Re: Descending aug and dim intervals

On Thu, 10 Apr 2008 12:55:57 +0100, "David Webber"
<dave@[EMAIL PROTECTED]
> wrote:

>
>"paramucho" <paramucho@[EMAIL PROTECTED]
> wrote in message 
>news:47ffcfaa.27560139@[EMAIL PROTECTED]
>> On Wed, 09 Apr 2008 22:46:49 -0400, Joey Goldstein
>> <nospam@[EMAIL PROTECTED]
> wrote:
>>
>
>> We had a long thread on the intricacies of this topic a few years
>> back. A google groups rec.music.theory search for the threads "Query
>> about compound intervals and inversions" and/or "crossed intervals"
>> will locate the threads. Dave Webber ended up exploring "directed
>> intervals"
>
>Yes :-)     I am still happy with them.   If you're playing two notes at 
>once, then the absolute interval between them is the natural concept. 
Those 
>of us who play woodwind don't:  we move from one note to another and can 
>jump down a 5th as easily as we can jump up one.   So a descending
interval 
>is a very natural concept in the melodic, rather than harmonic, context.
>
>>...
>> and interval arithmetic and I came up with "crossed
>> harmonic intervals" -- we argued about it all of course, but I recall
>> the thread with pleasure.
>
>So do I :-)
>
>Even though my concept of the diminished unison (moving through a
semitone 
>from C to Cb so that an upwards diminished unison moves down by a
semitone) 
>was always rather tongue in cheek, there are still some awkward problems
if 
>one gets hung up on the relation****p between intervals and pitch.    A 
>diminished 2nd for example:  F# to Gb.   Are there temperaments in which
the 
>higher note is lower than the lower one?  :-)  :-)
>
>But as abstract concepts intervals have a very elegant arithmetic.   
Part 
>of which is that octave complements are
>
>perfect+perfect
>major+minor
>aug+dim

It was amazing to see how rewarding such an utterly trivial topic
could be. I still have unfinished business from that thread though,
and that is to see if there is some criteria by which one say certain
intervals are meaningless.



 
Ian