An example of a perfect 5th interval is the interval from the note C to the
note G (basically 7 semi tones up). I can send you some stuff privately
that explains the exact physics of why it sounds good but basically it has
to do with the fact that a string (or column of air) vibrates at multiples
of its fundamental frequency (called overtones) and the first overtone that
is not the same note as the fundamental is the perfect 5th. Pythagoras
worked all this out back in his time and it is really basic maths and wave
theory from physics.
There is a similar relationship to the 4th (5 semitones up) e.g. C to F.
These intervals crop up all the time in music. The basic 12 bar blues
progression on which so much music (including a lot of jazz) is based is (in
C):
C|C|C|C|C|C|C|C
C|C|C|C|F|F|F|F
C|C|C|C|G|G|G|G
Jazz usually mutates the progression significantly but it is the basis of
tonnes of old blues and rock and roll songs. If you know the theme song to
Batman (who doesn't) then you know these intervals.
Steve
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