Re: Descending aug and dim intervals

On 10 Apr., 09:33, "David Webber" <d...@[EMAIL PROTECTED]
>
wrote:
> "Joey Goldstein" <nos...@[EMAIL PROTECTED]
> wrote in message
>
> news:ftjv2q$tao$1@[EMAIL PROTECTED]
>
> >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.
>
> Yes. =A0Complementary intervals which add to a perfect octave are
>
> perfect+perfect =A0(eg 4+5)
> major+minor =A0 (eg 3+6)
> dim+aug =A0(eg 3+6 as you have said)
>
> > Likewise, C up to Fb is an ascending dim 4th interval.
> > Is C down to Fb a "descending dim 5th"interval?
>
> No. =A0C down to Fb is a descending aug5.
>
> aug5+dim4 =3D perf8 =A0(it obeys the rule!)
>
> > C# up to Eb is an ascending dim 3rd interval.
> > Is C# down to Eb a descending aug 6th?
>
> Yes dim3+aug6 =3D perf8
>
> > Or is my brain just doing tricks on me because I'm tired?
>
> The Fb was the low point. =A0The rest is all fine :-) =A0 =A0 It is
actual=
ly a
> remarkably beautiful structure.
>
> Dave
> --
> David Webber
> Author of 'Mozart the Music Processor'http://www.mozart.co.uk
> For discussion/sup****t
seehttp://www.mozart.co.uk/mozartists/mailinglist.h=
tm

I suppose that this beautiful structure are partly tautological. I try
to explain why I think so.
Let us consider at first major scale. There are intervals with same
name which quantity of semitones differs on 1. It is natural to name
intervals with less quantity minor or diminished and intervals with
more quantity major or augmented. But how the names for intervals are
chosen?
The names for 3th intervals are taken from major and minor triads. The
6th interval is complementary  to 3th and it is natural that one
complementary to 3th major is named 6th  minor and vice versa.
The 2th interval may include 1 or 2 semitones. If it includes 1 one
then 3th interval which includes it is minor and therefore is named
minor. Complementary to it 7th interval is named major. If 2th
interval includes 2 semitones it is named major and....
 The perfect 4th and 5th intervals include accordingly 5 and 7
semitones and neutral to major and minor chord. Therefore interval
with 6 semitones may be named augmented 4th or diminished 7 th.
Apparently these intervals are complementary.
  Concerning intervals in minor scale the situation is more
complicated because of accidentals. But it seems to me that simple
rule may be used:
The names for perfect intervals are same as in  major scale. If
interval is more than same name major interval it is augmented major,
if it is less than same name minor interval it is diminished minor.

Best regards

Yuri Vilenkin