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A variety of musical terms are encountered in printed scores, music reviews, and program notes. Most of the terms are Italian, in accordance with the Italian origins of many European musical conventions. Sometimes, the special musical meanings of these phrases differ from the original or current Italian meanings.
Though ancient Chinese, Indians, Egyptians and Mesopotamians are known to have studied the mathematical principles of sound, [2] the Pythagoreans (in particular Philolaus and Archytas) [3] of ancient Greece were the first researchers known to have investigated the expression of musical scales in terms of numerical ratios, [4] particularly the ratios of small integers.
The resolution of binary integers increases exponentially as the word length increases: adding one bit doubles the resolution, adding two quadruples it, and so on. The number of possible values that an integer bit depth can represent can be calculated by using 2 n , where n is the bit depth. [ 1 ]
New Music in China and the C.C. Liu Collection at the University of Hong Kong. [full citation needed] ISBN 978-962-209-772-8. Clement, Brett (2009). A Study of the Instrumental Music of Frank Zappa (PhD dissertation). University of Cincinnati. Cohn, Richard (1991). "Bartók's Octatonic Strategies: A Motivic Approach."
Harmony – Aspect of music; Pure tone – Sound with a sinusoidal waveform; Pythagorean tuning – Method of tuning a musical instrument; Scale of harmonics; Spherical harmonics – Special mathematical functions defined on the surface of a sphere; Stretched octave; Subharmonic – Having a frequency that is a fraction of a fundamental frequency
Comparison between tunings: Pythagorean, equal-tempered, quarter-comma meantone, and others.For each, the common origin is arbitrarily chosen as C. The degrees are arranged in the order or the cycle of fifths; as in each of these tunings except just intonation all fifths are of the same size, the tunings appear as straight lines, the slope indicating the relative tempering with respect to ...
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Microtonality is the use in music of microtones — intervals smaller than a semitone, also called "microintervals".It may also be extended to include any music using intervals not found in the customary Western tuning of twelve equal intervals per octave.