User:TallKite/Solfeges: Difference between revisions

Line 9,524:

Genchains are distinct from fifthchains. Each pergen has one or more genchains, each of which contains one or more fifthchains. However if the octave is split in halves or quarters, the half-octave requires two names, and the pergen needs an additional vowel. The 13 consonants and 5 vowels cover 21 pergens. Of course, the genchains can only extend so far with only 13 consonants. But in general, it's enough to cover all the modes of any reasonably-sized MOS scale.

This pdf '''[https://tallkite.com/misc_files/notation guide for rank-2 pergens.pdf tallkite.com/misc_files/notation guide for rank-2 pergens.pdf]''' lists many pergens. The tuning of every interval and every accidental is defined in terms of c = P5 - 700¢. The EI (enharmonic ~~interval~~) can be added to or subtracted from any note or interval to get an equivalent note or interval. The entire solfege can be derived from the pergen, the EI and the vowel sequence.

This pdf '''[https://tallkite.com/misc_files/notation guide for rank-2 pergens.pdf tallkite.com/misc_files/notation guide for rank-2 pergens.pdf]''' lists many pergens. The tuning of every interval and every accidental is defined in terms of c = P5 - 700¢. The EU ([[enharmonic unison]]) can be added to or subtracted from any note or interval to get an equivalent note or interval. The entire solfege can be derived from the pergen, the EU and the vowel sequence.

Sometimes -i and -e mean lift/drop not dup/dud. -i never means mid, so there are only two vowel sequences, not three:

Line 9,867:

There are no ups and downs. The basic solfege has 13 notes. The extended solfege uses -u/-o to augment/diminish an -a interval. The solfege can be further extended with -i/-e meaning doubly augmented/diminished.

* G = P5, which = 700¢ + c for this and all other pergens

* EI = vA1 = 0¢ (extended solfege only)

* EU = vA1 = 0¢ (extended solfege only)

* ^ = # = 100 + 7c (extended solfege only)

Line 10,469:

* '''or''' vA1/^m2 (solfege #1) = 100¢ + c

* '''or''' ^A1/vm2 (solfege #2) = 100¢ + c

* EI = ^^d2 (solfege #1) = 0¢

* EU = ^^d2 (solfege #1) = 0¢

* '''or''' vvd2 (solfege #2) = 0¢

* ^ = 6 '''⋅''' |c|

Line 11,643:

|}

=== Solfege #3 (EI = vvM2) ===

=== Solfege #3 (EU = vvM2) ===

* P = ^4/v5 = 600¢

* G = ^1 = vM2 = 100¢ + c

* EI = vvM2 = 0¢

* EU = vvM2 = 0¢

* ^ = 100¢ + c

* # = 100¢ + 7c

Line 12,010:

* G = ^M2/vm3 = 250¢ - c/2

* EI = vvm2 = 0¢

* EU = vvm2 = 0¢

* ^ = 50¢ - 2.5c = 5G - P

Line 12,381:

== #4 (P8, P5/2) half-5th (list alternate pergens) ==

* G = ^m3/vM3 = ~3 = 350¢ + c/2

* EI = vvA1 = 0¢

* EU = vvA1 = 0¢

* ^ = 50¢ + 3.5c = 7G - 2P

Line 12,784:

* G = P4/2 = ^M2 = vm3 = 250¢ - c/2

* G' = P5/2 = /m3 = \M3 = 350¢ + c/2

* EI's: vvm2, \\A1

* EU's: vvm2, \\A1

* ^ = 50¢ - 2.5c = 5G - P

* / = 50¢ + 3.5c = 3P - 7G

Line 13,109:

* P = vM3/^^d4 (solfege #1) '''or''' ^M3/vvd4 (solfege #2) = 400¢

* G = P5 = 700¢ + c '''or''' vvA1/^m2 (solfege #1) '''or''' ^^A1/vm2 (solfege #2) = 100¢ - c

* EI = ^3d2 = 0¢

* EU = ^3d2 = 0¢

* ^ = 4 '''⋅''' |c|

Line 14,531:

* G = vM2/^^m2 = ^~2 = 167¢ - c/3

* EI = v3A1 = 0¢

* EU = v3A1 = 0¢

* ^ = (100¢ + 7c) / 3

Line 15,019:

* G = ^M2/vvm3 = 233¢ + c/3

* EI = v3m2 = 0¢

* EU = v3m2 = 0¢

* ^ = (100¢ - 5c) / 3

Line 15,296:

* G = ^4/vv5 = 567¢ - c/3

* EI = v3M2 = 0¢

* EU = v3M2 = 0¢

* ^ = (200¢ + 2c) / 3 (quite large, a literal third-tone)

Line 15,568:

* P = ^\M3 = v\4 = 400¢

* G = ^M2 = vm3 = 250¢ - c/2 '''or''' \M2 = 150¢ + c/2

* EI = vvm2, \6A2, ^\3A1 = 0¢

* EU = vvm2, \6A2, ^\3A1 = 0¢

* ^ = 50¢ - 2.5c

* / = 50¢ + 1.5c

Line 15,884:

* P = ^m3/v3A2 (solfege #1) '''or''' vm3/^3A2 (solfege #2) = 300¢

* G = P5 = 700¢ + c '''or''' vvA1/^^m2 (solfege #1) '''or''' ^^A1/vvm2 (solfege #2) = 100¢ + c

* EI = ^4d2 = 0¢

* EU = ^4d2 = 0¢

* ^ = 3 '''⋅''' |c|

Line 16,797:

== #17 (P8, P4/4) quarter-4th ==

* G = ^m2 = v3AA1 = v\M2 = v/A1 = 125¢ - c/4

* EI's = ^4dd2, \\m2, ^^\d2, vv\A1, etc.

* EU's = ^4dd2, \\m2, ^^\d2, vv\A1, etc.

* ^ = 25¢ + 4.75c

* / = 50¢ - 2.5c

Line 17,306:

== <nowiki>#</nowiki>18 (P8, P5/4) quarter-5th ==

* G = vM2 = ^3m2 = 175¢ + c/4

* EI = v4A1 = 0¢

* EU = v4A1 = 0¢

* ^ = 25¢ + 1.75c

Line 17,548:

== <nowiki>#</nowiki>19 (P8, P11/4) quarter-11th ==

* G = ^M3 = v34 = v\4 = v/d4 = ^//m3 = 425¢ - c/4

* EI's = v4dd3, \\A1, vv\m2, vv/d2, etc.

* EU's = v4dd3, \\A1, vv\m2, vv/d2, etc.

* ^ = 25¢ - 4.25c

* / = 50¢ + 3.5c

Line 18,020:

* G = v4 = ^3M3 = 475¢ + c/4

* EI = v4m2 = 0¢

* EU = v4m2 = 0¢

* ^ = 25¢ - 1.25c

Line 18,349:

* P = ^^4 = vv5 = 600¢

* G = ^1 = v3M2 = 50¢ + c/2

* EI = v4M2 = 0¢

* EU = v4M2 = 0¢

* ^ = 50¢ + c/2

Line 18,965:

* P = ^^M2 = v3m3 = 240¢

* G = P5 = 700¢ + c '''or''' ^1 = v4m2 = 20¢ - c

* EI = v5m2 = 0¢

* EU = v5m2 = 0¢

* ^ = 20¢ - c

Line 19,537:

* G = ^^m2 = v3A1 = 100¢ - c/5

* EI = ^5d2 = 0¢

* EU = ^5d2 = 0¢

* ^ = 2.4c

Line 19,985:

* G = vM2 = ^4d1 = 140¢ + c/5

* EI = v5A2 = 0¢

* EU = v5A2 = 0¢

* ^ = 60¢ + 1.8c

Line 20,355:

* G = ^^m3 = v3M3 = 340¢ - c/5

* EI = v5A1 = 0¢

* EU = v5A1 = 0¢

* ^ = 20¢ + 1.4c

Line 20,570:

This pergen can be thought of as "half-dudaug5th".

* G = vM3 = ^\d4 = //A2 = 380¢ + c/5

* EI's = ^5dd2, \5d34, ^^\d2, v\\m2, etc.

* EU's = ^5dd2, \5d34, ^^\d2, v\\m2, etc.

* ^ = 20¢ + 3.8c

* / = 40¢ - 4.4c

Line 20,942:

==<nowiki>#</nowiki>38 (P8, ccP4/5) fifth-coco-4th ==

* G = ^^4 = v35 = 580¢ - c/5

* EI = v5M2 = 0¢

* EU = v5M2 = 0¢

* ^ = 40¢ + 0.4c

Line 21,297:

*P = M2/m3 = 200¢

*G = ^1 = c (stands for 81/80 in Blackwood)

*EI = d2 = 0¢

*EU = d2 = 0¢

*^ = c

Line 21,752:

*P = M2/m2 = 171¢

*G = ^1 = c (stands for 135/128 in Whitewood)

*EI = A1 = 0¢

*EU = A1 = 0¢

*^ = c

Line 22,133:

!

! colspan="2" |pergen

!EI

!EU

!vowels

!perchain and/or genchain

Line 22,406:

Multi-edo pergens -- genchain is always De Do Da Du Di

! colspan="2" |pergen

!EI

!EU

!period

!perchain

@@ Line 9,524: / Line 9,524: @@
 Genchains are distinct from fifthchains. Each pergen has one or more genchains, each of which contains one or more fifthchains. However if the octave is split in halves or quarters, the half-octave requires two names, and the pergen needs an additional vowel. The 13 consonants and 5 vowels cover 21 pergens. Of course, the genchains can only extend so far with only 13 consonants. But in general, it's enough to cover all the modes of any reasonably-sized MOS scale.
-This pdf '''[https://tallkite.com/misc_files/notation&#x20;guide&#x20;for&#x20;rank-2&#x20;pergens.pdf tallkite.com/misc_files/notation guide for rank-2 pergens.pdf]''' lists many pergens. The tuning of every interval and every accidental is defined in terms of c = P5 - 700¢. The EI (enharmonic interval) can be added to or subtracted from any note or interval to get an equivalent note or interval. The entire solfege can be derived from the pergen, the EI and the vowel sequence.
+This pdf '''[https://tallkite.com/misc_files/notation&#x20;guide&#x20;for&#x20;rank-2&#x20;pergens.pdf tallkite.com/misc_files/notation guide for rank-2 pergens.pdf]''' lists many pergens. The tuning of every interval and every accidental is defined in terms of c = P5 - 700¢. The EU ([[enharmonic unison]]) can be added to or subtracted from any note or interval to get an equivalent note or interval. The entire solfege can be derived from the pergen, the EU and the vowel sequence.
 Sometimes -i and -e mean lift/drop not dup/dud. -i never means mid, so there are only two vowel sequences, not three:
@@ Line 9,867: / Line 9,867: @@
 There are no ups and downs. The basic solfege has 13 notes. The extended solfege uses -u/-o to augment/diminish an -a interval. The solfege can be further extended with -i/-e meaning doubly augmented/diminished.
 * G = P5, which = 700¢ + c for this and all other pergens
-* EI = vA1 = 0¢ (extended solfege only)
+* EU = vA1 = 0¢ (extended solfege only)
 * ^ = # = 100 + 7c (extended solfege only)
@@ Line 10,469: / Line 10,469: @@
 *   '''<u>or</u>''' vA1/^m2 (solfege #1) = 100¢ + c
 *   '''<u>or</u>''' ^A1/vm2 (solfege #2) = 100¢ + c
-* EI = ^^d2 (solfege #1) = 0¢
+* EU = ^^d2 (solfege #1) = 0¢
 * '''<u>or</u>''' vvd2 (solfege #2) = 0¢
 * ^ = 6 '''⋅''' |c|
@@ Line 11,643: / Line 11,643: @@
 |}
-=== Solfege #3 (EI = vvM2) ===
+=== Solfege #3 (EU = vvM2) ===
 * P = ^4/v5 = 600¢
 * G = ^1 = vM2 = 100¢ + c
-* EI = vvM2 = 0¢
+* EU = vvM2 = 0¢
 * ^ = 100¢ + c
 * # = 100¢ + 7c
@@ Line 12,010: / Line 12,010: @@
 * G = ^M2/vm3 = 250¢ - c/2
-* EI = vvm2 = 0¢
+* EU = vvm2 = 0¢
 * ^ = 50¢ - 2.5c = 5G - P
@@ Line 12,381: / Line 12,381: @@
 == #4 (P8, P5/2) half-5th (list alternate pergens) ==
 * G = ^m3/vM3 = ~3 = 350¢ + c/2
-* EI = vvA1 = 0¢
+* EU = vvA1 = 0¢
 * ^ = 50¢ + 3.5c = 7G - 2P
@@ Line 12,784: / Line 12,784: @@
 * G = P4/2 = ^M2 = vm3 = 250¢ - c/2
 * G' = P5/2 = /m3 = \M3 = 350¢ + c/2
-* EI's: vvm2, \\A1
+* EU's: vvm2, \\A1
 * ^ = 50¢ - 2.5c = 5G - P
 * / = 50¢ + 3.5c = 3P - 7G
@@ Line 13,109: / Line 13,109: @@
 * P = vM3/^^d4 (solfege #1) '''<u>or</u>''' ^M3/vvd4 (solfege #2) = 400¢
 * G = P5 = 700¢ + c '''<u>or</u>''' vvA1/^m2 (solfege #1) '''<u>or</u>''' ^^A1/vm2 (solfege #2) = 100¢ - c
-* EI = ^<sup>3</sup>d2 = 0¢
+* EU = ^<sup>3</sup>d2 = 0¢
 * ^ = 4 '''⋅''' |c|
@@ Line 14,531: / Line 14,531: @@
 * G = vM2/^^m2 = ^~2 = 167¢ - c/3
-* EI = v<sup>3</sup>A1 = 0¢
+* EU = v<sup>3</sup>A1 = 0¢
 * ^ = (100¢ + 7c) / 3
@@ Line 15,019: / Line 15,019: @@
 * G = ^M2/vvm3 = 233¢ + c/3
-* EI = v<sup>3</sup>m2 = 0¢
+* EU = v<sup>3</sup>m2 = 0¢
 * ^ = (100¢ - 5c) / 3
@@ Line 15,296: / Line 15,296: @@
 * G = ^4/vv5 = 567¢ - c/3
-* EI = v<sup>3</sup>M2 = 0¢
+* EU = v<sup>3</sup>M2 = 0¢
 * ^ = (200¢ + 2c) / 3 (quite large, a literal third-tone)
@@ Line 15,568: / Line 15,568: @@
 * P = ^\M3 = v\4 = 400¢
 * G = ^M2 = vm3 = 250¢ - c/2  '''<u>or</u>'''  \M2 = 150¢ + c/2
-* EI = vvm2, \<sup>6</sup>A2, ^\<sup>3</sup>A1 = 0¢
+* EU = vvm2, \<sup>6</sup>A2, ^\<sup>3</sup>A1 = 0¢
 * ^ = 50¢ - 2.5c
 * / = 50¢ + 1.5c
@@ Line 15,884: / Line 15,884: @@
 * P = ^m3/v<sup>3</sup>A2 (solfege #1) '''<u>or</u>''' vm3/^<sup>3</sup>A2 (solfege #2) = 300¢
 * G = P5 = 700¢ + c '''<u>or</u>''' vvA1/^^m2 (solfege #1) '''<u>or</u>''' ^^A1/vvm2 (solfege #2) = 100¢ + c
-* EI = ^<sup>4</sup>d2 = 0¢
+* EU = ^<sup>4</sup>d2 = 0¢
 * ^ = 3 '''⋅''' |c|
@@ Line 16,797: / Line 16,797: @@
 == #17 (P8, P4/4) quarter-4th ==
 * G = ^m2 = v<sup>3</sup>AA1 = v\M2 = v/A1 = 125¢ - c/4
-* EI's = ^<sup>4</sup>dd2, \\m2, ^^\d2, vv\A1, etc.
+* EU's = ^<sup>4</sup>dd2, \\m2, ^^\d2, vv\A1, etc.
 * ^ = 25¢ + 4.75c
 * / = 50¢ - 2.5c
@@ Line 17,306: / Line 17,306: @@
 == <nowiki>#</nowiki>18 (P8, P5/4) quarter-5th ==
 * G = vM2 = ^<sup>3</sup>m2 = 175¢ + c/4
-* EI = v<sup>4</sup>A1 = 0¢
+* EU = v<sup>4</sup>A1 = 0¢
 * ^ = 25¢ + 1.75c
@@ Line 17,548: / Line 17,548: @@
 == <nowiki>#</nowiki>19 (P8, P11/4) quarter-11th ==
 * G = ^M3 = v<sup>3</sup>4 = v\4 = v/d4 = ^//m3 = 425¢ - c/4
-* EI's = v<sup>4</sup>dd3, \\A1, vv\m2, vv/d2, etc.
+* EU's = v<sup>4</sup>dd3, \\A1, vv\m2, vv/d2, etc.
 * ^ = 25¢ - 4.25c
 * / = 50¢ + 3.5c
@@ Line 18,020: / Line 18,020: @@
 * G = v4 = ^<sup>3</sup>M3 = 475¢ + c/4
-* EI = v<sup>4</sup>m2 = 0¢
+* EU = v<sup>4</sup>m2 = 0¢
 * ^ = 25¢ - 1.25c
@@ Line 18,349: / Line 18,349: @@
 * P = ^^4 = vv5 = 600¢
 * G = ^1 = v<sup>3</sup>M2 = 50¢ + c/2
-* EI = v<sup>4</sup>M2 = 0¢
+* EU = v<sup>4</sup>M2 = 0¢
 * ^ = 50¢ + c/2
@@ Line 18,965: / Line 18,965: @@
 * P = ^^M2 = v<sup>3</sup>m3 = 240¢
 * G = P5 = 700¢ + c '''<u>or</u>''' ^1 = v<sup>4</sup>m2 = 20¢ - c
-* EI = v<sup>5</sup>m2 = 0¢
+* EU = v<sup>5</sup>m2 = 0¢
 * ^ = 20¢ - c
@@ Line 19,537: / Line 19,537: @@
 * G = ^^m2 = v<sup>3</sup>A1 = 100¢ - c/5
-* EI = ^<sup>5</sup>d2 = 0¢
+* EU = ^<sup>5</sup>d2 = 0¢
 * ^ = 2.4c
@@ Line 19,985: / Line 19,985: @@
 * G = vM2 = ^<sup>4</sup>d1 = 140¢ + c/5
-* EI = v<sup>5</sup>A2 = 0¢
+* EU = v<sup>5</sup>A2 = 0¢
 * ^ = 60¢ + 1.8c
@@ Line 20,355: / Line 20,355: @@
 * G = ^^m3 = v<sup>3</sup>M3 = 340¢ - c/5
-* EI = v<sup>5</sup>A1 = 0¢
+* EU = v<sup>5</sup>A1 = 0¢
 * ^ = 20¢ + 1.4c
@@ Line 20,570: / Line 20,570: @@
 This pergen can be thought of as "half-dudaug5th".
 * G = vM3 = ^\d4 = //A2 = 380¢ + c/5
-* EI's = ^<sup>5</sup>dd2, \<sup>5</sup>d<sup>3</sup>4, ^^\d2, v\\m2, etc.
+* EU's = ^<sup>5</sup>dd2, \<sup>5</sup>d<sup>3</sup>4, ^^\d2, v\\m2, etc.
 * ^ = 20¢ + 3.8c
 * / = 40¢ - 4.4c
@@ Line 20,942: / Line 20,942: @@
 ==<nowiki>#</nowiki>38 (P8, ccP4/5) fifth-coco-4th ==
 * G = ^^4 = v<sup>3</sup>5 = 580¢ - c/5
-* EI = v<sup>5</sup>M2 = 0¢
+* EU = v<sup>5</sup>M2 = 0¢
 * ^ = 40¢ + 0.4c
@@ Line 21,297: / Line 21,297: @@
 *P = M2/m3 = 200¢
 *G = ^1 = c (stands for 81/80 in Blackwood)
-*EI = d2 = 0¢
+*EU = d2 = 0¢
 *^ = c
@@ Line 21,752: / Line 21,752: @@
 *P = M2/m2 = 171¢
 *G = ^1 = c (stands for 135/128 in Whitewood)
-*EI = A1 = 0¢
+*EU = A1 = 0¢
 *^ = c
@@ Line 22,133: / Line 22,133: @@
 !
 ! colspan="2" |pergen
-!EI
+!EU
 !vowels
 !perchain and/or genchain
@@ Line 22,406: / Line 22,406: @@
 Multi-edo pergens -- genchain is always De Do Da Du Di
 ! colspan="2" |pergen
-!EI
+!EU
 !period
 !perchain