24edo solfege

Kite Giedraitis's solfege

Kite's 24edo solfege uses the conventional 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 same 33 note names as Kite's 31edo solfege.

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
Do	Da
	Ru	Ro	Ra	Re	Ri
					Mu	Mo	Ma	Me	Mi
									Fu	Fo	Fa	Fe	Fi
											Su	So	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 to a minor 2nd. Thus Fe + 5th = So + 5th = Ro. Dim 5ths may also 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	M6	^1	M3	^5	M7	^M2	A4/d5	vm7	m2	v4	m6	v8	m3	v5	m7	~2	P4	~6	P1
Do	Ma	Se	Ta	Re	Fa	Le	Da	Me	Si	Te	Ri	Fe/So	Tu	Ro	Fu	Lo	Du	Mo	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.