Universal solfege: Difference between revisions

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The principle is that we can divide the interval spectrum into discreet areas which can then be used to take subsets for most microtonal scales we can imagine. It's not an exhaustive solution but a practical and practicible one.  
The principle is that we can divide the interval spectrum into discreet areas which can then be used to take subsets for most microtonal scales we can imagine. It's not an exhaustive solution but a practical and practicible one.  


While the chart gives solfege syllables for 74 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, and solfege are ideally chosen in a heirarchy that prioritizes larger categories over smaller ones. For example, the "Small," "Medium," and "Large" categories aren't necessary unless a scale includes two kinds of an interval and the distinction is necessary.   
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 solfege 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 many contain more or less than 6 notes depending on the MOS.)  
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 many contain more or less than 6 notes depending on the MOS.)  


Finally, to quote Schulter: <blockquote>
Finally, to quote Schulter: <blockquote>
Line 44: Line 44:
|i
|i
|-
|-
| rowspan="13" |Second
| rowspan="10" |Second
| rowspan="4" |Minor
| rowspan="3" |Minor
|
|60-125
|Sai
|saɪ
|-
|Small
|Small
|60-80
|60-80
Line 56: Line 51:
|saɪs
|saɪs
|-
|-
|Medium
|'''Middle'''
|80-100
|'''80-100'''
|Saim
|'''Sai'''
|saɪm
|'''saɪ'''
|-
|-
|Large
|Large
|100-125
|100-125
|Sail
|Sail
|saɪ
|saɪl
|-
| rowspan="4" |Neutral
|
|125-170
|Soo
|su
|-
|-
| rowspan="3" |Neutral
|Small
|Small
|125-135
|125-135
Line 77: Line 67:
|sus
|sus
|-
|-
|Medium
|'''Middle'''
|135-160
|'''135-160'''
|Soom
|'''Soo'''
|sum
|'''su'''
|-
|-
|Large
|Large
Line 92: Line 82:
|ha
|ha
|-
|-
| rowspan="4" |Major
| rowspan="3" |Major
|
|180-240
|Say
|seɪ
|-
|Small
|Small
|180-200
|180-200
Line 103: Line 88:
|seɪs
|seɪs
|-
|-
|Medium
|'''Middle'''
|200-220
|'''200-220'''
|Saym
|'''Say'''
|seɪm
|'''seɪ'''
|-
|-
|Large
|Large
Line 118: Line 103:
|fɛ
|fɛ
|-
|-
| rowspan="12" |Thirds
| rowspan="9" |Thirds
| rowspan="4" |Minor
| rowspan="3" |Minor
|
|260-330
|Thai
|θaɪ
|-
|Small
|Small
|260-280
|260-280
Line 130: Line 110:
|θaɪs
|θaɪs
|-
|-
|Medium
|'''Middle'''
|280-300
|'''280-300'''
|Thaim
|'''Thai'''
|θaɪm
|'''θaɪ'''
|-
|-
|Large
|Large
Line 140: Line 120:
|θaɪl
|θaɪl
|-
|-
| rowspan="4" |Neutral
| rowspan="3" |Neutral
|
|330-372
|Thoo
|θu
|-
|Small
|Small
|330-342
|330-342
Line 151: Line 126:
|θus
|θus
|-
|-
|Medium
|'''Middle'''
|342-360
|'''342-360'''
|Thoom
|'''Thoo'''
|θum
|'''θu'''
|-
|-
|Large
|Large
Line 161: Line 136:
|θul
|θul
|-
|-
| rowspan="4" |Major
| rowspan="3" |Major
|
|372-440
|Thay
|θeɪ
|-
|Small
|Small
|372-400
|372-400
Line 172: Line 142:
|θeɪs
|θeɪs
|-
|-
|Medium
|'''Middle'''
|400-423
|'''400-423'''
|Thaym
|'''Thay'''
|θeɪm
|'''θeɪ'''
|-
|-
|Large
|Large
Line 187: Line 157:
|kɛ
|kɛ
|-
|-
| colspan="2" rowspan="4" |Fourths
| colspan="2" rowspan="3" |Fourths
|
|468-528
|Fo
|fɔ
|-
|Small
|Small
|468-491
|468-491
Line 198: Line 163:
|fɔs
|fɔs
|-
|-
|Medium
|'''Middle'''
|491-505
|'''491-505'''
|Fom
|'''Fo'''
|fɔm
|'''fɔ'''
|-
|-
|Large
|Large
Line 213: Line 178:
|fu
|fu
|-
|-
| colspan="2" rowspan="4" |Tritones
| colspan="2" rowspan="3" |Tritones
|
|560-640
|Trai
|traɪ
|-
|Small
|Small
|560-577
|560-577
Line 224: Line 184:
|traɪs
|traɪs
|-
|-
|Medium
|'''Middle'''
|577-623
|'''577-623'''
|Traim
|'''Trai'''
|traɪm
|'''traɪ'''
|-
|-
|Large
|Large
Line 239: Line 199:
|fʌ
|fʌ
|-
|-
| colspan="2" rowspan="4" |Fifths
| colspan="2" rowspan="3" |Fifths
|
|640-732
|Fi
|fɪ
|-
|Small
|Small
|640-695
|640-695
Line 250: Line 205:
|fɪs
|fɪs
|-
|-
|Medium
|'''Middle'''
|695-709
|'''695-709'''
|Fim
|'''Fim'''
|fɪm
|'''fɪ'''
|-
|-
|Large
|Large
Line 265: Line 220:
|tɛ
|tɛ
|-
|-
| rowspan="12" |Sixths
| rowspan="9" |Sixths
| rowspan="4" |Minor
| rowspan="3" |Minor
|
|760-828
|Kai
|kaɪ
|-
|Small
|Small
|760-777
|760-777
Line 277: Line 227:
|kaɪs
|kaɪs
|-
|-
|Medium
|'''Middle'''
|777-800
|'''777-800'''
|Kaim
|'''Kai'''
|kaɪm
|'''kaɪ'''
|-
|-
|Large
|Large
Line 287: Line 237:
|kaɪl
|kaɪl
|-
|-
| rowspan="4" |Neutral
| rowspan="3" |Neutral
|
|828-870
|Koo
|ku
|-
|Small
|Small
|828-840
|828-840
Line 298: Line 243:
|kus
|kus
|-
|-
|Medium
|'''Middle'''
|840-858
|'''840-858'''
|Koom
|'''Koo'''
|kum
|'''ku'''
|-
|-
|Large
|Large
Line 308: Line 253:
|kul
|kul
|-
|-
| rowspan="4" |Major
| rowspan="3" |Major
|
|870-940
|Kay
|keɪ
|-
|Small
|Small
|870-900
|870-900
Line 319: Line 259:
|keɪs
|keɪs
|-
|-
|Medium
|'''Middle'''
|900-920
|'''900-920'''
|Kaym
|'''Kay'''
|keɪm
|'''keɪ'''
|-
|-
|Large
|Large
Line 334: Line 274:
|twɛ
|twɛ
|-
|-
| rowspan="13" |Sevenths
| rowspan="10" |Sevenths
| rowspan="4" |Minor
| rowspan="3" |Minor
|
|960-1025
|Vai
|vaɪ
|-
|Small
|Small
|960-987
|960-987
Line 346: Line 281:
|vaɪs
|vaɪs
|-
|-
|Medium
|'''Middle'''
|987-1000
|'''987-1000'''
|Vaim
|'''Vai'''
|vaɪm
|'''vaɪ'''
|-
|-
|Large
|Large
Line 361: Line 296:
|hɒ
|hɒ
|-
|-
| rowspan="4" |Neutral
| rowspan="3" |Neutral
|
|1030-1075
|Voo
|vu
|-
|Small
|Small
|1030-1043
|1030-1043
Line 372: Line 302:
|vus
|vus
|-
|-
|Medium
|'''Middle'''
|1043-1065
|'''1043-1065'''
|Voom
|'''Voo'''
|vum
|'''vu'''
|-
|-
|Large
|Large
Line 382: Line 312:
|vul
|vul
|-
|-
| rowspan="4" |Major
| rowspan="3" |Major
|
|1075-1140
|Vay
|veɪ
|-
|Small
|Small
|1075-1100
|1075-1100
Line 393: Line 318:
|veɪs
|veɪs
|-
|-
|Medium
|'''Middle'''
|1100-1120
|'''1100-1120'''
|Vaym
|'''Vay'''
|veɪm
|'''veɪ'''
|-
|-
|Large
|Large
Line 436: Line 361:
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."
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 small medium and large versions, which we can denote with the consonant affixes "s" "m" and "l"
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, medium, or small versions. These are denoted as follows:
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
* "O" and "Co" for the commatic ranges
Line 452: Line 377:
** "Twe" for semitwelfth  
** "Twe" for semitwelfth  


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


{| 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
|}
{| 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
|}
{| 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
|}
{| class="wikitable"
{| class="wikitable"
|+
|+
! colspan="4" |<nowiki>24edo 3L4s 3|3</nowiki>
! colspan="3" |<nowiki>24edo 3L4s 3|3</nowiki>
|-
|-
!Cents
!Cents
!Solfege
!Solfege
!Interval name
!Interval name
!
|-
|-
|0
|0
|A  
|A
|Unison
|Unison
|
|-
|-
|150
|150
|Soo
|Soo
|Neutral Second
|Neutral Second
|
|-
|-
|350
|350
|Thoo
|Thoo
|Neutral Third
|Neutral Third
|
|-
|-
|500
|500
|Fo
|Fo
|Fourth
|Fourth
|
|-
|-
|700
|700
|Fi
|Fi
|Fifth
|Fifth
|
|-
|-
|850
|850
|Koo
|Koo
|Neutral Sixth
|Neutral Sixth
|
|-
|-
|1050
|1050
|Voo
|Voo
|Neutral Seventh
|Neutral Seventh
|
|-
|-
|1200
|1200
|A
|A
|Octave
|Octave
|
|}
{| 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
|}
{| 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
|}
{| 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
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 516: Line 650:
|-
|-
|184.615
|184.615
|Say
|Says
|Major Second
|Small Major Second
|-
|-
|276.923
|276.923
|Thai
|Thais
|Minor Third
|Small Minor Third
|-
|-
|461.538
|461.538
|Nai
|Ke
|Semisixth
|Semisixth
|-
|-
Line 532: Line 666:
|-
|-
|738.462
|738.462
|Noo
|Te
|Semitenth
|Semitenth
|-
|-
|923.077
|923.077
|Kay
|Kayl
|Major Sixth
|Large Major Sixth
|-
|-
|1107.692
|1107.692

Revision as of 18:30, 18 November 2023

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 discreet areas which can then be used to take subsets for most microtonal scales we can imagine. 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 many 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.[1]

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 Fim 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
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
  1. ↑ https://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt
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