Minor-maj7 tetrad

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.

1 6/5 3/2 15/8

The most obvious,one third up and one down from the fifth.

1 6/5 3/2 48/25

Two thirds down!I�m not sure about how useful this is.Any opinions?

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MATS �LJARE
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--- In tuning@y..., "Mats Öljare" <oljare@h...> wrote:
> 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?

Mats �ljare wrote,

<<1 7/6 3/2 15/8>>

Hmm, you might also be interested in a 7 - 14 all overtone scale that
uses the 6:7:9:11... ?

1/1 13/12 7/6 4/3 3/2 5/3 11/6 2/1
1/1 14/13 16/13 18/13 20/13 22/13 24/13 2/1
1/1 8/7 9/7 10/7 11/7 12/7 13/7 2/1
1/1 9/8 5/4 11/8 3/2 13/8 7/4 2/1
1/1 10/9 11/9 4/3 13/9 14/9 16/9 2/1
1/1 11/10 6/5 13/10 7/5 8/5 9/5 2/1
1/1 12/11 13/11 14/11 16/11 18/11 20/11 2/1

<<1 6/5 3/2 15/8>>

This would make sense with a

15/8
/ \
/ \
4/3---1/1---3/2---9/8
\ / \ /
\ / \ /
8/5---6/5

interpretation of the harmonic minor.

As always, there's an awful lot of possibilities... I'll be interested
to hear what you come up with.

--Dan Stearns

Mats �ljare wrote,

<<Two thirds down!I�m not sure about how useful this is.Any
opinions?>>

Dave Keenan wrote,

<<Opinion: not useful.>>

(Another) opinion: Dave just gave about as good a reason as any that I
can think of to assume that it's about ten times more useful than it
was an opinion ago...

--Dan Stearns

Hi Mats,

When I posted the tetrads which were local minima of dyadic harmonic entropy
(which you can hear at the bottom of
http://artists.mp3s.com/artists/140/tuning_lab.html),
the tuning that came up as optimal (to within 2 cents) for the minor-maj7
tetrad was

0 314 702 1090

This is very close to 1/1:6/5:3/2:15/8 or 40:48:60:75, though the augmented
fifth seems expanded a touch to mitigate its harshness a bit.