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The concept of harmonic function originates in theories about just intonation.It was realized that three perfect major triads, distant from each other by a perfect fifth, produced the seven degrees of the major scale in one of the possible forms of just intonation: for instance, the triads F–A–C, C–E–G and G–B–D (subdominant, tonic, and dominant respectively) produce the seven ...
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average .
Riemannian theory, in general, refers to the musical theories of German theorist Hugo Riemann (1849–1919). His theoretical writings cover many topics, including musical logic, [ 1 ] notation, [ 2 ] harmony, [ 3 ] melody, [ 4 ] phraseology, [ 5 ] the history of music theory, [ 6 ] etc.
Music theory analyzes the pitch, timing, and structure of music. It uses mathematics to study elements of music such as tempo , chord progression , form , and meter . 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 .
The Oxford Companion to Music describes three interrelated uses of the term "music theory": The first is the "rudiments", that are needed to understand music notation (key signatures, time signatures, and rhythmic notation); the second is learning scholars' views on music from antiquity to the present; the third is a sub-topic of musicology ...
In Greek music it was used to tune tetrachords, which were composed into scales spanning an octave. [6] A distinction can be made between extended Pythagorean tuning and a 12-tone Pythagorean temperament. Extended Pythagorean tuning corresponds 1-on-1 with western music notation and there is no limit to the number of fifths.
The Phrygian mode (pronounced / ˈ f r ɪ dʒ i ə n /) can refer to three different musical modes: the ancient Greek tonos or harmonia, sometimes called Phrygian, formed on a particular set of octave species or scales; the medieval Phrygian mode, and the modern conception of the Phrygian mode as a diatonic scale, based on the latter.
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 Tonality ...