Stretched tuning experiments (was: First melodic spring results)

[Paul wrote:]
>John, what did you think of Herman's "1/7-comma meantone with 1/7-
>comma-stretched octaves" version, as compared with, say, 55-tET?

Pulling them up right now! Stretched 1/7 comma meantone: bright, but
not as lovely or as vivid as 34-tET. I have to say that octave stretch
doesn't seem to help as far as I can tell; it adds a tension to my ear.
This new voicing is a bit shrill on my synth, and stretch makes it even
more shrill.

55-tET - s***: I've downloaded the whole set three times, last on the
16th, and I don't have it! Standby... Aha, I see there are some
adaptive versions up as well, by some guy with a long name.

Well, 55 sounds pretty good too! And it's racked into narrow fifths
and quite narrow minor thirds. Yarrgh.

I try 7-limit adaptive - yow, those 7ths are flat!! OK, 5-limit COFT
and 5-limit adaptive sound pretty good to me (is this like movie studios
using their own employees to pose as excited movie-goers and/or
reviewers? ;-> )

Conclusion: confusion. Maybe I'll pick a slow piano piece to try some
experiments with 34-like intervals, with and without overall stretch.

JdL

--- In tuning-math@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> [Paul wrote:]
> >John, what did you think of Herman's "1/7-comma meantone with 1/7-
> >comma-stretched octaves" version, as compared with, say, 55-tET?
>
> Pulling them up right now! Stretched 1/7 comma meantone:

Oops -- Herman should really clarify -- this is not stretched 1/7-
comma meantone, but rather a tuning where the fifths are 1/7-comma
narrow and the octaves are 1/7-comma wide.

[Paul wrote:]
>>>John, what did you think of Herman's "1/7-comma meantone with 1/7-
>>>comma-stretched octaves" version, as compared with, say, 55-tET?

[I wrote:]
>>Pulling them up right now! Stretched 1/7 comma meantone:

[Paul:]
>Oops -- Herman should really clarify -- this is not stretched 1/7-
>comma meantone, but rather a tuning where the fifths are 1/7-comma
>narrow and the octaves are 1/7-comma wide.

Oh, I meant that, despite fewer words. Although, I see that Herman
is saying "1/7-comma meantone with 1/7-comma tempered octaves"; perhaps
if the word "tempered" were changed to "stretched", it'd be clearer...

BTW, a slight glitch in the files, including my own COFT, is that the
D note (tonic) has no bend message whatever till later in the file, as
channels are reused. On some modules, including my VSC-88, stale bend
messages from the previous sequence can sour the first few seconds of a
newly tuned sequence. If in doubt, a reset is a good idea between
tunings.

JdL

On Tue, 19 Jun 2001 14:48:00 -0600, "John A. deLaubenfels"
<jdl@adaptune.com> wrote:

>[Paul:]
>>Oops -- Herman should really clarify -- this is not stretched 1/7-
>>comma meantone, but rather a tuning where the fifths are 1/7-comma
>>narrow and the octaves are 1/7-comma wide.

Right; this is actually one of my favorite tunings for playing
traditionally notated music on the DX7II. 1/7-comma wide octaves and
1/7-comma narrow fifths. Although sometimes I just call it "1/7-comma
stretched meantone" out of laziness.

>Oh, I meant that, despite fewer words. Although, I see that Herman
>is saying "1/7-comma meantone with 1/7-comma tempered octaves"; perhaps
>if the word "tempered" were changed to "stretched", it'd be clearer...

Done.

--- In tuning-math@y..., Herman Miller <hmiller@I...> wrote:
> On Tue, 19 Jun 2001 14:48:00 -0600, "John A. deLaubenfels"
> >Oh, I meant that, despite fewer words. Although, I see that Herman
> >is saying "1/7-comma meantone with 1/7-comma tempered octaves";
perhaps
> >if the word "tempered" were changed to "stretched", it'd be
clearer...
>
> Done.

No. I think maybe John still doesn't get it. It's definitely "with
octaves tempered 1/7-comma wide" and _not_ "with a stretch of 1/7
comma per octave". These are very different things.

A "stretch" is in fact applied to _all_ intervals, not merely the
octave. However it is usually specified as so many cents per octave.
Its purpose is usually to compensate for a stretched inharmonic timbre
or a property of human pitch perception.

A meantone with a tempered octave means that for a given note we not
only need to know where it is on the chain of fifths, but how many
octaves one has to reduce its stacked fifths by, to bring it back to
the "home" octave. Herman's scale gives the optimum distributiion of
the syntonic comma for the intervals 1:2, 2:3 and 4:5. It essentially
doesn't give a damn about other 5-limit intervals like 3:4, 5:6, 3:5,
5:8.

Dan Stearns, are you reading? This is an excellent example of a tuning
that optimises only the rooted intervals (in this case including the
octave), giving them all equal weight.

Here are the three scales to the nearest cent
1. Ordinary 1/7 comma meantone
2. 1/7 comma meantone with a stretch of 1/7 comma per octave
3. 1/7 comma meantone with octaves tempered 1/7 comma wide.

Name Octaves Fifths 1/7 with with
comma stretch tempered octaves
-----------------------------------------------
C 0 0 0 0 0
C# -4 7 92 92 80
D -1 2 198 198 195
Eb 2 -3 303 304 309
E -2 4 396 397 389
F 1 -1 501 502 504
F# -3 6 593 595 584
G 0 1 699 701 699
G# -4 8 791 793 779
A -1 3 897 899 894
Bb 2 -2 1002 1005 1008
B -2 5 1094 1097 1088
C 1 0 1200 1203 1203

Look at E. Notice how stretch makes the major thirds (4:5 = 386c)
slightly worse, but wide-tempered-octaves makes them significantly
better.

Regards,
-- Dave Keenan

On Thu, 21 Jun 2001 01:54:56 -0000, "Dave Keenan" <D.KEENAN@UQ.NET.AU>
wrote:

>A "stretch" is in fact applied to _all_ intervals, not merely the
>octave. However it is usually specified as so many cents per octave.
>Its purpose is usually to compensate for a stretched inharmonic timbre
>or a property of human pitch perception.

Hmm, good point. I guess I'll call it a "widened" octave rather than a
"stretched" one.