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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 :
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 ]
Building on of Sethares (2004), [5] dynamic tonality introduces the notion of pseudo-harmonic partials, in which the frequency of each partial is aligned to match the pitch of a corresponding note in a pseudo-just tuning, thereby maximizing the consonance of that pseudo-harmonic timbre with notes of that pseudo-just tuning. [6] [7] [8] [9]
In this book, Aristoxenus refers to previous experiments conducted by Pythagoreans to determine the relationship between small integer ratios and consonant notes (e.g., 1:2 describes an octave relationship, which is a doubling of frequency). While identifying as a Pythagorean, Aristoxenus claims that numerical ratios are not the ultimate ...
Some non-mel auditory-frequency-scale formulas use the same form but with much lower break frequency, not necessarily mapping to 1000 at 1000 Hz; for example the ERB-rate scale of Glasberg and Moore (1990) uses a break point of 228.8 Hz, [15] and the cochlear frequency–place map of Greenwood (1990) uses 165.3 Hz.
Tuning is the process of adjusting the pitch of one or many tones from musical instruments to establish typical intervals between these tones. Tuning is usually based on a fixed reference, such as A = 440 Hz. The term "out of tune" refers to a pitch/tone that is either too high or too low in relation to a given reference pitch. While an ...
In musical notation, the different vertical positions of notes indicate different pitches. Play top: Play bottom: Pitch is a perceptual property that allows sounds to be ordered on a frequency-related scale, [1] or more commonly, pitch is the quality that makes it possible to judge sounds as "higher" and "lower" in the sense associated with musical melodies. [2]