Digital Sound & Music: Concepts, Applications, & Science, Chapter 2, last updated 6/25/2013
frequency components in the next second. The upshot of this fact is that for complex non-
periodic sounds, you have to analyze frequencies over a specified time period, called a window.
When you ask your sound analysis software to provide a frequency analysis, you have to set the
window size. The window size in Adobe Audition‟s frequency analysis view is called “FFT
size.” In the examples above, the window size is set to 65536, indicating that the analysis is
done over a span of 65,536 audio samples. The meaning of this window size is explained in
more detail in Chapter 7. What is important to know at this point is that there‟s a tradeoff
between choosing a large window and a small one. A larger window gives higher resolution
across the frequency spectrum – breaking down the spectrum into smaller bands – but the
disadvantage is that it “blurs” its analysis of the constantly changing frequencies across a larger
span of time. A smaller window focuses on what the frequency components are in a more
precise, short frame of time, but it doesn‟t yield as many frequency bands in its analysis.
2.2.4 Frequency Components of Non-Sinusoidal Waves
In Section 2.1.3, we categorized waves by the relationship between the direction of the medium‟s
movement and the direction of the wave‟s propagation. Another useful way to categorize waves
is by their shape – square, sawtooth, and triangle, for example. These waves are easily described
in mathematical terms and can be constructed artificially by adding certain
harmonic frequency components in the right proportions. You may encounter
square, sawtooth, and triangle waves in your work with software synthesizers.
Although these waves are non-sinusoidal – i.e., they don‟t take the shape of a
perfect sine wave – they still can be manipulated and played as sound waves, and
they‟re useful in simulating the sounds of musical instruments.
A square wave rises and falls regularly between two levels (Figure 2.20,
left). A sawtooth wave rises and falls at an angle, like the teeth of a saw (Figure
2.20, center). A triangle wave rises and falls in a slope in the shape of a triangle
(Figure 2.20, right). Square waves create a hollow sound that can be adapted to
resemble wind instruments. Sawtooth waves can be the basis for the synthesis of violin sounds.
A triangle wave sounds very similar to a perfect sine wave, but with more body and depth,
making it suitable for simulating a flute or trumpet. The suitability of these waves to simulate
particular instruments varies according to the ways in which they are modulated and combined.
Figure 2.20 Square, sawtooth, and triangle waves
Non-sinusoidal waves can be generated by
computer-based tools – for example, Reason or Logic,
which have built-in synthesizers for simulating musical
instruments. Mathematically, non-sinusoidal waveforms
are constructed by adding or subtracting harmonic
frequencies in various patterns. A perfect square wave, for
0 5 10 15 20 25 30
0 5 10 15 20 25 30
0 1 2 3 4 5 6 7 8 9 10
Aside: If you add the even
numbered frequencies, you still
get a sawtooth wave, but with
double the frequency compared
to the sawtooth wave with all