Yer: Difference between revisions

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== Tritave-Based Yer ==

One could imagine a tritave-repeating variation of Yer, where 2's are out but 3's are in (the EFG of 11, 13, 17, 19 remains but is tritave-reduced instead).

== 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]]":

[ ⟨ 1 0 0 0 -7 ]

⟨ 0 1 0 0 1 ]

⟨ 0 0 1 0 1 ]

⟨ 0 0 0 1 1 ] ⟩

Expressed as a [[join]] 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:

[ ⟨ 1 0 0 11 4 ]

⟨ 0 1 0 -2 -1 ]

⟨ 0 0 1 0 1 ] ⟩

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 ==

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 == Tritave-Based Yer ==
 One could imagine a tritave-repeating variation of Yer, where 2's are out but 3's are in (the EFG of 11, 13, 17, 19 remains but is tritave-reduced instead).
+== 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]]":
+[ ⟨	1	0	0	0	-7	]
+⟨	0	1	0	0	1	]
+⟨	0	0	1	0	1	]
+⟨	0	0	0	1	1	] ⟩
+Expressed as a [[join]] 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:
+[ ⟨	1	0	0	11	4	]
+⟨	0	1	0	-2	-1	]
+⟨	0	0	1	0	1	] ⟩
+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 ==