Re: minor major seventh

> > What kind of ratios do you suggest as target for a minor+major
> seventh
> > tetrad?There are 3 ones that i_ve considered.
> >
> > 1 7/6 3/2 15/8
> >
> > A 7-limit approximation through"positive"major thirds,assuming a
> 225/224
> > bridge.
>
> I don't think so. I'd call this a subminor major seventh, a different
> chord altogether.
>
> > 1 6/5 3/2 15/8
> >
> > The most obvious,one third up and one down from the fifth.
>
> Sure. Why not?
>
> > 1 6/5 3/2 48/25
> >
> > Two thirds down!I_m not sure about how useful this is.Any opinions?
>
> Opinion: not useful.
>
> What about 10:12:15:19 or (closer to 12-tET) 16:19:24:30?
>
>

I like the way the first (1 7/6 3/2 15/8) sounds though I'm not sure
that all listeners would feel that this settles as a tonic minor. I
didn't like the obvious 1 6/5 3/2 15/8 on listennings.

I think Pauls second proposal would have a lot of stability being
a complete otonal series. A version I came up with that also uses
the 'psuedo-12tet 19 identities' is 1/1 19/16 3/2 36/19 which
in cents is 0 297 702 1106 vs Pauls 0 297 702 1088.

For MY useage, I feel that the pun between the "minor third above
the 1/1" being a "major third above the major seventh", is an
important feature of this chord (part of its buzz).

This is why I believe I didn't like the obvious 1 6/5 3/2 15/8 on
listennings, due to the very wide implied "major third" between
the seventh and third. Your last proposal fixes that, at the cost
of placing a very wide major third above the fifth. I believe this
too would lack the restfulness of a tonic minor.

Basically, you are revealing the basic problem with just/rational
ways to interpret an augmented triad. A stack of 5/4's puts a
very wide 428c third on the outside. A single 5/4 leaves 814c
to fit two major thirds into.

Using this result and my preference that the minor third pun as
"major third above the major seventh", and assuming that I want
that major third to be 5/4 (and it may very well be preferable to
have it a bit sharper major third than the JI one) then I can
draw up a temperring of this chord at 0 295 702 1109 cents.
This puts the 5/4 between the major seventh and minor third
and splits the minor sixth symmetrically around the perfect fifth.

The most interesting RI (rational intonation) view of this
chord is as a Pythagorean 1/1 32/27 3/2 243/128 with (in C)
the B<->Eb diminished fourth is a schismic? major third.

Bob Valentine

Robert wrote,

>I think Pauls second proposal

I only made one proposal: 0 314 702 1090. Perhaps you mean Dave K.?

>would have a lot of stability being
>a complete otonal series.

Yes, 16:19:24:30 has extra stability since the lowest note is a power of 2.

>This is why I believe I didn't like the obvious 1 6/5 3/2 15/8 on
>listennings, due to the very wide implied "major third" between
>the seventh and third. Your last proposal fixes that, at the cost
>of placing a very wide major third above the fifth. I believe this
>too would lack the restfulness of a tonic minor.

Now I really don't know whose "last proposal" you're talking about!

>Basically, you are revealing the basic problem with just/rational
>ways to interpret an augmented triad. A stack of 5/4's puts a
>very wide 428c third on the outside. A single 5/4 leaves 814c
>to fit two major thirds into.

This is one of the reasons my program widened both of the 5:4s a bit, to get
that outer minor sixth a bit more concordant.

> Subject: RE: Re: minor major seventh
>

> Robert wrote,
>
> >I think Pauls second proposal
>
> I only made one proposal: 0 314 702 1090. Perhaps you mean Dave K.?
>

Oooops, I thought it was you who wrote you wrote...

> >
> > What about 10:12:15:19 or (closer to 12-tET) 16:19:24:30?
> >

> >This is why I believe I didn't like the obvious 1 6/5 3/2 15/8 on
> >listennings, due to the very wide implied "major third" between
> >the seventh and third. Your last proposal fixes that, at the cost
> >of placing a very wide major third above the fifth. I believe this
> >too would lack the restfulness of a tonic minor.
>
> Now I really don't know whose "last proposal" you're talking about!
>

This was the last proposal of the original poster, which was

1 6/5 3/2 48/25
>
> >Basically, you are revealing the basic problem with just/rational
> >ways to interpret an augmented triad. A stack of 5/4's puts a
> >very wide 428c third on the outside. A single 5/4 leaves 814c
> >to fit two major thirds into.
>
> This is one of the reasons my program widened both of the 5:4s a bit, to get
> that outer minor sixth a bit more concordant.
>

...which someone (I thought you) correctly named augmented fifth. One
could make the claim that my preference for a 5/4 diminished fourth is
a 12tet brainwashing. I did say that it may be that it may be
preferable to have the diminished fourth somewhat wider.

Bob Valentine

Robert Valentine wrote,

>One
>could make the claim that my preference for a 5/4 diminished fourth is
>a 12tet brainwashing.

Perhaps, but I do believe that perference for an augmented fifth wider than
25/16 is _not_ due to any brainwashing.