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Music and mathematics. A spectrogram of a violin waveform, with linear frequency on the vertical axis and time on the horizontal axis. The bright lines show how the spectral components change over time. The intensity colouring is logarithmic (black is −120 dBFS). Music theory analyzes the pitch, timing, and structure of music.
Musical analysis is the study of musical structure in either compositions or performances. [ 1 ] According to music theorist Ian Bent, music analysis "is the means of answering directly the question 'How does it work?'". [ 2 ] The method employed to answer this question, and indeed exactly what is meant by the question, differs from analyst to ...
In music theory, the spiral array model is an extended type of pitch space. A mathematical model involving concentric helices (an "array of spirals "), it represents human perceptions of pitches, chords, and keys in the same geometric space. It was proposed in 2000 by Elaine Chew in her MIT doctoral thesis Toward a Mathematical Model of ...
Comparison of equal-tempered (black) and Pythagorean (green) intervals showing the relationship between frequency ratio and the intervals' values, in cents. 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 .
In modern academia, music theory is a subfield of musicology, the wider study of musical cultures and history. Music theory is often concerned with abstract musical aspects such as tuning and tonal systems, scales, consonance and dissonance, and rhythmic relationships. In addition, there is also a body of theory concerning practical aspects ...
Godfried Toussaint (1944–2019) was a Belgian–Canadian computer scientist who worked as a professor of computer science for McGill University and New York University.His main professional expertise was in computational geometry, [2] but he was also a jazz drummer, [3] held a long-term interest in the mathematics of music and musical rhythm, and since 2005 held an affiliation as a researcher ...
Computational musicology includes any disciplines that use computation in order to study music. It includes sub-disciplines such as mathematical music theory, computer music, systematic musicology, music information retrieval, digital musicology, sound and music computing, and music informatics. [2] As this area of research is defined by the ...
Fibonacci sequence. In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes ...