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Psychoacoustics, we hope you'll remember this word,
is founded on the basic observation that the human auditory
system and other species' auditory systems exhibit tonotopicity.
Tonotopicity is a frequency to place mapping in the cochlea.
That means that a given frequency is going to have a sweet spot on the basilar membrane,
where that particular frequency reaches the height of
its activity as a traveling wave is carried down the basilar membrane.
The hair cell that is sitting at that particular sweet spot,
let's go ahead and call it 1K,
the hair cell that's at the 1K spot,
is going to be the hair cell that will be most sensitive to one kilohertz.
It's going to be activated to other frequencies.
If it's little neighbor over there,
is most sensitive to 1.1K,
the 1K hair cell is going to have some activity going on,
but his neighbor's going to have more activity.
This tonotopicity helps explain theories of pitch perception.
It also helps explain the origin of consonance and dissonance,
musical consonance and dissonance,
also called cognitive consonance and dissonance,
is based on tonal music systems and it's based on theory.
Small integer ratio dyads,
meaning two simultaneous frequencies
whose relationship can be described by small integers such as a one to two ratio,
two to three ratio,
a three to four ratio,
and I just described the octave,
the perfect fifth, the perfect fourth.
Those small integer ratio dyads to simultaneous tones are
regarded by most listeners to be harmonious and pleasant.
In Western tonal music theory,
they would be called consonant.
But consonance and dissonance also have a sensory origin.
When two frequencies are very closely spaced,
we say that it's impossible to resolve those two frequency components,
meaning that you cannot hear them apart.
If we were to play simultaneously 1,000 hertz plus 1,004 hertz,
the resulting wave would look like this.
There'd be two fine components,
1,000 hertz and 1,004 hertz,
we cannot hear those apart,
because our auditory system can't resolve those components.
Think of it like two colors that are so closely spaced,
it's very difficult to see them apart.
But what's of interest to us in psychoacoustics,
is their difference product.
The difference product is four hertz,
they're separated by four hertz.
So, this wave is going to have,
on its temporal envelope,
it's going to have an amplitude modulation at around four hertz,
and we're going to perceive,
we can't hear four hertz,
it's below a perception,
but we're going to perceive [NOISE] this beating tone.
It explains why minor seconds, major seconds,
and some minor thirds are considered more
dissonant than consonant because of that byproduct, that beating.
Beating goes up to about 15 hertz or
20 hertz or so depending on which researchers work you're reading,
the higher frequencies from about 20 hertz to
about 150 or 200 hertz are also perceptible,
but they're harder to perceive,
and they are called roughness.
Roughness components helps to explain why a tritone was once called the devil's chord,
diabolus in musica, it's the devil.
It's the devil in part because it's difficult to sing as I understand,
but also because the math that explains the frequency ratio relationship between
the two tones that together form
a tritone dyad is described in adjust tuning system by the numbers 32 and 45,
unlike a nice octave,
the one to two ratio,
the 32 to 45 ratio is describing two tones, complex tones,
let's say, that have partials harmonic overtones that are rather closely separated,
and what that gives rise to is a very slight,
but obvious sensation of roughness that [NOISE],
the really fast amplitude modulations.
You can think of it in another modality,
the modality of touch.
An octave would be running your fingers across silk,
minor second would be running your fingers across corduroy,
really thick corduroy where you can feel the bumps [NOISE].
Roughness would be like running your fingers across denim.
Denim jeans is obviously rougher than silk,
harder to detect on your fingertips.
So, think of the tritone like jeans,
the octave like silk,
minor second like corduroy.
I hope that helps rather than confuses.
But, the basic principle of this auditory filtering,
the fact that when two frequencies are closely separated within a certain bandwidth,
they will interact with one another,
is the dominant theory that helps explain psychoacoustics.
So, please remember the words tonotopicity, auditory filtering,
critical band, and the origins of consonance and dissonance.
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