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Ascending by fifths in equal temperament leads to a return to the starting pitch class—starting with a C and ascending by fifths leads to another C after a certain number of iterations. This does not occur if an exact 3:2 ratio is used (just intonation). The adjustment made in equal temperament tuning is called the Pythagorean comma.
A standard order is often called ascending (corresponding to the fact that the standard order of numbers is ascending, i.e. A to Z, 0 to 9), the reverse order descending (Z to A, 9 to 0). For dates and times, ascending means that earlier values precede later ones e.g. 1/1/2000 will sort ahead of 1/1/2001.
The same placement pattern, alternating between descending and ascending placements of , applies for any larger value of . [2] In sequences of permutations with this recursive structure, each permutation differs from the previous one either by the single-position-at-a-time motion of n {\displaystyle n} , or by a change of two smaller numbers ...
In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. [1] [2] Each iteration starts with a number, sorts the digits into descending and ascending order, and calculates the difference between the two new numbers.
This tuning dates to Ancient Mesopotamia [5] (see Music of Mesopotamia § Music theory), and was done by alternating ascending fifths with descending fourths (equal to an ascending fifth followed by a descending octave), resulting in the notes of a pentatonic or heptatonic scale falling within an octave.
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Melodic minor scale (ascending) on A Play ⓘ In traditional classical theory, the melodic minor scale has two forms, as noted above, an ascending form and a descending form. Although each of these forms of itself comprises seven pitches, together they comprise nine, which might seem to call into question the scale's status as a heptatonic scale.
Ascending Descending 1/minor second: Theme of the One Ring from The Lord of the Rings [citation needed] Theme from Jaws [9] [10] "Nice Work If You Can Get It" [9]
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