2197/2187: Difference between revisions

@@ Line 1: / Line 1: @@
-The '''Threedie''', which is the interval '''2197/2187''' (13^3/3^7), is a 3.13 analog of the 2.5 [[128/125|diesis]], 2^7/5^3. Tempering by it, instead of chopping the octave into three sharp 5/4s, chops the tritave (3) into three slightly flat 13/9s, since (13/9)^3/3 = 2197/2187. 596 provides the optimal patent val for the corresponding rank five temperament.
+{{Infobox Interval
+| Icon =
+| Ratio = 2197/2187
+| Monzo = 0 -7 0 0 0 3
+| Cents = 7.89798
+| Name = threedie
+| Color name =
+| FJS name = dd2<sup>13,13,13</sup>
+| Sound =
+}}
+The '''threedie''', '''2197/2187''', is a 3.13 analog of the 2.5 [[128/125|diesis]]. Analogously to tempering the diesis, which divides the octave into three sharp 5/4s, tempering the threedie divides the [[tritave]] into three slightly flat 13/9s, since (13/9)<sup>3</sup>/3 = 2197/2187. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.