On 4/6/07, Atte André Jensen wrote:
> I strongly believe that the overtone series is the basis of all harmony.
The 12-tone ET fifth is actually off by about 3 cents.
> is not neseccarily the only "good" relationship between intervals, but
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
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
> However the equal temperament is just one approximation of the intervals
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.