Kite's uniform solfege: Difference between revisions
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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. | ||
'''Genchains''' are distinct from fifthchains. Each pergen has one or more genchains, each of which contains one or more fifthchains. The 13 consonants and 5 vowels without compound vowels cover 20 pergens. Of course, the genchains can only extend so far with only 13 consonants. But in general, it's enough to cover all the modes of any reasonably-sized MOS scale. | '''Genchains''' are distinct from fifthchains. Each pergen has one or more genchains, each of which contains one or more fifthchains. The number of genchains always equals the number of periods per octave. In general, the number of fifthchains per genchain equals the number of generators per '''multigen''', which is the 2nd interval in the pergen. Thus (P8, P4/3) has 1 genchain that contains 3 interwoven fifthchains. But an exception arises when the multigen is not perfect (i.e. major or minor). Then the fifthchains hop from one genchain to the next. The only such pergen that has a uniform solfege is (P8/2, M2/4). It has 2 genchains and a total of 4 fifthchains. | ||
'''[https://Tallkite.com/misc files/notation guide for rank-2 pergens.pdf TallKite.com/misc_files/notation guide for rank-2 pergens.pdf]''' lists many pergens. The tuning of every interval and every accidental is defined in terms of c = P5 - 700¢. The EI (enharmonic interval) can be added to or subtracted from any note or interval to get an equivalent note or interval. The entire solfege can be derived from the pergen, the EI and the vowel sequence. | |||
The 13 consonants and 5 vowels without compound vowels cover 20 pergens. Of course, the genchains can only extend so far with only 13 consonants. But in general, it's enough to cover all the modes of any reasonably-sized MOS scale. | |||
'''[https://Tallkite.com/misc files/notation guide for rank-2 pergens.pdf TallKite.com/misc_files/notation guide for rank-2 pergens.pdf]''' lists many pergens. The tuning of every interval and every accidental is defined in terms of c = P5 - 700¢. The EI (enharmonic interval, "E" in the pdf) can be added to or subtracted from any note or interval to get an equivalent note or interval. The entire solfege can be derived from the pergen, the EI and the vowel sequence. For each pergen, there is one "official" solfege. | |||
Sometimes -i and -e mean lift/drop not dup/dud. -i never means mid, so there are only two vowel sequences: | Sometimes -i and -e mean lift/drop not dup/dud. -i never means mid, so there are only two vowel sequences: | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+single-pair solfeges | |+single-pair solfeges | ||
!-3 | !-3 | ||
!-2 | !-2 | ||
| Line 502: | Line 471: | ||
!2 | !2 | ||
!3 | !3 | ||
|- | |- | ||
!trud | !trud | ||
!dud | !dud | ||
| Line 512: | Line 479: | ||
!dup | !dup | ||
!trup | !trup | ||
|- | |- | ||
| | | -eyo | ||
| -e | |||
| -e | | -o | ||
| -o | | -a | ||
| -a | | -u | ||
| -u | | -i | ||
| -i | | -iyu | ||
| -iyu | |||
|} | |} | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+double-pair solfeges | |+double-pair solfeges | ||
! | |||
!down | !down | ||
!plain | !plain | ||
| Line 532: | Line 496: | ||
|- | |- | ||
!lift | !lift | ||
| -owi | | -owi | ||
| -i | | -i | ||
| -uwi | | -uwi | ||
|- | |- | ||
!plain | !plain | ||
| -o | | -o | ||
| -a | | -a | ||
| -u | | -u | ||
|- | |- | ||
! drop | ! drop | ||
| -owe | | -owe | ||
| -e | | -e | ||
| -uwe | | -uwe | ||
|} | |} | ||
Any compound vowel with a "w" is for double-pair only. Mnemonic: w = "double-U" = double-pair. | Any compound vowel with a "w" is for double-pair only. Mnemonic: w = "double-U" = double-pair. | ||
The whole (or unsplit) pergen (P8, P5) doesn't use ups and downs. It uses the single-pair vowel sequence, with -u and -o repurposed to mean augmented and diminished: | |||
{| class="wikitable center-all" | |||
|+(P8, P5) solfege | |||
!-3 | |||
!-2 | |||
!-1 | |||
!0 | |||
! 1 | |||
!2 | |||
!3 | |||
|- | |||
!ddd | |||
!dd | |||
!dim | |||
!plain | |||
!aug | |||
!AA | |||
!AAA | |||
|- | |||
| -eyo | |||
| -e | |||
| -o | |||
| -a | |||
| -u | |||
| -i | |||
| -iyu | |||
|} | |||
[[Category:Solfege]] | [[Category:Solfege]] | ||