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As another example, the otonal harmonic fragment 5 ⁄ 4, 6 ⁄ 4, 7 ⁄ 4, 8 ⁄ 4 is strictly proper, with the one step intervals varying in size from 8 ⁄ 7 to 5 ⁄ 4, two step intervals vary from 4 ⁄ 3 to 3 ⁄ 2, three step intervals from 8 ⁄ 5 to 7 ⁄ 4.
The harmonic seventh interval, also known as the septimal minor seventh, [2] [3] or subminor seventh, [4] [5] [6] is one with an exact 7:4 ratio [7] (about 969 cents). [8] This is somewhat narrower than and is, "particularly sweet", [ 9 ] "sweeter in quality" than an "ordinary" [ 10 ] just minor seventh , which has an intonation ratio of 9:5 ...
[12] [13] In general, a common fraction is said to be a proper fraction, if the absolute value of the fraction is strictly less than one—that is, if the fraction is greater than −1 and less than 1. [14] [15] It is said to be an improper fraction, or sometimes top-heavy fraction, [16] if the absolute value of the fraction is greater than or ...
The suspect in the New Orleans attack that killed 14 people on New Year's Day is believed to have acted alone in a "premeditated and evil act," the FBI has said.
The Helmholtz decomposition in three dimensions was first described in 1849 [9] by George Gabriel Stokes for a theory of diffraction. Hermann von Helmholtz published his paper on some hydrodynamic basic equations in 1858, [10] [11] which was part of his research on the Helmholtz's theorems describing the motion of fluid in the vicinity of vortex lines. [11]
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