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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 ...
The difference between these two definitions resides in whether "formants" characterise the production mechanisms of a sound or the produced sound itself. In practice, the frequency of a spectral peak differs slightly from the associated resonance frequency, except when, by luck, harmonics are aligned with the resonance frequency, or when the ...
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]
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 .
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 ...
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.
A tablet with the Hymn to Nikkal inscribed [1]. The earliest form of musical notation can be found in a cuneiform tablet that was created at Nippur, in Babylonia (today's Iraq), in about 1400 BCE.
Sound waves may be viewed using parabolic mirrors and objects that produce sound. [ 9 ] The energy carried by an oscillating sound wave converts back and forth between the potential energy of the extra compression (in case of longitudinal waves) or lateral displacement strain (in case of transverse waves) of the matter, and the kinetic energy ...