Draft of FAQ: what is adaptive tuning?

I invite help from many list members (Margo, Paul E, etc., etc.) who
can fill in for gaps in my knowledge! And of course, all other comments
are welcome as well.

=====================================================================

Adaptive tuning (also called dynamic tuning) is the process of modifying
the tuning of pitches as a piece is played, to best suit the intervals
and chords at each moment.

There are many types of adaptive tuning:

. Discrete Adaptive Tuning (DAT), also called Fixed Adaptive Tuning
(FAT) vs. Continuous Adaptive Tuning (CAT), also called Variable
Adaptive Tuning (VAT).

. Method of making tuning choices: performer vs. computer program.

. Real-time adaptive tuning vs. "leisure" tuning, with the latter
able to make choices based on an entire work, and the former able
to see only the past and present.

DAT/FAT achieves adaptive tuning by making dynamic use of a fixed set of
available pitches, almost always on a keyboard instrument. The number
of possible pitches is determined by the number of physical keys
available to the player. This has the advantage of giving the artist
complete control over the adaptive tuning used, at the expense of
limiting to some extent the range of what can be done.

A practical method for DAT/FAT was first proposed by Nicoli Vicentino in
1555. One keyboard manual is tuned in 1/4 comma meantone, or actually
the almost identical 31-tET; the other corrects for the flat fifths by
being tuned 1/4 comma higher.

CAT/VAT can be produced by some acoustic instruments, and by the human
voice, and by electronic instruments. Barbershop singing makes heavy
use of CAT/VAT, and to some extent, so do jazz and blues singing and
playing. More recently, there have been experiments with retuning
programs that apply CAT/VAT to MIDI files.

The challenges of adaptive tuning are easily illustrated: consider the
sequence C->A->D->G->C, either with bare notes or with the chords Cmaj,
Amin, Dmaj, Gmaj, Cmaj. The ideal tunings for the four sequential
intervals are 5:6, 4:3, 4:3, 4:3, but the product of these, corrected
for octave, is 80:81, the famous (or infamous) syntonic comma. One way
to deal with this challenge is to let the absolute tuning "drift" over
time, in this case downward by about 1/5 semitone each time the sequence
is played. Over the course of a reasonably long piece, drift of this
sort can easily amount to a large fraction of an octave, if not more.
There is a school that accepts such drift in order never to compromise
simultaneous intervals or retune sounding notes. If drift is considered
unacceptable, however, then difficult choices have to be made, both in
modifying the tuning of notes which are continuously sounding, and in
compromising to some extent the tuning of intervals.

Real-time adaptive tuning by program is superior to leisure tuning in
that one need not wait for the results: as a piece is played, it is
tuned. However, since chord transitions often involve a few
milliseconds of overlap, a real-time program can easily become confused
and make bad choices that have to be corrected with painful motion of
notes already sounding. These challenges are particularly intense when
tuning targets 7 or higher limits, in which tuning deviations are much
greater than in 5-limit music.

At least one commercial program is available for real-time CAT/VAT,
and at least one list member has dabbled in leisure retuning of MIDI
files. The field of adaptive tuning is still in its infancy, however,
and many refinements have yet to be made. Also, there is a great deal
of controversy regarding what target adaptive tunings (if any) are
suitable, or appropriate, for works of past masters.

Oops! Make that Nicola Vicentino, not Nicoli Vicentino! And in the
comma pump sequence I meant to use Dmin, not Dmaj.

JdL

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

/tuning/topicId_19260.html#19260

>
> There are many types of adaptive tuning:
>
>Discrete Adaptive Tuning (DAT), also called Fixed Adaptive
Tuning(FAT) vs. Continuous Adaptive Tuning (CAT), also called
Variable Adaptive Tuning (VAT).
>

John... did you ever read the CAT in the HAT?? I like your acronyms,
but I hope they won't only be enjoyed by FAT CATS...
_______ ____ ____ ___
Joseph Pehrson

[I wrote:]
>> There are many types of adaptive tuning:
>>
>>Discrete Adaptive Tuning (DAT), also called Fixed Adaptive
>>Tuning(FAT) vs. Continuous Adaptive Tuning (CAT), also called
>>Variable Adaptive Tuning (VAT).

[Joseph Pehrson:]
>John... did you ever read the CAT in the HAT?? I like your acronyms,
>but I hope they won't only be enjoyed by FAT CATS...

O'course I did - didn't everybody? Actually, it came out when I was
9 or 10, but my baby sister was the perfect age, so we all used to
read it to her.

These terms actually aren't mine: Dave Keenan suggested DAT/CAT, and
Margo suggested FAT/VAT. I'd like to reduce it down to one set if
possible, but no one else has expressed a preference of one over the
other, so I'm gonna keep'm both till it gets sorted out.

(Funny, the words from Dr. Seuss are coming back into my head, after all
these years... Someday I plan to get a complete set of his books -
which one had the Patrol Cats? How about Bartholomew and the Oobleck?
That one was very scary to me as a child...)

JdL

Hi John deLaubenfels:

I see a lot of potential for confusion with your FAQ entry.

For example, one might read what you've written and come up with the
usual strict-JI "solution" to your Cmaj-Amin-Dmin-Gmaj-Cmaj problem:
simply allow the D in D minor to be 10/9 and the D in G major to be
9/8. There's no drift there. It would seem to be a DAT/FAT solution
according to what you've written! Is it? I don't know . . . though
Eivind Groven's adaptively-tuned "JI" keyboard would make use of this
kind of solution (except in 1/8-schisma temperament), clearly it
doesn't satisfy my ears or the goals of your program . . . so perhaps
you need to decide whether adaptive tuning is defined as something
that has to improve upon strict JI when it comes to retune motion, or
whether strict JI can sometimes be considered a subset of adaptive
tuning . . .

. . . One should mention "necessarily tempered chords" too . . .

It might be better to start really slowly, with examples -- your
writing could be intimidating to someone who hasn't thought about
these issues and might barely have a grasp of the concepts involved.

> A practical method for DAT/FAT was first proposed by Nicol[a]
Vicentino in
> 1555. One keyboard manual is tuned in 1/4 comma meantone, or
actually
> the almost identical 31-tET; the other corrects for the flat fifths
> by
> being tuned 1/4 comma higher.

And the flat minor thirds! P.S. this is not a very practical method
at all -- how do you handle sustained pitches when they have to move
from one keyboard to the other -- but it is an outstanding
theoretical method, preserving the triadic purity of JI while audibly
matching the melodic integrity of meantone, which Vicentino
recommended for singers (Margo, did I remember that correctly?).

[Paul E:]
>I see a lot of potential for confusion with your FAQ entry.

>For example, one might read what you've written and come up with the
>usual strict-JI "solution" to your Cmaj-Amin-Dmin-Gmaj-Cmaj problem:
>simply allow the D in D minor to be 10/9 and the D in G major to be
>9/8. There's no drift there. It would seem to be a DAT/FAT solution
>according to what you've written! Is it? I don't know . . . though
>Eivind Groven's adaptively-tuned "JI" keyboard would make use of this
>kind of solution (except in 1/8-schisma temperament), clearly it
>doesn't satisfy my ears or the goals of your program . . . so perhaps
>you need to decide whether adaptive tuning is defined as something
>that has to improve upon strict JI when it comes to retune motion, or
>whether strict JI can sometimes be considered a subset of adaptive
>tuning . . .

At the suggestion of Daniel Wolf off-list, I've condensed the terms;
I think I'll just use FAT and VAT, if no one objects. I must admit that
I'd never considered whether strict JI, with its unchecked drift, would
be considered a subset of adaptive tuning. I'd prefer that someone who
uses strict JI decide that, but, for the moment, I've included the drift
option under the adaptive tuning umbrella.

What I'm trying to illustrate with the comma-pump sequence is that
SOMETHING has to give. I do explicitly mention drift as an option, but
perhaps I need to say more clearly that the alternative, the retuning
of existing notes, is painful? I had thought that was clear, but maybe
not.

>. . . One should mention "necessarily tempered chords" too . . .

>It might be better to start really slowly, with examples -- your
>writing could be intimidating to someone who hasn't thought about
>these issues and might barely have a grasp of the concepts involved.

Well, I'm torn: it would be easy to write something three times as long,
or even much longer, but we have other list members saying "Less is
more", and seeming to imply that a single sentence should suffice. We
are, of course, still waiting for more specific suggestions from the
list member who has been most vocal in this regard.

>>A practical method for DAT/FAT was first proposed by Nicol[a]
>>Vicentino in 1555. One keyboard manual is tuned in 1/4 comma
>>meantone, or actually the almost identical 31-tET; the other corrects
>>for the flat fifths by being tuned 1/4 comma higher.

>And the flat minor thirds!

OK, I'll add mention of them. In fact, since Margo has written up a
piece on Vicentino, I'll just point to hers, after a brief mention in my
write-up.

>P.S. this is not a very practical method at all -- how do you handle
>sustained pitches when they have to move from one keyboard to the other

Paul, I really have to chuckle at this, because a few months ago you
seemed very upset at me when I pointed out this limitation - do you
remember?

>-- but it is an outstanding
>theoretical method, preserving the triadic purity of JI while audibly
>matching the melodic integrity of meantone, which Vicentino
>recommended for singers (Margo, did I remember that correctly?).

OK, I'll change the word "practical" to "theoretical", but mainly I'll
point to Margo's entry.

I do of course realize that a newcomer to tuning will be left with more
questions than answers after reading this FAQ about adaptive tuning.
My hope is at least to give some kind of underpinning for the subject,
knowing that further study will be necessary. Again at Daniel's
suggestion off-list, I've added links to my own and others' web pages;
I'll post rev. 1 in a moment.

Again, I'd be glad to expand, and/or to invite others to add specific
clarifications, either as separate entries or as suggested inclusions
for the entry I've begun (or, for that matter, as a replacement!). This
will be an HTML document, with links possible, and it might be less
intimidating to keep the main entry no more than a page or so long,
with liberal links to other pages with more details.

BTW: Paul, whether or not you act as editor for this FAQ, I hope you'll
write up some entries for it! If it is considered unacceptable for one
person to be both editor and author, I'd rather see you use your
expertise to be an author.

JdL

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

> Paul, I really have to chuckle at this, because a few months ago you
> seemed very upset at me when I pointed out this limitation - do you
> remember?
>
I remember you pointing it out, but I don't remember being very upset!

> >-- but it is an outstanding
> >theoretical method, preserving the triadic purity of JI while
audibly
> >matching the melodic integrity of meantone, which Vicentino
> >recommended for singers (Margo, did I remember that correctly?).
>
> OK, I'll change the word "practical" to "theoretical", but mainly
I'll
> point to Margo's entry.

Maybe you could just get the salient point in there, as in my
sentence above (which Margo appeared to echo in her recent post).

> BTW: Paul, whether or not you act as editor for this FAQ, I hope
you'll
> write up some entries for it! If it is considered unacceptable for
one
> person to be both editor and author, I'd rather see you use your
> expertise to be an author.

Well, I'll wait and see if there are any holes that need filling, but
for now I'll satisfy myself by making suggestions to other people's
FAQs.