Distortion Caused by Too Much Mic Gain - Can This Be Removed

[brianejsmith]

OK. Now that's settled can I address one thing I have never understood about sound?

Pure sound - like the concert hall "take your seats" A - is pretty uninteresting and the ear is drawn to harmonies (and unresolved sequences like the leading 7th).

Harmony means more than one frequency being played or heard at the same time but I've never understood how this can be.

The ear and a loudspeaker cone are single planar (2 dimensional effectively) surfaces and can only vibrate at a single freqency at a time otherwise they would tear or break up. A magnet driving a loudspeaker can only resonate at a single frequency at a time so how do we get harmonies?

Is it an illusion where each frequency we detect in fact follows the preceding one at millisecond intervals and the brain adds them together? A bit like sampling say, where so many samples are taken and then "played back" all at once fooling the brain into thinking they've been played together?

(If sound does indeed work like this then clipping should be removable by finding the right samples to get rid off?)

If the multiple frequencies are really heard simultaneously how does that work? Wouldn't they just add up to a different frequency? And physically, how can a microphone diaphram, an ear drum or a loudspeaker vibrate at multiple frequencies at the same time without as I say tearing or breaking up?

When I look at the sound trace in Audacity I see a horizontal sequence of spikes of varying heights which I think represent amplitude or volume or sound pressure? I know that within each spike there appears to be a number of frequencies which my ear hears simultaneoulsy giving the harmonic effect humans find so pleasing. But how does it happen?

This has troubled me since school days and physics classes. It would be nice to get an answer.

[steve]

The ear and a loudspeaker cone are single planar (2 dimensional effectively) surfaces and can only vibrate at a single freqency at a time otherwise they would tear or break up. A magnet driving a loudspeaker can only resonate at a single frequency at a time so how do we get harmonies?

The eardrum is essentially 2 dimensional planar, but the inner ear is a complex 3 dimensional form. http://en.wikipedia.org/wiki/Eardrum

A loudspeaker cone does not, or should not vibrate at its resonant frequency. For a well designed loudspeaker the resonant frequency of the speaker cone will be below the operating range of the speaker. Using various mechanisms, the speaker unit is "damped" to prevent the cone from resonating at its primary resonant frequency - this is important to prevent the speaker from "booming" at the resonant frequency.

Rather than "resonating", the speaker is designed to "follow" as accurately as possible the signal that is driving it, which is usually not a single frequency, but a complex waveform made up of many frequencies superimposed on each other. Similarly the eardrum "follows" the complex waveform that is transmitted through the air.

The eardrum is coupled to the inner ear, where tuned receptors called "hair cells" within the cochlea respond to the multiple frequencies within the sound and send signals through the auditory nerve to the brain, where "hearing" occurs.

[brianejsmith]

It's the "complex waveform made up of many frequencies superimposed on each other" bit I don't understand.

How can a single physical device - like an eardrum or loudspeaker - vibrate at several frequencies, all at the same time?

If the frequencies occur at the identical same moment why don't they just add up to another frequency?

If we could see the wave form there would be a single moving crest not lots of different crests all moving at the same time?

There are billions of molecules in air so I can understand multiple streams of them arriving at the ear drum or microphone diaphram each stream resonating separately at a different frequency.

But why don't they bump into each other and knock each other off frequency?

I assume that the vocal chords can only vibrate at a single frequency at any given moment but the note they produce is then corrupted by the various cavities and physical structures in the body which produces a mix of frequencies.

These frequencies will be supportive because they all came from/are variations on the original pure note or single frequency but when other voices and instruments are added we must surely end up with lots of vibrating molecule streams all banging into each other?

And, and this is the crux of my non-understanding, how then does a single physical surface capture or reproduce them (the ones that survive)?

[steve]

You're asking difficult questions, but I'll do my best to explain

When we talk about a "frequency", we are referring to a simple oscillating "cycle" known as a "sine tone". The "Tone Generator" in the Audacity Generate menu creates "sine tones" by default. If you generate a sine tone and zoom in close on it you will see something like this:

firsttrack000.png (7.66 KiB) Viewed 678 times

In the "Analyze" menu there is a tool called "Plot Spectrum".
With the "Axis" set to "Log Frequency" you should see something like this:

sine-tone.png (40.68 KiB) Viewed 678 times

The "spike" indicates the single tone frequency. Theoretically it should just be a single vertical line, but due to limitations of the frequency analysis the spike appears to spread out at the bottom - that is just a limitation of the tool - with a bit of tweaking of the Spectrum settings you can get a more accurate plot. This is the same audio, but it shows the single frequency a bit more accurately:

sine-tone-better-plot.png (41.41 KiB) Viewed 678 times

Now try generating a "Square No Alias" tone.
Select the Tone Generator and in the "Waveform" selection choose "Square No Alias".
Play the tone and you will hear that it sounds much "harsher" than the Sine tone, though the "note" (the fundamental frequency) is the same (by default it is 440 Hz "A".)

Zoom in close and you will see that the shape of the waveform is quite different - it looks "square":

firsttrack001.png (7.01 KiB) Viewed 678 times

Why does it sound so different, but still the same "note"?
If we look at "Plot Spectrum" we can see that the "fundamental" frequency (the biggest, lowest spike) is the same frequency as for the sine tone, but there are many other frequencies present also. These other frequencies are "harmonics" and give the sound its different timbre.

square-tone.png (42.21 KiB) Viewed 678 times

Does that help at all?

[brianejsmith]

That's a lot of work; really appreciate it.

But doesn't it just confirm that the sounds we typically hear in music are made up up of lots of frequencies combining somehow? Which is my starting point.

If in a single heard or listened to instant there are multiple frequencies generated each carried on their own resonating or vibrating stream of molecules how does a single solid surface like a loudspeaker cone reproduce them?

I understand about the hairs in the ear touching, or almost, the eardrum, each one tuned to a different set of frequencies but the ear drum has to (re)produce those different frequencies to make the individual hairs react. How does it do that? All at the same time?

How does one, solid microphone diaphram send the electrical equivalent of multiple streams of vibrating air molecules down a single wire? At the same time?

[steve]

The loudspeaker / eardrum are not responding to multiple separate streams, but to the combined effect of those frequencies, so they are responding to the waveform (as shown graphically in the track) rather than to the individual frequencies (as shown in the spectrum).
In the inner ear, the hair cells respond to the individual frequencies (as shown in the spectrum) with different hair cells "tuned" to respond to different frequencies.