Joe's Blog

Advantages of hearing over seeing.

October 17, 2018

The miracle of the octave, and the richness and variety of structure in music:

In the domain of colors, red is very close to violet in appearance.   Similarly, in the domain of sound, two notes that are exactly one octave apart bear resemble each other more closely that any other two distinct pitches.  The only interval that can sound more similar  is the perfect unison, when two strings, instruments or voices sound at the same pitch.

If we relate these two similarities to the frequencies of the light waves on the one hand and the sound waves on the other hand, it turns that violet as about twice the frequency of red, and the note an octave higher than a second note has twice the frequency of the lower note in the octave.

Is this a coincidence?  We are often too tempted to make comparisons between a physical cause of a sensation with the way we experience that sensation in our consciousness.  Certainly, when we look at red and violet side by side, the number 2.0 (two times) does not occur to us as being relevant to what we are seeing.   When we hear consonance of the octave in our consciousness,  as in the case of the other sense, the number two does leap to mind.

However, just to indulge myself, I would like to conjecture further about this coincidence.  The spectrum of sound frequencies includes many octaves: about seven octaves on a piano, and basically an unlimited  umber of octaves in principle, only we cannot hear most of those.  The electromagnetic spectrum of frequencies, which includes visible light and colors, has many more “octaves” of frequencies as well, except that we cannot see them with our eyes.

At the “high” end of the visible spectrum, the frequency of light wave causing us to see violet is almost twice that of red, red notably being approximately at the extreme low end of the visible spectrum.  Unfortunately we cannot see “colors” when they are higher than violet or lower than red.

What if we could see other octaves-worth of visible light?  What would these new colors look like to us, and perhaps more interestingly, if there were, would the ‘color’ of ‘light’ we experience that has twice the frequency of violet, resemble violet in a way how violet resembles red.

Perhaps in our galaxy there are creates who could answer this question for us.  Meanwhile, I just have an analogy between the senses, and it only holds for one octave.

However, there is magic enough in the phenomenon of just the octave in sound:

For instance, with colors and light, we cannot see, at the same time, two different colors as well as automatically also seeing the third color that represents the mixture of both.   Of course there is such a third color, but it doesn’t spring to life automatically, we would have another splotch of color separate in space, a third one, next to the original two.

Let’s compare this with sound.  When we hear two sounds at once, we are aware of two very different types of things, both at the same time:

#1

That there are two distinct sounds, and each one, if we concentrate, can be heard “separately” (as if it were ‘alone’ and apart from the other.  Except not alone in space, but simultaneously in time.   With colors, we can only see two different colors, if they are in different places in space in our visible field.

#2

The other, which is also true of sound but not of sight, is that at the same time that we can hear two sounds, we can hear something else that is neither the one sound or the other, but a new an unique sound quality that is the result of the combination of both.  And this isn’t limited to two sounds an octave apart, but of any number sounds, at any distances apart from each other*.

In fact, music seems to be the only art that has been created by homo sapiens that is in time alone but is richer for that reason.

Summary:

The octave is a miracle.  It is a  pristine example of something that is equally the same as, and yet equally different than, something else.

As much as space may have the seeming advantage of three dimensions while time may have no dimensions whatsoever (or some say just ‘one’ dimension), time, hearing, and music have an advantage over space.   If we consider the possible of forms in structure that exist for the composer, we find that, because of the phenomenon of ‘octave’, its forms can be more endlessly evolved, forms that are both various and complex, and with more emergent forms** arising out of it, than any art.

* … at least until the frequencies of the sounds become too close together, at which point the separate sounds become inseparable to the ear and we are left just with the effect of their combination.  A Perfect example is “white noise” when it is composed at the same time of many different frequencies and those frequencies are “spaced” close together.

** Wikipedia’s (cc) article on emergence begins with these words: “emergence occurs when “the whole is greater than the sum of the parts.”

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