New Bach tuning for Paul E

(Paul, if you want to listen before you hear my opinion, don't read very
far down yet.)

I just did the Bach/Busoni Chaconne in two tunings for comparison:

. Paul E's requested combination: 5-limit with no tuning files,
negligible melody springs, negligible horizontal springs, and
rather soft vertical springs. Grounded to COFT.

. The same but with the usual quite rigid horizontal springs.

To listen, download b-b-bjh.zip from

/tuning/files/JdL/

Here are some of the numbers that result:

With negligible horizontal springs (b-b-bjes3h.mid):

COFTbig Total spring pain: 446192.988
After relaxing, Total spring pain: 232105.639
nSpring Strength Pain RMS deviation
------- -------- ---- -------------
Vertical 8820 14736.907 154070.028 4.573 cent
Horizontal 9903 26.122 35.536 1.650 cent
Melodic 3909 53.517 1018.816 6.170 cent
Grounding 9915 25842.068 76981.258 2.441 cent
TOTAL 32547 40658.613 232105.639 3.379 cent

Normal rigid horizontal springs (b-b-bjes3.mid):

COFTbig Total spring pain: 446192.990
After relaxing, Total spring pain: 271524.260
nSpring Strength Pain RMS deviation
------- -------- ---- -------------
Vertical 8820 14736.907 194414.526 5.137 cent
Horizontal 9903 261215.184 15451.585 0.344 cent
Melodic 3909 53.517 980.011 6.052 cent
Grounding 9915 25842.068 60678.138 2.167 cent
TOTAL 32547 301847.675 271524.260 1.341 cent

Funny! Dropping the horizontal springs did of course reduce vertical
pain, BUT melodic and grounding pain both went UP.

Note: I could have omitted horizontal springs and melodic springs
altogether, but by leaving them in place with negligible strength,
they become a gauge without significantly distorting the results.
Melodic springs here are 1% of "nominal" (where I've picked a tentative
nominal value from listening experiments), and horizontal springs in
the first tuning are a mere .01% of nominal.

My assessment: the first tuning is quite good, much better than I
expected when Paul suggested the experiment, but there are passages
where a sounding note wavers audibly. Try around 5:30 to 6:00, for
instance, where there is a mix of sustained melodic notes and rapid,
harmonically varying background notes which push the long notes around
in tuning to an excessive degree, IMO. The second, more usual treatment
sounds very clean and lovely to me (though I miss the 7:4 7ths of a
7-limit tuning ;-> ).

Well, Paul, for the Nth time (N >> 1), your suggestion has lead to a
very interesting listening experience. Don't look for a retiring of
horizontal springs any time soon, however!

JdL

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

/tuning/topicId_27453.html#27453

Curiously enough, the file that did *not* have horizontal springs in
it seemed more "justy" than the other file. Could it have been the
7:4 situation?

Dunno.... I'm going to listen again on a better sound card...

__________ __________ _____
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
>
> /tuning/topicId_27453.html#27453
>
>
> Curiously enough, the file that did *not* have horizontal springs
in
> it seemed more "justy" than the other file.

That's not odd at all. Horizontal = melody, vertical = harmony.

[Joseph Pehrson wrote:]
>>Curiously enough, the file that did *not* have horizontal springs in
>>it seemed more "justy" than the other file. Could it have been the
>>7:4 situation?

[Paul E:]
>That's not odd at all. Horizontal = melody, vertical = harmony.

Right. The version without horizontal springs is showing vertical
pain at 79% of the "normal" version. It is indeed more "justy". There
are probably certain places where horizontal forces cause a particularly
large deviation from just in the normal file, which are absent entirely
from the version without horizontal springs.

Joe, did you experience any horizontal pain in the file without
horizontal springs? Or were sounding notes steady enough in pitch for
your taste throughout?

JdL

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_27453.html#27476

> --- In tuning@y..., jpehrson@r... wrote:
> > --- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> >
> > /tuning/topicId_27453.html#27453
> >
> >
> > Curiously enough, the file that did *not* have horizontal springs
> in
> > it seemed more "justy" than the other file.
>
> That's not odd at all. Horizontal = melody, vertical = harmony.

Well... that's good, since what I'm hearing makes some sense... In
that case, for what it's worth, although both files sound quite nice,
I prefer the one *without* the horizontal springs. The harmonies
made more of an impression...

_________ ________ ______
Joseph Pehrson

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

/tuning/topicId_27453.html#27480

> [Joseph Pehrson wrote:]
> >>Curiously enough, the file that did *not* have horizontal springs
in
> >>it seemed more "justy" than the other file. Could it have been
the
> >>7:4 situation?
>
> [Paul E:]
> >That's not odd at all. Horizontal = melody, vertical = harmony.
>
> Right. The version without horizontal springs is showing vertical
> pain at 79% of the "normal" version. It is indeed more "justy".
There
> are probably certain places where horizontal forces cause a
particularly
> large deviation from just in the normal file, which are absent
entirely
> from the version without horizontal springs.
>
> Joe, did you experience any horizontal pain in the file without
> horizontal springs? Or were sounding notes steady enough in pitch
for
> your taste throughout?
>
> JdL

Well... to be perfectly honest about it, I was so "mesmerized" with
the harmonies in the file without the horizontal springs that I
really didn't care or think about the horizontal "steadiness..."

The file with the horizontal springs made less of an impression...

If I'm understanding this at all correctly, 12-tET would,
essentially, be the "steadiest" horizontally in all this, correct?

So, the file without the horizontal springs is the most "justy" and
also the furthest from 12-tET... correct??

Oh... I listened with a better sound card and still had exactly the
same impressions...

_________ _______ _______
Joseph Pehrson

[Paul wrote:]
>>That's not odd at all. Horizontal = melody, vertical = harmony.

[Joseph Pehrson:]
>Well... that's good, since what I'm hearing makes some sense... In
>that case, for what it's worth, although both files sound quite nice,
>I prefer the one *without* the horizontal springs. The harmonies
>made more of an impression...

[I wrote:]
>>Joe, did you experience any horizontal pain in the file without
>>horizontal springs? Or were sounding notes steady enough in pitch for
>>your taste throughout?

[Joe:]
>Well... to be perfectly honest about it, I was so "mesmerized" with
>the harmonies in the file without the horizontal springs that I
>really didn't care or think about the horizontal "steadiness..."

>The file with the horizontal springs made less of an impression...

>If I'm understanding this at all correctly, 12-tET would,
>essentially, be the "steadiest" horizontally in all this, correct?

Any fixed tuning would be rock-steady; only adaptive tuning is not.

>So, the file without the horizontal springs is the most "justy" and
>also the furthest from 12-tET... correct??

Well, of course the tuning varies throughout the piece, but on average,
your statement is true.

>Oh... I listened with a better sound card and still had exactly the
>same impressions...

Joe, thanks for listening! The wavering that I'm experiencing is an
elusive thing: sometimes I hear it, sometimes I don't. I think that
exposure to Paul E has caused some of his sensitivity to "rub off" on
me. ;->

Would you like to hear even more vertical consonance? I ran the same
file with fairly rigid vertical springs, with and without horizontal
springs. Here are some of the numbers that result:

With negligible horizontal springs (b-b-bjer3h.mid):

COFTbig Total spring pain: 1782085.436
After relaxing, Total spring pain: 591073.517
nSpring Strength Pain RMS deviation
------- -------- ---- -------------
Vertical 8820 58947.627 425182.111 3.798 cent
Horizontal 9903 26.122 77.735 2.440 cent
Melodic 3909 53.517 1297.047 6.962 cent
Grounding 9915 25842.068 164516.624 3.568 cent
TOTAL 32547 84869.333 591073.517 3.732 cent

Normal rigid horizontal springs (b-b-bjer3.mid):

COFTbig Total spring pain: 1782085.190
After relaxing, Total spring pain: 714244.637
nSpring Strength Pain RMS deviation
------- -------- ---- -------------
Vertical 8820 58947.627 505191.831 4.140 cent
Horizontal 9903 261215.184 56761.774 0.659 cent
Melodic 3909 53.517 1388.717 7.204 cent
Grounding 9915 25842.068 150902.314 3.417 cent
TOTAL 32547 346058.395 714244.637 2.032 cent

If we compare these to the 's' numbers from yesterday, we see that here
RMS vertical deviation from ideal is nearly equal to RMS grounding
deviation; there, grounding deviations were much smaller than vertical,
on average.

Would you be interested in hearing these versions (both more "justy"
than either of yesterday's)? If so, I'll upload 'em.

JdL

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

/tuning/topicId_27453.html#27508

>
> Would you be interested in hearing these versions (both more "justy"
> than either of yesterday's)? If so, I'll upload 'em.
>
> JdL

Sure! I guess that means that *eventually* I'll start hearing
the "wobblies," yes?? So far, I'm not getting that effect....

________ ______ _____
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

> Well... to be perfectly honest about it, I was so "mesmerized" with
> the harmonies in the file without the horizontal springs that I
> really didn't care or think about the horizontal "steadiness..."
>
> The file with the horizontal springs made less of an impression...
>
> If I'm understanding this at all correctly, 12-tET would,
> essentially, be the "steadiest" horizontally in all this, correct?

The COFT would be just as steady, but with better harmonies than 12-
tET.
>
> So, the file without the horizontal springs is the most "justy" and
> also the furthest from 12-tET... correct??

Not necessarily.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
>
> /tuning/topicId_27453.html#27508
>
> >
> > Would you be interested in hearing these versions (both
more "justy"
> > than either of yesterday's)? If so, I'll upload 'em.
> >
> > JdL
>
> Sure! I guess that means that *eventually* I'll start hearing
> the "wobblies," yes?? So far, I'm not getting that effect....

For music that doesn't go all the way around the circle of fifths,
you may never hear the "wobblies", no matter how "justy" the
harmonies get . . . we know from Vicentino's adaptive JI proposal
(his second tuning of 1555) that for such music, we can get all
triads just and limit all wobbles to 1/4-comma, or 5.4 cents . . .
this is a typically imperceptible melodic interval . . .

So rather than Bach, you may want to try, say Schubert, if you're
interested in hearing "wobblies" that can't be eliminated.

[Joseph Pehrson wrote:]
>>Sure! I guess that means that *eventually* I'll start hearing
>>the "wobblies," yes?? So far, I'm not getting that effect....

[Paul E:]
>For music that doesn't go all the way around the circle of fifths,
>you may never hear the "wobblies", no matter how "justy" the
>harmonies get . . . we know from Vicentino's adaptive JI proposal
>(his second tuning of 1555) that for such music, we can get all
>triads just and limit all wobbles to 1/4-comma, or 5.4 cents . . .
>this is a typically imperceptible melodic interval . . .

>So rather than Bach, you may want to try, say Schubert, if you're
>interested in hearing "wobblies" that can't be eliminated.

Well, if I'm understanding what you're saying correctly, both the Bach
and the Mozart would seem to challenge your assertions (I gather you've
not yet had a chance to listen). Vicentino's methods do allow for a
significant addition of consonances compared to meantone alone, but...
I won't say more till you've heard the tunings.

JdL

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> [Joseph Pehrson wrote:]
> >>Sure! I guess that means that *eventually* I'll start hearing
> >>the "wobblies," yes?? So far, I'm not getting that effect....
>
> [Paul E:]
> >For music that doesn't go all the way around the circle of fifths,
> >you may never hear the "wobblies", no matter how "justy" the
> >harmonies get . . . we know from Vicentino's adaptive JI proposal
> >(his second tuning of 1555) that for such music, we can get all
> >triads just and limit all wobbles to 1/4-comma, or 5.4 cents . . .
> >this is a typically imperceptible melodic interval . . .
>
> >So rather than Bach, you may want to try, say Schubert, if you're
> >interested in hearing "wobblies" that can't be eliminated.
>
> Well, if I'm understanding what you're saying correctly, both the
Bach
> and the Mozart would seem to challenge your assertions (I gather
you've
> not yet had a chance to listen).

Not yet -- anyway, I didn't assert anything here, and since Joseph
_did_ hear the wobblies in your adaptive JI versions, the point is
moot.

> Vicentino's methods do allow for a
> significant addition of consonances compared to meantone alone,
but...

I know, it can't even give you a just sus4 chord, unless you modify
it further.