41edo solfege - Revision history

Wilh3lm: /* Shasavistic harmononyms */ Filled in missing harmononyms (though I really hope 3 and 38 have better approximations than Xcyli and Jus)

2025-04-07T22:37:34Z

Shasavistic harmononyms: Filled in missing harmononyms (though I really hope 3 and 38 have better approximations than Xcyli and Jus)

← Older revision		Revision as of 22:37, 7 April 2025
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	\|-		\|-
	\|3		\|3
	\|		\|Xcyli
	\|		\|135/128
	\|-		\|-
	\|4		\|4
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	\|-		\|-
	\|14		\|14
	\|		\|Myk
	\|		\|14/11
	\|-		\|-
	\|15		\|15
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	\|-		\|-
	\|18		\|18
	\|		\|Xcys
	\|		\|27/20
	\|-		\|-
	\|19		\|19
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	\|-		\|-
	\|23		\|23
	\|		\|Juli
	\|		\|40/27
	\|-		\|-
	\|24		\|24
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	\|-		\|-
	\|27		\|27
	\|		\|Puzi
	\|		\|11/7
	\|-		\|-
	\|28		\|28
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	\|-		\|-
	\|38		\|38
	\|		\|Jus
	\|		\|256/135
	\|-		\|-
	\|39		\|39

Wilh3lm: Added section on Shasavistic harmononyms

2025-04-07T22:21:41Z

Added section on Shasavistic harmononyms

Show changes

TallKite: /* Adding/subtracting other intervals */

2023-10-27T00:56:46Z

Adding/subtracting other intervals

← Older revision		Revision as of 00:56, 27 October 2023
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	In general, one can add or subtract any conventional (i.e. plain) interval from any note, and the result will be as expected. But only if the expected answer exists in the solfege. It must exist on the 13-note chain of 5ths from dim5 to aug4. In other words, the expected answer must not be augmented or diminished, unless it's an aug4 or a dim5. (Otherwise, one must use an enharmonic equivalent.) For example, one can easily add a M3 to any note other than a L-, M-, T- or P- note. Thus Ro + M3 = Po and Na + M3 = Sa, but La + M3 = Fru. Beware, because the -i chain is only 6 notes long, when adding to or subtracting from an -i note, the expected answer must exist on the P5-A4 chain.		In general, one can add or subtract any conventional (i.e. plain) interval from any note, and the result will be as expected. But only if the expected answer exists in the solfege. It must exist on the 13-note chain of 5ths from dim5 to aug4. In other words, the expected answer must not be augmented or diminished, unless it's an aug4 or a dim5. (Otherwise, one must use an enharmonic equivalent.) For example, one can easily add a M3 to any note other than a L-, M-, T- or P- note. Thus Ro + M3 = Po and Na + M3 = Sa, but La + M3 = Fru. Beware, because the -i chain is only 6 notes long, when adding to or subtracting from an -i note, the expected answer must exist on the P5-A4 chain.

	One can often easily add/subtract an unconventional (upped or downed) interval as well. The ups and downs add up and cancel out as expected. Thus Ra + vM2 = Mo and Ru + vM2 = Ma. Obviously the vowel will change. Again, the expected answer must exist in the solfege. No ~~double-upmajor~~, ~~double-upminor~~ or ~~double-downminor~~ intervals! (~~Double-downmajor~~ is mid, thus Ro + vM2 = Mi.)		One can often easily add/subtract an unconventional (upped or downed) interval as well. The ups and downs add up and cancel out as expected. Thus Ra + vM2 = Mo and Ru + vM2 = Ma. Obviously the vowel will change. Again, the expected answer must exist in the solfege. No dupmajor, dupminor or dudminor intervals! (Dudmajor is mid, thus Ro + vM2 = Mi.)

	==Andrew Heathwaite's Solfege==		==Andrew Heathwaite's Solfege==

TallKite: added note names to the first chart, added the off-zone to the fretboard chart

2022-11-22T19:53:02Z

added note names to the first chart, added the off-zone to the fretboard chart

Show changes

TallKite: explained the Ti - Fi issue more

2022-10-19T09:16:40Z

explained the Ti - Fi issue more

← Older revision		Revision as of 09:16, 19 October 2022
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	*change the '''degree''' as usual: 2nd <--> 7th, 3rd <--> 6th, and 4th <--> 5th		*change the '''degree''' as usual: 2nd <--> 7th, 3rd <--> 6th, and 4th <--> 5th
	*change the '''quality''' as usual: major <--> minor, aug <--> dim, but perfect and mid are unchanged		*change the '''quality''' as usual: major <--> minor, aug <--> dim, but perfect and mid are unchanged
			*get the new '''consonant''' from the degree and quality
	* change the '''vowel''' as expected: -o <--> -u, but -a and -i are unchanged		* change the '''vowel''' as expected: -o <--> -u, but -a and -i are unchanged

	For example, Fru = minor-Re-up becomes major-Ti-down = To.		For example, Fru = minor-Re-up becomes major-Ti-down = To. Likewise, Si becomes Fi.

	===The Circle of Fifths===		===The Circle of Fifths===
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	Because the aforementioned 4 chains connect up, it's very easy to find the note a 4th or 5th above any note. It always rhymes, and the consonant is as would be expected from conventional interval arithmetic. Ra plus a 4th is Sa, Fro plus a 5th is Flo, etc. Thus in the example scales above, the 3rd, 6th and 7th always rhyme, as do the tonic, 2nd, 4th and 5th.		Because the aforementioned 4 chains connect up, it's very easy to find the note a 4th or 5th above any note. It always rhymes, and the consonant is as would be expected from conventional interval arithmetic. Ra plus a 4th is Sa, Fro plus a 5th is Flo, etc. Thus in the example scales above, the 3rd, 6th and 7th always rhyme, as do the tonic, 2nd, 4th and 5th.

	However, consider the 4 tritones Fi, Po, Pa and Pu. The note a 5th above any of these would be some sort of augmented or mid 8ve, which doesn't exist in this solfege. Therefore one must rename the tritone as a dim or mid 5th. Thus Po + 5th = Sha + 5th = Fra. Likewise, Sho, Sha, Shu and Si need renaming when adding a 4th: Shu + 4th = Pa + 4th = Ta.		However, consider the four tritones Fi, Po, Pa and Pu. The note a 5th above any of these would be some sort of augmented or mid 8ve, which doesn't exist in this solfege. Therefore one must rename the tritone as a dim or mid 5th. Thus Po + 5th = Sha + 5th = Fra. Likewise, Sho, Sha, Shu and Si need renaming when adding a 4th: Shu + 4th = Pa + 4th = Ta.

	One minor exception arises with Ti and Fi. Conventionally, M7 + 5th = A4, and indeed Tu/Ta/To + 5th = Pu/Pa/Po. But Ti + 5th = Fi not Pi. Likewise Fu/Fa/Fo + 4th = Thu/Tha/Tho, minor 7ths as expected, but Fi + 4th = Ti not Thi. These exceptions are not an issue as long as you remember that there is no Pi or Thi in the solfege.		One minor exception arises with Ti and Fi. Conventionally, M7 + 5th = A4, and indeed Tu/Ta/To + 5th = Pu/Pa/Po. But Ti + 5th = Fi not Pi. Likewise Fu/Fa/Fo + 4th = Thu/Tha/Tho, minor 7ths as expected, but Fi + 4th = Ti not Thi. These exceptions are not an issue as long as you remember that there is no Pi or Thi in the solfege. (What if we fix this by renaming Fi as Pi? Another issue arises: one would expect that Pi's octave complement would be Shi, but instead it's Si. What if Si were renamed Shi? Then Shi plus a 5th would make not Fri but rather Ri. So some sort of minor exception is inevitable.)

	===Adding/subtracting other intervals===		===Adding/subtracting other intervals===

TallKite: /* Overview */

2022-10-08T04:09:29Z

Overview

← Older revision		Revision as of 04:09, 8 October 2022
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	===Overview ===		===Overview ===
	See [[Uniform ~~Solfege~~]] for a full explanation.		See [[Uniform solfege]] for a full explanation.
	{\| class="wikitable" style="text-align:center;"		{\| class="wikitable" style="text-align:center;"
	\|+		\|+

TallKite at 11:17, 5 October 2022

2022-10-05T11:17:34Z

← Older revision		Revision as of 11:17, 5 October 2022
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	![[41edo]]		![[41edo]]
	!edosteps		!edosteps
	! colspan="2" \|~~Da Ra Mo names~~		! colspan="2" \|solfege
	! colspan="2" \|[[Ups and downs notation\|ups and downs]] names		! colspan="2" \|[[Ups and downs notation\|ups and downs]] names
	\|-		\|-
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	\|}		\|}

	===Suggestion for learning ~~Da Ra Mo~~===		===Suggestion for learning===
	Even with many familiar consonants and a consistent vowel sequence, it can take a while to master 45 syllables. One might want to take a divide-and-conquer approach. Start with replacing Do Re Mi etc. with this solfege:		Even with many familiar consonants and a consistent vowel sequence, it can take a while to master 45 syllables. One might want to take a divide-and-conquer approach. Start with replacing Do Re Mi etc. with this solfege:

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	\|}		\|}

	See also Andrew's [[31edo solfege]], which is a subset of this solfege, and <bdi>Phylingual</bdi>‎'s [[53edo solfege]], which is very nearly a superset. (It names the M7 as Tih.)		See also Andrew's [[31edo\|31edo solfege]], which is a subset of this solfege, and <bdi>Phylingual</bdi>‎'s [[53edo\|53edo solfege]], which is very nearly a superset. (It names the M7 as Tih.)

	===Example scales===		===Example scales===

TallKite: updated

2022-10-05T11:09:56Z

updated

← Older revision		Revision as of 11:09, 5 October 2022
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	==~~Kite Giedraitis's~~ Solfege==		==Uniform Solfege==

	===Overview ===		===Overview ===
	[[~~Kite Giedraitis\|Kite~~]]'s solfege is nicknamed "Da Ra Mo" after harmonics 8:9:10. It uses the conventional consonants D, R, M, F, S, L and T. But most consonants have an alternate form that indicates flattening or sharpening. The vowels are unconventional: "oo" = u = '''u'''p, "ah" = a ~~= pl'''a'''in, "oh" = o = d'''o'''wn and "ee" = i = m'''i'''d~~.		See [[Uniform Solfege]] for a full explanation.
	{\| class="wikitable" style="text-align:center;"		{\| class="wikitable" style="text-align:center;"
	\|+		\|+
	![[41edo]]		![[41edo]]
			!edosteps
	! colspan="2" \|Da Ra Mo names		! colspan="2" \|Da Ra Mo names
	! colspan="2" \|[[Ups and downs notation\|ups and downs]] names		! colspan="2" \|[[Ups and downs notation\|ups and downs]] names
	~~!edosteps~~
	\|-		\|-
	!unisons		!unisons
			\|0-1
	\| colspan="2" \|Da Du		\| colspan="2" \|Da Du
	\| colspan="2" \|P1 ^1		\| colspan="2" \|P1 ^1
	~~\|0-1~~
	\|-		\|-
	!2nds		!2nds
			\|2-8
	\|Fro Fra Fru		\|Fro Fra Fru
	\|Ri Ro Ra Ru		\|Ri Ro Ra Ru
	\| vm2 m2 ^m2		\| vm2 m2 ^m2
	\|~2 vM2 M2 ^M2		\|~2 vM2 M2 ^M2
	~~\|2-8~~
	\|-		\|-
	!3rds		!3rds
			\|9-15
	\|No Na Nu		\|No Na Nu
	\|Mi Mo Ma Mu		\|Mi Mo Ma Mu
	\|vm3 m3 ^m3		\|vm3 m3 ^m3
	\|~3 vM3 M3 ^M3		\|~3 vM3 M3 ^M3
	~~\|9-15~~
	\|-		\|-
	!4ths		!4ths
			\|16-18
	\| colspan="2" \| Fo Fa Fu		\| colspan="2" \| Fo Fa Fu
	\| colspan="2" \| v4 P4 ^4		\| colspan="2" \| v4 P4 ^4
	~~\|16-18~~
	\|-		\|-
	!tritones		!tritones
			\|19-22
	\| colspan="2" \| Fi/Sho Po/Sha Pa/Shu Pu/Si		\| colspan="2" \| Fi/Sho Po/Sha Pa/Shu Pu/Si
	\| colspan="2" \| ~4/vd5 vA4/d5 A4/^d5 ^A4/~5		\| colspan="2" \| ~4/vd5 vA4/d5 A4/^d5 ^A4/~5
	~~\|19-22~~
	\|-		\|-
	!5ths		!5ths
			\|23-25
	\| colspan="2" \| So Sa Su		\| colspan="2" \| So Sa Su
	\| colspan="2" \| v5 P5 ^5		\| colspan="2" \| v5 P5 ^5
	~~\|23-25~~
	\|-		\|-
	!6ths		!6ths
			\|26-32
	\|Flo Fla Flu		\|Flo Fla Flu
	\|Li Lo La Lu		\|Li Lo La Lu
	\|vm6 m6 ^m6		\|vm6 m6 ^m6
	\|~6 vM6 M6 ^M6		\|~6 vM6 M6 ^M6
	~~\|26-32~~
	\|-		\|-
	!7ths		!7ths
			\|33-39
	\|Tho Tha Thu		\|Tho Tha Thu
	\|Ti To Ta Tu		\|Ti To Ta Tu
	\|vm7 m7 ^m7		\|vm7 m7 ^m7
	\|~7 vM7 M7 ^M7		\|~7 vM7 M7 ^M7
	~~\|33-39~~
	\|-		\|-
	!8ves		!8ves
	\| colspan="2" \|Do Da ~~(Du)~~		\|40-41
	\| colspan="2" \|v8 P8 ~~(^8)~~		\| colspan="2" \|Do Da
	~~\|40-41 (42)~~		\| colspan="2" \|v8 P8
	\|}		\|}
	The seven 2nds illustrate the solfege's logic:		The seven 2nds illustrate the solfege's logic:
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	The vowels relate to [[color notation]]: -a = w'''a''', -o = y'''o''' or z'''o''' = '''o'''ver/'''o'''tonal, -u = g'''u''' or r'''u''' = '''u'''nder/'''u'''tonal, and -i = '''i'''la. The zogu 5th is Sha because the -o and -u in zogu cancel to make -a.		The vowels relate to [[color notation]]: -a = w'''a''', -o = y'''o''' or z'''o''' = '''o'''ver/'''o'''tonal, -u = g'''u''' or r'''u''' = '''u'''nder/'''u'''tonal, and -i = '''i'''la. The zogu 5th is Sha because the -o and -u in zogu cancel to make -a.

	Da Ra Mo is a subset of Kite's [[53edo solfege]]. The idea of 12 consonants is inspired by Erv Wilson's 41edo solfege (see page 54 of http://www.anaphoria.com/41notes.pdf). However Kite added a 13th consonant P- to indicate a sharpened 4th. Mnemonic: Sha sharpens to Sa, and Tha sharpens to Ta, so if Fa were spelled Pha, it would sharpen to Pa.

	===Example scales & tags===		===Example scales & tags===

TallKite at 04:58, 6 September 2022

2022-09-06T04:58:43Z

← Older revision		Revision as of 04:58, 6 September 2022
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	\|40-41 (42)		\|40-41 (42)
	\|}		\|}
	~~Th- is unvoiced as in <u>th</u>ink.~~ The seven 2nds illustrate the solfege's logic:		The seven 2nds illustrate the solfege's logic:

	*Fro = '''f'''lat-'''R'''e-d'''o'''wn = vm2		*Fro = '''f'''lat-'''R'''e-d'''o'''wn = vm2
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	However, consider the 4 tritones Fi, Po, Pa and Pu. The note a 5th above any of these would be some sort of augmented or mid 8ve, which doesn't exist in this solfege. Therefore one must rename the tritone as a dim or mid 5th. Thus Po + 5th = Sha + 5th = Fra. Likewise, Sho, Sha, Shu and Si need renaming when adding a 4th: Shu + 4th = Pa + 4th = Ta.		However, consider the 4 tritones Fi, Po, Pa and Pu. The note a 5th above any of these would be some sort of augmented or mid 8ve, which doesn't exist in this solfege. Therefore one must rename the tritone as a dim or mid 5th. Thus Po + 5th = Sha + 5th = Fra. Likewise, Sho, Sha, Shu and Si need renaming when adding a 4th: Shu + 4th = Pa + 4th = Ta.

	~~A few~~ minor ~~exceptions arise~~ with ~~the -i notes~~. Conventionally, M7 + 5th = A4, and indeed Ta + 5th = Pa. But Ti + 5th = Fi not Pi. Likewise Fa + 4th = Tha, a minor ~~7th~~ as expected, but Fi + 4th = Ti not Thi. These exceptions are not an issue as long as you remember that there is no Pi or Thi in the solfege.		One minor exception arises with Ti and Fi. Conventionally, M7 + 5th = A4, and indeed Tu/Ta/To + 5th = Pu/Pa/Po. But Ti + 5th = Fi not Pi. Likewise Fu/Fa/Fo + 4th = Thu/Tha/Tho, minor 7ths as expected, but Fi + 4th = Ti not Thi. These exceptions are not an issue as long as you remember that there is no Pi or Thi in the solfege.

	===Adding/subtracting other intervals===		===Adding/subtracting other intervals===
	The same rule for 4ths and 5ths mostly holds for plain major 2nds. Keep the vowel, and change the consonant as expected. Ra + M2 = Ma. But again the 4 tritones must be named as 5ths not 4ths: Fi + M2 = Sho + M2 = Flo. Note that Fi to Si is a <u>minor</u> 2nd. Beware, this rule breaks down entirely for major~~-ish~~ and mid 7ths (the four T- notes), due to the lack of aug and mid 8ves:		The same rule for 4ths and 5ths mostly holds for plain major 2nds. Keep the vowel, and change the consonant as expected. Ra + M2 = Ma. But again the 4 tritones must be named as 5ths not 4ths: Fi + M2 = Sho + M2 = Flo. Note that Fi to Si is a <u>minor</u> 2nd. Beware, this rule breaks down entirely for major and mid 7ths (the four T- notes), due to the lack of aug and mid 8ves:

	* Tu + M2 = Ri (^M7 + M2 = ~9)		* Tu + M2 = Ri (^M7 + M2 = ~9)

TallKite: added an edosteps column to the main solfege tables

2022-08-31T05:52:43Z

added an edosteps column to the main solfege tables

← Older revision		Revision as of 05:52, 31 August 2022
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	! colspan="2" \|Da Ra Mo names		! colspan="2" \|Da Ra Mo names
	! colspan="2" \|[[Ups and downs notation\|ups and downs]] names		! colspan="2" \|[[Ups and downs notation\|ups and downs]] names
			!edosteps
	\|-		\|-
	!unisons		!unisons
	\| colspan="2" \|Da Du		\| colspan="2" \|Da Du
	\| colspan="2" \|P1 ^1		\| colspan="2" \|P1 ^1
			\|0-1
	\|-		\|-
	!2nds		!2nds
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	\| vm2 m2 ^m2		\| vm2 m2 ^m2
	\|~2 vM2 M2 ^M2		\|~2 vM2 M2 ^M2
			\|2-8
	\|-		\|-
	!3rds		!3rds
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	\|vm3 m3 ^m3		\|vm3 m3 ^m3
	\|~3 vM3 M3 ^M3		\|~3 vM3 M3 ^M3
			\|9-15
	\|-		\|-
	!4ths		!4ths
	\| colspan="2" \| Fo Fa Fu		\| colspan="2" \| Fo Fa Fu
	\| colspan="2" \| v4 P4 ^4		\| colspan="2" \| v4 P4 ^4
			\|16-18
	\|-		\|-
	!tritones		!tritones
	\| colspan="2" \| Fi/Sho Po/Sha Pa/Shu Pu/Si		\| colspan="2" \| Fi/Sho Po/Sha Pa/Shu Pu/Si
	\| colspan="2" \| ~4/vd5 vA4/d5 A4/^d5 ^A4/~5		\| colspan="2" \| ~4/vd5 vA4/d5 A4/^d5 ^A4/~5
			\|19-22
	\|-		\|-
	!5ths		!5ths
	\| colspan="2" \| So Sa Su		\| colspan="2" \| So Sa Su
	\| colspan="2" \| v5 P5 ^5		\| colspan="2" \| v5 P5 ^5
			\|23-25
	\|-		\|-
	!6ths		!6ths
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	\|vm6 m6 ^m6		\|vm6 m6 ^m6
	\|~6 vM6 M6 ^M6		\|~6 vM6 M6 ^M6
			\|26-32
	\|-		\|-
	!7ths		!7ths
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	\|vm7 m7 ^m7		\|vm7 m7 ^m7
	\|~7 vM7 M7 ^M7		\|~7 vM7 M7 ^M7
			\|33-39
	\|-		\|-
	!8ves		!8ves
	\| colspan="2" \|Do Da (Du)		\| colspan="2" \|Do Da (Du)
	\| colspan="2" \|v8 P8 (^8)		\| colspan="2" \|v8 P8 (^8)
			\|40-41 (42)
	\|}		\|}
	Th- is unvoiced as in <u>th</u>ink. The seven 2nds illustrate the solfege's logic:		Th- is unvoiced as in <u>th</u>ink. The seven 2nds illustrate the solfege's logic:
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	!solfege names		!solfege names
	![[Ups and downs notation\|ups and downs]] names		![[Ups and downs notation\|ups and downs]] names
			!edosteps
	\|-		\|-
	!unisons		!unisons
	\|Do Di		\|Do Di
	\|P1 ^1		\|P1 ^1
			\|0-1
	\|-		\|-
	!2nds		!2nds
	\|Ro Rih Ra Ru Reh Re Ri		\|Ro Rih Ra Ru Reh Re Ri
	\|vm2 m2 ^m2 ~2 vM2 M2 ^M2		\|vm2 m2 ^m2 ~2 vM2 M2 ^M2
			\|2-8
	\|-		\|-
	!3rds		!3rds
	\|Ma Meh Me Mu Mi Maa Mo		\|Ma Meh Me Mu Mi Maa Mo
	\|vm3 m3 ^m3 ~3 vM3 M3 ^M3		\|vm3 m3 ^m3 ~3 vM3 M3 ^M3
			\|9-15
	\|-		\|-
	!4ths		!4ths
	\|Fe Fa Fih Fu Fi		\|Fe Fa Fih Fu Fi
	\|v4 P4 ^4 ~4 vA4		\|v4 P4 ^4 ~4 vA4
			\|16-20
	\|-		\|-
	!5ths		!5ths
	\|Se Su Sih So (or Sol) Si		\|Se Su Sih So (or Sol) Si
	\|^d5 ~5 v5 P5 ^5		\|^d5 ~5 v5 P5 ^5
			\|21-25
	\|-		\|-
	!6ths		!6ths
	\|Lo Leh Le Lu La Laa Li		\|Lo Leh Le Lu La Laa Li
	\|vm6 m6 ^m6 ~6 vM6 M6 ^M6		\|vm6 m6 ^m6 ~6 vM6 M6 ^M6
			\|26-32
	\|-		\|-
	!7ths		!7ths
	\|Ta Teh Te Tu Ti Taa To		\|Ta Teh Te Tu Ti Taa To
	\| vm7 m7 ^m7 ~7 vM7 M7 ^M7		\| vm7 m7 ^m7 ~7 vM7 M7 ^M7
			\|33-39
	\|-		\|-
	!8ves		!8ves
	\|Da Do (Di)		\|Da Do (Di)
	\|v8 P8 (^8)		\|v8 P8 (^8)
			\|40-41 (42)
	\|}		\|}