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This list of frequencies is for a theoretically ideal piano. On an actual piano, the ratio between semitones is slightly larger, especially at the high and low ends, where string stiffness causes inharmonicity , i.e., the tendency for the harmonic makeup of each note to run sharp .
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 h {\displaystyle h} or v {\displaystyle v} :
The notes of a scale form intervals with each of the other notes of the chord in combination. A 5-note scale has 10 of these harmonic intervals, a 6-note scale has 15, a 7-note scale has 21, an 8-note scale has 28. [8]
The tables above only show the frequency ratios of each note with respect to the base note. However, intervals can start from any note and so twelve intervals can be defined for each interval type – twelve unisons, twelve semitones , twelve 2-semitone intervals, etc.
A "complex tone" (the sound of a note with a timbre particular to the instrument playing the note) "can be described as a combination of many simple periodic waves (i.e., sine waves) or partials, each with its own frequency of vibration, amplitude, and phase". [1] (See also, Fourier analysis.)
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 notes used in music can be more complex than musical tones, as they may include aperiodic aspects, such as attack transients, vibrato, and envelope modulation. A simple tone, or pure tone, has a sinusoidal waveform. A complex tone is a combination of two or more pure tones that have a periodic pattern of repetition, unless specified otherwise.
For an instrument in equal temperament tuned to the A440 pitch standard widely adopted in 1939, middle C has a frequency around 261.63 Hz [1] (for other notes see piano key frequencies). Scientific pitch was originally proposed in 1713 by French physicist Joseph Sauveur and based on the numerically convenient frequency of 256 Hz for middle C ...