Universal solfege

WORK IN PROGRESS

Universal Solfege was invented by Nick Vuci. It builds on Margo Schulter's "Regions of the Interval Spectrum" to create a systematic solfege which can be applied to a variety of microtonal scales.

The principle is that we can divide the interval spectrum into discrete areas which can then be used to take subsets for most microtonal scales we can imagine (although it works best with scales that have around 5-9 notes). It's not an exhaustive solution but a practical and practicible one.

While the chart gives solfege syllables for 59 distinct intervals, the entire gamut is not meant to be used in one instance. Instead it is meant to be used via selection of a subset relevant to a main scale.

When using MOS, the system can be used in conjunction with "hexachords" to create a microtonal "hexachordal solfeggio." (Of course, "hexachord" is the common term but here it is insufficient since the set may contain more or less than 6 notes depending on the MOS.)

Finally, to quote Schulter:

A main caution is that the borders are inevitably "fuzzy," so that one region shades into another and suggested values in cents are more illustrative than definitive.

This means that ultimately you should define the intervals as you hear them and as they function to you, not necessarily as they strictly fall on this chart. If a scale contains an interval that is 259 cents, but you hear it as a minor third in context, then give it the solfege syllable of a minor third instead of a semifourth.

A chart below lays things out:

Interval	Class	Subcategory	Cent Range	Solfege	IPA
Unison			0	A	a
Comma			0-30	O	ɒ
Dieses			30-60	Ee	i
Second	Minor	Small	60-80	Sais	saɪs
		Middle	80-100	Sai	saɪ
		Large	100-125	Sail	saɪl
	Neutral	Small	125-135	Soos	sus
		Middle	135-160	Soo	su
		Large	160-170	Sool	sul
	Equable Heptatonic		160-182	Ha	ha
	Major	Small	180-200	Says	seɪs
		Middle	200-220	Say	seɪ
		Large	220-240	Sayl	seɪl
Semifourth (Interseptimal Maj2-min3)			240-260	Fe	fɛ
Thirds	Minor	Small	260-280	Thais	θaɪs
		Middle	280-300	Thai	θaɪ
		Large	300-330	Thail	θaɪl
	Neutral	Small	330-342	Thoos	θus
		Middle	342-360	Thoo	θu
		Large	360-372	Thool	θul
	Major	Small	372-400	Thays	θeɪs
		Middle	400-423	Thay	θeɪ
		Large	423-440	Thayl	θeɪl
Semisixth (Interseptimal Maj3-4)			440-468	Ke	kɛ
Fourths		Small	468-491	Fos	fɔs
		Middle	491-505	Fo	fɔ
		Large	505-528	Fol	fɔl
Superfourths			528-560	Foo	fu
Tritones		Small	560-577	Trais	traɪs
		Middle	577-623	Trai	traɪ
		Large	623-640	Trail	traɪl
Subfifths			640-672	Fu	fʌ
Fifths		Small	640-695	Fis	fɪs
		Middle	695-709	Fi	fɪ
		Large	709-732	Fil	fɪl
Semitenth (Interseptimal 5-min6)			732-760	Te	tɛ
Sixths	Minor	Small	760-777	Kais	kaɪs
		Middle	777-800	Kai	kaɪ
		Large	800-828	Kail	kaɪl
	Neutral	Small	828-840	Koos	kus
		Middle	840-858	Koo	ku
		Large	858-870	Kool	kul
	Major	Small	870-900	Kays	keɪs
		Middle	900-920	Kay	keɪ
		Large	920-940	Kayl	keɪl
(Semitwelfth Interseptimal Maj6-min7)			940-960	Twe	twɛ
Sevenths	Minor	Small	960-987	Vais	vaɪs
		Middle	987-1000	Vai	vaɪ
		Large	1000-1025	Vail	vaɪl
	Equable heptatonic		1018-1040	Ho	hɒ
	Neutral	Small	1030-1043	Voos	vus
		Middle	1043-1065	Voo	vu
		Large	1065-1075	Vool	vul
	Major	Small	1075-1100	Vays	veɪs
		Middle	1100-1120	Vay	veɪ
		Large	1120-1140	Vayl	veɪl
Octave less diesis			1140-1170	Dee	di
Octave less comma			1170-1200	Co	kɒ
Octave			1200	A	a

The Unison and the Octave (ie the "tonic") is always denoted with "A." (IPA: a)

For the main intervals which do not have major or minor forms, we give the following syllables:

• "Fo" for fourths
• "Trai" for tritones
• "Fi" for fifths

For the main intervals which have major, neutral, and minor versions we assign evocative and distinct consonant affixes:

• "S-" for seconds
• "Th-" for thirds
• "K-" for sixths
• "V-" for sevenths

To denote major, neutral, and minor versions of these intervals we add the vowels "ay" "oo" and "ai" (IPA "eɪ," "u," and "aɪ") which mimic the distinct vowels of the words "major," "neutral," and "minor."

All of these main categories have primary versions (which can optionally be specified as the "middle" version) but also small and large versions, which we can denote with the consonant suffixes "s" and "l."

For the more esoteric categories we do not do not have major, minor, neutral, nor do we have large or small versions. These are denoted as follows:

• "O" and "Co" for the commatic ranges
• "Ee" and "Dee" for the dieses ranges
• "Foo" for the superfourth range
• "Fu" for the subfifth range
• "Ha" and Hoo" for the higher and lower equable heptatonic ranges  

• The four interseptimal ranges
  • "Fe" for semifourth
  • "Ke" for semisixth
  • "Te" for semitenth
  • "Twe" for semitwelfth

We will now show some examples of how this system can be used in practice.

12edo 5L2s 5|1
Cents	Solfege	Interval name
0	A	Unison
200	Say	Major Second
400	Thay	Major Third
500	Fo	Fourth
700	Fi	Fifth
900	Kay	Major Sixth
1100	Vay	Major Seventh
1200	A	Octave

31edo 5L2s 5|1
Cents	Solfege	Interval name
0	A	Unison
193.548	Says	Small Major Second
387.097	Thays	Small Major Third
503.226	Fo	Fourth
696.774	Fi	Fifth
890.323	Kays	Small Major Sixth
1083.871	Vays	Small Major Seventh
1200	A	Octave

31edo 3L4s 3|3
Cents	Solfege	Interval name
0	A	Unison
154.839	Soo	Neutral Second
348.387	Thoo	Neutral Third
503.226	Fo	Fourth
696.774	Fi	Fifth
851.613	Koo	Neutral Sixth
1045.161	Voo	Neutral Seventh
1200	A	Octave

24edo 3L4s 3|3
Cents	Solfege	Interval name
0	A	Unison
150	Soo	Neutral Second
350	Thoo	Neutral Third
500	Fo	Fourth
700	Fi	Fifth
850	Koo	Neutral Sixth
1050	Voo	Neutral Seventh
1200	A	Octave

24edo 4L1s 2|2
Cents	Solfege	Interval name
0	A	Unison
250	Fe	Semifourth
500	Fo	Fourth
700	Fi	Fifth
950	Twe	Semitwelfth
1200	A	Octave

19edo 4L1s 2|2
Cents	Solfege	Interval name
0	A	Unison
252.632	Fe	Semifourth
505.263	Fol	Large Fourth
694.737	Fis	Small Fifth
947.368	Twe	Semitwelfth
1200	A	Octave

19edo 5L2s 5|1
Cents	Solfege	Interval name
0	A	Unison
189.474	Says	Small Major Second
378.947	Thays	Small Major Third
505.263	Fol	Large Fourth
694.737	Fis	Small Fifth
884.211	Kays	Small Major Sixth
1073.684	Vool	Large Neutral Seventh
1200	A	Octave

Harmonics 8::16
Cents	Solfege	Interval name
0	A	Unison
203.91	Say	Major Second
386.314	Thays	Small Major Third
551.318	Foo	Superfourth
701.955	Fi	Fifth
840.528	Koo	Neutral Sixth
968.826	Vais	Small Minor Seventh
1088.269	Vays	Small Major Seventh
1200	A	Octave

13edo 5L3s 5|2
Cents	Solfege	Interval name
0	A	Unison
184.615	Says	Small Major Second
276.923	Thais	Small Minor Third
461.538	Ke	Semisixth
646.154	Fu	Subfifth
738.462	Te	Semitenth
923.077	Kayl	Large Major Sixth
1107.692	Vay	Major Seventh