On 4/6/07, Atte André Jensen <atte.jensen@xxxxxxxxx> wrote:
Chuckk Hubbard wrote: > I agree. If there are harmonics common to almost all music, it's more > like 3 or 4 of them than 12.
Hi Atte.
I strongly believe that the overtone series is the basis of all harmony. In there you'll find the octave, fifth, major/minor thirds and seconds (actually only our octave and fifth are the only equal tempered intervals that are tuned as in the overtone series). The overtone series
The 12-tone ET fifth is actually off by about 3 cents.
is not neseccarily the only "good" relationship between intervals, but it the one build into everything we and our forefathers surround(ed) ourselves with. An early man hitting a hollow piece of wood 40,000 years ago would hear the overtone series. Same with Josquin de Prez hearing a single voice singing a single note. Same with Cage. It's the common harmonic reference from which no hearing person cannot escape (although we can try, and make interesting music exploring along the way).
Many materials actually do not make this perfect overtone series. Gongs, bells, drums, and even plucked strings tend to be a little off. The whole appeal of Tibetan singing bowls is that the materials have slightly different frequencies. Gamelans are typically tuned uniquely, but studies have shown that often the octave does not appear on them. They tune them to partials, and the partials are not purely harmonic. My understanding is that some energy is dispersed when waves change planes or something. Like a wave that faces uneven pressure fron 3 dimensions will have a longer or shorter path depending on how many cycles it goes through in that volume... I think. So that overtones resonate at a different rate than you would expect. I think this is why I despise handbell ensembles like I do. The fundamentals are tuned to 12-tone ET, and the overtones are all over the place.
However the equal temperament is just one approximation of the intervals found in the overtone series, one that for obvious reasons was so practical that it has enjoyed wide spread use. Different cultures (for reasons I will make no attempt to understand) made different approximations of the overtone series and/or made use of it's intervalic relationships in different ways, which brought us Bach, Miles, the Ragas of Indian music and then some more.
I still agree with this though. Most tuning systems are based in some way on harmonic overtones. The exceptions are usually deliberate (like Easley Blackwood's album I mentioned in the previous thread). I think it's just that some explore higher harmonics than others; 12-tone ET doesn't imitate any prime-numbered partials higher than 5. Peace -Chuckk -- http://www.badmuthahubbard.com
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