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Thx
i am familiar with the pathagorian comma. Actually the 5th is a 3/2 ratio, not 2/3 meaning the third harmonic of the lower note is the same friquency as the second harmonic of the upper note of the interval being played but that is not so important.
the pure fifth don’t exist on pianos – I tune them regular. If you picture the sine wave like in the article the line drawn depicts the dilemma. It is an imaginary line. In the real world on monochords, harpsichords, violins or pianos the line becomes a string or a wire and has physical properties like diameter, stiffness and length. This forces the harmonics sharp of the theoretical frequency. so in the world of tuning the theoretical harmonics become partials which is more descriptive of what’s happening. That means that all intervals must be tempered and the perfect fifth don’t really exist – even on tuning forks.
On another note I know that science has gone to great length to try to generate a pure tone with zero harmonics or partials. Don’t know if they had success or not.
in regard to healing power all I can say is the fifth is probably the second most pleasing almost pure interval to listen to next to an octave but if you get beyond the mid range or the normal melody frequencies everything changes. Harmonics or partials can range beyond our normal hearing range in friquency and the interesting thing is – in tuning anyway – our brain can fill in where our ears leave off.
Very interesting stuff.
One more thought and this gets into perception: had a chance to work for Urlich Sauter the Sauter piano maker from Germany. He makes a very unique piano for special order, maybe only a few like it in the world- he calls it a Microtonal Piano.
Its unique because it is a full keyboard like the Bosendorfer Imperial with 97 rather than the traditional 88 notes but it’s true uniqueness is that those 97 notes spans only one octave, from A-3 to A-4
talk about a chromatic scale.
it takes two hands to play a perfect fifth. Even a third.
what is also unique is that someone can play it.
and what it s also unique is that someone actually writes music for it.
to me, no matter what the artist was doing it made no musical sense but it certainly did to the composer and the artist who interpreted it.
Go figure
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