"Steve Latham" <llatham@[EMAIL PROTECTED]
> wrote in message
news:paPLj.40$iI3.22@[EMAIL PROTECTED]
>
> "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.
>
That's where it breaks down, because...
> This makes a bunch of assumptions - for instance, that the unison itself
> is considered a "distance".
The "distance" is zero - how do you diminish zero?
> 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.
Why? You can have more than nothing, but how can you have less than
nothing?
> 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!
But is debt a musical analog?
Tom K.
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