Introduction to Computer Music: Volume One

Pitch is our perceptual interpretation of frequency. As mentioned, ideal human hearing ranges from 20 to 20,000 Hz, yet we have our greatest sensitivity to frequencies which lie within 200 to 2000 Hz, which takes up two-thirds of the distance on the basilar membrane. One proof of this is the “just noticeable difference” or JND. The JND is the smallest change in frequency of a single sine tone that is perceptible by the average listener. Most studies place is around 3% in the 100 Hz range, but only 0.5% in the 2000 Hz range. One might extrapolate that a bass player has more liberty to play out of tune than a violinist.

In general, we perceive pitch logarithmically in relation to frequency. The formula for successive semitones is a frquency ratio of 1:12th Root of 2 or 1:1.05946. Every doubling in Hz is perceived as an equivalent octave. It is thought that because a doublings of frequency causes a response at equal distance on the basilar membrane, we hear octaves as related. In fact, because of the logarithmic spacing of pitch placement on the membrane it can be extrapolated that we perceive differences in pitches not as differences frequency, but as the ratio of pitches separating them or musical intervals (which are ratios of frequencies and not linear differences). So A220 to A440 is perceived as the “same” interval as A440 to A880, even though one pair has a difference of 220 Hz and the other a difference of 440 Hz. View a chart of frequency vs. pitch here.

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For further study, see Hyperphysics->Hearing