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 | '''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]]. | |||
== See also == | == See also == | ||
Revision as of 11:19, 2 January 2025
| Interval information |
retroptolemaic whole tone
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 cents 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) = [-115 96 -16⟩ (lela-quadquadgu negative 6th, ~6.66 cents). In addition, this interval differs from 256/225 (Neapolitan diminished third) by the schisma.