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PostPosted: Wed Jun 20, 2007 6:41 pm 

Joined: Sun Mar 27, 2005 12:45 am
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Location: Ithaca, NY
Twelve Tone Music: The Coin of Music: A Response from Mark Gould: A Composer’s Journal Entry May 26, 2007


Received this e-mail from Mark today. To give a bit of background: Mark had written, in our previous discussion on twelve tone music, "You mention the increase of tonal elements in your own work. I believe that this is entirely natural - I don't think there is any distinction - merely that these two dissimilar methods are opposite sides of the same coin." I had answered, “ As for both methods being opposite sides of the same coin: I am not sure that I would put it that way, but it is a good image. Are you putting the overtone series as the coin? And that composers then can choose how to use the natural laws of sound of this earth, choose which side of the coin to use in their music - i.e. tonal or atonal, atonal or serial, bitonal or polytonal etc.?” Here is Mark’s response and my comments to him:

Mark: Hello Laurie!

the coin of music....

As you know I studied Acoustics at university, and also continued my interest in microtonal music. As part of my studies, I was constantly reminded of the mathematics involved in sound. This mathematics was always of one form: that some kind of oscillation was set up by allowing the energy in an elastic object to be stored by tensing it and then releasing it - the plucked string, the compressed column of air in a pipe. Like a swing, this energy moved from being potential - tensed, to moving - kinetic. As the swing passes through the low point, the kinetic energy gets transferred to potential, until there is no kinetic left. At this point the oscillation repeats, due to the tensing of the medium - string or air moving to release. Thus they counterbalance one another until friction or other losses drain the oscillation of energy, and the oscillation ceases.

All this physics was repeatedly taught to me. All music is based on the mathematics behind an 'elastic' medium and its ability to store and release energy. Every elastic system is capable of oscillation, and often the mathematics states that there are different modes of oscillation. For strings and pipes these modes occur at whole number multiples of the mode with the lowest frequency (pitch).

And so we have harmonic series. For gongs, plates of metal, xylophones, vibraphones and all instruments of this type their modes of oscillation do not occur at whole number multiples of the lowest frequency, and are called 'inharmonic'. Of course the physics of a harp or piano or violin string are not perfect - even they are 'inharmonic', as they drift slightly from the perfect elastic string. So the real world is imperfect, that the mathematics indicates that sounds in this corporeal world are imperfect.

And so it goes. For western music, the harmonic series is king, it governs the generation of temperament in terms of the favoured intervals that a pitch-system must have - hence historical concentration on temperaments with 12, 19, 31 and 53 notes. But in the Eastern world there is a different emphasis. It has often been stated that such music is pentatonic, and therefore backward in some way, but that is because the emphasis is on the intricacy of the melody not the subtlety of the harmonic variety. But also the oriental mind is set upon sounds that the western ear has only used in one context - that of the bell. Bells are notoriously inharmonic. The casting of bells is a complex and refined process, as is their grinding to produce a clear and ringing tone. Why base a music on the harmonic series and employ inharmonic instruments to realise it?

But in the west, our twelve notes, being the approximation of the harmonic series - up to a point - means that the combinations of tones will perpetually be extracts and small sections of the harmonic series - at every point the combinations of tones are in some way the upper elements of fundamentals located far in the bass.

Therefore, whether we choose tonality or twelve note methods, these fundamentals sound in our minds, and perhaps in twelve note music they lie far lower than in tonal music, so low as to be perceptually inaudible - as if the music has moved up the harmonic series in some way. And once these fundamentals disappear from our perception, so does tonality.

LC: A beautifully written and very interesting discussion, dear Mark. I had never considered that the fundamental tone might be lower in twelve tone music, and inaudible. I had always thought about it a bit differently: that the chromatics we twelve tone composers use are so high up in the overtone series (before they manifest) that many of them are inaudible to us. Therefore, in a way, the twelve tones we serial composers use for establishing our row manifest in a more transparent, spiritual realm - because the chromatics are so high in the overtone series.

Mark: The return to tonality spoken of by many composers is a perhaps a product of the modern world - and it is strange that in this age of reproducing media - CD/radio/mp3 files - music from all ages is around us - no longer do we have to listen only to modern music as we would have in earlier times, but now we can appreciate Gregorian and even Ancient Greek music in the same time frame as Stockhausen, or Adams.
The coin of music is in those vibrations - and the sides are simple to 'behold' - one side for music where these vibrations are concerted, where their natures are constantly reinforced, and the other, where they are juxtaposed, placed in sculptural opposition. Both are valid ways of understanding the vibrations - each has a beauty of its own. But the harmonic vibrations (and the inharmonic ones of bells and plates and bars) stand independent of how human beings use them.
with all best wishes,


LC: Thank you for this discussion and all the best to you!


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