Re: Adaptive tempering and tuning

[Paul wrote:]
>>John deLaubenfels' program already does this to a great extent.
>>All "commas" are tempered out, using a combination of melodic and
>>harmonic tempering.

[Gene wrote:]
>I thought his idea worked on notes. I was proposing to lift a piece
>to JI, and then vary the generators slightly. Does his program do
>something like this?

My methods set up an impossible combination of desires, using springs to
allow for flexibility, then attempt to find the best compromise. My
model is an analog of physical springs, with the goal to reach minimum
energy ("pain").

[Paul:]
>>Comma slides identified? I object to the idea that any piece of
>>Western common-practice music "implies" comma slides at any
>>particular points in the score.

[Gene:]
>In C major take the chord sequence I-IV-II-V-I. Each of these chords
>has at least one note in common with each neighboring chord, so the
>harmonic meaning is rigidly enforced; I would say the sequence
>clearly transposes down a comma if lifted to JI. Even if you don't
>agree, wouldn't you think such a sequence should be identified?

The infamous "comma pump". Here's what happens in my treatment: the
vertical springs target JI intervals, and the horizontal springs try to
hold each note to a consistent tuning. This of course leads to a shift
in absolute pitch of 80:81 each time the sequence repeats. To
counteract this tendency, I add grounding springs, which connect each
instance of each pitch class to a particular tuning. The grounding
springs are loose enough to allow significant deviation at a particular
moment, but strong enough that, over time, their influence effectively
stops drift.

The "price" of grounding is expressed both in slightly less than just
vertical intervals and some shift in notes continuously sounding. The
relative coefficients of spring stiffness can be adjusted so that the
price is paid all vertically, or all horizontally (within some very
small tolerance) if one desires.

JdL

>To counteract this tendency, I add grounding springs, which connect
>each instance of each pitch class to a particular tuning. The
>grounding springs are loose enough to allow significant deviation at a
>particular moment, but strong enough that, over time, their influence
>effectively stops drift.

John, do you think an approach is possible where you don't have a
grounding spring to each individual pitch class, but instead
calculate a "centre of gravity" first, in some clever way or
another, and connect that point to the earth with a single spring,
and a damper if you like (or a resistor and a capacitor in electrical
terms)? That means you will have the same drift counteracting term
to add to all notes, and no need to compromise the vertical
intervals.

Manuel

Bob Wendell here. Yes, Manuel, I like that idea. It may be closer to
what actually happens when singers or string players whose
ears are trained to prefer just harmonies adjust naturally over time
to keep pitch from drifting and maintain a sense of pitch return or
"key closure", as we might call it.

I do think the "fudging" happens melodically at strategic times, but
spread out and not usually involving "slides" on one pitch, at least
not so great as to be easily perceptible.

--- In tuning@y..., <manuel.op.de.coul@e...> wrote:
>
> >To counteract this tendency, I add grounding springs, which connect
> >each instance of each pitch class to a particular tuning. The
> >grounding springs are loose enough to allow significant deviation
at a
> >particular moment, but strong enough that, over time, their
influence
> >effectively stops drift.
>
> John, do you think an approach is possible where you don't have a
> grounding spring to each individual pitch class, but instead
> calculate a "centre of gravity" first, in some clever way or
> another, and connect that point to the earth with a single spring,
> and a damper if you like (or a resistor and a capacitor in
electrical
> terms)? That means you will have the same drift counteracting term
> to add to all notes, and no need to compromise the vertical
> intervals.
>
> Manuel

[I wrote:]
>>To counteract this tendency, I add grounding springs, which connect
>>each instance of each pitch class to a particular tuning. The
>>grounding springs are loose enough to allow significant deviation at a
>>particular moment, but strong enough that, over time, their influence
>>effectively stops drift.

[Manuel Op de Coul wrote:]
>John, do you think an approach is possible where you don't have a
>grounding spring to each individual pitch class, but instead
>calculate a "centre of gravity" first, in some clever way or
>another, and connect that point to the earth with a single spring,
>and a damper if you like (or a resistor and a capacitor in electrical
>terms)? That means you will have the same drift counteracting term
>to add to all notes, and no need to compromise the vertical
>intervals.

You know, I've been struggling with the grounding issue for a long time,
but I'm not sure I've ever considered exactly what I think you're
saying! Each pitch class would be evaluated for ideal grounding via
the COFT calculation, but a given combination of notes sounding together
would get a calculated optimal grounding position (some kind of weighted
average of the individual notes), which would be expressed as a single
grounding spring. For about the 10-billionth time in my life, "Why
didn't I think of that?" Although, come to think of it, that may be
what is achieved in my existing model when vertical springs are made
very stiff.

Let me ask you this: would you allow horizontal issues to pull vertical
intervals away from JI at all? In my model, as it now exists,
horizontal springs and grounding springs both tend to contain the
deviation of a given pitch class from some calculated ideal value, but
horizontal springs act as "capacitors" (or inductors, depending upon
how the analogous electrical circuit is wired), stabilizing the tuning
of a pitch class in localized time, where grounding springs are the
analog of resistors. If the action of grounding is rewired so that it
exerts no vertical pull, would the issue of not retuning a sounding note
still have vertical sway?

If grounding were not allowed to cause vertical deviation but horizontal
forces _were_, then I think your suggestion could only be implemented
with a change to my program (as opposed to jiggering the relative
stiffnesses of the spring classes).

Very interesting!

JdL

John deLaubenfels wrote:
>Let me ask you this: would you allow horizontal issues to pull vertical
>intervals away from JI at all?

Yes certainly. Perhaps the horizontal springs can be made a bit weaker
if you add a damper to the drift spring.

>If the action of grounding is rewired so that it
>exerts no vertical pull, would the issue of not retuning a sounding note
>still have vertical sway?

Yes, so it might be beneficial to make the action against drift like
almost continuously, so at a higher rate than the notes, and also retune
sounding notes.
I bought a nice CD with Haydn sonatas on clavichord recently and the
pitch of tones is often far from stable. But it's not ugly, I can get
used to it.

>If grounding were not allowed to cause vertical deviation but horizontal
>forces _were_, then I think your suggestion could only be implemented
>with a change to my program.

Indeed, I haven't thought about it further other than that estimating the
drift is not trivial. But if you want to generalize to non-12 adaptive
retuning it might be a good change.

Manuel

--- In tuning@y..., <manuel.op.de.coul@e...> wrote:
>
> >To counteract this tendency, I add grounding springs, which connect
> >each instance of each pitch class to a particular tuning. The
> >grounding springs are loose enough to allow significant deviation
at a
> >particular moment, but strong enough that, over time, their
influence
> >effectively stops drift.
>
> John, do you think an approach is possible where you don't have a
> grounding spring to each individual pitch class, but instead
> calculate a "centre of gravity" first, in some clever way or
> another, and connect that point to the earth with a single spring,
> and a damper if you like (or a resistor and a capacitor in
electrical
> terms)? That means you will have the same drift counteracting term
> to add to all notes, and no need to compromise the vertical
> intervals.
>
> Manuel

Manuel -- this is the approach taken in John deLaubenfels' old real-
time retuning program. His new, leisure-tine program can always do
better because the horizontal retuning motions can always be reduced
relative to the old method, given harmonies as close to just as
desired.

[I wrote:]
>>Let me ask you this: would you allow horizontal issues to pull
>>vertical intervals away from JI at all?

[Manuel wrote:]
>Yes certainly. Perhaps the horizontal springs can be made a bit weaker
>if you add a damper to the drift spring.

Is what you're saying that you'd allow grounding spring targets to
change slowly? That's something I've been thinking of doing for
real-time tuning, an area I've long neglected.

[JdL:]
>>If the action of grounding is rewired so that it exerts no vertical
>>pull, would the issue of not retuning a sounding note still have
>>vertical sway?

[Manuel:]
>Yes, so it might be beneficial to make the action against drift like
>almost continuously, so at a higher rate than the notes, and also
>retune sounding notes.

Sorry, not following you here.

[Paul wrote:]
>Manuel -- this is the approach taken in John deLaubenfels' old real-
>time retuning program. His new, leisure-tine program can always do
>better because the horizontal retuning motions can always be reduced
>relative to the old method, given harmonies as close to just as
>desired.

Manuel's proposal _does_ allow for horizontal springs to pull intervals
away from JI, but does not allow grounding springs to. I'm not sure
this will give better results than the matrix I'm now using (because
the particular grounding position of a particular scale degree _is_
important in its own right, I think), but I'm very intrigued.

JdL

John wrote:
>Is what you're saying that you'd allow grounding spring targets to
>change slowly? That's something I've been thinking of doing for
>real-time tuning, an area I've long neglected.

I meant to let the excitation of the grounding spring to change
slowly, just like a car is damped on a bumpy road. Don't know if
that amounts to the same as you're saying to change the target
though.

>>Yes, so it might be beneficial to make the action against drift like
>>almost continuously, so at a higher rate than the notes, and also
>>retune sounding notes.

>Sorry, not following you here.

Think of it in terms of lowpass filtering the drift. Your model
has springs for discrete points in time. I was suggesting to act
against the drift at smaller time steps than those springs, to make
it appear more continuously. So to have a higher sampling frequency
for the drift.

>I'm not sure
>this will give better results than the matrix I'm now using (because
>the particular grounding position of a particular scale degree _is_
>important in its own right, I think), but I'm very intrigued.

Neither am I, the effect might well be negligible. But an advantage may
be that if you want to retune a piece in 15-tET for example, you don't
need to worry about using 15 grounding springs or whatever instead of
12.

Manuel