User:TallKite/Solfeges: Difference between revisions
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Da - Ra - Ma - Fa - Sa - La - Ta - Da | Da - Ra - Ma - Fa - Sa - La - Ta - Da | ||
This helps with <u>un</u>learning the | This helps with <u>un</u>learning the traditional vowels. Next add in the 6 altered consonants, making a 12-edo-like solfege: | ||
Next add in the 6 altered consonants, making a 12-edo-like solfege: | |||
Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da | Da - Fra - Ra - Na - Ma - Fa - Pa/Sha - Sa - Fla - La - Tha - Ta - Da | ||
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== Rank-2 Uniform Solfeges by Pergen == | == Rank-2 Uniform Solfeges by Pergen == | ||
Rank-2 temperaments have an infinite number of notes, so a solfege can only cover a fraction of them. But often one only uses enough notes to make a MOS scale. [[Pergen|Pergens]] tell us how to use ups and downs to notate | Rank-2 temperaments have an infinite number of notes, so a solfege can only cover a fraction of them. But often one only uses 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. | ||
Genchains are distinct from fifthchains. Each pergen has one or more genchains, each of which contains one or more fifthchains. However if the octave is split in halves or quarters, the half-octave requires two names, and the pergen needs an additional vowel. The 13 consonants and 5 vowels cover | Genchains are distinct from fifthchains. Each pergen has one or more genchains, each of which contains one or more fifthchains. However if the octave is split in halves or quarters, the half-octave requires two names, and the pergen needs an additional vowel. The 13 consonants and 5 vowels cover 21 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. | ||
Sometimes -i and -e mean lift/drop not dup/dud | This pdf '''[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. | ||
Sometimes -i and -e mean lift/drop not dup/dud. -i never means mid, so there are only two vowel sequences, not three: | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+the two vowel sequences | |+the two vowel sequences | ||
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|<nowiki>-u = up</nowiki> | |<nowiki>-u = up</nowiki> | ||
| -i = dup or lift | | -i = dup or lift | ||
|}In | |}In certain pergens, there are compound vowels like -iyu for trup or -uwi for uplift. | ||
In the MOS scale tables, any note that changes from one mode to the next is '''bolded'''. The mode numbers are defined such that the 1st mode always has Sa and not Fa, and the last mode always has Fa and not Sa. | |||
A pergen's solfege can suggest an edo's solfege. For example, 22edo supports (P8, P4/3), and the pergen's solfege has 27 notes in it. Since the generator is 3\22, simply apply the genchain to every 3rd edostep of 22edo. The extra 5 names make duplicate names. | A pergen's solfege can suggest an edo's solfege. For example, 22edo supports (P8, P4/3), and the pergen's solfege has 27 notes in it. Since the generator is 3\22, simply apply the genchain to every 3rd edostep of 22edo. The extra 5 names make duplicate names. | ||
To Do: | |||
* make a table of pergens and what MOS scales each one covers | * make a table of pergens and what MOS scales each one covers | ||
* discuss using numeric solfeges with non-diatonic-friendly MOSes | * discuss using numeric solfeges with non-diatonic-friendly MOSes | ||
* for each pergen, list the entire genchain in melodic order, if possible? | * for each pergen, list the entire genchain in melodic order, if possible? | ||
=== List of MOS scales === | === List of MOS scales === | ||
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== #1 (P8, P5) unsplit == | == #1 (P8, P5) unsplit == | ||
There are no ups and downs. The basic solfege has 13 notes. The extended solfege uses -u/-o to augment/diminish an -a interval. The solfege can be further extended with -i/-e meaning doubly augmented/diminished. | There are no ups and downs. The basic solfege has 13 notes. The extended solfege uses -u/-o to augment/diminish an -a interval. The solfege can be further extended with -i/-e meaning doubly augmented/diminished. | ||
* G = P5 = 700¢ + c for this and all other pergens | * G = P5, which = 700¢ + c for this and all other pergens | ||
* EI = vA1 = 0¢ (extended solfege only) | * EI = vA1 = 0¢ (extended solfege only) | ||
* ^ = # = 100 + 7c (extended solfege only) | * ^ = # = 100 + 7c (extended solfege only) | ||
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|Da | |Da | ||
|} | |} | ||
== #4 (P8, P5/2) half-5th (list alternate pergens) == | == #4 (P8, P5/2) half-5th (list alternate pergens) == | ||
* G = ^m3/vM3 = ~3 = 350¢ + c/2 | * G = ^m3/vM3 = ~3 = 350¢ + c/2 | ||
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|^D | |^D | ||
|} | |} | ||
Implied 22edo solfege: Da - Du - Fru - Ro - Ra - Ru/Na - Nu - Mo - Ma/Fo - Fa - Fu - Po/Shu - So - Sa - Su/Fla - Flu - Lo - La/Tho - Tha - Thu - To - Do - Da | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+ | |+ | ||
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|Da | |Da | ||
|} | |} | ||
== #8 (P8, P5/3) third-5th == | == #8 (P8, P5/3) third-5th == | ||