Reply to Carl L on adaptive tuning

[I wrote:]
>>Mmmm. I'm not using a chord list per se; rather, each set of sounding
>>notes tries to fit itself to one of the tuning files loaded, in each
>>of the possible 12 keys the file can be transposed to.

[Carl Lumma, TD 496.4:]
>You've got to have something that pairs 12-tone chords with just ones.
>The question is, do you consider all just verions equally consonant?

No, I don't. My just7.tun, for example, tunes C to 0.00 cents deviation
from 12-tET, and tunes E -13.69 cents from 12-tET, thus forming an
exact 4:5 from C, and rates that ratio as "+32 goodness units", where
"goodness units" are arbitrarily defined, scale-adjusted by trial and
error. The same file tunes Bb as -31.16 cents from 12-tET, so that it
forms a 7:9 interval against D (tuned +3.91 cents from 12-tET), and it
rates that interval as "0 goodness units", in other words, it is less
favored if all you're playing is a major third. But when playing a
dom7, the program tries all alignments with the just7.tun file, summing
the goodness for all the intervals formed, and finds that the best
alignment comes when the 7:9 is tuned, well, as 7:9.

I use the same pre-processing before going into the spring world, as I
did before the program HAD springs. Then I wire the ideal interval of
each spring to match the tuning file selected previously. Having
selected a 4:5 spring in one place and a 7:9 spring in another, I don't
at present modify the spring constants based upon the interval; EXCEPT
that I have some slightly kludgy code that relaxes the spring constants
of 5-limit tritones (since from what people on the list say, having a
dissonant tritone is considered desirable in 5-limit, the opposite of
7-limit).

[Carl:]
>What if I didn't want to zero from 12-tet? What if I consider meantone
>ideal? 12 zaps the pythagorean and syntonic commas, but say I want to
>keep the pythagorean comma? Would it be difficult to let the user
>specify the ideal case in a file? In general could this be done for
>for all deviations, not just horizontal motion?

Paul E's idea of floating all but one pitch12 is one approach to this,
but I think you're asking for more. I'm not sure how to "keep the
pythagorean comma", without having the program explicitly follow the
modulations of the piece, which would be possible, though it's not
something I'm doing now.

I've done some more reading of your "adaptive.txt", and I have some
questions. Your idea of having a lookup table that has complete chords,
as opposed to my tuning tables which accommodate all chords "at once",
would seem to have both strengths and weaknesses. It's stronger in that
in theory you could provide more tuning possibilities (you've mentioned
going up to 19, where, for me, even 11 is a stretch). Weaker, in that
I see the number of chords you would need expanding rapidly in real-
life. What, for example, do you plan to do when two successive chords
overlap slightly? One option, which in fact I do, is to seek out such
overlaps, evaluate them for duration, and essentially throw away the
very brief complex chords formed when they don't last longer than some
preset time, which I typically set to 64 msec.

Do you plan to have any chords actually tuned to 12-tET? You know the
typical examples: augmented triads, full diminished tetrads, and strings
of four or more notes connected by fifths.

Depending upon your answer to that, how does volume of notes come into
play? For example, suppose I play C and E very loudly, but then play
G# very softly? This is sort of an augmented triad, sort of not.

What is your thought about considering the duration of chords? If I
play a chord for a very brief length of time, should it have as much
pull on tuning as a long sustained chord?

How will you handle drift? The ol' comma pump, repeated many times?

Will you consider the length of time between chords? Two conflicting
chords back-to-back vs. separated by a long silence, say.

In your scheme, can chords, or the notes within them, interact when
something else intervenes? If there are three successive chords, and
only the outer two have a C, say, will the two C's consider their
relative tuning?

When you refer to "ticks" in a MIDI file, what does this mean? I'm
aware of the MIDI time scheme, but if nothing is changing, there's
nothing to focus on, yes?

OK, that's enough for one posting! I'll be glad to continue to dig into
your scheme based on your response. Let's keep it on-list, if nobody
objects; I think others would be interested in what you're planning to
do, and perhaps others will bring forth their own ideas.

JdL

John deLaubenfels wrote,

>EXCEPT
>that I have some slightly kludgy code that relaxes the spring constants
>of 5-limit tritones (since from what people on the list say, having a
>dissonant tritone is considered desirable in 5-limit, the opposite of
>7-limit).

I don't see why you need to make an exception here. There is no consonant
tritone in 5-limit; the only consonances in 5-limit are ratios of numbers
five or below (after removing factors of two). Why do you need to handle it
differently that, say, major or minor seconds, which are also dissonant in
5-limit?

[I wrote:]
>>EXCEPT that I have some slightly kludgy code that relaxes the spring
>>constants of 5-limit tritones (since from what people on the list say,
>>having a dissonant tritone is considered desirable in 5-limit, the
>>opposite of 7-limit).

[Paul Erlich, TD 497.13:]
>I don't see why you need to make an exception here. There is no
>consonant tritone in 5-limit; the only consonances in 5-limit are
>ratios of numbers five or below (after removing factors of two). Why
>do you need to handle it differently that, say, major or minor seconds,
>which are also dissonant in 5-limit?

Back when we were first discussing the Chaconne (Bach? Busoni?), it
became clear that my method was suffering because I made the 5-limit
seventh degree 8/9 of the root above and tried hard to hold it there.
That, of course, results in a dissonant tritone. Since it's dissonant,
it's pointless to hold it rigidly in space; that only makes sense for
consonant notes.

In point of fact, I do also relax major and minor seconds in both
5-limit and 7-limit. The contrast between the two is the 7th degree:
in 7-limit (where, as I once said, to a firestorm of protest, "tuning
really MEANS something"), it's important to hold it about as tightly as,
say, a 4:5.

JdL