Chapter One: An Acoustics Primer

### 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 (2^{1/12}), 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