Subminor and supermajor (was: Graylessness and limit)

JdL wrote:

>This whole minor question is interesting. I missed your sample files,
>but can generate some via midi. 6:7:9 is of course another option,
>with a wonderfully dark minor sound, but terrible problems doing the
>ol' A,C,E -> A,C,E,G -> C,E,G transition without ending on a horrible
>"car horn" major triad (14:18:21) or forcing painful retuning motion.

I suppose, if you accept 4:5:6:7 as a possible tuning of a major 7th chord
(which I don't, at least not as a dominant 7th unless you are seeking the
barbershop style of adaptive JI) then I suppose you would have to allow
that 6:7:9 is a form of minor chord. But it sounds quite distinct to me,
from either 16:19:24 or 1/(6:5:4) = 1/6 : 1/5 : 1/4 = 10:12:15. I don't
think even barbershop ever uses 6:7:9 as a tuning of a minor triad.

I (and many others) prefer to call 6:7:9 a subminor triad and 14:18:21 a
supermajor triad. 14:18:21 may better be understood utonally as 1/(9:7:6) =
1/9 : 1/7 : 1/6.

So of course I call 4:5:6:7 a subminor 7th (sm7) or augmented 6th (aug6)
chord depending on the context.

Regards,
-- Dave Keenan
http://dkeenan.com

[I wrote:]
>>This whole minor question is interesting. I missed your sample files,
>>but can generate some via midi. 6:7:9 is of course another option,
>>with a wonderfully dark minor sound, but terrible problems doing the
>>ol' A,C,E -> A,C,E,G -> C,E,G transition without ending on a horrible
>>"car horn" major triad (14:18:21) or forcing painful retuning motion.

[Dave Keenan:]
>I suppose, if you accept 4:5:6:7 as a possible tuning of a major 7th
>chord (which I don't, at least not as a dominant 7th unless you are
>seeking the barbershop style of adaptive JI) then I suppose you would
>have to allow that 6:7:9 is a form of minor chord.

Gee, Dave, I don't consciously seek a "barbershop" sound, but on the
other hand I DO like properly tuned sevenths. And I think that 6:7:9
sounds wonderful.

[Dave:]
>But it sounds quite distinct to me, from either 16:19:24 or 1/(6:5:4) =
>1/6 : 1/5 : 1/4 = 10:12:15. I don't think even barbershop ever uses
>6:7:9 as a tuning of a minor triad.

Maybe they don't, but I'd like to!

[Dave:]
>I (and many others) prefer to call 6:7:9 a subminor triad and 14:18:21
>a supermajor triad.

I've used the same terminology.

>14:18:21 may better be understood utonally as 1/(9:7:6) =
>1/9 : 1/7 : 1/6.

Quite true.

>So of course I call 4:5:6:7 a subminor 7th (sm7) or augmented 6th
>(aug6) chord depending on the context.

There I would not choose the same terminology as you. Look at those
small integer ratios: they are not deserving of being called "sub"-
anything. To my ears, anything else is a compromise.

JdL

--- In tuning@egroups.com, David C Keenan <D.KEENAN@U...> wrote:

> http://www.egroups.com/message/tuning/15732
>
> JdL wrote:
>
> > This whole minor question is interesting. I missed your sample
> > files, but can generate some via midi. 6:7:9 is of course
> > another option, with a wonderfully dark minor sound, but
> > terrible problems doing the ol' A,C,E -> A,C,E,G -> C,E,G
> > transition without ending on a horrible "car horn" major triad
> > (14:18:21) or forcing painful retuning motion.
>
> I suppose, if you accept 4:5:6:7 as a possible tuning of a major
> 7th chord (which I don't, at least not as a dominant 7th unless
> you are seeking the barbershop style of adaptive JI) then I
> suppose you would have to allow that 6:7:9 is a form of minor
> chord. But it sounds quite distinct to me, from either 16:19:24
> or 1/(6:5:4) = 1/6 : 1/5 : 1/4 = 10:12:15. I don't think even
> barbershop ever uses 6:7:9 as a tuning of a minor triad.

I've been reading the discussion of various flavors of minor
triad with interest, and just thought I'd add that one which
I really liked in a particular context was the 64:75:96 which
I used at the climactic point in the melody of _3 Plus 4_:

http://www.ixpres.com/interval/monzo/3plus4/3plus4ji.mid

This chord makes its first appearance at 20 seconds into the tune.

(An mp3 version is available on the Tuning Punks site.)

When I first uploaded this JI-retuned version at the very end
of last year, I discussed this chord a bit on this list; check
the archives. The point I found most interesting was that
75/64 is much closer in frequency to 7/6 than to 19/16 - both
of which I tried first - but it sounds far more different (to my
ears) from the former than from the latter. I never did figure
out how to explain that.

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'