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  2. Music and mathematics - Wikipedia

    en.wikipedia.org/wiki/Music_and_mathematics

    The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory. While music theory has no axiomatic foundation in modern mathematics, the basis of musical sound can be described mathematically (using acoustics ) and exhibits "a remarkable array ...

  3. Multiphonic - Wikipedia

    en.wikipedia.org/wiki/Multiphonic

    In brass instruments, the most common method of producing multiphonics is by simultaneously playing the instrument and singing into it. When the sung note has a different frequency than the played note (preferably within the harmonic series of the played note), several new notes that are the sums/differences of the frequencies of the sung note and the played note are produced; leading to the ...

  4. Music theory - Wikipedia

    en.wikipedia.org/wiki/Music_theory

    Music theorists sometimes use mathematics to understand music, and although music has no axiomatic foundation in modern mathematics, mathematics is "the basis of sound" and sound itself "in its musical aspects... exhibits a remarkable array of number properties", simply because nature itself "is amazingly mathematical". [87]

  5. Circle of fifths - Wikipedia

    en.wikipedia.org/wiki/Circle_of_fifths

    The standard tempered fifth has a frequency ratio of 2 7/12:1 (or about 1.498307077:1), approximately two cents narrower than a justly tuned fifth. Ascending by twelve justly tuned fifths fails to close the circle by an excess of approximately 23.46 cents , roughly a quarter of a semitone , an interval known as the Pythagorean comma .

  6. Variations (Cage) - Wikipedia

    en.wikipedia.org/wiki/Variations_(Cage)

    This work is intended "for any number of players and any sound producing means." The score consists of eleven transparent sheets: six with lines and five with points. The mechanism is the same as in Variations I : perpendiculars are dropped from points to lines to determine sound characteristics, except that the list of characteristics is ...

  7. Musical acoustics - Wikipedia

    en.wikipedia.org/wiki/Musical_acoustics

    Musical acoustics or music acoustics is a multidisciplinary field that combines knowledge from physics, [1] [2] [3] psychophysics, [4] organology [5] (classification of the instruments), physiology, [6] music theory, [7] ethnomusicology, [8] signal processing and instrument building, [9] among other disciplines.