Adaptive treatment for 19-tET

[Paul E:]
>One good way of doing the former might be to compose in an ET and then
>use an adaptive tuning program (John deLaubenfels' is only set up for
>12-tone now, but perhaps eventually 19-tone will be feasible) to
>determine the final tuning.

I seem to remember that when I first joined the list, you mentioned an
interest in adaptive treatment of 19-tET. Now, as then, this is
something I'd be glad to consider, time permitting. There are two big
issues involved:

. What target tuning is ideal for each interval represented in the
ET? Can a "tuning file free" method, which blindly assigns each
dyad in the ET to a target JI interval, do justice? If not, it's
harder.

. In what form will the program receive a sequence in non-12 ET?

Looking at the intervals for 19-tET, for example,

19-tET Raw Target
interval cents cents
------- ---- ------
1 63.16 70.67 (25:24)
2 126.32 111.73 (16:15)
3 189.47 182.40 (10:9) or 203.91 (9:8)
4 252.63 266.87 (7:6) or 231.17 (8:7)
5 315.79 315.64 (6:5)
6 378.95 386.31 (5:4)
7 442.11 435.08 (9:7)
8 505.26 498.04 (4:3)
9 568.42 582.51 (7:5)
10 631.58
11 694.74 701.96 (3:2)
12 757.89
13 821.05 813.69 (8:5)
14 884.21 884.36 (5:3)
15 947.37 (ambiguous - see above)
16 1010.53 (ambiguous - see above)
17 1073.68 1088.27 (15:8)
18 1136.84
19 1200.00 1200.00 (2:1)

OK: in 5-limit, we're fine - everything smaller than 5 would be given
zero spring strength; in fact, only 5, 6, 8, and inversions thereof are
considered important, right? Unfortunately, I'm only really interested
if there's a plausibility in 7-limit as well, and there the ambiguity
of 7:6 and 8:7 means that springs can't reasonably be "blindly"
targeted. Thus, for 19-tET in 7-limit, my tuning file method or some
good substitute is required. That's more work than the blind method.

And what of the second question? Pitch bends? This I could handle.

JdL

John deLaubenfels wrote,

> . What target tuning is ideal for each interval represented in the
> ET? Can a "tuning file free" method, which blindly assigns each
> dyad in the ET to a target JI interval, do justice? If not, it's
> harder.

The situation is much as in 12-tone. For 5-limit, one can go "tuning file
free". For 7-limit, one has to look at triads or larger chords. With 31
tones can one go "tuning file free" in the 7-limit; with 41 tones one can go
"tuning file free" in the 9-limit, and with 72 tones one can go "tuning file
free" in the 11-limit.

>. In what form will the program receive a sequence in non-12 ET?

How about a mapping where a perfect twelfth on the keyboard represents a
19-tone octave (2:1)?

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

/tuning/topicId_19011.html#19011

> [Paul E:]
> >One good way of doing the former might be to compose in an ET and
then use an adaptive tuning program (John deLaubenfels' is only set
up for 12-tone now, but perhaps eventually 19-tone will be feasible)
to determine the final tuning.
>
> I seem to remember that when I first joined the list, you mentioned
an interest in adaptive treatment of 19-tET. Now, as then, this is
> something I'd be glad to consider, time permitting. There are two
big issues involved:
>
>What target tuning is ideal for each interval represented in
the ET? Can a "tuning file free" method, which blindly assigns
each dyad in the ET to a target JI interval, do justice? If not,
it's harder.
>
In what form will the program receive a sequence in non-12 ET?
>

This is, of course, an interesting proposal, but it might get a
little complex. For the type of work I am, personally, going to
be doing, I will be using a synthesizer with an adjustable tuning
table. So it's going to be hard to work with the MIDI file... that
is, unless the pitch bends for 19-tET could be added LATER and then
manipulated from there... I suppose that's a possibility...

And then, there is the live performer. Of course, that line could
simply be done in MIDI and then the pitch bend "deviations"
transferred to the printed score... but it does add another
"complexity..."

________ ______ _____ __
Joseph Pehrson

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:

/tuning/topicId_19011.html#19012

>
In what form will the program receive a sequence in non-12 ET?
>
> How about a mapping where a perfect twelfth on the keyboard
represents a 19-tone octave (2:1)?

Actually, this looks now like it would be a bit easier than I thought
it would be. It should be pretty easy to assign 19-tET pitch bends
to this 19-note MIDI note numbers (or maybe about 3 "octaves" of
them...), and go from there...

It would be quite fascinating to write a 19-tET piece and then
compare it with a true "adjusted" JI version. That certainly would
solve the problems of the "wolves" and "irregularities" arising in
the various JI scales posted in SCALA (!!)

________ ______ _____ ___
Joseph Pehrson

[Joseph Pehrson wrote:]
>This is, of course, an interesting proposal, but it might get a
>little complex. For the type of work I am, personally, going to
>be doing, I will be using a synthesizer with an adjustable tuning
>table. So it's going to be hard to work with the MIDI file... that
>is, unless the pitch bends for 19-tET could be added LATER and then
>manipulated from there... I suppose that's a possibility...

>And then, there is the live performer. Of course, that line could
>simply be done in MIDI and then the pitch bend "deviations"
>transferred to the printed score... but it does add another
>"complexity..."

Right - I'm not surprised it wouldn't be useful for the work you're
doing. And there's not much stuff out there in the MIDI world in
19-tET to make the effort worthwhile. I'll probably stick to 12-tET
source files for awhile.

JdL

>I seem to remember that when I first joined the list, you mentioned an >interest in adaptive treatment of 19-tET. Now, as then, this is

I have also mentioned adaptive 19-based tuning,when posting some of my pieces here.

>In what form will the program receive a sequence in non-12 ET?

As individual midi note numbers,1-128.Each midi note representing one 1/19 octave step.I usually use note number 60(c)as a reference,though this should of course be adjustable.Range is a problem,since 128 notes are not enough for a full piano range with 19 tones,but that is more a problem for the composers.

If you are going to extend your adaptive tuning utilities for non-12 tunings,you should consider supporting other tunings as well(17,22,24?)that could all benefit from this kind of treatment.

Just a few suggestions,

-=-=-=-=-=-=-
MATS �LJARE
http://www.angelfire.com/mo/oljare
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