View source for Universal solfege

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{{Distinguish|Uniform solfege}}

'''Universal Solfege'''{{idiosyncratic}} was invented by [[User:Nick Vuci|Nick Vuci]]. It builds on [[Margo Schulter]]'s [https://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt "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:

<blockquote>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.<ref>https://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt</ref></blockquote>

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. 

== Full gamut ==
A chart below lays things out:
{| class="wikitable"
!Interval
!Class
!Subcategory
!Cent Range
!Solfege
!IPA
|-
|Unison
|
|
|0
|A
|a
|-
|Comma
|
|
|0-30
|O
|ɒ
|-
|Dieses
|
|
|30-60
|Ee
|i
|-
| rowspan="10" |Second
| rowspan="3" |Minor
|Small
|60-80
|Sais
|saɪs
|-
|'''Middle'''
|'''80-100'''
|'''Sai'''
|'''saɪ'''
|-
|Large
|100-125
|Sail
|saɪl
|-
| rowspan="3" |Neutral
|Small
|125-135
|Soos
|sus
|-
|'''Middle'''
|'''135-160'''
|'''Soo'''
|'''su'''
|-
|Large
|160-170
|Sool
|sul
|-
| colspan="2" |Equable Heptatonic
|160-182
|Ha
|ha
|-
| rowspan="3" |Major
|Small
|180-200
|Says
|seɪs
|-
|'''Middle'''
|'''200-220'''
|'''Say'''
|'''seɪ'''
|-
|Large
|220-240
|Sayl
|seɪl
|-
| colspan="3" |Semifourth (Interseptimal Maj2-min3)     
|240-260
|Fe
|fɛ
|-
| rowspan="9" |Thirds
| rowspan="3" |Minor
|Small
|260-280
|Thais
|θaɪs
|-
|'''Middle'''
|'''280-300'''
|'''Thai'''
|'''θaɪ'''
|-
|Large
|300-330
|Thail
|θaɪl
|-
| rowspan="3" |Neutral
|Small
|330-342
|Thoos
|θus
|-
|'''Middle'''
|'''342-360'''
|'''Thoo'''
|'''θu'''
|-
|Large
|360-372
|Thool
|θul
|-
| rowspan="3" |Major
|Small
|372-400
|Thays
|θeɪs
|-
|'''Middle'''
|'''400-423'''
|'''Thay'''
|'''θeɪ'''
|-
|Large
|423-440
|Thayl
|θeɪl
|-
| colspan="3" |Semisixth (Interseptimal Maj3-4)
|440-468
|Ke
|kɛ
|-
| colspan="2" rowspan="3" |Fourths
|Small
|468-491
|Fos
|fɔs
|-
|'''Middle'''
|'''491-505'''
|'''Fo'''
|'''fɔ'''
|-
|Large
|505-528
|Fol
|fɔl
|-
| colspan="3" |Superfourths
|528-560
|Foo
|fu
|-
| colspan="2" rowspan="3" |Tritones
|Small
|560-577
|Trais
|traɪs
|-
|'''Middle'''
|'''577-623'''
|'''Trai'''
|'''traɪ'''
|-
|Large
|623-640
|Trail
|traɪl
|-
| colspan="3" |Subfifths
|640-672
|Fu
|fʌ
|-
| colspan="2" rowspan="3" |Fifths
|Small
|640-695
|Fis
|fɪs
|-
|'''Middle'''
|'''695-709'''
|'''Fi'''
|'''fɪ'''
|-
|Large
|709-732
|Fil
|fɪl
|-
| colspan="3" |Semitenth (Interseptimal 5-min6)
|732-760
|Te
|tɛ
|-
| rowspan="9" |Sixths
| rowspan="3" |Minor
|Small
|760-777
|Kais
|kaɪs
|-
|'''Middle'''
|'''777-800'''
|'''Kai'''
|'''kaɪ'''
|-
|Large
|800-828
|Kail
|kaɪl
|-
| rowspan="3" |Neutral
|Small
|828-840
|Koos
|kus
|-
|'''Middle'''
|'''840-858'''
|'''Koo'''
|'''ku'''
|-
|Large
|858-870
|Kool
|kul
|-
| rowspan="3" |Major
|Small
|870-900
|Kays
|keɪs
|-
|'''Middle'''
|'''900-920'''
|'''Kay'''
|'''keɪ'''
|-
|Large
|920-940
|Kayl
|keɪl
|-
| colspan="3" |(Semitwelfth Interseptimal Maj6-min7)
|940-960
|Twe
|twɛ
|-
| rowspan="10" |Sevenths
| rowspan="3" |Minor
|Small
|960-987
|Vais
|vaɪs
|-
|'''Middle'''
|'''987-1000'''
|'''Vai'''
|'''vaɪ'''
|-
|Large
|1000-1025
|Vail
|vaɪl
|-
| colspan="2" |Equable heptatonic
|1018-1040
|Ho
|hɒ
|-
| rowspan="3" |Neutral
|Small
|1030-1043
|Voos
|vus
|-
|'''Middle'''
|'''1043-1065'''
|'''Voo'''
|'''vu'''
|-
|Large
|1065-1075
|Vool
|vul
|-
| rowspan="3" |Major
|Small
|1075-1100
|Vays
|veɪs
|-
|'''Middle'''
|'''1100-1120'''
|'''Vay'''
|'''veɪ'''
|-
|Large
|1120-1140
|Vayl
|veɪl
|-
| colspan="3" |Octave less diesis
|1140-1170
|Dee
|di
|-
| colspan="3" |Octave less comma
|1170-1200
|Co
|kɒ
|-
| colspan="3" |Octave
|1200
|A
|a
|}

The unison and the octave (i.e. 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 

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

=== 12edo diatonic (major mode) ===
{| class="wikitable"
! colspan="3" |<nowiki>12edo 5L2s 5|1</nowiki>
|-
!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 diatonic (major mode) ===
{| class="wikitable"
! colspan="3" |<nowiki>31edo 5L2s 5|1</nowiki>
|-
!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 mosh (bish mode) ===
{| class="wikitable"
! colspan="3" |<nowiki>31edo 3L4s 3|3</nowiki>
|-
!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 mosh (bish mode) ===
{| class="wikitable"
|+
! colspan="3" |<nowiki>24edo 3L4s 3|3</nowiki>
|-
!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 manual (medial mode) ===
{| class="wikitable"
! colspan="3" |<nowiki>24edo 4L1s 2|2</nowiki>
|-
!Cents
!Solfege
!Interval name
|-
|0
|A
|Unison
|-
|250
|Fe
|Semifourth
|-
|500
|Fo
|Fourth
|-
|700
|Fi
|Fifth
|-
|950
|Twe
|Semitwelfth
|-
|1200
|A
|Octave
|}

=== 19edo manual (medial mode) ===
{| class="wikitable"
! colspan="3" |<nowiki>19edo 4L1s 2|2</nowiki>
|-
!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 diatonic (major mode) ===
{| class="wikitable"
! colspan="3" |<nowiki>19edo 5L2s 5|1</nowiki>
|-
!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 ===
{| class="wikitable"
! colspan="3" |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 oneirotonic (Celephaïsian mode) ===
{| class="wikitable"
|+
! colspan="3" |<nowiki>13edo 5L3s 5|2</nowiki>
|-
!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
|}

== References ==
<references />

[[Category:Solfege]]