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Fusion

Pitch and the perception of harmonic, nearly harmonic and inharmonic spectra.

by REGINALD BAIN

Fusion
"This processes by which the brain combines a previously analyzed set of pure tones into a sound with only one pitch is known as fusion."

"A set of pure tones fuse into a single pitch only if they are members of a harmonic series (or a close approximation)."

Murray Campbell and Clive Greated
The Musician's Guide to Acoustics
The QuickTime animation in Fig. 1 displays three closely-related complex tones made from six pure tone components (all with equal amplitudes). The exact frequency relationships are shown in blue superimposed on the musical staff. Notice how each of the frequency components in the first complex tone are odd members of a harmonic series on C2 (partials 3-13). Now play the animation. Listen to how the pure tone components in the first and second complex tones seem to fuse together to produce a single sense of pitch at the 'missing fundamental' pitch. By contrast, the pure tone components in the third complex tone does not produce a sense of a single pitch, all six frequency components can be heard. Using the series notation introduced in the first section of the harmonic series article, we can represent the frequency relationships between the tone components is shown below in Fig. 2.
Fig. 1. Three general classes of spectra: 1. harmonic, 2. nearly harmonic, and 3. inharmonic

Fig. 2. Equivalent series notation for the three tones in Fig. 1
Spectral TypeSeries Notation
Tone 1Harmonicf0, 3 f0, 5 f0, 7 f0, 9 f0, 11 f0, 13 f0,
Tone 2Nearly-harmonicf0, 2.9 f0, 5.1 f0, 6.9 f0, 9.1 f0, 10.9 f0, 13.1 f0,
Tone 3Inharmonicf0, 2.7 f0, 5.4 f0, 7.3 f0, 8.8 f0, 11.3 f0, 12.6 f0,

Updated: September 17, 2002

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