modes

Bill Alves wrote,

>Given that there are seven pitches in the diatonic set, there are thus
>seven possible diatonic modes, of which major and minor are only two. I
>don't see how they are different than the other diatonic modes.

They are very different. The tritone (the only exception in the
classification of generic interval sizes according to 5-limit consonance)
is disjoint from the tonic triad in only these modes. Thus the tonic triad
of either mode is more stable against the scale than any other triad. The
tritone resolves to two notes of the tonic triad of these modes in contrary
motion through both instances of the rarer step size (the half step) -- and
the position of the rarer step sizes is what tells the listener "where we
are" in the mode. So the cadence is a way of saying, "we've been traveling
around for a while, but now that we know where we are, we're home!" If you
want two tritones disjoint from the tonic triad, so that they can both
resolve to it, you use the harmonic minor or harmonic major (major flat 6)
modes, although one of the notes of one of the tritones will have to
resolve by a whole step, albeit to a note that is being approached by half
step from a note of the other tritone.

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