Re: Stretched meantones [WAS> Draft: What is meantone (MT)?]

Herman Miller wrote:

> Stretched octave meantone tunings, with octaves greater than
> 1200 cents, are also useful in certain contexts, although
> strictly speaking they're not really meantone scales. The
> benefit of tempering the octave is that the fifths don't need to
> be tempered as much if the octaves are tuned slightly sharp.

YES! Hello Herman! Thank you. So! I am not
the _only_ one to use stretched meantones. Well
well. This is a delight indeed.

Right -- if you temper the octave instead of
the fifth you can get pythagorean quality fifths
AND all your nice little pure thirds. Good stuff.
The ancients even considered it (per Jorgensen)
but decided against it as to their ears a tempered
octave was unacceptable.

- Jeff

On Thu, 22 Feb 2001 00:53:03 -0500, "J Scott" <xjscott@earthlink.net>
wrote:

>Right -- if you temper the octave instead of
>the fifth you can get pythagorean quality fifths
>AND all your nice little pure thirds. Good stuff.
>The ancients even considered it (per Jorgensen)
>but decided against it as to their ears a tempered
>octave was unacceptable.

I've played with that scale, too, but you have to temper the octave by 1/2
comma to get that effect, which is quite noticeable. When I play in
"stretched" meantone, I usually use a scale with octaves and fifths both
tempered by 1/7 of a comma -- the fifths a little flat, the octaves a
little sharp, and the major thirds a little sharp by the same amount.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

--- In tuning@y..., Herman Miller <hmiller@I...> wrote:
> When I play in
> "stretched" meantone, I usually use a scale with octaves and fifths
both
> tempered by 1/7 of a comma -- the fifths a little flat, the octaves
a
> little sharp, and the major thirds a little sharp by the same
amount.

Hi Herman,

Can you explain why you favour that tuning over one with octaves
1/6-comma wide, fifths 1/6-comma narrow and just major thirds. The
disadvantage I see is that the 1/7-comma "stretched" meantone gives
just 5:8 minor sixths at the expense of the major and minor thirds and
minor sixth (4:5, 5:6, 3:5).

Thanks again for introducing me to these "stretched" or
tempered-octave meantones.

-- Dave Keenan

On Fri, 23 Feb 2001 03:48:32 -0000, "Dave Keenan" <D.KEENAN@UQ.NET.AU>
wrote:

>Hi Herman,
>
>Can you explain why you favour that tuning over one with octaves
>1/6-comma wide, fifths 1/6-comma narrow and just major thirds. The
>disadvantage I see is that the 1/7-comma "stretched" meantone gives
>just 5:8 minor sixths at the expense of the major and minor thirds and
>minor sixth (4:5, 5:6, 3:5).
>
>Thanks again for introducing me to these "stretched" or
>tempered-octave meantones.

I haven't tried that specific tuning, so I can't say whether I'd prefer one
or the other. I suspect it would depend on the style of music.

In general when exploring non-equal scales, I start out by trying to
minimize the maximum error of the set of intervals I'm interested in (in
this case the major third, fifth, and octave). So I'm sure I'm probably
missing out on some nice scales. But I'll try that 1/6-comma scale over the
weekend and see how it compares with the others.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

--- In tuning@y..., Herman Miller <hmiller@I...> wrote:
> In general when exploring non-equal scales, I start out by trying to
> minimize the maximum error of the set of intervals I'm interested in
(in
> this case the major third, fifth, and octave).

Me too. It's hard for me to conceive that you wouldn't also be
interested in at least the 5:6 minor third, but when I accepted that
you weren't, I found that my own algorithm gives the wrong answer!

http://dkeenan.com/Music/DistributingCommas.htm

It says to widen the octave by 1/5-comma, narrow the fifths by
1/5-comma and thereby arrive at major thirds which are 1/5-comma
_narrow_, as opposed to your 1/7-comma _wide_ which is indeed optimal.

My algorithm goes wrong in step 6, in this case. Are you there Manuel
Op de Coul?

A weight of 1/3 on the factors of 2 gives the optimal result in this
case. At this stage it isn't clear how to fix my algorithm, but
thankyou very much for finding this counterexample.

Regards,
-- Dave Keenan