729/640: Difference between revisions

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{{Infobox Interval

| Name = acute whole tone

| Name = acute whole tone, retroptolemaic whole tone

| Color name = Lg2, lagu 2nd

}}

'''729/640''' is the interval that results from stacking [[16/15]] (classical diatonic semitone) and [[2187/2048]] (Pythagorean apotome), or [[27/25]] (large limma) and [[135/128]] (major limma). It is equal to [[9/8]] raised by a [[syntonic comma]], about 225.4 [[cent]]s in size~~, and~~ well approximated by three steps of [[16edo]], and 16 of them exceed three octaves by the comma (729/640)16/23 = 396/(2115×516) = {{monzo|-115 96 -16}} (lela-quadquadgu negative 6th, ~6.66 cents).

'''729/640''', the '''retroptolemaic whole tone''', is the interval that results from stacking [[16/15]] (classical diatonic semitone) and [[2187/2048]] (Pythagorean apotome), or [[27/25]] (large limma) and [[135/128]] (major limma). It is equal to [[9/8]] raised by a [[syntonic comma]], about 225.4 [[cent]]s in size.

== Approximation ==

This interval is well approximated by three steps of [[16edo]], and 16 of them exceed three octaves by the comma (729/640)16/23 = 396/(2115×516) = {{monzo|-115 96 -16}} (lela-quadquadgu negative 6th, ~6.66 cents). In addition, this interval differs from [[256/225]] (Neapolitan diminished third) by the [[schisma]]. Furthermore, it exceeds [[25/22]] by [[8019/8000]], the minortone comma, and falls short of [[8/7]] by [[5120/5103]], the hemifamity comma.

== See also ==

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = acute whole tone
+| Name = acute whole tone, retroptolemaic whole tone
 | Color name = Lg2, lagu 2nd
 }}
-'''729/640''' is the interval that results from stacking [[16/15]] (classical diatonic semitone) and [[2187/2048]] (Pythagorean apotome), or [[27/25]] (large limma) and [[135/128]] (major limma). It is equal to [[9/8]] raised by a [[syntonic comma]], about 225.4 [[cent]]s in size, and well approximated by three steps of [[16edo]], and 16 of them exceed three octaves by the comma (729/640)<sup>16</sup>/2<sup>3</sup> = 3<sup>96</sup>/(2<sup>115</sup>×5<sup>16</sup>) = {{monzo|-115 96 -16}} (lela-quadquadgu negative 6th, ~6.66 cents).
+'''729/640''', the '''retroptolemaic whole tone''', is the interval that results from stacking [[16/15]] (classical diatonic semitone) and [[2187/2048]] (Pythagorean apotome), or [[27/25]] (large limma) and [[135/128]] (major limma). It is equal to [[9/8]] raised by a [[syntonic comma]], about 225.4 [[cent]]s in size.
+== Approximation ==
+This interval is well approximated by three steps of [[16edo]], and 16 of them exceed three octaves by the comma (729/640)<sup>16</sup>/2<sup>3</sup> = 3<sup>96</sup>/(2<sup>115</sup>×5<sup>16</sup>) = {{monzo|-115 96 -16}} (lela-quadquadgu negative 6th, ~6.66 cents).  In addition, this interval differs from [[256/225]] (Neapolitan diminished third) by the [[schisma]]. Furthermore, it exceeds [[25/22]] by [[8019/8000]], the minortone comma, and falls short of [[8/7]] by [[5120/5103]], the hemifamity comma.
 == See also ==