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On 5/17/06, Rob Haden <[log in to unmask]> wrote:
> On Wed, 17 May 2006 09:25:42 +0100, Peter Bleackley
> <[log in to unmask]> wrote:
> >As for a tritone, it's also called a diminished fifth, an augmented fourth,
> >or  the diabolus in musica. It's the interval of 3 whole tones or 6
> >semitones, corresponding to a pitch ratio of sqrt(2) in the equally
> >tempered scale (64/45 or 45/32 in rational-interval scales), eg C to F#,
> >and is generally considered the most discordant inteval in the entire scale.

Note that you cannot play a tritone with just the white notes on a piano.

> I wonder if it's possible for there to be a creature which does not find the
> tritone to be the most discordant interval...

Well, IIRC, notes are considered discordant depending on how close
they and their harmonics are to each other without being exactly the
same.  This must be to do with the way our ears detect frequency by
the resonance of parts of the ear that are tuned to certain
frequencies -- they will pick up multiple of those frequencies too
(i.e. harmonics), so harmonics become associated with the notes in out
brains. (BTW, timbre depends on the relative power of harmonics of a
note, so the same notes can sound more or less discordant on different
instruments).  If you compare multiples of 2 to the integers, you
will find that many are close, but none of the early ones are *very*
close (except 0).  Ultimately it could come from the sound of screams,
warning cries, wolves howling, or something like that.