Re: Descending aug and dim intervals

"Tom K." <tkorth1@[EMAIL PROTECTED]
> wrote in message 
news:Z-edncsoOfh7JWLanZ2dnUVZ_s2tnZ2d@[EMAIL PROTECTED]
> What is a "negative distance" in terms of musical intervals, Dave? 
Sounds 
> a bit like like our late, unlamented "Diminished Prime"!

You guys got me thinking about this again (oh brother).

So:

You have a Major 3rd.

If you increase the distance of this interval by raising the upper note an

octave, or lowering the lower note an octave, you create a "compound 
interval", in this case, a Major 10th.

If you consider a Perfect Unison to be a "simple" interval, than
performing 
the same operation will yield a Perfect 8ve.

It stands to reason that, in order to simplify a compound interval, you 
would perform the opposite operation - decreasing the distance by an
octave.

If we decrease Perfect 12th by a half step, thus making it a diminished 
12th, then "simplifying" it by decreasing the distance by an octave, we
are 
left with a diminished 5th.

If we decrease a Perfect 8ve by a half step, thus making it a diminished 
8ve, then simplifying it makes - a diminished Unison.

This makes a bunch of assumptions - for instance, that the unison itself
is 
considered a "distance". From a practical standpoint, two people can play 
the same note, and lines can cross, so unisons are at least practical from

that standpoint.

Can you augment a unison? If so, it should allow for being diminished too.

The practicality of such would be pretty meaningless in almost any context
I 
can think of though. It's kind of like saying -1 = 1-2. It does, but
either 
way you're left in debt!

Steve