Alternative Tuning and How We Hear
The waveform generated by a bell is aperiodic.
There are a bunch of non-harmonic partials, and if you listen closely, you often can hear a low "hum tone" that seems to bear no relationship to the fundamental.
The fact that people can attribute a definite pitch to a bell is somewhat mysterious.
Not all bells are that way; some produce a non-melodic clank that can really only be used for percussive effects at best.
The reason seems to be that a well-crafted bell produces a few partials that fit the human brain's harmony template.
The brain then believes that the fundamental is present when in fact it is not.
The other partials that don't really fit the template are of low enough amplitude or are far enough away in frequency that the mind ignores them - they instead become part of the quality of the sound, rather than a contributor to the pitch.
Here is a list of partials for a bell (from The Science of Musical Sound.)
| 1st | 2nd | imagined! | 3rd | 4th | 5th | 6th | 7th |
| the actual partials | 1 | 2.76 | not
present | 5.40 | 8.93 | 13.34 | 18.64 | 31.87 |
how the mind
perceives them | ignored
(hum tone) | ignored | 4.5 | ignored | 2 * 4.47 | 3 * 4.45 | 4 * 4.66 | 7 * 4.55 |
Give it a listen.
The mind imagines there is a fundamental at 4.5 times the true fundamental frequency, where in fact no such partial exists.
The extra true fundamental is perceived as the "hum tone". The second and third partials are also ignored.
Since bell-like tones are "messy," in that they contain lots of non-harmonic partials, they usually cannot be combined to play chords.
It think this is because there are so many non-harmonic partials that the brain can't strongly match any templates in all the clutter.
Listen to these three bell tones separately:
listen to C
listen to E
listen to G
and now listen to them combined into a chord:
listen to CEG.
And yet it may be possible to build wind chimes with
barbershop 7th chords.
This document is ©2003 by Bill Grundmann.
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