Harmonic - Understanding Resonance

By Richard Merrick

What is Resonance?

Example: Acoustical resonance of different frequencies in a cello.
Resonance Cello

1. A phenomenon of reflected energy
2. Always occurs inside some kind of container
3. Has a prime resonant frequency
4. Represented as squared magnitudes (E=mc2)
5. Responsible for all coherence in nature
6. Universal to ALL types of waves (air, water, electricity, light, atoms, plasma, etc.)

Neural Resonance

Resonance Brain

• Holonomic brain theory (Karl Pribram, David Bohm)
'Cognitive function is guided by a matrix of neurological wave interference patterns.'
• Harmonic resonance theory (Steven Lehar)
'Spatial patterns in perception and behavior are mediated by spatial standing waves in neural tissue.'

What is a Standing Wave?

As waves reflect in a container, the prime resonant frequency reflects back on itself (adding and subtracting in opposition) to create a stationary oscillating wave pattern. Similarly, all interference patterns are composed of standing waves that are similarly stable and stationary as well.

Resonance Container

As a standing wave forms, additional waves can form in the same medium. These waves are called 'harmonics,' 'wave partials' or in music 'overtones.' Harmonic partials to the standing wave are not random frequencies, but instead whole number multiples (1x, 2x, 3x, … nx) of the prime resonant frequency. This is called the harmonic series.

Resonance Harmonics

This is what the harmonic series looks like when both opposing phases of interference are superimposed at a constant energy level or amplitude. Notice the stable pattern it creates and the gaps that form around the nodes and other locations. This is universal to all kinds of waves as they 'resonate' inside some container.

Question is, what causes standing waves to form in such a regular pattern? What is the underlying physics that prevents fractional or enharmonic waves from forming on the prime resonant frequency?

Further Reading

Interference - A Grand Scientific Musical Theory
, By Richard Merrick

Content courtesy of Richard Merrick
Copyright (c) 2011. All Rights Reserved.

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