Introduction to Computer Music: Volume One

14. How do we perceive pitch?

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 it 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 equal temperament 12-notes-to-an-octave semitones is a frequency ratio of one to the twelfth root of two (21/12), or 1:1.05946. For example, to find the frequency of the A# semitone above A440, multiple 440 by 1.05946 to get ~466.163. Every doubling in Hz is perceived as an equivalent octave. It is thought that because a doubling of frequency causes a response at equal distance on the basilar membrane, we hear octaves as related. Because of the logarithmic spacing of pitch placement on the membrane, we perceive musical intervals not as differences in frequency, but as ratios between frequencies. 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 because they share a 2:1 frequency ratio. Below is a chart of frequency vs. pitch. Click here to dowload as an Excel spreadsheet of the chart below for copying and pasting specific frequencies if needed.

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For further study, see Hyperphysics->Hearing