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The twelfth root of two or (or equivalently /) is an algebraic irrational number, approximately equal to 1.0594631.It is most important in Western music theory, where it represents the frequency ratio (musical interval) of a semitone (Play ⓘ) in twelve-tone equal temperament.
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifths [2] which are "pure" or perfect, with ratio :. This is chosen because it is the next harmonic of a vibrating string, after the octave (which is the ratio 2 : 1 {\displaystyle 2:1} ), and hence is the ...
In musical tuning theory, a Pythagorean interval is a musical interval with a frequency ratio equal to a power of two divided by a power of three, or vice versa. [1] For instance, the perfect fifth with ratio 3/2 (equivalent to 3 1 / 2 1 ) and the perfect fourth with ratio 4/3 (equivalent to 2 2 / 3 1 ) are Pythagorean intervals.
12-tone equal temperament chromatic scale on C, one full octave ascending, notated only with sharps. Play ascending and descending ⓘ. 12 equal temperament (12-ET) [a] is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 (≈ 1.05946).
The reason for this is that the frequency of the first overtone is about 5 2 / 2 2 = 25 / 4 = 6 + 1 ⁄ 4 times the fundamental (about 2 + 1 ⁄ 2 octaves above it). [2] By comparison, the first overtone of a vibrating string or metal bar is one octave above (twice) the fundamental, so when the string is plucked or the bar is ...
Intuitively, if one starts with a tiny object around the point (1, 2, 3) and apply F to that object, one will get a resulting object with approximately 40 × 1 × 2 = 80 times the volume of the original one, with orientation reversed.
The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1) 2 = x 2 ...
The result of fitting a set of data points with a quadratic function. Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum based on a least-squares fit of sinusoids to data samples, similar to Fourier analysis.