Yer: Difference between revisions
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== Introduction == | == Introduction == | ||
Yer is an octave-reduced EFG ([[wikipedia:Euler–Fokker_genus|Euler-Fokker genus]]) of 11, 13, 17, and 19. As such it is a 2.11.13.17.19 limit just intonation tuning (ignoring the 3rd, 5th, and 7th harmonics) which is octave-repeating. | Yer is an octave-reduced EFG ([[wikipedia:Euler–Fokker_genus|Euler-Fokker genus]]) of 11, 13, 17, and 19. As such it is a 2.11.13.17.19 limit just intonation tuning (ignoring the 3rd, 5th, and 7th harmonics) which is octave-repeating. | ||
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== Blumeyer comma == | == Blumeyer comma == | ||
Those pitches right on top of each other are a feature, not a bug. The pitch 11 * 13 * 17 is 2431, only one off from the pitch 19, which when octave adjusted is 2432. So we end up with this superparticular ratio, 2432:2431, called the Blumeyer comma. | Those pitches right on top of each other are a feature, not a bug. The pitch 11 * 13 * 17 is 2431, only one off from the pitch 19, which when octave adjusted is 2432. So we end up with this superparticular ratio, 2432:2431, called the Blumeyer comma. | ||
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|- | |- | ||
|Blumeyer comma | |Blumeyer comma | ||
|2432/2431 | |[[2432/2431]] | ||
|0.71200249782 | |0.71200249782 | ||
|<nowiki> | |<nowiki>[ 7 0 0 0 -1 -1 -1 1 ></nowiki> | ||
|} | |} | ||
[[File:Blumeyer comma.png|none|thumb| | [[File:Blumeyer comma.png|none|thumb| | ||
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|- | |- | ||
|yama comma | |yama comma | ||
|209/208 | |[[209/208]] | ||
|8.303296728 | |8.303296728 | ||
|<nowiki> | |<nowiki>[ -4 0 0 0 1 -1 0 1 ></nowiki> | ||
|} | |} | ||
Another consequence of the yama comma is that a couple “extra” lattice connections appear. These are drawn in dotted green on the lattices in the introduction. | Another consequence of the yama comma is that a couple “extra” lattice connections appear. These are drawn in dotted green on the lattices in the introduction. | ||
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|- | |- | ||
|Blume comma | |Blume comma | ||
|2057/2048 | |[[2057/2048]] | ||
|7.59129422992 | |7.59129422992 | ||
|<nowiki> | |<nowiki>[ -11 0 0 0 2 0 1 ></nowiki> | ||
|} | |} | ||
[[File:Blume comma.png|none|thumb| | [[File:Blume comma.png|none|thumb| | ||
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== Comma pumps == | == Comma pumps == | ||
Yer is pure JI, but due to the five places where it boasts two pitches very close together but with very different harmonic compositions, it can achieve [[Zero comma pump|zero comma pumps]] by “comma shifting” at those key points, returning to exactly their original pitch. | Yer is pure JI, but due to the five places where it boasts two pitches very close together but with very different harmonic compositions, it can achieve [[Zero comma pump|zero comma pumps]] by “comma shifting” at those key points, returning to exactly their original pitch. | ||
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|3v1 | |3v1 | ||
|1 | |1 | ||
|<nowiki> | |<nowiki>[ 7 0 0 0 -1 -1 -1 1 ></nowiki> | ||
|0.7120024978 | |0.7120024978 | ||
|0.7120024978 | |0.7120024978 | ||
| Line 1,195: | Line 1,192: | ||
|4v0 | |4v0 | ||
|1 | |1 | ||
|<nowiki> | |<nowiki>[ 15 0 0 0 1 1 1 1 ></nowiki> | ||
|594.3140298 | |594.3140298 | ||
|7.5912943 | |7.5912943 | ||
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== Scala file == | == Scala file == | ||
<pre> | |||
! yer.scl | ! yer.scl | ||
! | ! | ||
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247/128 | 247/128 | ||
2/1 | 2/1 | ||
</pre> | |||
== Video explanation == | == Video explanation == | ||
More details are presented in this video: [https://vimeo.com/184148765 Yer (pitch system)] | More details are presented in this video: [https://vimeo.com/184148765 Yer (pitch system)] | ||
== Listening == | == Listening == | ||
* [https://soundcloud.com/cmloegcmluin/tsraxcfaubdj Douglas Blumeyer - Tsraxcfaubdj] | |||
[https://soundcloud.com/cmloegcmluin/tsraxcfaubdj Douglas Blumeyer - Tsraxcfaubdj] | * [https://soundcloud.com/cmloegcmluin/blumeyer-comma-ji-unpump Douglas Blumeyer - Blumeyer Comma JI Unpump] | ||
* [https://chrisvaisvil.com/the-figment-for-woodwinds-muted-strings-and-choir-in-just-intonation-tuning Chris Vaisvil - The Figment] | |||
[https://soundcloud.com/cmloegcmluin/blumeyer-comma-ji-unpump Douglas Blumeyer - Blumeyer Comma JI Unpump] | * [http://chrisvaisvil.com/now-yer-talkin-ji-piano Chris Vaisvil - Now Yer Talkin'] | ||
[https://chrisvaisvil.com/the-figment-for-woodwinds-muted-strings-and-choir-in-just-intonation-tuning Chris Vaisvil - The Figment] | |||
[http://chrisvaisvil.com/now-yer-talkin-ji-piano Chris Vaisvil - Now Yer Talkin'] | |||
== Tritave-Based Yer == | == Tritave-Based Yer == | ||
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== Yer as a temperament == | == Yer as a temperament == | ||
If you [[temper out]] only the Blumeyer comma, you get this 2.11.13.17.19 [[subgroup]] [[mapping]], which naturally should be called "Blumeyer [[regular temperament|temperament]]": | If you [[temper out]] only the Blumeyer comma, you get this 2.11.13.17.19 [[subgroup]] [[mapping]], which naturally should be called "Blumeyer [[regular temperament|temperament]]": | ||
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⟨ 0 0 0 1 1 ] ⟩ | ⟨ 0 0 0 1 1 ] ⟩ | ||
Expressed as a [[map-merging|map-merge]] of [[ET]]s, that's 13&113&137&194. So one ~19 is up one each of the ~11, ~13, and ~17 here. | Expressed as a [[map-merging|map-merge]] of [[ET]]s, that's 13&113&137&194. So one ~19 is up one each of the ~11, ~13, and ~17 here. | ||
Now if you temper out the Blumeyer comma and the yama comma (and therefore also the blume comma; in fact, the [[canonical form]] of the [[comma basis]] appears to be blume and yama, with the Blumeyer comma being a linear combination of them), then you get a [[rank-3 temperament]], with mapping: | Now if you temper out the Blumeyer comma and the yama comma (and therefore also the blume comma; in fact, the [[canonical form]] of the [[comma basis]] appears to be blume and yama, with the Blumeyer comma being a linear combination of them), then you get a [[rank-3 temperament]], with mapping: | ||
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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¢: | 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¢: | ||
<pre> | |||
! yerMV3.scl | ! yerMV3.scl | ||
! | ! | ||
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1133.7 | 1133.7 | ||
(2/1) | (2/1) | ||
</pre> | |||
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. | 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. | ||
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|} | |} | ||
==See also== | == 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) | * [[Hilim13]], another tridecatonic tuning in the [[2.11.13.17.19 subgroup]], [[Just intonation|JI]], designed by [[Gene Ward Smith]] | ||
* [[Gjaeck]], another tuning in the [[2.11.13.17.19 subgroup]], a tempered [[MOS scale|MOS]] of [[57edo|57ed2]], also designed by [[Douglas Blumeyer]] | |||
[[Hilim13]], another tridecatonic tuning in the [[2.11.13.17.19 subgroup]], [[Just intonation|JI]], designed by [[Gene Ward Smith]] | |||
[[Category:Euler-Fokker genera]] | [[Category:Euler-Fokker genera]] | ||
[[Category:Tables]] | [[Category:Tables]] | ||
[[Category:19-limit]] | [[Category:19-limit]] | ||
[[Category:Just intonation scales]] | [[Category:Just intonation scales]] | ||
[[Category: | [[Category:Blumeyer]] | ||
[[Category:Combination product sets]] | [[Category:Combination product sets]] | ||
[[Category:Comma pump]] | [[Category:Comma pump]] | ||