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.
|3-limit||Plain major scale||Da||Ra||Ma||Fa||Sa||La||Ta||Da|
|Plain minor scale||Da||Ra||Na||Fa||Sa||Fla||Tha||Da|
Kite Guitar fretboard
The various rainbows run either -o -u -o -u or else -a -i -a.
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.
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.
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 double-upmajor, double-upminor or double-downminor intervals! (Double-downmajor 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)|
|3- limit||Plain major scale||Do||Re||Maa||Fa||Sol||Laa||Taa||Do|
|Plain minor scale||Do||Re||Meh||Fa||Sol||Leh||Teh||Do|
The two 5-limit scales are the same as conventional solfege.