Yer: Difference between revisions

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== Introduction ==

Yer is an octave-reduced [[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).

Yer is an octave-reduced [[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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Yer - lattice view

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It has a minor third of 19:16 and a minor second 17:16.

== EFG, CPS ==

Every pitch in the system is a combination of either zero, one, two, three, or four of 11, 13, 17, or 19, for a total of 1 + 4 + 6 + 4 + 1 = 16 pitches. In other words it is the [[wikipedia:Power_set|powerset]] of {11, 13, 17, 19}.

If anyone is familiar with [[Erv Wilson|Erv Wilson]]’s [[Combination_product_sets|Combination Product Sets]], or CPS's, it may help to think of an Euler-Fokker Genus as the intersection of the choose-1 tetrany, the choose-2 hexany, and the choose-3 tetrany, plus the unison, plus 11 * 13 * 17 * 19 all together which may be called the aota, an acronym for “all of the above”.

As an EFG, it has no subharmonic factors, that is, no division - only multiplication of them together, which leads to it being [https://en.xen.wiki/w/Otonality_and_utonality#Ambitonal ambitonal], not otonal or utonal leaning. While it is nicely “balanced/symmetrical” as all CPSs are, pitches in the resultant system are not evenly distributed. There are two massive gaps of 185 cents, and two places where pitches land almost directly on top of each other.

== Commas ==

@@ Line 1: / Line 1: @@
 == Introduction ==
-Yer is an octave-reduced [[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).
+Yer is an octave-reduced [[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.
 {| class="wikitable"
@@ Line 96: / Line 96: @@
 Yer - lattice view
 ]]
+It has a minor third of 19:16 and a minor second 17:16.
+== EFG, CPS ==
+Every pitch in the system is a combination of either zero, one, two, three, or four of 11, 13, 17, or 19, for a total of 1 + 4 + 6 + 4 + 1 = 16 pitches. In other words it is the [[wikipedia:Power_set|powerset]] of {11, 13, 17, 19}.
+If anyone is familiar with [[Erv Wilson|Erv Wilson]]’s [[Combination_product_sets|Combination Product Sets]], or CPS's, it may help to think of an Euler-Fokker Genus as the intersection of the choose-1 tetrany, the choose-2 hexany, and the choose-3 tetrany, plus the unison, plus 11 * 13 * 17 * 19 all together which may be called the aota, an acronym for “all of the above”.
+As an EFG, it has no subharmonic factors, that is, no division - only multiplication of them together, which leads to it being [https://en.xen.wiki/w/Otonality_and_utonality#Ambitonal ambitonal], not otonal or utonal leaning. While it is nicely “balanced/symmetrical” as all CPSs are, pitches in the resultant system are not evenly distributed. There are two massive gaps of 185 cents, and two places where pitches land almost directly on top of each other.
 == Commas ==