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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 the formulas, the ratios 3:2 or 2:3 represent an ascending or descending perfect fifth (i.e. an increase or decrease in frequency by a perfect fifth, while 2:1 or 1:2 represent a rising or lowering octave). The formulas can also be expressed in terms of powers of the third and the second harmonics.
In music, an octave (Latin: octavus: eighth) or perfect octave (sometimes called the diapason) [2] is a series of eight notes occupying the interval between (and including) two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music ...
The musical system of ancient Greece evolved over a period of more than 500 years from simple scales of tetrachords, or divisions of the perfect fourth, into several complex systems encompassing tetrachords and octaves, as well as octave scales divided into seven to thirteen intervals.
The opposition between consonance and dissonance can be made in different contexts: In acoustics or psychophysiology, the distinction may be objective.In modern times, it usually is based on the perception of harmonic partials of the sounds considered, to such an extent that the distinction really holds only in the case of harmonic sounds (i.e. sounds with harmonic partials).
Sympathetic resonance has been applied to musical instruments from many cultures and time periods, and to string instruments in particular. In instruments with undamped strings (e.g. harps, guitars and kotos), strings will resonate at their fundamental or overtone frequencies when other nearby strings are sounded.
On the other hand, the octave series is a geometric progression (2f, 4f, 8f, 16f, ...), and people perceive these distances as "the same" in the sense of musical interval. In terms of what one hears, each octave in the harmonic series is divided into increasingly "smaller" and more numerous intervals.
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.