# Introduction to Computer Music: Volume One

### 8. What is phase?

Phase denotes a particular point in the cycle of a waveform, measured as an angle in degrees. It is normally not an audible characteristic of a single wave (but can be when we use very low-frequency waves as controls in synthesis). Phase is a very important factor in the interaction of one wave with another, either acoustically or electronically.

The Flash example below traces a sine wave by plotting the height of the tip of a spoke (or radius) of a rotating wheel (y-axis) against time (x-axis). The height of the spoke-tip corresponds to the waveform's relative amplitude, here plotted between an imaginary +1 to -1. To measure the phase angle, we start with the reference of the spoke pointing completly to the right and refer to that as 0º, with a relative height or amplitude of 0 as well. As the wheel rotates couterclockwise, the sine wave reaches its peak positive amplitude when the spoke has traveled 90º from its starting point (click on the 90º button), with a relative amplitude of +1. At 180º from the starting point, the amplitude of the sine wave has returned to 0 (click on the 180º button). At 270º, the sine wave reaches its peak negative amplitude of -1 (click on the 270º button) and then returns to 0 as it returns to its starting point of 360º or 0º.1

Another common sinusoidal waveform used in synthesis or measurement is the cosine wave, which is exactly the same shape as a sine wave and would sound exactly the same all by itself, but is distinguished by the fact that its cycle begins 90° out of phase to a sine wave, or at +1.

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1 Dodge p. 29-32

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