Digital Sound & Music: Concepts, Applications, & Science, Chapter 2, last updated 6/25/2013

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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

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Tutorial:

Non-

Sinusoidal

Waves

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

frequency components.