12. 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 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 relations to frequency. 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.

In the range of 20 to 2000 Hz, the ear has the ability to fuse harmonically-related frequencies into a single entity (i.e. a single note with a particular timbre) with a fundamental frequency, even if the fundamental is missing.

When we listen to a violin section, we are hopefully hearing numerous instruments playing approximately the same pitch, with some very slight differences in frequency (called chorusing) that give the sound a depth and richness beyond what a single instrument would produce. As mentioned above, a slight difference in frequency will lead to the phenomenon of beating. We perceive the mistuned notes as a single chorused pitch up to the limit of discrimination, a difference of approximately 10 to 15 Hz, beyond which we hear two separate tones. At the very point of such a perceptual separation lies an area of tonal roughness. While a single pitch may maximally stimulate a specific spot on the basilar membrane, it also stimulates some adjacent hair cells as well. These lie within what is called the critical band. Other pitches which are close in frequency may also share some hair cells in common, which is theorized to cause intervalically close tones to sound more complex that more widely separated tones. The intervallic width of the critical band varies with register, being a large percentage of the frequencies of two low tones, and a smaller percentage of the frequencies at a higher register (it is about a minor 3rd above A440). This may account for our orchestrational penchant for using wider intervals in lower registers. Another applicable phenomenon is that when two sounds of equal loudness are close in pitch, thereby in the critical band, their combined loudness will be only slightly greater than one of them alone.

In preparing this article it became clear that the complete and exact mechanism for our extraordinary pitch resolution and discrimination is not completely understood and is still being investigated. The placement theory coupled with the critical band does not completely explain our ability to detect the minute frequency changes we are capable of.

Our perception of pitch is also effected by the duration and intensity of a sound. Sustained sounds above 2 kHz may be perceived as rising in pitch as their intensity increases, whereas sounds below 2 kHz may be perceived as dropping in pitch. I might theorize that this phenomenon contributes to the intonation difficulties all high school band or choral conductors experience with changes in dynamics.

ADD TUNING SECTION HERE

For further study, see Hyperphysics->Hearing




An Acoustics Primer, Chapter 12
URL: www.indiana.edu/~emusic/acoustics/pitch.htm
Copyright 2003 Prof. Jeffrey Hass
Center for Electronic and Computer Music, School of Music
Indiana University, Bloomington, Indiana