24edo solfege

Kite Giedraitis's diatonic solfege

Kite's diatonic solfege uses the conventional 7 consonants D, R, M, F, S, L and T. It uses unconventional vowels. For each degree, the sequence runs front to back (i.e. bright to dim) -i -e -a -o -u for upmajor-major-mid-minor-downminor. It uses the exact same 33 note names as Kite's 31edo solfege.

Kite's diatonic solfege (-i -e -a -o -u = ^M M ~ m vm), see 31edo

24edo	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
notes	C	^C vDb	Db	vD	D	^D vEb	Eb	vE	E	^E vF	F	^F vGb	F# Gb	^F# vG	G	^G vAb	Ab	vA	A	^A vBb	Bb	vB	B	^B vC	C
intervals	P1	^1 vm2	m2	~2	M2	^M2 vm3	m3	~3	M3	^M3 v4	P4	^4 vd5	A4 d5	^A4 v5	P5	^5 vm6	m6	~6	M6	^M6 vm7	m7	~7	M7	^M7 v8	P8
solfege	Do	Da Ru	Ro	Ra	Re	Ri Mu	Mo	Ma	Me	Mi Fu	Fo	Fa Su	Fe So	Fi Sa	Se	Si Lu	Lo	La	Le	Li Tu	To	Ta	Te	Ti Du	Do

Beware: Mi, Fa, So, La and Ti all have new meanings.

Example scales

Upmajor scale	Do	Re	Mi	Fo	Se	Li	Ti	Do
Major scale	Do	Re	Me	Fo	Se	Le	Te	Do
Mid scale	Do	Re	Ma	Fo	Se	La	Ta	Do
Minor scale	Do	Re	Mo	Fo	Se	Lo	To	Do
Downminor scale	Do	Re	Mu	Fo	Se	Lu	Tu	Do

To find the octave complement of any interval:

• change the degree as usual: 2nd <--> 7th, 3rd <--> 6th, and 4th <--> 5th
• change the vowel as expected: -i <--> -u and -e <--> -o (-a is unchanged)

The two circles of fifths

The plain circle lacks ups and downs, hence the name.

The plain circle of 5ths

P1	P5	M2	M6	M3	M7	A4/d5	m2	m6	m3	m7	P4	P1
Do	Se	Re	Le	Me	Te	Fe/So	Ro	Lo	Mo	To	Fo	Do

The "off" circle contains the 6 offperfect intervals (^1 ^4 v4 ^5 v5 v8). The other 6 notes could be thought of as offmajor or offminor. Most of the notes in this circle have two names.

The "off" circle of 5ths

vm2 ^1	vm6 ^5	vm3 ^M2	vm7 ^M6	v4 ^M3	v8 ^M7	v5 ^A4	~2	~6	~3	~7	vd5 ^4	vm2 ^1
											Su	Ru
Ru	Lu	Mu	Tu	Fu	Du	Sa	Ra	La	Ma	Ta	Fa	Da
Da	Si	Ri	Li	Mi	Ti	Fi

Viewed as chains instead of circles:

• plain chain: So Ro Lo Mo To Fo Do Se Re Le Me Te Fe
• off chain: Su Ru Lu Mu Tu Fu Du Sa Ra La Ma Ta Fa Da Si Ri Li Mi Ti Fi

It's fairly easy to find the note a 4th or 5th above any note. The consonant is as would be expected from conventional interval arithmetic. There are only 3 fifths that don't rhyme:

• Do - Se (P1 to P5)
• Da - Si (^1 to ^5)
• Du - Sa (v1 to v5)

Thus Re plus a 4th is Se, Ro plus a 5th is Lo, etc. And in the example scales above, the 3rd, 6th and 7th always rhyme, as do the tonic and 4th, as do the 2nd and 5th.

However going a 5th up from an aug or upaug 4th would go to an aug or upaug 8ve, which doesn't exist in this solfege. Therefore one must rename the 4th as a dim 5th, then go up a 5th to a minor 2nd. Thus Fe + 5th = So + 5th = Ro. Likewise when adding a 4th, dim 5ths need renaming: So + 4th = Fe + 4th = Te.

Other circles

The two circles of 5ths can be interwoven to make a circle of mid 3rds.

P1	~3	P5	~7	M2	^4 vd5	M6	^1 vm2	M3	^5 vm6	M7	^M2 vm3	A4 d5	^M6 vm7	m2	^M3 v4	m6	^M7 v8	m3	^A4 v5	m7	~2	P4	~6	P1
Do	Ma	Se	Ta	Re	Fa Shu	Le	Da Ru	Me	Si Lu	Te	Ri Mu	Fe So	Li Tu	Ro	Mi Fu	Lo	Ti Du	Mo	Fi Sa	To	Ra	Fo	La	Do

The two circles of 4ths can be interwoven to make a circle of half-4ths.

P1	^M2 vm3	P4	^5 vm6	m7	^1 vm2	m3	^4 vd5	m6	~7	m2	~3	A4 d5	~6	M7	~2	M3	^A4 v5	M6	^M7 v8	M2	^M3 v4	P5	^M6 vm7	P1
Do	Ri Mu	Fo	Si Lu	To	Da Ru	Mo	Fa Su	Lo	Ta	Ro	Ma	Fe So	La	Te	Ra	Me	Fi Sa	Le	Ti Du	Re	Mi Fu	Se	Li Tu	Do

There is also a circle of down 5ths.

Kite Giedraitis's chromatic solfege

Kite's chromatic solfege uses the 7 conventional consonants D, R, M, F, S, L and T, plus 5 altered consonants that indicate flattening. It uses unconventional vowels: "oo" = u = up, "oh" = o = down, and "ah" = a = plain. It's a subset of Kite's 41edo solfege.

• Fr- = flat Re
• Fl- = flat La
• Sh- = flat So = sharp Fa
• Th = flat Ti
• N- = flat Mi

24edo	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
notes	C	^C vDb	Db	vD	D	^D vEb	Eb	vE	E	^E vF	F	^F vGb	F# Gb	^F# vG	G	^G vAb	Ab	vA	A	^A vBb	Bb	vB	B	^B vC	C
intervals	P1	^1 vm2	m2	~2	M2	^M2 vm3	m3	~3	M3	^M3 v4	P4	^4 vd5	A4 d5	^A4 v5	P5	^5 vm6	m6	~6	M6	^M6 vm7	m7	~7	M7	^M7 v8	P8
solfege	Da	Du Fro	Fra	Ro	Ra	Ru No	Na	Mo	Ma	Mu Fo	Fa	Fu Sho	Sha	Shu So	Sa	Su Flo	Fla	Lo	La	Lu Tho	Tha	To	Ta	Tu Do	Da

Beware, Do and So have new meanings.

Example scales

Upmajor scale	Da	Ra	Mu	Fa	Sa	Lu	Tu	Da
Major scale	Da	Ra	Ma	Fa	Sa	La	Ta	Da
Mid scale	Da	Ra	Mo	Fa	Sa	Lo	To	Da
Minor scale	Da	Ra	Na	Fa	Sa	Fla	Tha	Da
Downminor scale	Da	Ra	No	Fa	Sa	Flo	Tho	Da

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
• change the vowel as expected: -i <--> -u and -e <--> -o (-a is unchanged)
• if you get an aug 4th, change it to a dim 5th with the same vowel
• if you get an upminor interval Fru, Nu, Flu or Thu, change it to downmajor: Ro, Mo, Lo or To

The two circles of fifths

The plain circle lacks ups and downs, hence the name.

The plain circle of 5ths

P1	P5	M2	M6	M3	M7	A4/d5	m2	m6	m3	m7	P4	P1
Da	Sa	Ra	La	Ma	Ta	Sha	Fra	Fla	Na	Tha	Fa	Da

The "off" circle contains the 6 offperfect intervals (^1 ^4 v4 ^5 v5 v8). The other 6 notes could be thought of as offmajor or offminor. Most of the notes in this circle have two names.

The "off" circle of 5ths

vm2 ^1	vm6 ^5	vm3 ^M2	vm7 ^M6	v4 ^M3	v8 ^M7	v5 ^d5	~2	~6	~3	~7	vd5 ^4	vm2 ^1
Fro	Flo	No	Tho	Fo	Do	So	Ro	Lo	Mo	To	Sho	Fro
Du	Su	Ru	Lu	Mu	Tu	Shu					Fu	Du

Viewed as chains instead of circles:

• plain chain: Sha Fra Fla Na Tha Fa Da Sa Ra La Ma Ta
• off chain: Sho Fro Flo No Tho Fo Do So Ro Lo Mo To and Fu Du Su Ru Lu Mu Tu Shu

It's fairly easy to find the note a 4th or 5th above any note. The vowels match, i.e. the syllables rhyme. The consonant is as would be expected from conventional interval arithmetic. However, remember that an aug 4th is named as a dim 5th:

• To + P5 = Sho
• Ta + P5 = Sha
• Tu + P5 = Shu

Thus Ra plus a 4th is Sa, Ro plus a 5th is Lo, etc. And in the example scales above, the 3rd, 6th and 7th always rhyme, as do the tonic, 2nd, 4th and 5th.

Other circles

The two circles of 5ths can be interwoven to make a circle of mid 3rds.

P1	~3	P5	~7	M2	^4 vd5	M6	^1 vm2	M3	^5 vm6	M7	^M2 vm3	d5	^M6 vm7	m2	^M3 v4	m6	^M7 v8	m3	^d5 v5	m7	~2	P4	~6	P1
Da	Mo	Sa	To	Ra	Fu Sho	La	Du Fro	Ma	Su Flo	Ta	Ru No	Sha	Lu Tho	Fra	Mu Fo	Fla	Tu Do	Na	Shu So	Tha	Ro	Fa	Lo	Da

The two circles of 4ths can be interwoven to make a circle of half-4ths.

P1	^M2 vm3	P4	^5 vm6	m7	^1 vm2	m3	^4 vd5	m6	~7	m2	~3	d5	~6	M7	~2	M3	^d5 v5	M6	^M7 v8	M2	^M3 v4	P5	^M6 vm7	P1
Da	Ru No	Fa	Su Flo	Tha	Du Fro	Na	Fu Sho	Fla	To	Fra	Mo	Sha	Lo	Ta	Ro	Ma	Shu So	La	Tu Do	Ra	Mu Fo	Sa	Lu Tho	Da

There is also a circle of down 5ths.