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A jump from the lowest semitone to the highest semitone in one octave doubles the frequency (for example, the fifth A is 440 Hz and the sixth A is 880 Hz). The frequency of a pitch is derived by multiplying (ascending) or dividing (descending) the frequency of the previous pitch by the twelfth root of two (approximately 1.059463).
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 :
During phonation, the vocal folds vibrate at a certain rate. This vibration results in a periodic acoustic waveform comprising a fundamental frequency and its harmonics. The fundamental frequency of the acoustic wave can be controlled by adjusting the muscles of the larynx, and listeners perceive this fundamental frequency as pitch.
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 ]
An octave is the interval between one musical pitch and another with double or half its frequency. For example, if one note has a frequency of 440 Hz, the note one octave above is at 880 Hz, and the note one octave below is at 220 Hz. The ratio of frequencies of two notes an octave apart is therefore 2:1.
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 ...
Pitch is a major auditory attribute of musical tones, along with duration, loudness, and timbre. [3] Pitch may be quantified as a frequency, but pitch is not a purely objective physical property; it is a subjective psychoacoustical attribute of sound. Historically, the study of pitch and pitch perception has been a central problem in ...
The unique characteristics of octaves gave rise to the concept of pitch class: pitches of the same letter name that occur in different octaves may be grouped into a single "class" by ignoring the difference in octave. For example, a high C and a low C are members of the same pitch class—the class that contains all C's. [29]