeRiyuPi. This tells us that primes 5, 7 and perhaps 13 are placed similarly, but prime 11 differs. Thus any 7-limit chord's shape is the same in both 41edo and 53edo.

[[Category:Solfege]]

@@ Line 561: / Line 561: @@
 == 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.
+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 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
@@ Line 572: / Line 572: @@
 !prime 13
 !solfege string
+!alternates
 |-
 ![[19-edo]]
@@ Line 581: / Line 582: @@
 | -4
 |MaThoPaFla
+|Tho=Lu
 |-
 ![[22-edo]]
@@ Line 590: / Line 592: @@
 | -9
 |RuThaShaTho
+|Ru=Sho, Tho=Pu
 |-
 ![[31-edo]]
@@ Line 599: / Line 602: @@
 |15
 |MaLuShoSi
+|Sho=Mi, Si=The
 |-
 ![[41-edo]]
@@ Line 608: / Line 612: @@
 |20
 |FoDeFlePi
+|Fle=Riyu, Pi=Deyo
 |-
 ![[53edo|53-edo]]
@@ Line 617: / Line 622: @@
 |20
 |FoDeRiyuPi
+|Riyu=Theye
 |}
 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.
+The solfege string for all meantone edos starts with Ma, all [[archy]] edos have Tha as the 2nd syllable, etc.
-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.
+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 alternate solfege string is MaLuShoThe. The alternate fifthspan is usually only of interest if the smaller fifthspan approaches half the edo, and the alternate fifthspan is only slightly more remote.
+In a multi-ring edo such as 72, -u/-o must be repurposed to mean up/down. The alternates in the table below are exactly as remote as the primary names.
 {| class="wikitable"
 |+Solfege strings for various multi-ring edos
@@ Line 631: / Line 639: @@
 !prime 13
 !solfege string
+!alternates
 |-
 ![[15-edo]]
@@ Line 638: / Line 647: @@
 |(N/A)
 |MoThaFu
+|
 |-
 ![[24-edo]]
@@ Line 644: / Line 654: @@
 |^4 or vA4
 |^m6 or vM6
-|MaThoFuFlu or
+|MaThoPoLo
-MaThoPoLo
+|Po=Fu, Lo=Flu
 |-
 ![[34-edo]]
 |vM3
-|m7
+|(N/A)
-|~4
+|^^4
-|~6
+|^^m6
-|MoThaFiLi
+|MeAPoLo
+|Po=Fu, Lo=Flu
 |-
 ![[72-edo]]
@@ Line 659: / Line 670: @@
 |^^^P4 or vvvA4
 |^^^m6 or vvvM6
-|MoTheFiyuFliyu or
+|MoThePeyoLeyo
-MoThePeyoLeyo
+|Peyo=Fiyu, Leyo=Fliyu
 |}
-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.
+edo is an unusual case. Each ring has 17 notes, which is more than 13 consonants and 1 vowel can cover. So -u/-o means up/down within the ring, and -i/-e means lift/drop by an edostep from one ring to the next. Note the use of -A- to exclude prime 7, which in 34edo has a huge relative error of 45%.
 == Application to Bosanquet keyboards ==
-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.
+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. For example, in 31edo an up equals a step in the 5:00 direction, but in 41edo it's the opposite, a step in the 11:00 direction.
+This picture shows the solfege 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 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.
@@ Line 671: / Line 684: @@
 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.
-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.
+<u>Solfege strings</u>: The placement of various primes on a Bosanquet keyboard is determined by the fifthspan mapping (see the previous section). Thus an edo's solfege string tells a lumatone player the physical placement of various primes. Notes ending in -u/-i lie on the top half of the keyboard and those ending-o/-e lie on the bottom half. The alternate fifthspan is sometimes useful to bring one prime nearer the others. For example, 41edo's solfege string is FoDeFlePi, with prime 13 being an outlier. It's alternate string is FoDeFleDeyo, which makes for more compact chord shapes.
+The solfege string can be used to compare edos. For example 41edo is FoDeFlePi (or FoDeFleDeyo) and 53edo is FoDeRiyuPi. This tells us that primes 5, 7 and perhaps 13 are placed similarly, but prime 11 differs. Thus any 7-limit chord's shape is the same in both 41edo and 53edo.
 [[Category:Solfege]]