Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013

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4.1.6 Sound Perception

4.1.6.1 Frequency Perception

In Chapter 3, we discussed the non-linear nature of pitch perception when we looked at octaves

as defined in traditional Western music. The A above middle C (call it A4) on a piano keyboard

sounds very much like the note that is 12 semitones above it, A5, except that A5 has a higher

pitch. A5 is one octave higher than A4. A6 sounds like A5 and A4, but it's an octave higher

than A5. The progression between octaves is not linear with respect to frequency. A2's

frequency is twice the frequency of A1. A3's frequency is twice the frequency of A2, and so

forth. A simple way to think of this is that as the frequencies increase by multiplication, the

perception of the pitch change increases by addition. In any case, the relationship is non-linear,

as you can clearly see if you plot frequencies against octaves, as shown in Figure 4.7.

Figure 4.7 Non-linear nature of pitch perception

The fact that this is a non-linear relationship implies that the higher up you go in

frequencies, the bigger the difference in frequency between neighboring octaves. The difference

between A2 and A1 is 110 – 55 = 55 Hz while the difference between A7 and A6 is 3520 – 1760

= 1760 Hz. Because of the non-linearity of our perception, frequency response graphs often

show the frequency axis on a logarithmic scale, or you're given a choice between a linear and a

logarithmic scale, as shown in Figure 4.8. Notice that you can select or deselect "linear" in the

upper left hand corner. In the figure on the right, the distance between 10 and 100 Hz on the

horizontal axis is the same as the distance between 100 and 1000, which is the same as 1000 and

10000. This is more in keeping with how our perception of the pitch changes as the frequencies

get higher. You should always pay attention to the scale of the frequency axis in graphs such as

this.