41edo solfege

Uniform Solfege

Overview

See Uniform solfege for a full explanation.


41edo	edosteps	solfege		ups and downs names
unisons	0-1	Da Du		P1 ^1		C ^C
2nds	2-8	Fro Fra Fru	Ri Ro Ra Ru	vm2 m2 ^m2	~2 vM2 M2 ^M2	vDb Db ^Db	vvD vD D ^D
3rds	9-15	No Na Nu	Mi Mo Ma Mu	vm3 m3 ^m3	~3 vM3 M3 ^M3	vEb Eb ^Eb	vvE vE E ^E
4ths	16-18	Fo Fa Fu		v4 P4 ^4		vF F ^F
tritones	19-22	Fi/Sho Po/Sha Pa/Shu Pu/Si		~4/vd5 vA4/d5 A4/^d5 ^A4/~5		^^F/vGb vF#/Gb F#/^Gb ^F#/vvG
5ths	23-25	So Sa Su		v5 P5 ^5		vG G ^G
6ths	26-32	Flo Fla Flu	Li Lo La Lu	vm6 m6 ^m6	~6 vM6 M6 ^M6	vAb Ab ^Ab	vvA vA A ^A
7ths	33-39	Tho Tha Thu	Ti To Ta Tu	vm7 m7 ^m7	~7 vM7 M7 ^M7	vBb Bb ^Bb	vvB vB B ^B
8ves	40-41	Do Da		v8 P8		vC C

The seven 2nds illustrate the solfege's logic:

Fro = flat-Re-down = vm2
Fra = flat-Re-plain = m2
Fru = flat-Re-up = ^m2
Ri = Re-mid = ~2
Ro = Re-down = vM2
Ra = Re-plain = M2
Ru = Re-up = ^M2

The vowels relate to color notation: -a = wa, -o = yo or zo = over/otonal, -u = gu or ru = under/utonal, and -i = ila. The zogu 5th is Sha because the -o and -u in zogu cancel to make -a.

Example scales & tags


3-limit	Plain major scale	Da	Ra	Ma	Fa	Sa	La	Ta	Da
3-limit	Plain minor scale	Da	Ra	Na	Fa	Sa	Fla	Tha	Da
5-limit	Downmajor scale	Da	Ra	Mo	Fa	Sa	Lo	To	Da
5-limit	Upminor scale	Da	Ra	Nu	Fa	Sa	Flu	Thu	Da
7-limit	Upmajor scale	Da	Ra	Mu	Fa	Sa	Lu	Tu	Da
7-limit	Downminor scale	Da	Ra	No	Fa	Sa	Flo	Tho	Da
11-limit	Mid scale	Da	Ra	Mi	Fa	Sa	Li	Ti	Da

See also these barbershop tags: Sweet Sweet Harmony (original tag) and Kite's translations of barbershop tags.

Kite Guitar fretboard

The various rainbows run either -o -u -o -u or else -a -i -a.

<-- nut bridge -->
Pa	So	Su	Fla	Li	La	Tho	Thu	To	Tu	Da
Ru	Na	Mi	Ma	Fo	Fu	Sha	Si	Sa	Flo	Flu	Lo	Lu	Tha	Ti	Ta	Do	Du	Fra	Ri
Ti	Ta	Do	Du	Fra	Ri	Ra	No	Nu	Mo	Mu	Fa	Fi	Pa	So	Su	Fla	Li	La	Tho
									Da	Fro	Fru	Ro	Ru	Na	Mi	Ma	Fo	Fu	Sha

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:

Da - Ra - Ma - Fa - Sa - La - Ta - Da

This helps with unlearning 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 also present but changed.)

Once this solfege feels natural, 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

Once this is fully memorized, add in the other 3 vowels.

Octave Complements

To find the octave complement of any interval:

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
get the new consonant from the degree and quality
change the vowel as expected: -o <--> -u, but -a and -i are unchanged

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

The Circle of Fifths

The 13 -a notes form a chain of 5ths running from the dim 5th to the aug 4th:

Sha - Fra - Fla - Na - Tha - Fa - Da - Sa - Ra - La - Ma - Ta - Pa

The aug 4th Pa is also the updim 5th Shu, which is the starting point for another 13-note chain of 5ths, all -u notes. Since the ending point Pu is also Si, this leads to a 6-note chain of -i notes. This in turn leads to a 13-note -o chain, which leads back to the -a chain. 13 -a notes + 13 -u notes + 6 -i notes + 13 -o notes = 45 names = 41 notes with duplicate names for the 4 tritones.

To summarize, the 4 vowels create 4 separate chains of 5ths, and the 4 tritones with duplicate names connect those 4 chains into one 41-note circle. This is one rationale for the 13th consonant P-, for it supplies most of the duplicate names.

The 45 note names in circle-of-5ths order
(read left-to-right, top-row-to-bottom-row)
	d5	m2	m6	m3	m7	P4	P1	P5	M2	M6	M3	M7	A4 (d5)
-a							Da	Sa	Ra	La	Ma	Ta	Pa (Shu)
-u	Shu	Fru	Flu	Nu	Thu	Fu	Du	Su	Ru	Lu	Mu	Tu	Pu (Si)
-i								Si	Ri	Li	Mi	Ti	Fi (Sho)
-o	Sho	Fro	Flo	No	Tho	Fo	Do	So	Ro	Lo	Mo	To	Po (Sha)
-a	Sha	Fra	Fla	Na	Tha	Fa	Da

Adding/subtracting 4ths and 5ths

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 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. (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

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 minor 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)
Ta + M2 = Fru (M7 + M2 = ^m9)
To + M2 = Fra (vM7 + M2 = m9)
Ti + M2 = Fro (~7 + M2 = vm9)

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 dupmajor, dupminor or dudminor intervals! (Dudmajor is mid, thus Ro + vM2 = Mi.)

Andrew Heathwaite's Solfege

Andrew's solfege expands on the conventional Do - Di/Ra - Re - Ri/Me - Mi - Fa - Fi/Se - Sol - Si/Le - La - Li/Te - Ti - Do. There are 8 vowels, with -ih, -eh, -aa and -u added. There are 6 different vowel sequences.


41edo	solfege names	ups and downs names	edosteps
unisons	Do Di	P1 ^1	0-1
2nds	Ro Rih Ra Ru Reh Re Ri	vm2 m2 ^m2 ~2 vM2 M2 ^M2	2-8
3rds	Ma Meh Me Mu Mi Maa Mo	vm3 m3 ^m3 ~3 vM3 M3 ^M3	9-15
4ths	Fe Fa Fih Fu Fi	v4 P4 ^4 ~4 vA4	16-20
5ths	Se Su Sih So (or Sol) Si	^d5 ~5 v5 P5 ^5	21-25
6ths	Lo Leh Le Lu La Laa Li	vm6 m6 ^m6 ~6 vM6 M6 ^M6	26-32
7ths	Ta Teh Te Tu Ti Taa To	vm7 m7 ^m7 ~7 vM7 M7 ^M7	33-39
8ves	Da Do (Di)	v8 P8 (^8)	40-41 (42)

See also Andrew's 31edo solfege, which is a subset of this solfege, and Phylingual‎'s 53edo solfege, which is very nearly a superset. (It names the M7 as Tih.)

Example scales


3- limit	Plain major scale	Do	Re	Maa	Fa	Sol	Laa	Taa	Do
3- limit	Plain minor scale	Do	Re	Meh	Fa	Sol	Leh	Teh	Do
5-limit	Downmajor scale	Do	Re	Mi	Fa	Sol	La	Ti	Do
5-limit	Upminor scale	Do	Re	Me	Fa	Sol	Le	Te	Do
7-limit	Upmajor scale	Do	Re	Mo	Fa	Sol	Li	To	Do
7-limit	Downminor scale	Do	Re	Ma	Fa	Sol	Lo	Ta	Do
11-limit	Mid scale	Do	Re	Mu	Fa	Sol	Lu	Tu	Do

The two 5-limit scales are the same as conventional solfege.