Kite's uniform solfege: Difference between revisions
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==Overview== | ==Overview== | ||
Uniform solfeges are a type of solfege devised by [[Kite Giedraitis]]. They are closely related to his [[ups and downs notation]]. Like the notation, they work with both rank-1 and rank-2 temperaments. They use a uniform vowel sequence for each degree, hence the name. A uniform solfege lets one perform basic interval arithmetic directly within the solfege, without having to translate to note names or interval names and back. | Uniform solfeges are a type of [[solfege]] devised by [[Kite Giedraitis]]. They are closely related to his [[ups and downs notation]]. Like the notation, they work with both rank-1 and rank-2 temperaments. They use a uniform vowel sequence for each degree, hence the name. A uniform solfege lets one perform basic interval arithmetic directly within the solfege, without having to translate to note names or interval names and back. | ||
Uniform solfeges use the conventional consonants D R M F S L T. But all consonants except D have an alternate form that indicates flattening or sharpening: | Uniform solfeges use the conventional consonants D R M F S L T. But all consonants except D have an alternate form that indicates flattening or sharpening: | ||
*Fr- = '''f'''lat Re = minor 2nd (mnemonic: F stands for flat) | *Fr- = '''f'''lat Re = minor 2nd (mnemonic: F stands for flat) | ||
*N- = flat Mi = minor 3rd | * N- = flat Mi = minor 3rd | ||
*P- = sharp Fa = aug 4th | *P- = sharp Fa = aug 4th | ||
*Sh- = flat So = dim 5th | *Sh- = flat So = dim 5th | ||
*Fl- = '''f'''lat La = minor 6th (mnemonic: F stands for flat) | *Fl- = '''f'''lat La = minor 6th (mnemonic: F stands for flat) | ||
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The vowel sequence varies slightly depending on the context. From high to low: | The vowel sequence varies slightly depending on the context. From high to low: | ||
* -i = dup (double-up) or double-augmented (or for rank-2, possibly lift) | *-i = dup (double-up) or double-augmented (or for rank-2, possibly lift) | ||
* -u = '''u'''p or augmented | *-u = '''u'''p or augmented | ||
* -a = pl'''a'''in i.e. 3-limit | *-a = pl'''a'''in i.e. 3-limit | ||
* -o = d'''o'''wn or diminished | *-o = d'''o'''wn or diminished | ||
* -e = dud (double-down) or double-diminished (or for rank-2, possibly drop) | *-e = dud (double-down) or double-diminished (or for rank-2, possibly drop) | ||
The augmented and diminished meanings only apply to tunings that don't require ups and downs, such as sharp-1 edos and unsplit pergens. | The augmented and diminished meanings only apply to tunings that don't require ups and downs, such as sharp-1 edos and unsplit pergens. | ||
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The 5 vowels are like those in Spanish or Italian. There are only 5 vowels because those are the most singable, and also additional vowels would make the solfeges harder to learn. Shi is pronounced "she" and She is "shay". Fri is "free". | The 5 vowels are like those in Spanish or Italian. There are only 5 vowels because those are the most singable, and also additional vowels would make the solfeges harder to learn. Shi is pronounced "she" and She is "shay". Fri is "free". | ||
=== Example Scales === | ===Example Scales=== | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+ | |+ | ||
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|La | |La | ||
|Ta | |Ta | ||
|Da | | Da | ||
|- | |- | ||
!Plain minor scale | !Plain minor scale | ||
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|Sa | |Sa | ||
|Fla | |Fla | ||
|Tha | | Tha | ||
|Da | |Da | ||
|- | |- | ||
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|Sa | |Sa | ||
|Flu | |Flu | ||
|Thu | | Thu | ||
|Da | |Da | ||
|- | |- | ||
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==Interval Arithmetic== | ==Interval Arithmetic== | ||
===Octave Complements=== | ===Octave Complements === | ||
To find the [[octave complement]] of any interval: | To find the [[octave complement]] of any interval: | ||
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One can often easily add/subtract an unconventional (upped or downed) interval as well. The ups and downs add up and cancel out as expected. Thus Ra + vM2 = Mo and Ru + vM2 = Ma. Obviously the vowel will change. Again, the expected answer must exist in the solfege. 3-vowel solfeges lack double-ups and double-downs. 4-vowel solfeges lack double-upmajor and double-downminor. | One can often easily add/subtract an unconventional (upped or downed) interval as well. The ups and downs add up and cancel out as expected. Thus Ra + vM2 = Mo and Ru + vM2 = Ma. Obviously the vowel will change. Again, the expected answer must exist in the solfege. 3-vowel solfeges lack double-ups and double-downs. 4-vowel solfeges lack double-upmajor and double-downminor. | ||
==Solfeges for Edos== | == Solfeges for Edos== | ||
{{Main|List of uniform solfeges for EDOs}} | |||
In the perfect edos (7, 14, 21, 28 and 35), there is no need for the altered consonants, since Lw1 is tempered out. Some other edos (12, ??) also omit them. | In the perfect edos (7, 14, 21, 28 and 35), there is no need for the altered consonants, since Lw1 is tempered out. Some other edos (12, ??) also omit them. | ||
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|- | |- | ||
!5 vowels | !5 vowels | ||
! 53, 60 | !53, 60 | ||
| -e = dud | | -e = dud | ||
|<nowiki>-o = down</nowiki> | |<nowiki>-o = down</nowiki> | ||
|<nowiki>-a = plain</nowiki> | |<nowiki>-a = plain</nowiki> | ||
|<nowiki>-u = up</nowiki> | |<nowiki>-u = up</nowiki> | ||
| -i = dup | | -i = dup | ||
|} | |} | ||
There is only so much one can do with 5 vowels and 13 consonants. Not all edos are covered. The number of vowels an edo's solfege needs equals the edo's [[sharpness|sharpness or penta-sharpness]], whichever is larger. Thus an edo with a (penta)sharpness of 6 or higher needs 6 or more vowels and isn't covered. Every edo above 60 is such an edo. The excluded edos are the less efficient ones, with a fairly inaccurate 5th for their size. Thus they tend to be the less popular edos. | There is only so much one can do with 5 vowels and 13 consonants. Not all edos are covered. The number of vowels an edo's solfege needs equals the edo's [[sharpness|sharpness or penta-sharpness]], whichever is larger. Thus an edo with a (penta)sharpness of 6 or higher needs 6 or more vowels and isn't covered. Every edo above 60 is such an edo. The excluded edos are the less efficient ones, with a fairly inaccurate 5th for their size. Thus they tend to be the less popular edos. | ||
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Because 72edo is such a popular edo, an exception is made and it has 2 additional vowels. | Because 72edo is such a popular edo, an exception is made and it has 2 additional vowels. | ||
=== Examples=== | ===Examples=== | ||
*12edo: Da Fra Ra Na Ma Fa Pa/Sha Sa Fla La Tha Ta Da | *12edo: Da Fra Ra Na Ma Fa Pa/Sha Sa Fla La Tha Ta Da | ||
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In edos with an even [[Sharpness|penta-sharpness]], there are "in-between" notes with two names. For example, 4\19 is named as both a 2nd and a 3rd (Ru/No). | In edos with an even [[Sharpness|penta-sharpness]], there are "in-between" notes with two names. For example, 4\19 is named as both a 2nd and a 3rd (Ru/No). | ||
=== Correlations with Color Notation=== | === Correlations with Color Notation === | ||
-u/-o can mean not only up/down, but also under/over, meaning in the ratio's denominator or numerator. A [[color notation]] review: | -u/-o can mean not only up/down, but also under/over, meaning in the ratio's denominator or numerator. A [[color notation]] review: | ||
* yo/gu = 5-over/5-under = subtract/add 81/80 | *yo/gu = 5-over/5-under = subtract/add 81/80 | ||
*zo/ru = 7-over/7-under = subtract/add 64/63 | *zo/ru = 7-over/7-under = subtract/add 64/63 | ||
*ilo/lu = 11-over/11-under = subtract/add [[729/704]] | *ilo/lu = 11-over/11-under = subtract/add [[729/704]] | ||
*tho/thu = 13-over/13-under = subtract/add 27/26 | * tho/thu = 13-over/13-under = subtract/add 27/26 | ||
(In color notation, the last two commas could instead be 33/32 and [[1053/1024]], but these are "over" commas, and they must be under to keep the -o/-u correlation.) | (In color notation, the last two commas could instead be 33/32 and [[1053/1024]], but these are "over" commas, and they must be under to keep the -o/-u correlation.) | ||
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!17 | !17 | ||
!19 | !19 | ||
! 22 | !22 | ||
!24 | !24 | ||
!26 | !26 | ||
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!60 | !60 | ||
|- | |- | ||
! rowspan="2" |ya | ! rowspan="2" | ya | ||
| | | | ||
|(yo) | |(yo) | ||
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|gu | |gu | ||
|- | |- | ||
! rowspan="2" |za | ! rowspan="2" | za | ||
| | | | ||
| | | | ||
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| | | | ||
|- | |- | ||
! rowspan="2" |ila | ! rowspan="2" | ila | ||
|(ilo) | |(ilo) | ||
|ilo | | ilo | ||
| | | | ||
| | | | ||
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| | | | ||
|- | |- | ||
! rowspan="2" |tha | ! rowspan="2" | tha | ||
| | | | ||
|tho | |tho | ||
|tho | | tho | ||
| | | | ||
|tho | |tho | ||
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==Solfeges for Rank-2 Temperaments== | ==Solfeges for Rank-2 Temperaments== | ||
{{Main|List of Uniform Solfeges For Pergens}} | |||
Rank-2 temperaments have an infinite number of notes, so a solfege can only cover a fraction of them. But often one only needs enough notes to make a MOS scale. [[Pergen|Pergens]] tell us how to use ups and downs to notate these temperaments, and the same consonants and vowels can be used. Instead of circles of 5ths, there are '''fifthchains'''. Each fifthchain requires its own vowel, so there is a maximum of 5 fifthchains. However this can be extended to 9 fifthchains by using compound vowels such as -iyu, see below. | Rank-2 temperaments have an infinite number of notes, so a solfege can only cover a fraction of them. But often one only needs enough notes to make a MOS scale. [[Pergen|Pergens]] tell us how to use ups and downs to notate these temperaments, and the same consonants and vowels can be used. Instead of circles of 5ths, there are '''fifthchains'''. Each fifthchain requires its own vowel, so there is a maximum of 5 fifthchains. However this can be extended to 9 fifthchains by using compound vowels such as -iyu, see below. | ||
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{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+unsplit (no-pair) solfege | |+unsplit (no-pair) solfege | ||
! -4 | !-4 | ||
!-3 | !-3 | ||
!-2 | !-2 | ||
!-1 | !-1 | ||
!0 | !0 | ||
!1 | ! 1 | ||
!2 | !2 | ||
!3 | !3 | ||
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| -e | | -e | ||
| -o | | -o | ||
| | | -a | ||
| -u | | -u | ||
| -i | | -i | ||
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| -u | | -u | ||
|- | |- | ||
!drop | ! drop | ||
| -owe | | -owe | ||
| -e | | -e | ||
| -uwe | | -uwe | ||
|} | |} | ||
Any compound vowel with a "w" is for double-pair only. Mnemonic: w = double- | Any compound vowel with a "w" is for double-pair only. Mnemonic: w = "double-U" = double-pair. | ||
[[Category:Solfege]] | [[Category:Solfege]] | ||