Alternative Tuning and How We Hear
Alternative Tuning and How We Hear
You can hear this effect when a plane is flying overhead. Just crouch down and stand back up. While you are moving, you will hear the characteristic sweep of phase shifting. The plane's sound goes directly into your ears and is mixed with the sound that reflects off the ground first. By crouching, you change the distance from the ground, and so change the delay.
The effect can arise if multiple microphones are mixed together and one or more of the microphones are moving. (It shows up on television or movies occasionally if someone messed up the mix.) It can be heard while walking past multiple loudspeakers too. The effect can happen any time that sounds are delayed and mixed.
Sound propagates through air at about 1000 feet per second. That translates to about 1 foot in 1/1000 second. Short times like this are usually expressed in mS (or milliseconds, 1/1000 of a second). Imagine there is a wall 3 feet from your right ear, and sounds are coming from your left. The sound directly enters your left ear. Some of the sound can bend around your head and enter your right ear after a delay of roughly 1 mS, because the distance is roughly a foot from ear to ear. Only low frequencies can bend this sharply. The higher frequencies travel on to the wall, bounce off and then enter your right ear. The total extra distance is roughly 1+3+3 or 7 feet. This is 7 mS of delay.
This is not the same sort of delay that your brain uses for stereoscopic sound location. That delay is some fraction of the transit time around your head, which is something less than 1 mS.
I believe the brain uses this information to help you understand that there is a wall 3 feet away to the right. It adds to what your eyes tell you is there, and I think in some cases, it can allow you to acoustically "see behind your back." The effect is strongest when the reflecting surface moves relative to your ears, as would happen if an object is approaching you. This is a strong benefit that evolution might have selected for.
Why am I mentioning all this? Because the process of delaying a sound 7 ms and mixing it with the original is precisely the "phase shift" effect. I think the brain is attuned to this phenomenon and uses it the glean information about the surroundings. It can help warn of the approach of an unseen object, and reinforce one's sense of position in one's surroundings. Recognition of this phenomenon is a template matching process. This idea is discussed further in the section on partials.
The graph shows the transfer function of a comb filter.
This is a way of describing how a sound is modified by a device such as a comb filter.
The frequencies where the graph is high are enhanced and get through, the frequencies where the graph is low are blocked or diminished.
The reason it does this is because of cancellation and reinforcement.
If you take a sine wave and delay it by exactly 1/2 its period, you will find that it has been "flipped" upside-down.
If you add it to the original sine wave, each point exactly cancels out to zero.
The same thing happens if you delay the sine wave by 3/2 of its period, or 5/2, 7/2, etc.
If you take a sine wave and delay it by exactly 2/2 its period, you will find that it is the same as the original.
If you add it to the original sine wave, each point exactly doubles.
The same thing happens if you delay the sine wave by 4/2 of its period, or 6/2, 8/2, etc.
By taking a sound and adding a delayed version of it to itself, certain partials are cancelled.
If 1/2, 3/2, 5/2, 7/2, etc. of the partial's period is equal to the delay, it is cancelled.
Other partials are enhanced.
If 2/2, 4/2, 6/2, 8/2, etc. of the partial's period is equal to the delay, it is reinforced.
For example, if the delay is 10 mS, a partial having a frequency of 50 Hz would be cancelled.
Its period is 20 mS, 1/2 of that is 10 mS.
A partial at 100 Hz would be reinforced.
Its period is 10 mS, 2/2 of that is 10 mS.
A partial at 150 Hz would also be cancelled.
Its period is 6.66 mS, 3/2 of that is 10 mS.
A partial at 200 Hz would also be reinforced.
Its period is 5 mS, 4/2 of that is 10 mS.
A partial at 250 Hz would also be cancelled.
Its period is 4 mS, 5/2 of that is 10 mS.
The section on partials discusses the idea of templates in more detail.
For pure sine waves, separations beyond this amount sound smooth.
But for complex waves, more effects begin to appear.
This document is ©2003 by Bill Grundmann.
RELATION TO HARMONICS
The pattern of reinforcement and cancellation creates artificial partials from a sound with many frequencies present.
These partials exactly match the pattern of the template that the brain uses to identify fundamental frequencies.
This is why the phase shift effect seems to impose a strong pitch on the sound that goes through it.
As the delay is changed, the artificial partials move in a way that is consistent with a fundamental moving in pitch.
TWO SOMEWHAT SIMILAR TONES
As we increase the frequency difference between two tones, the phase shifting effect becomes so fast that it is imperceptible.
A new effect is perceived instead.
BEAT FREQUENCY
We hear the average of the two tones' frequencies and a new low frequency pitch appears.
This beat frequency is the difference between the two tones' frequencies.
I believe this may be a mode where the cilia of the inner ear are reporting volume changes (the beat) of one frequency (the average).
CRITICAL BANDWIDTH
As we further increase the frequency difference between two tones, an unpleasant, coarse sound is perceived.
I believe this may be the transition point where the cilia of the inner ear are switching to the mode of reporting two separate frequencies.
TWO SOMEWHAT DIFFERENT TONES
We've now separated the frequencies enough that the human ear is detecting two different notes happening together.
At this point there are many possible intervals.
They all seem to have musical meaning and usefulness.
INTERVALS
Some intervals sound better than others.
People long ago recognized unison and octave intervals as being very pleasant and very stable.
The fifth and fourth soon enjoyed a similar importance.
The fourth is commonly perceived as being less stable than the fifth, although I suspect that may be more of a convention (in many musical styles the fourth is supposed to resolve to the third).
The third also plays an important role, but this is apparently fairly recent in musical history, and I suspect it may be a somewhat artificial convention too.
WHOLE NUMBER RATIOS
People have noted that the frequency ratios of the important, more stable intervals seem to be dictated by small whole number fractions.
I think this was an empirical observation that didn't have any particularly good explanation on its own.
Numerology notwithstanding.
TWO VERY DIFFERENT TONES
If tones are several octaves apart, it seems that pretty much anything goes.
Usually there needs to be something filling in the space between them to constrain them in any strong way.
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