Pitch (music) - Labeling Pitches

Labeling Pitches

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For a comprehensive list of frequencies of musical notes, see Scientific pitch notation and Frequencies of notes.

Pitches can be labeled using letters, as in Helmholtz pitch notation; using a combination of letters and numbers, as in scientific pitch notation, where notes are labelled upwards from C0, the 16 Hz C; or by a number representing the frequency in hertz (Hz), the number of cycles per second. For example, one might refer to the A above middle C as "a'", "A4", or "440 Hz". In standard Western equal temperament, the notion of pitch is insensitive to "spelling": the description "G4 double sharp" refers to the same pitch as "A4"; in other temperaments, these may be distinct pitches.

Human perception of musical intervals is approximately logarithmic with respect to fundamental frequency: the perceived interval between the pitches "A220" and "A440" is the same as the perceived interval between the pitches "A440" and "A880". Motivated by this logarithmic perception, music theorists sometimes represent pitches using a numerical scale based on the logarithm of fundamental frequency. For example, one can adopt the widely used MIDI standard to map fundamental frequency, f, to a real number, p, as follows

This creates a linear pitch space in which octaves have size 12, semitones (the distance between adjacent keys on the piano keyboard) have size 1, and A440 is assigned the number 69. (See Frequencies of notes.) Distance in this space corresponds to musical intervals as understood by musicians. An equal-tempered semitone is subdivided into 100 cents. The system is flexible enough to include "microtones" not found on standard piano keyboards. For example, the pitch halfway between C (60) and C♯ (61) can be labeled 60.5.