thesis

>From: Robert C Valentine <BVAL@IIL.INTEL.COM>
>I'm sure you've already been forwarded to the Harmonic Entropy list
>where you can see curves similar to what you describe

No, I haven't been, but I remember reading about that some time ago.
My system is centered on the idea of:
1. Defining exactly what you mean by certain intervals by
defining them fuzzily.
2. Defining a tuning by connecting the scalar degrees with fuzzy
intervals, and stating how important each is to you.
3. Letting an algorithm find the best compromise, either before the
performance or in response to which degrees are sounding.

I'd like to see what you think about how my system compares
with yours. My url is:
http://members.fortunecity.com/odradek5/pp/rustyprogress.html

What's yours?

Thanks for the interst,

-m

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--- In tuning@y..., "Michael Saunders" <michaelsaunders7@h...> wrote:
>
> >From: Robert C Valentine <BVAL@I...>
> >I'm sure you've already been forwarded to the Harmonic Entropy list
> >where you can see curves similar to what you describe
>
> No, I haven't been, but I remember reading about that some time ago.
> My system is centered on the idea of:
> 1. Defining exactly what you mean by certain intervals by
> defining them fuzzily.
> 2. Defining a tuning by connecting the scalar degrees with fuzzy
> intervals, and stating how important each is to you.
> 3. Letting an algorithm find the best compromise, either before the
> performance or in response to which degrees are sounding.

This sounds exactly like what John deLaubenfels is achieving for 12-
tET MIDI files and various paradigms of vertical tuning. And we've
discussed the possible extension to scores notated in meantone (i.e.,
most anything from 1480-1720) and more exotic notational systems. I
invite John to join in this discussion for he and Michael may have
much to share and perhaps much to learn from one another.

[Michael Saunders wrote:]
>>My system is centered on the idea of:
>>1. Defining exactly what you mean by certain intervals by
>> defining them fuzzily.
>>2. Defining a tuning by connecting the scalar degrees with fuzzy
>> intervals, and stating how important each is to you.
>>3. Letting an algorithm find the best compromise, either before the
>> performance or in response to which degrees are sounding.

[Paul E:]
>This sounds exactly like what John deLaubenfels is achieving for 12-
>tET MIDI files and various paradigms of vertical tuning. And we've
>discussed the possible extension to scores notated in meantone (i.e.,
>most anything from 1480-1720) and more exotic notational systems. I
>invite John to join in this discussion for he and Michael may have
>much to share and perhaps much to learn from one another.

Hi, Michael. Welcome to the list! What you're doing does sound a lot
like my field of interest. I do have your web address written down, but
won't have time to read it in depth for the rest of this week at least.
May I ask some questions about what you do?

. Are you able to process existing MIDI files?

. How do/would you handle a chain of fifths chord, ex. C-G-D-A, where
the fifths and the minor third conflict?

. What about augmented triads and full diminished tetrads?

. How do/would you handle the "comma pump" sequence: Cmaj, Amin,
Dmin, Gmaj, Cmaj, which tends to impose downward drift on the
tuning?

. Do you do 5-limit tuning, or do you go into higher limits, as, for
example, a 4:5:6:7 chord?

. It sounds above as if you do (or plan on doing) both real-time
adaptive tuning, and what I call "leisure" tuning (with knowledge
of the entire piece, able to "look forward" in time); is this
correct?

As Paul has mentioned, I'm at http://www.adaptune.com. Links from there
describe more detail on how I approach these challenges.

I look forward to further discussion of your methods!

JdL

>Thanks, there was something wrong with the PDF link (for me).

Sorry---fortunecity can be very screwy. I'll try uploading it again
this morning. There are also postscript and html versions up there,
and, if you have it at hand, Xenharmonikon #17 has an overview
article about it.

>finding 'good' tunings for diatonic scales, where good would mainly
>be aimed at having many good approximations of small fractions.

>I built a curve where the points of simple small ratios are
>minima...

That sounds great (I think I remember having read about it some
time ago). My system is for representing tunings in a general way,
in the way I think we really think about them, as networks of
fuzzy intervals. So, my system doesn't serch for optimal tunings the
way yours does; it searches for optimal tunings for a given network
of fuzzy intervals. I suppose if you weighted every possible interval
equally, and used standard dissonance curves for them, and masked
these so that they could only fall in a certain range, then you'd
probably get similar results with my algorithm.

>Shore, hope to have something intelligent to say when
>I read more in your paper.

I look forward to it!

-m

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>>My system is centered on the idea of:
>>1. Defining exactly what you mean by certain intervals by
>> defining them fuzzily.
>>2. Defining a tuning by connecting the scalar degrees with fuzzy
>> intervals, and stating how important each is to you.
>>3. Letting an algorithm find the best compromise, either before the
>> performance or in response to which degrees are sounding.

>This sounds exactly like what John deLaubenfels is achieving for 12-
>tET MIDI files and various paradigms of vertical tuning. And we've
>discussed the possible extension to scores notated in meantone (i.e.,
>most anything from 1480-1720) and more exotic notational systems. I
>invite John to join in this discussion for he and Michael may have
>much to share and perhaps much to learn from one another.

Yes---I'll have to see how his system compares with my unstable tuning.

thanks,

-m

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>Welcome to the list!

Thanks! (actually, I've been lurking for more years than
I can remember.)

> . Are you able to process existing MIDI files?

No (no desire to work with midi, really---I'm a csounder).
A little background:
My system, Rusty, hasn't yet been coded (well, a little bit has);
I've been trying to find support to continue the research, trying
to find a job, etc. It's not specifically for tuning---it's for representing
many different types of musical object in a very general, rigorous
way---the short paper on my site gives a good 1.5 page overview
of this. Of course, objects like intervals, scales and tunings are
a big part of the story. So, the goal, for me, is to be able to
_represent_ any imaginable instance of one of these objects (and
to represent it in the computer in the same way we think of it).
Also, the behavior of objects is important, so my scales know
how to tune themselves. Very roughly, it works like this:

-You define some intervals fuzzily (as a function of suitability
(on [0,1]) vs. pitch distance. This curve can have any shape at
all, perhaps representing your opinion about what a given interval
is or some objectively-generated dissonance curve. Generally
speaking, if you have a peak in the graph, that means that the
location of the peak is a suitable instance of the interval you're
defining. The width of the peak relates to how far you're willing
to temper it---the suitability drops off as you move away from the
peak.

-You have a scale (i.e., an indexing system) you want to use.

-You define a tuning by connecting some of the scalar degrees with
fuzzy intervals. You need only define the intervals that are
important to you, and you can weight them according to importance.

-Then, my algorithm finds the optimal tuning (absolute pitches)
_given_the_user_definitions_. The resulting scale is correct in
the sense that it's exactly what the user defined. In a nutshell,
the algorithm works like this: it finds all the pathways through
defined-intervals between an anchor (a degree with a defined
fixed pitch) and the degree being tuned. It adds the fuzzy intervals
on each pathway together by convolution (i.e., adding their
abscissae). It takes all of these (possibly conflicting) pathways
and combines them together by multiplication, generating a
curve of suitability vs. pitch for that degree. This is defuzzified by
finding the median of the maxima (the shape of the curve may
be interesting too).

And that's how I think we thing about tunings, deep-down, in
a very prcatical way.

> . How do/would you handle a chain of fifths chord, ex. C-G-D-A, where
> the fifths and the minor third conflict?

I'm not tied to any particular scale or interval definitions, so it
depends on how you define it. Let's say each of the possible intervals
gets a definition of a Gaussian curve peaking at:
CG---3/2 GD---3/2
CD---9/8 GA---9/8
CA---5/3 DA---3/2
with widths representing how far I think each can be tempered.
Then I throw it to the algorithm and let the computer worry
about it---I'll get the optimal compromise according to my definitions.

> . What about augmented triads and full diminished tetrads?

A similar story. You define what you mean by "maj/min third"
and "octave" using fuzzy intervals, then let the algorithm make
the compromise. Maybe you might like to make the interval
definitions based on dissonance curves, for example.

> . How do/would you handle the "comma pump" sequence: Cmaj, Amin,
> Dmin, Gmaj, Cmaj, which tends to impose downward drift on the
> tuning?

Drift is a big issue! My adaptive algorithm is in there. (I called my
fixed and adaptive systems "stable" and "unstable" in the thesis,
since the term "adaptive wasn't in use (or at least wasn't widespread)
when I wrote it.) It's something like 30 pages long, but roughly:
I process the score to determine to what degree (in a fuzzy sense)
each scalar degree is present at a given time, according to lots of
parameters about things that affect memory, etc. (there are several
ways notes can "persist"). Then the score is broken up into a series of
"harmonic contexts"---sections when the same set of degrees is sounding
---according to a lot of rules. Then it's a matter of anchoring each
context to a "fiducial" note. There are several categories of candidates
and the rules are quite Byzantine but, I think, rational---and controllable
with many parameters. Drift is a big issue in this. Then, my stable
tuning algorithm operates within this structure to tune notes only in
reference to what is sounding and the degree to which it is sounding.
There are versions where the pitches of notes are nominally constant
and where they are allowed to vary with time to improve the intonation.
I think it's quite general and covers everything---everything I could
think of anyway.

> . Do you do 5-limit tuning, or do you go into higher limits, as, for
> example, a 4:5:6:7 chord?

It's all a matter of what the user defines.

> . It sounds above as if you do (or plan on doing) both real-time
> adaptive tuning, and what I call "leisure" tuning (with knowledge
> of the entire piece, able to "look forward" in time); is this
> correct?

Yes, though I'm no fan of real-time, I designed the algorithms so
they never _require_ future information, though they can take
advantage of it (you'll notice in the handling of drift, there's no
bais towards forward/backward, for example).

>As Paul has mentioned, I'm at http://www.adaptune.com. Links from there
>describe more detail on how I approach these challenges.

Thanks---I'll be reading up on it!

>I look forward to further discussion of your methods!

Me too!

-m

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