5L 3s: Difference between revisions

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VisualWikitext

@@ Line 501: / Line 501: @@
 | 104.25
 | 18/17, 17/16
+|}
+=== Buzzard (48&53) ===
+In the broad sense, Buzzard can be viewed as any tuning that divides the 3rd harmonic into 4 equal parts. [[28edo]] and [[33edo]] can nominally be viewed as supporting it, but are still very flat and in an ambiguous zone between A-Team and true Buzzard in terms of harmonies. [[38edo]] & [[43edo]] are good compromises between melodic utility and harmonic accuracy, as the small step is still large enough to be obvious to the untrained ear, but [[48edo]] is where it really comes into it's own in terms of harmonies, providing not only an excellent [[3/2]], but also [[7/4]] and [[The_Archipelago|archipelago]] harmonies, as by dividing the 5th in 4 it obviously also divides it in two as well. Beyond that, it's a question of which intervals you want to favor. [[53edo]] has an essentially perfect [[3/2]], [[58edo]] gives the lowest overall error for the Barbados triads 10:13:15 and 26:30:39, while [[63edo]] does the same for the basic 4:6:7 triad. You could in theory go up to [[83edo]] if you want to favor the [[7/4]] above everything else, but beyond that, general accuracy drops off rapidly and you might as well be playing equal pentatonic.
+The sizes of the generator, large step and small step of oneirotonic are as follows in various buzzard tunings.
+{| class="wikitable right-2 right-3 right-4 right-5"
+|-
+!
+! [[38edo]]
+! [[53edo]]
+! [[63edo]]
+! Optimal ([[POTE]]) tuning
+! JI intervals represented (2.3.5.7.13 subgroup)
+|-
+| generator (g)
+| 15\38, 473.68
+| 21\53, 475.47
+| 25\63, 476.19
+| 475.69
+| 3/2 21/16
+|-
+| L (3g - octave)
+| 7/38, 221.04
+| 10/53, 226.41
+| 12/63, 228.57
+| 227.07
+| 8/7
+|-
+| s (-5g + 2 octaves)
+| 1/38 31.57
+| 1/53 22.64
+| 1/63 19.05
+| 21.55
+| 55/54 81/80 91/90
 |}