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The simplest pitch space model is the real line. A fundamental frequency f is mapped to a real number p according to the equation = + (/) This creates a linear space in which octaves have size 12, semitones (the distance between adjacent keys on the piano keyboard) have size 1, and middle C is assigned the number 60, as it is in MIDI. 440 Hz is the standard frequency of 'concert A', which ...
The spaces described in this article are pitch class spaces which model the relationships between pitch classes in some musical system. These models are often graphs, groups or lattices. Closely related to pitch class space is pitch space, which represents pitches rather than pitch classes, and chordal space, which models relationships between ...
The octave of any pitch refers to a frequency exactly twice that of the given pitch. Succeeding superoctaves are pitches found at frequencies four, eight, sixteen times, and so on, of the fundamental frequency. Pitches at frequencies of half, a quarter, an eighth and so on of the fundamental are called suboctaves.
On Things Heard, generally ascribed to Strato of Lampsacus, states that the pitch is related to the frequency of vibrations of the air and to the speed of sound. [ 9 ] In about 20 BC, the Roman architect and engineer Vitruvius wrote a treatise on the acoustic properties of theaters including discussion of interference, echoes, and reverberation ...
Logarithmic plot of frequency in hertz versus pitch of a chromatic scale starting on middle C. Each subsequent note has a pitch equal to the frequency of the prior note's pitch multiplied by 12 √ 2. The base-2 logarithm of the above frequency–pitch relation conveniently results in a linear relationship with or :
A pure tone's pressure waveform versus time looks like this; its frequency determines the x axis scale; its amplitude determines the y axis scale; and its phase determines the x origin. In psychoacoustics , a pure tone is a sound with a sinusoidal waveform ; that is, a sine wave of constant frequency , phase-shift , and amplitude . [ 1 ]
If one starts on any equal-tempered pitch and repeatedly ascends by the musical interval of a semitone, one will eventually land on a pitch with the same pitch class as the initial one, having passed through all the other equal-tempered chromatic pitch classes in between. Since the space is circular, it is also possible to descend by semitone.
The complement of set X is the set consisting of all the pitch classes not contained in X. [12] The product of two pitch classes is the product of their pitch-class numbers modulo 12. Since complementation and multiplication are not isometries of pitch-class space, they do not necessarily preserve the musical character of the objects they ...
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