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    When listening to music, there are several aspects that one can glean from the experience. There is the melody, which is most payed attention to. There is also the harmony. There may also be the isolation of the rythm. Or in the case of songs, the words. In certain cases however, there may be a focusing of ones attention to a particular instrument.

    Occasionally I pay attention to the way a particular instrument is being played in a certain piece of music. I notice how the notes the instrument is being played to follow works either in contrast or in concert with the rest of the instruments. I note (no pun intended) how it has its own individuality while contributing to the theme as a whole. It is fascinating to hear such combinations of individuality making the whole, since it speaks of the genius that was the composer. How he could make so many separate minor variations come into the greater whole of a symphony is one of the most awe inspiring aspects of music, its connections to mathematics and physics and psychology notwithstanding. It seems as though musical composers have an intrinsic knowledge of Chaos theory and fractals.

    In order to fully appreciate the affect of music and audio on the human psyche, one needs to appreciate at least in a basic way the composition of sound and how we interpret the difference between a musical sound and noise. Pythagorus had been the first to document the discovery of harmonics. He postulated that a string on a harp could be made to produce not only its fundamental note but whole integer multiples of it by pressing on a part of the string corresponding to the length divided by the whole number integer. For instance, if one were to press on the string in the center, then pluck one half, the string would vibrate at twice the frequency of the fundamntal.

    Several millenia later Fourier made up a few formulae to show that complex waves could be broken down into multiple sine waves that were summed together. It is this transform formula that is at the heart of today's audio analyzers. It can be shown that musical instruments make harmonics and with a particular pattern.

    Typically, a musical note consists of the fundamental frequency, the one we usually hear as the note's pitch, and harmonics, the composition of which we discern as the tone's timbre (pronounced TAHM-ber). What I mean by this is that the harmonics can vary in amplitude and quantity. The amplitude of the harmonics is what is most noticeable by our ears followed by number. Our ears can only discern up to seven harmonics, though. By this I mean that if I were to remove the harmonics of a tone, which theoretically can go to infinity, I could get down to the seventh one before you would start noticing a change in the sound of the tone. Also, if I start to change the amplitude, or loudness, of the harmonics, you would begin to notice this very easily (The Psychology of Music - Diana Deutsch).

    It is the patern of the amplitude of the harmonics I wish to address here. Looking at the chart below one can see what the typical theoretical pattern is:


    The F, F1, F2 etc. represents the fundamental frequency and the harmonics. This is the fundamental frequency multiplied by 1,2,3, etc. respectively. The vertical bar represents the relative amplitudes of a typical tone. There are varieties based on the instrument being used, but this is merely a representation. The point here is to recognize a pattern. Any variation of the pattern of harmonics, say to non-whole integer multiples (for instance 1.2 times the fundamental, 2.3 times, 3.1 times, 3.8 times etc) would result not in a musical tone but in a noise or a sound from another source.

    One can now easily see that changing the amplitude of any of the harmonics could make it sound different to us. The difference between an "A" from a guitar and one from a horn is merely the amplitude levels of the harmonics, since only seven of them can be discerned by our ears.

    Before we get further into the implications of this, however, I would like to introduce a fact of nature on earth. There is a condition of the earth that in essence makes it an instrument in its own right. Between the ground and the ionosphere, there is a cavity, our atmoshpere. The ionosphere and the ground are electrically and magnetically conductive. The atmosphere in between creates a cavity. Like any cavity in a structure, there exists a resonance. Helmholtz had demonstrated this with his resonator. You can demonstrate this by blowing across the opening of an empty bottle. Although the previous examples are acoustic resonances, the princile applies. This cavity between the earth and ionosphere have electromagnetic resonance frequencies. They are now known as the Schumann Resonances. The fundamental frequency is about 8 hertz and as the frequencies increase, the amplitude decreases. The following chart shows the relationship:


    As one can see, there seems to be a coincidence in the pattern of the resonances and the tone of a musical instrument. But there is more.

    According to at least one source, the EEG pattern of the brain resembles the charts of the Schumann Resonances. Interesting to note also is that the fundamental frequency is within the frequency range of a mental state known as the Alpha state, where the frequency of our brain is anywhere between 7 and 12 Hertz.

    It would seem reasonable that our brains, electromagnetic in nature, would be shaped and influenced by the earth's magnetic field resonances, and should resemble the same.

    Here is another interesting fact. The Triode tube has a harmonics distortion pattern similar to both the Schumann Resonances and a musical tone. Tube amplifiers, particularly those made exclusively with triodes and such circuitry design that does not minimize distortion, is most pleasing to the listener. It is said to be most "musical". Interestingly, audiophiles that listen to tube amplifiers that produce a large amount of distortion (up to 10%) claimthat the sound had worsened when the distortion product has been minimized.

    Solid state amplifiers have a pattern where every other harmonic is strong, where the others are weak. That is, all the odd harmoncis are strong and the even ones are weaker. So there is no longer a proportional decrease but a jagged one, as can be seen by the following chart:

    As can be seen here, the odd harmonics dominate (represented by the F2, F4, F6, which are the third, fifth, and seventh harmonics respectively, the fundamental being considered the first harmonic). Even with the reduction of these harmonics by distortion reduction techniques, the sound of solid state amplifiers is slightly different when compared to a tube amplifier of similar distorition reduction characteristics.
    The conclusion one can reach here therefore is that anything that displays the pattern of the Shumann Resonances of the earth will be regarded by us as being music. Anything that displays this pattern as a reproductive device will be considered as sounding best, or musical.

    This is why, in my opinion, we made music what it is, and why many audiophiles prefer tube amplifiers over transistor amplifiers.

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Copyright 1998, Gabriel Velez III