User:TallKite/Solfeges - Revision history

TallKite: updated EI to EU

2024-12-29T00:06:34Z

updated EI to EU

TallKite: /* Pergens Summary */

2022-10-02T18:42:35Z

Pergens Summary

← Older revision		Revision as of 18:42, 2 October 2022
Line 22,177:		Line 22,177:
	!5		!5
	\|(P8/2, P4/2)		\|(P8/2, P4/2)
			true double
	\|half-everything		\|half-everything
	\|vvm2, \\A1, vv\\M2		\|vvm2, \\A1, vv\\M2
	\| -a -u -o -i -e<br>-uwi -owe		\| -a -u -o -i -e<br>-uwi -owe
	\|Da - ~~Fuwi~~/~~Sowe~~ - Da<br>Da - Ru/No - Fa<br>Da - Ni/Me - Sa		\|Da - Ru/No - Fa<br>Fuwi/Sowe - Fli/Le - Duwi/Rowe<br>Da - Ni/Me - Sa
	\|(2 4...) (0 -2...)		\|(2 4...) (0 -2...)
	\|		\|
Line 22,223:		Line 22,224:
	\|(P8/3, P4/2)		\|(P8/3, P4/2)
	\|third-8ve<br>half-4th		\|third-8ve<br>half-4th
	\|~~'''^~~<sup>3</sup>~~d2''', \\m2~~		\|vvm2, \<sup>6</sup>A2
	\| -a -u -o -i -e<br>-~~uwi~~ -~~owe~~		\| -a -u -o -i -e<br>-owi -uwe
	\|~~'''Da~~ - Mo - ~~Flu - Da'''~~<br>Da - Ri/Ne - Fa		\|Muwe - Se - Luwe<br>Da - Ru/No - Fa<br>Flowi - Thi - Frowi
	\|(3 6...) (0 -2...)		\|(3 6...) (0 -2...)
	\|~~7\12 = 700¢~~		\|
	\|-		\|-
	!12		!12
Line 22,235:		Line 22,236:
	\|'''^^d2''', \<sup>3</sup>A1		\|'''^^d2''', \<sup>3</sup>A1
	\| -a -u -o -i -e<br>-uwi -uwe -owi -owe		\| -a -u -o -i -e<br>-uwi -uwe -owi -owe
	\|~~'''Da - Po/Shu - Da'''<br>~~Da - Re - Ni - Fa<br>Po/Shu - Fluwe - Lowi - To		\|Da - Re - Ni - Fa<br>'''Po/Shu - Fluwe - Lowi - To'''
	\|(2 4...) (0 -3...)		\|(2 4...) (0 -3...)
	\|7\12 = 700¢		\|7\12 = 700¢

TallKite: added 72edo

2022-10-02T07:38:42Z

added 72edo

Show changes

TallKite: added pergen #10

2022-10-02T06:21:00Z

added pergen #10

Show changes

TallKite: /* Pergens Summary */

2022-10-01T21:32:30Z

Pergens Summary

← Older revision		Revision as of 21:32, 1 October 2022
Line 21,356:		Line 21,356:
	!4		!4
	\| (P8, P5/2)		\| (P8, P5/2)
	\|half-~~4th~~		\|half-5th
	\|vvA1		\|vvA1
	\| -a -u -o		\| -a -u -o
Line 21,367:		Line 21,367:
	\|half-everything		\|half-everything
	\|vvm2, \\A1, vv\\M2		\|vvm2, \\A1, vv\\M2
	\| -a -u -o -i -e		\| -a -u -o -i -e<br>-uwi -owe
	-uwi -owe
	\|Da - Fuwi/Sowe - Da<br>Da - Ru/No - Fa<br>Da - Ni/Me - Sa		\|Da - Fuwi/Sowe - Da<br>Da - Ru/No - Fa<br>Da - Ni/Me - Sa
	\|(2 4...) (0 -2...)		\|(2 4...) (0 -2...)
Line 21,411:		Line 21,410:
	!10		!10
	\|(P8/3, P4/2)		\|(P8/3, P4/2)
	\|third-8ve		\|third-8ve<br>half-4th
	half-4th
	\|'''^<sup>3</sup>d2''', \\m2		\|'''^<sup>3</sup>d2''', \\m2
	\| -a -u -o -i -e		\| -a -u -o -i -e<br>-uwi -owe
	-uwi -owe		\|'''Da - Mo - Flu - Da'''<br>Da - Ri/Ne - Fa
	\|'''Da - Mo - Flu - Da'''
	Da - Ri/Ne - Fa
	\|(3 6...) (0 -2...)		\|(3 6...) (0 -2...)
	\|7\12 = 700¢		\|7\12 = 700¢
Line 21,426:		Line 21,422:
	third-4th		third-4th
	\|'''^^d2''', \<sup>3</sup>A1		\|'''^^d2''', \<sup>3</sup>A1
	\| -a -u -o -i -e		\| -a -u -o -i -e<br>-uwi -uwe -owi -owe
	-uwi -uwe -owi -owe		\|'''Da - Po/Shu - Da'''<br>Da - Re - Ni - Fa<br>Po/Shu - Fluwe - Lowi - To
	\|'''Da - Po/Shu - Da'''
	Da - Re - Ni - Fa

	Po/Shu - Fluwe - Lowi - To
	\|(2 4...) (0 -3...)		\|(2 4...) (0 -3...)
	\|7\12 = 700¢		\|7\12 = 700¢
Line 21,547:		Line 21,539:
	\|sixth-4th		\|sixth-4th
	\|v<sup>3</sup>A1, \\m2		\|v<sup>3</sup>A1, \\m2
	\| -a -u -o -i -e		\| -a -u -o -i -e<br>-uwi -uwe -owi -owe
	-uwi -uwe -owi -owe		\|Da - Duwi/Fruwe - Ro - Ri/Ne -<br>- Nu - Mowi/Fowe - Fa
	\|Da - Duwi/Fruwe - Ro - Ri/Ne
	- Nu - Mowi/Fowe - Fa
	\|(1 2...) (0 -6...)		\|(1 2...) (0 -6...)
	\|		\|
Line 21,559:		Line 21,549:
	\|vvvm2, \\A1		\|vvvm2, \\A1
	\| -a -u -o -i -e<br>-uwe -owi		\| -a -u -o -i -e<br>-uwe -owi
	\|Da - Frowi - Ru - Ni/Me -		\|Da - Frowi - Ru - Ni/Me -<br>- Fo - Puwe - Sa
	- Fo - Puwe - Sa
	\|(1 1...) (0 6...)		\|(1 1...) (0 6...)
	\|		\|
Line 21,569:		Line 21,558:
	\|vvA1, \<sup>3</sup>M2		\|vvA1, \<sup>3</sup>M2
	\| -a -u -o -i -e<br>-uwe -owi		\| -a -u -o -i -e<br>-uwe -owi
	\|Da - Nuwe - Fi - Flu/Lo -		\|Da - Nuwe - Fi - Flu/Lo -<br>- Do - Rowi - Fa
	- Do - Rowi - Fa
	\|(1 3...) (0 -6...)		\|(1 3...) (0 -6...)
	\|		\|
Line 21,588:		Line 21,576:
	\|v<sup>6</sup>A1		\|v<sup>6</sup>A1
	\| -a -u -o -i -e<br>-iyu -eyo		\| -a -u -o -i -e<br>-iyu -eyo
	\|Da - Fu - Thi - Niyu/Meyo -		\|Da - Fu - Thi - Niyu/Meyo -<br>- Le - Ro - Sa
	- Le - Ro - Sa
	\|(1 -1...) (0 -6...)		\|(1 -1...) (0 -6...)
	\|		\|
Line 21,598:		Line 21,585:
	\|v<sup>7</sup>A2		\|v<sup>7</sup>A2
	\| -a -u -o -i -e<br>-iyu -eyo		\| -a -u -o -i -e<br>-iyu -eyo
	\|Da - Meyo - Fu - Le -		\|Da - Meyo - Fu - Le -<br>- Thi - Ro - Niyu - Sa
	- Thi - Ro - Niyu - Sa
	\|(1 0...) (0 7...)		\|(1 0...) (0 7...)
	\|		\|
Line 21,618:		Line 21,604:
	\|P4 / P5		\|P4 / P5
	\|Da - Fa/Sa - Da		\|Da - Fa/Sa - Da
	\|(2 3...)		\|(2 3...) (0 0...)
	(0 0...)
	\|silly, 9/8 vanishes		\|silly, 9/8 vanishes
	\|-		\|-
Line 21,627:		Line 21,612:
	\|M2 / P4		\|M2 / P4
	\|Da - Fa - Sa - Da		\|Da - Fa - Sa - Da
	\|(3 5...)		\|(3 5...) (0 0...)
	(0 0...)
	\|silly, 32/27 vanishes		\|silly, 32/27 vanishes
	\|-		\|-
Line 21,636:		Line 21,620:
	\|??		\|??
	\|Da - ?? - Fa/Sa - ?? - Da		\|Da - ?? - Fa/Sa - ?? - Da
	\|(4 6...)		\|(4 6...) (0 0...)
	(0 0...)		\|silly, 9/8 vanishes<br>multi-ring
	\|silly, 9/8 vanishes
	multi-ring
	\|-		\|-
	\| (P8/5, ^1)		\| (P8/5, ^1)
Line 21,646:		Line 21,628:
	\|M2 / m3		\|M2 / m3
	\|Da - Ra/Na - Ma/Fa - Sa/Fla - La/Tha- Da		\|Da - Ra/Na - Ma/Fa - Sa/Fla - La/Tha- Da
	\|(5 8...)		\|(5 8...) (0 0...)
			\|if Blackwood,<br>generator = 16/15
	(0 0...)
	\|if Blackwood,
	generator = 16/15
	\|-		\|-
	\|(P8/7, ^1)		\|(P8/7, ^1)
Line 21,657:		Line 21,636:
	\|M2 / m2		\|M2 / m2
	\|Da - Ra - Ma - Fa - Sa - La - Ta - Da		\|Da - Ra - Ma - Fa - Sa - La - Ta - Da
	\|(7 11...)		\|(7 11...) (0 0...)
	(0 0...)		\|if Whitewood,<br>generator = 135/128
	\|if Whitewood,
	generator = 135/128
	\|-		\|-
	\|(P8/10, ^1)		\|(P8/10, ^1)
Line 21,667:		Line 21,644:
	\|???		\|???
	\|Da - Fra - Ra/Na - Ma - Fa - Pa/Sha - Sa - Fla - La/Tha - Ta - Da		\|Da - Fra - Ra/Na - Ma - Fa - Pa/Sha - Sa - Fla - La/Tha - Ta - Da
	\|(10 16...)		\|(10 16...) (0 0...)
	(0 0...)		\|'''solfege names'''<br>'''may be wrong'''
	\|'''solfege names'''
	'''may be wrong'''
	\|-		\|-
	\|(P8/12, ^1)		\|(P8/12, ^1)
Line 21,677:		Line 21,652:
	\|A1 / m2		\|A1 / m2
	\|Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da		\|Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da
	\|(12 19 28...)		\|(12 19 28...) (0 0 -1...)
	(0 0 -1...)		\|if Compton,<br>generator = 81/80
	\|if Compton,
	generator = 81/80
	\|}		\|}

TallKite: /* Pergens Summary */

2022-09-27T20:18:27Z

Pergens Summary

@@ Line 21,562: / Line 21,562: @@
 - Fo - Puwe - Sa
 |(1 1...) (0 6...)
+|
 |-
@@ Line 21,571: / Line 21,581: @@
 |Da - Nowi - Se - Lu/Tho -<br>- Di - Muwe - Sa
 |(1 0...) (0 6...)
+|
 |-

TallKite: /* Pergens Summary */

2022-09-27T19:15:31Z

Pergens Summary

Show changes

TallKite: /* 41edo */

2022-09-27T04:36:19Z

41edo

← Older revision		Revision as of 04:36, 27 September 2022
Line 1:		Line 1:
	'''<big>This page is a work in progress!</big>'''		'''<big>This page is a work in progress!</big>'''

	To do: ~~check all edo pages for others' solfeges, done up to 19~~		To do:

	include subset solfeges (8 of 24, 9/18 of 36, 16 of 48, 15/20 of 60, ~~others?~~ 11 of 22? 13 of 26?)		check all edo pages for others' solfeges, done up to 19

			figure out the format for inbetween notes in edo tables: list once or list twice?

			include subset solfeges? (8 of 24, 9/18 of 36, 16 of 48, 15/20 of 60, maybe 11 of 22? 13 of 26?)

	discuss advantages and disadvantages of lots of enharmonic equivalences (the "extra" notes)		discuss advantages and disadvantages of lots of enharmonic equivalences (the "extra" notes)

	discuss ~~performerr~~ vs composer solfeges? example: subset solfege and 12-edo numeric solfege, the ultimate performer solfege		discuss performer vs composer solfeges? example: subset solfege and 12-edo numeric solfege, the ultimate performer solfege

	maybe break up into 2 pages?		maybe break up into 2 pages?
Line 19:		Line 23:
	'''BC (backwards-compatible)''' solfeges are for mid-sized edos like 17 and 19. They expand on the conventional Do Re Mi (and Do Di/Ra Re RiMa Mi) and use traditional vowels plus new ones.		'''BC (backwards-compatible)''' solfeges are for mid-sized edos like 17 and 19. They expand on the conventional Do Re Mi (and Do Di/Ra Re RiMa Mi) and use traditional vowels plus new ones.

	'''Uniform''' solfeges are for ~~larger~~ edos like 41 and 53. They use a uniform vowel sequence for all degrees. They add 6 altered consonants: Fr- N- P- Sh- Fl- and Th-. '''Uniform diatonic''' solfeges don't add them.		'''Uniform''' solfeges are for almost edos, especially large ones like 41 and 53. They are also for rank-2 temperaments. They use a uniform vowel sequence for all degrees. They add 6 altered consonants: Fr- N- P- Sh- Fl- and Th-. '''Uniform diatonic''' solfeges don't add them.

	== Uniform solfeges ==		== Uniform solfeges ==
Line 7,704:		Line 7,708:
	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|+		\|+
	~~Kite's~~ solfege (-a = plain, -u = up, -o = down, -i = mid), see also 53edo		uniform solfege (-a = plain, -u = up, -o = down, -i = mid), see also 53edo
	![[41edo]]		![[41edo]]
	!edosteps		!edosteps

TallKite: /* Rank-2 Uniform Solfeges by Pergen */

2022-09-27T04:02:33Z

Rank-2 Uniform Solfeges by Pergen

← Older revision		Revision as of 04:02, 27 September 2022
Line 9,119:		Line 9,119:

	A pergen's solfege can suggest an edo's solfege. For example, 22edo supports (P8, P4/3), and the pergen's solfege has 27 notes in it. Since the generator is 3\22, simply apply the genchain to every 3rd edostep of 22edo. The extra 5 names make duplicate names.		A pergen's solfege can suggest an edo's solfege. For example, 22edo supports (P8, P4/3), and the pergen's solfege has 27 notes in it. Since the generator is 3\22, simply apply the genchain to every 3rd edostep of 22edo. The extra 5 names make duplicate names.

			Every solfege syllable that ends in -o indicates a correlation with colorspeak. Thus temperaments that start with Mo have -o/-u = yo/gu, those that have 2nd syllable Tho have -o/-u = zo/ru, etc.

	To Do:		To Do:

TallKite at 03:40, 27 September 2022

2022-09-27T03:40:03Z

← Older revision		Revision as of 03:40, 27 September 2022
Line 154:		Line 154:
	Da - Ra - Ma - Fa - Sa - La - Ta - Da		Da - Ra - Ma - Fa - Sa - La - Ta - Da

	This helps with <u>un</u>learning the ~~syllables Do, Mi, So and Ti, which are still present but have a changed meaning~~. ~~(For those familiar with the full 17-name solfege, note that Ra, Ri, Fi, Si and Li are often present but changed.)~~		This helps with <u>un</u>learning the traditional vowels. Next add in the 6 altered consonants, making a 12-edo-like solfege:

	Next add in the 6 altered consonants, making a 12-edo-like solfege:

	Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da		Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da
Line 9,094:		Line 9,092:

	== Rank-2 Uniform Solfeges by Pergen ==		== Rank-2 Uniform Solfeges by Pergen ==
	Rank-2 temperaments have an infinite number of notes, so a solfege can only cover a fraction of them. But often one only uses enough notes to make a MOS scale. [[Pergen\|Pergens]] tell us how to use ups and downs to notate ~~them~~, and the same consonants and vowels can be used. Instead of circles of 5ths, there are fifthchains. Each fifthchain requires its own vowel, so there is a maximum of 5 fifthchains.		Rank-2 temperaments have an infinite number of notes, so a solfege can only cover a fraction of them. But often one only uses enough notes to make a MOS scale. [[Pergen\|Pergens]] tell us how to use ups and downs to notate these temperaments, and the same consonants and vowels can be used. Instead of circles of 5ths, there are fifthchains. Each fifthchain requires its own vowel, so there is a maximum of 5 fifthchains.

	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 ~~about 20~~ 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.		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.

	Sometimes -i and -e mean lift/drop not dup/dud~~. If so, note that there are no words for uplift, downlift, etc~~. -i never means mid, so there are only two vowel sequences, not three:		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.

			Sometimes -i and -e mean lift/drop not dup/dud. -i never means mid, so there are only two vowel sequences, not three:
	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|+the two vowel sequences		\|+the two vowel sequences
Line 9,114:		Line 9,114:
	\|<nowiki>-u = up</nowiki>		\|<nowiki>-u = up</nowiki>
	\| -i = dup or lift		\| -i = dup or lift
	\|}In ~~the MOS scale tables~~, ~~any note that changes from one mode to the next is '''bolded'''~~.		\|}In certain pergens, there are compound vowels like -iyu for trup or -uwi for uplift.

	~~The EI (enharmonic interval) can be added to or subtracted from~~ any note ~~or interval~~ to ~~get an equivalent note or interval~~.		In the MOS scale tables, any note that changes from one mode to the next is '''bolded'''. The mode numbers are defined such that the 1st mode always has Sa and not Fa, and the last mode always has Fa and not Sa.

	A pergen's solfege can suggest an edo's solfege. For example, 22edo supports (P8, P4/3), and the pergen's solfege has 27 notes in it. Since the generator is 3\22, simply apply the genchain to every 3rd edostep of 22edo. The extra 5 names make duplicate names.~~to do~~:		A pergen's solfege can suggest an edo's solfege. For example, 22edo supports (P8, P4/3), and the pergen's solfege has 27 notes in it. Since the generator is 3\22, simply apply the genchain to every 3rd edostep of 22edo. The extra 5 names make duplicate names.

			To Do:

	* explain c is P5 - 700¢
	* explain the 1st mode always has Sa and not Fa, and the last mode always has Fa and not Sa.
	* make a table of pergens and what MOS scales each one covers		* make a table of pergens and what MOS scales each one covers
	* discuss using numeric solfeges with non-diatonic-friendly MOSes		* discuss using numeric solfeges with non-diatonic-friendly MOSes
	* for each pergen, list the entire genchain in melodic order, if possible?		* for each pergen, list the entire genchain in melodic order, if possible?
	* explain temperament naming: can use Aug and Dim syllables to extend the genchains, can use -a- for an omitted prime.

	=== List of MOS scales ===		=== List of MOS scales ===
Line 9,364:		Line 9,363:
	== #1 (P8, P5) unsplit ==		== #1 (P8, P5) unsplit ==
	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.		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 = 700¢ + c for this and all other pergens		* G = P5, which = 700¢ + c for this and all other pergens
	* EI = vA1 = 0¢ (extended solfege only)		* EI = vA1 = 0¢ (extended solfege only)
	* ^ = # = 100 + 7c (extended solfege only)		* ^ = # = 100 + 7c (extended solfege only)
Line 11,877:		Line 11,876:
	\|Da		\|Da
	\|}		\|}
	~~A similar table can be made for 5L9s. The same solfege can be used for 9L5s, but Sa will be < 4\7 = 686¢.~~

	== #4 (P8, P5/2) half-5th (list alternate pergens) ==		== #4 (P8, P5/2) half-5th (list alternate pergens) ==
	* G = ^m3/vM3 = ~3 = 350¢ + c/2		* G = ^m3/vM3 = ~3 = 350¢ + c/2
Line 14,160:		Line 14,157:
	\|^D		\|^D
	\|}		\|}
			Implied 22edo solfege: Da - Du - Fru - Ro - Ra - Ru/Na - Nu - Mo - Ma/Fo - Fa - Fu - Po/Shu - So - Sa - Su/Fla - Flu - Lo - La/Tho - Tha - Thu - To - Do - Da
	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|+		\|+
Line 14,515:		Line 14,513:
	\|Da		\|Da
	\|}		\|}
	~~A similar table can be made for 7L8s, but it will lack the 1st and 15th modes.~~

	== #8 (P8, P5/3) third-5th ==		== #8 (P8, P5/3) third-5th ==