729/640: Difference between revisions

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'''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, 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, 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).  In addition, this interval differs from [[256/225]] (Neapolitan diminished third) by the [[schisma]].


== See also ==
== See also ==