42edo: Difference between revisions

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42edo is on the [[optimal ET sequence]] of the [[Augmented family#eugene|eugene]], [[joan]], [[lemba]], [[neutron]], [[qeema]], [[seville]], [[sevond]], [[skateboard]], [[tritikleismic]] and [[vines]] temperaments.

While not an accurate tuning on the full 7-limit, 42edo does an excellent job on the 2.9.15.7.33.39 [[k*N subgroups|2*42 subgroup]], having the same tuning on it as does [[84edo]]. On this subgroup 42 has the same [[comma]]s as 84.

42edo is a diatonic edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. 42edo is one of the most difficult diatonic edos to notate, because no other diatonic edo's 5th is as sharp (see [[47edo]] for the opposite extreme).

=== Odd harmonics ===

While not an accurate tuning on the full [[7-limit]], 42edo does an excellent job on the 2.9.15.7.33.39 [[k*N subgroups|2*42 subgroup]], having the same tuning on it as does [[84edo]]. On this subgroup 42 has the same [[comma]]s as 84.

~~=== Subsets and supersets ===~~

~~Since 42 factors into {{factorization|42}}, 42edo contains subset edos {{EDOs| 2, 3, 6, 7, 14, and 21 }}.~~

=== Octave stretch ===

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For a more detailed comparison see [[Table of stretched 42edo tunings]].

=== Subsets and supersets ===

Since 42 factors into {{factorization|42}}, 42edo contains subset edos {{EDOs| 2, 3, 6, 7, 14, and 21 }}.

==Intervals==

@@ Line 6: / Line 6: @@
 edo is on the [[optimal ET sequence]] of the [[Augmented family#eugene|eugene]], [[joan]], [[lemba]], [[neutron]], [[qeema]], [[seville]], [[sevond]], [[skateboard]], [[tritikleismic]] and [[vines]] temperaments.
-While not an accurate tuning on the full 7-limit, 42edo does an excellent job on the 2.9.15.7.33.39 [[k*N subgroups|2*42 subgroup]], having the same tuning on it as does [[84edo]]. On this subgroup 42 has the same [[comma]]s as 84.
 edo is a diatonic edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. 42edo is one of the most difficult diatonic edos to notate, because no other diatonic edo's 5th is as sharp (see [[47edo]] for the opposite extreme).
 === Odd harmonics ===
+While not an accurate tuning on the full [[7-limit]], 42edo does an excellent job on the 2.9.15.7.33.39 [[k*N subgroups|2*42 subgroup]], having the same tuning on it as does [[84edo]]. On this subgroup 42 has the same [[comma]]s as 84.
 {{Harmonics in equal|42}}
-=== Subsets and supersets ===
-Since 42 factors into {{factorization|42}}, 42edo contains subset edos {{EDOs| 2, 3, 6, 7, 14, and 21 }}.
 === Octave stretch ===
@@ Line 52: / Line 48: @@
 For a more detailed comparison see [[Table of stretched 42edo tunings]].
+=== Subsets and supersets ===
+Since 42 factors into {{factorization|42}}, 42edo contains subset edos {{EDOs| 2, 3, 6, 7, 14, and 21 }}.
 ==Intervals==