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2.4.5 Musical acoustics
Standard musical pitch is based
on a frequency of 440 Hz for A in the treble stave (a′) (see ISO
16: 1975). Wind instruments should be constructed to conform to this frequency
Diatonic major scale. The frequency ratios of musical intervals in the diatonic major scale are shown below; the upper row shows the ratio between adjacent steps, the lower row the ratio to the keynote.
Diatonic major scale
The interval between a major and a
minor tone, 81/80, is called a comma.
Equally tempered major scale. A semitone of equal temperament = 21/12 = 1.059 46. A tone of equal temperament = 2 semitones of ET = 21/6 = 1.122 46. The table below gives the frequencies (Hz) of musical notes in equal temperament for the octave starting at c'.
Frequencies of notes in equal temperament (Hz)
Any pitch interval may be expressed in cents, a cent being defined as the ratio 21/1200:1. Thus there are 100 cents to the ET semitone (see Wood and Bowsher, The Physics of Music, 1975).
ISO 16: 1975 Acoustics–standard tuning
frequency (standard musical pitch).
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