729/640: Difference between revisions
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Created page with "{{Infobox Interval | Name = acute whole tone | Color name = Lg2, lagu 2nd }} '''729/640''' is the interval that results from stacking 16/15 (classical diatonic semitone)..." |
Provided an additional name, which is now reflected in the article |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = acute whole tone | | Name = acute whole tone, retroptolemaic whole tone | ||
| Color name = Lg2, lagu 2nd | | 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, 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). | ||
== See also == | == See also == | ||
Revision as of 23:39, 1 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, 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) = [-115 96 -16⟩ (lela-quadquadgu negative 6th, ~6.66 cents).