Re: That tuning method you (Carl L)'ve been pitching

[I wrote:]
>>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.

[Carl Lumma, TD 498.4:]
>My procedure only tunes the five loudest notes at a given time; less if
>there are less than five unique (after octave equivalence) pitches
>sounding.

Mmmm. My experience has been that, if you don't explicitly go after
and neutralize those small overlap points, you end up with tuning you
don't want when the dying notes die. Real-time schemes don't, of
course, "know", when a new chord starts, whether the old one is about to
die or not, which is one of the really tough challenges of real-time
adaptive JI, as opposed to what I call leisure retuning.

[JdL:]
>>Do you plan to have any chords actually tuned to 12-tET?

[Carl:]
>Nope.

So... if the first chord is an augmented triad, or full diminished
chord, how will it be tuned? Symmetry in, asymmetry out: a tough
proposition.

[JdL:]
>>How will you handle drift? The ol' comma pump, repeated many times?

[Carl:]
>Ignores drift entirely. Repeated pump makes the music go flat.

It's hard for me to believe you'll be satisfied with that! Drift
control is challenging, but, IMHO, all but essential.

[JdL:]
>>If there are three successive chords, and only the outer two have a C,
>>say, will the two C's consider their relative tuning?

[Carl:]
>Nope. In a way, I'm actually after "strict" JI here. I call it
>adaptive because it's getting at JI with only 12-pitches, moving the
>tonic is all over the place. But I'm trying more to access high-limit
>pitch sets than I am trying to get JI to conform to meantone logic.

Hmmm, I don't quite follow the whole paragraph. But listeners like Paul
E are likely to find mismatches if your method doesn't, I fear. Of
course, you may or may not want to get excited about that...

[JdL:]
>>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?

[Carl:]
>Just the shortest unit of action in the MIDI-verse. Yes, many ticks
>will not feature a change (although not as many as one might think,
>since event loudness is sampled at each tick), but the thing is: ain't
>nothin' gettin' past this baby.

OK, fine... As I've written on this list, I tend to bypass the MIDI
time scheme in favor of naked .001 sec "ticks", to prevent undesired
shoe-horning of rolled chords into block ones. Your method could just
go from midi event to midi event, skipping past empty ticks.

As always, I say, go for it, Carl! None of these challenges, or the
other ones you face, are insurmountable.

JdL

>Mmmm. My experience has been that, if you don't explicitly go after
>and neutralize those small overlap points, you end up with tuning you
>don't want when the dying notes die. Real-time schemes don't, of
>course, "know", when a new chord starts, whether the old one is about to
>die or not, which is one of the really tough challenges of real-time
>adaptive JI, as opposed to what I call leisure retuning.

Obviously, I have no idea how my method will sound. But, keeping in mind
that it re-evaluates the type of chord sounding at every tick, I don't
think it would suffer from the problem you're thinking of.

>So... if the first chord is an augmented triad, or full diminished
>chord, how will it be tuned? Symmetry in, asymmetry out: a tough
>proposition.

The chords are tuned by way of a lookup table. There may be several
19-limit chords that resemble a "full diminished chord" in sound (if you
mean a diminished 7th chord, 10:12:14:17 is one example).

My method trys to squeeze as many consonant relationships out of 12-tone as
possible. Erlich's method takes the opposite approach, ignoring anything
that isn't a simple 5-limit consonance. That seems the ideal method for
rendering classical music as it was meant to be heard. Of course, extended
meantone already does an excellent job, but it makes sense to hide the
errors horizontally rather than vertically, since you can, and the improved
fifths do make a difference.

>It's hard for me to believe you'll be satisfied with that! Drift
>control is challenging, but, IMHO, all but essential.

The important thing is: drift from what? Not all music depends on the
vanishing of the syntonic comma. Progressions are possible that would go
sharp in meantone.

The other thing is, my version doesn't completely ignore drift. As I said,
I use 12-tet as the ideal in horizontal motion. How? 1.) In the lookup
table, chords are penalized for their deviation from 12, and 2.) if there
aren't any common tones between adjacent chords, the 12-tet motion is taken
as ideal (see adaptive.txt).

>>Nope. In a way, I'm actually after "strict" JI here. I call it
>>adaptive because it's getting at JI with only 12-pitches, moving the
>>tonic is all over the place. But I'm trying more to access high-limit
>>pitch sets than I am trying to get JI to conform to meantone logic.
>
>Hmmm, I don't quite follow the whole paragraph. But listeners like Paul
>E are likely to find mismatches if your method doesn't, I fear. Of
>course, you may or may not want to get excited about that...

Let me turn you on to Erv Wilson's pitch-space diagrams (if you're not
already hip). Go to...

http://www.anaphoria.com/dal12.html

Figure 14 depicts the 11-limit Partchian tonality diamond. The diamond is
a pitch set formed by a group of connected hexads. In Wilson's chart each
hexad is a pentagon, and each vertex is a note (the 6th note is at the
center of the pentagon). Otonal hexads point up, utonal hexads point down.
See them in there? Notice the progression of hexads around the outside of
star -- each pair of chords is connected by a common dyad. The point is,
there are progressions which do not require temperament to work!

>As always, I say, go for it, Carl! None of these challenges, or the
>other ones you face, are insurmountable.

Thanks for your encouragement!

-Carl

On Sat, 22 Jan 2000 03:36:49 -0500, Carl Lumma <clumma@nni.com> wrote:

>The important thing is: drift from what? Not all music depends on the
>vanishing of the syntonic comma. Progressions are possible that would go
>sharp in meantone.

I don't know if this is the sort of thing you had in mind, but it reminds
me of the harmonic progression at the end of the Mizarian Porcupine
Overture. I wanted to take advantage of the enharmonic equivalents
available in 15tet but not 12tet. The sequence I came up with doesn't rely
on any of the exotic harmonies available in 15tet, so it's possible to play
it entirely in 12tet, but instead of closing the loop and continuing back
at Eb where it began, the 12tet version migrates upward one semitone at a
time!

Eb-- D C--- B C#-- C# E
Bb-- Bb G--- G# A--- G# A# B--- B
G--- G E--- E E--- E# F#----- G#
Eb-- D C--- B A C#-- C# D D# E

A JI version of this sequence without reference to 12tet would start at Eb+
6/5 and end up at E-- 100/81, a "drift" upwards of only 49 cents (half of
the 12tet-based drift).

--
see my music page ---> +--<http://www.io.com/~hmiller/music/music.html>--
Thryomanes /"If all Printers were determin'd not to print any
(Herman Miller) / thing till they were sure it would offend no body,
moc.oi @ rellimh <-/ there would be very little printed." -Ben Franklin

>I don't know if this is the sort of thing you had in mind, but it reminds
>me of the harmonic progression at the end of the Mizarian Porcupine
>Overture. I wanted to take advantage of the enharmonic equivalents
>available in 15tet but not 12tet. The sequence I came up with doesn't rely
>on any of the exotic harmonies available in 15tet, so it's possible to play
>it entirely in 12tet, but instead of closing the loop and continuing back
>at Eb where it began, the 12tet version migrates upward one semitone at a
>time!
>
>Eb-- D C--- B C#-- C# E
>Bb-- Bb G--- G# A--- G# A# B--- B
>G--- G E--- E E--- E# F#----- G#
>Eb-- D C--- B A C#-- C# D D# E
>
>A JI version of this sequence without reference to 12tet would start at Eb+
>6/5 and end up at E-- 100/81, a "drift" upwards of only 49 cents (half of
>the 12tet-based drift).

That's exactly what I had in mind. Nifty progression!

-Carl

Herman Miller wrote,

>The sequence I came up with doesn't rely
>on any of the exotic harmonies available in 15tet, so it's possible to play
>it entirely in 12tet, but instead of closing the loop and continuing back
>at Eb where it began, the 12tet version migrates upward one semitone at a
>time!

>Eb-- D C--- B C#-- C# E
>Bb-- Bb G--- G# A--- G# A# B--- B
>G--- G E--- E E--- E# F#----- G#
>Eb-- D C--- B A C#-- C# D D# E

>A JI version of this sequence without reference to 12tet would start at Eb+
>6/5 and end up at E-- 100/81, a "drift" upwards of only 49 cents (half of
>the 12tet-based drift).

Cool! So you're exploiting the vanishing of the 250:243 in 15-tET. This is
one of the great things about alternative tunings, in my opinion