Yer: Difference between revisions
Cmloegcmluin (talk | contribs) Yer as a temperament |
Cmloegcmluin (talk | contribs) |
||
| Line 7: | Line 7: | ||
Yer was developed by [[Douglas Blumeyer|Douglas Blumeyer]] as a system to explore the [[unnoticeable comma]] 2432/2431, the Blumeyer comma, which appears twice as a step in the scale. | Yer was developed by [[Douglas Blumeyer|Douglas Blumeyer]] as a system to explore the [[unnoticeable comma]] 2432/2431, the Blumeyer comma, which appears twice as a step in the scale. | ||
{| class="wikitable" | {| class="wikitable center-all" | ||
|+ | |+ | ||
!name | !name | ||
| Line 1,265: | Line 1,265: | ||
Again that's still in the 2.11.13.17.19 subgroup. And this one is the join of 13&24&33, with [[generators]] 1200.4457, 4149.8305, 4442.6991 (that 1st generator modulo the [[period]] is 548.4934 and the 2nd generator is 841.362). So one ~17 is down two ~11, and one ~19 is down one ~11 and up a ~13. Cool! This you'd call "Yer temperament" then. It has been registered here: [[Subgroup_temperaments#Yer_.28rank_3.29]] | Again that's still in the 2.11.13.17.19 subgroup. And this one is the join of 13&24&33, with [[generators]] 1200.4457, 4149.8305, 4442.6991 (that 1st generator modulo the [[period]] is 548.4934 and the 2nd generator is 841.362). So one ~17 is down two ~11, and one ~19 is down one ~11 and up a ~13. Cool! This you'd call "Yer temperament" then. It has been registered here: [[Subgroup_temperaments#Yer_.28rank_3.29]] | ||
== See also == | A 13-note scale with only three scale step sizes is possible here. It's 7L 4M 2s, with the pattern LMLLMLsLMLMLs, where L ≈ 103.4¢, M ≈ 85.9¢, and s ≈ 66.2¢: | ||
<nowiki> | |||
! yerMV3.scl | |||
! | |||
yer temperament 13-note scale | |||
13 | |||
! | |||
103.4 | |||
189.3 | |||
292.7 | |||
396.1 | |||
482.0 | |||
585.4 | |||
651.7 | |||
755.1 | |||
841.0 | |||
944.4 | |||
1030.3 | |||
1133.7 | |||
(2/1) | |||
</nowiki> | |||
However this is not quite an [[MV3]] scale. It is a rotation of the "LLMLsLMLMLsLM" pattern which is identified [[User:Xenoindex/Tridecatonic_MV3|here]] as "Conditional (MM=Ls)", and while it's quite close, L + s = 103.4 + 66.2 = 169.6 but 169.6/2 = 84.8, not 85.9 which is the M here. | |||
The lattice for this scale looks like: | |||
{| class="wikitable" | |||
|+ | |||
| - | |||
|(-2,2) | |||
11·13·17·19 | |||
13·19/11 | |||
585.4¢ | |||
|(-1,2) | |||
13·19 | |||
1133.7¢ | |||
|(0,2) | |||
11·13·19 | |||
482.0¢ | |||
|(1,2) | |||
11·13² | |||
1030.3¢ | |||
|- | |||
|(-3,1) | |||
17·19 | |||
396.1¢ | |||
|(-2,1) | |||
13·17 | |||
11·17·19 | |||
944.4¢ | |||
|(-1,1) | |||
11·13·17 | |||
19 | |||
292.7¢ | |||
|(0,1) | |||
13 | |||
11·19 | |||
841.0¢ | |||
|(1,1) | |||
11·13 | |||
189.3¢ | |||
|- | |||
|(-3,0) | |||
17·19/13 | |||
17/11 | |||
755.1¢ | |||
|(-2,0) | |||
17 | |||
103.4¢ | |||
|(-1,0) | |||
11·17 | |||
651.7¢ | |||
|(0,0) | |||
1 | |||
11²·17 | |||
0¢ | |||
| - | |||
|} | |||
==See also== | |||
[https://musical-patterns.douglasblumeyer.com Musical Patterns] - select Tsraxcfaubdj (GitHub page is here to explore the programmatic reasoning behind how this piece uses Yer: https://github.com/MusicalPatterns/pattern-tsraxcfaubdj) | [https://musical-patterns.douglasblumeyer.com Musical Patterns] - select Tsraxcfaubdj (GitHub page is here to explore the programmatic reasoning behind how this piece uses Yer: https://github.com/MusicalPatterns/pattern-tsraxcfaubdj) | ||