Re: Descending aug and dim intervals

On Wed, 09 Apr 2008 22:46:49 -0400, Joey Goldstein
<nospam@[EMAIL PROTECTED]
> wrote:

>I can't believe that this is stumping me, but I guess I haven't had to 
>think about this stuff since being a music student myself.
>
>Cb up to E is an ascending augmented 3rd interval.
>
>But, is Cb down to E a descending "diminished 6th" interval?
>I think that's probably correct, but it seems really weird to me.
Correct

>Likewise, C up to Fb is an ascending dim 4th interval.
>Is C down to Fb a "descending dim 5th"interval?
Augmented 5th

>C# up to Eb is an ascending dim 3rd interval.
>Is C# down to Eb a descending aug 6th?
Correct
>
>Or is my brain just doing tricks on me because I'm tired?

While we can use the terms "ascending" and "descending" to help
picture the notes, intervals are always reckoned from the low pitch to
the high pitch (with the obvious exception for the unison).

Widening: major -> augmented
Narrowing: minor -> diminished

C up to E is a major 3rd, widening with Cb to E augments.
E up to C is a minor 6th, narrowing with E to Cb diminishes.

Widening: perfect -> augmented
Narrowing: perfect -> diminished

C up to F is a perfect 4th, narrowing with C to Fb diminishes.
F up to C is a perfect 5th, widening with Fb to C augments.

C up to Eb is a minor 3rd, narrowing with C# to Eb diminishes.
Eb up to C is a major 6th, widening with Eb to C# augments.

Note, you can't "narrow" a unison, so there is no such thing as a
diminished unison.

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" 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. 


Ian