Jon Harris
Guest
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 Posted:
Tue Dec 14, 2004 11:50 pm Post subject:
Re: Struggling with waveform questions. |
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"Richard Dobson" <richarddobson@blueyonder.co.uk> wrote in message
news:rrGvd.37130$up1.34693@text.news.blueyonder.co.uk...
| Quote: | Jon Harris wrote:
Yes, I've always found it interesting that Europeans several hundred years
ago
considered the major third to be a dissonant interval, whereas today it is
one
of the most harmonious.
This is partly because during the mediaeval period tuning was based on
Pythagorean principles. The Pythagorean third is created from four ascending
perfect fifths ((3/2)^4 --> 81/64 after octave reduction), which is a very
much
wider interval than the "perfect major third" of ratio 5/4, and it is indeed
pretty out of tune. Later on just intonation took over, based on the quest for
"pure" intervals, and the major third became consonant enough to be acceptable
for a final chord. Note also the practice of "tierce de Picardie" - a minor
mode piece will end with a major third as the minor third is less consonant
than
the major third. Whereas previously the fifth was preferred over the third for
the same reason, and so on.
12-note/Octave Equal Temperament (ET) is the solution to the tuning problem
that
we have come (grudgingly!) to accept; here the third is not quite as wide as
the
Pythagorean third, but is still the single most out of tune interval in ET.
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Thanks for the explanation--makes good sense. I used to just think those old
dudes were weird! :-)
BTW, a group of top-flight wind (especially brass) players who know how to
micro-adjust their pitch on-the-fly to obtain just intonation produces an
amazing sound! Harmonic-rich timbres will all the harmonics in-tune! |
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