Re: Descending aug and dim intervals

<vilen@[EMAIL PROTECTED]
> wrote in message 
news:cec4a948-e56b-4664-bea6-2f806854bf7a@[EMAIL PROTECTED]
>
> Nevertheless i have doubts concerning addition of intervals. I repeat
> your examples,
>> maj7+dim7=min13
>> maj7+aug6=aug12
>
> Gives "maj+dim" always "min" and "maj+aug"-"aug"? Where can one the
> rules find?

You just have to add the intervals and see what results :-)   In general
you 
don't have anything like "maj+dim" = "min" but octave complements
(min,maj) 
(perf,perf)  (aug,dim) *are* very regular.

More generally let's look at a few:

CDE      maj2+maj2 = maj3
CDEb    maj2+min2 = min3
CDEbb   maj2+dim2 = dim3
CDF       maj2+min3 = perf4
CDF#    maj2+maj3 = aug4

CEF      maj3+min2 = perf4
CEG     maj3+min3 = perf5

In fact it looks like any perfect interval  can be split  (maj+min) or 
(perf+perf) or (dim+aug)  though the converse is not true  (see CDEb above

where maj+min->min).

CEA   maj3+perf4 = maj6
CDG  maj2+perf4 = perf5
CDA   maj2+perf5 = maj6


It looks like
    maj+maj is always either maj or aug.

But this is only indicative: I'll leave the proof as an exercise.  :-)

But it is part of the richness that you can't say that maj+maj and others 
are always *something*.   That would factorise the interval 2nd 3rd 4th
etc 
from the qualifier (maj,min,...)  and the whole algebra of intervals would

factorise into two separate algebras.  The fact that it doesn't makes it 
more interesting from the mathematical (and, I suspect, musical)
viewpoint.

> And if add three intervals? Isn't better add semitones from the first.

No.  You can add semitones by adding intervals, but you can't add
intervals 
just by adding semitones.

Dave
-- 
David Webber
Author of 'Mozart the Music Processor'
http://www.mozart.co.uk
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