need dissonant 72-tET scale

Well, my "prediction" is that many, many composers are going to be
writing "requiems" for the World Trade Center. There will be some
*huge* pieces, and many of them. In fact, many of our most visible
composers will have at least one.

Other composers, perhaps not needing to make quite as big a "splash"
will be writing their own personal pieces, dealing internally with
the tragedy.

It is more in this spirit that I need a little help getting some
scales together.

I need a scale that is expansive, resonant and pretty dissonant. I
thought at first of possibly a non-octave scale, but really they are
much too difficult to notate, if I decide to include a live
performer...

Similarly, although I know there are people on this list who feel 19-
tET is easy to notate and learn for specifically "non-xenharmonic"
performers, but I have some doubts there, too. 19-tET might have the
right "sound" for such a project, but I need something even more
practical...

I have *no* doubts, however, about the feasibility of performers
learning 72-tET... None whatsoever.

However, my favorite "blackjack" subset would surely not be right for
such a project. It is much too "sunny" a scale, much too consonant.

What I need is the "dark brother" of blackjack... another scale
subset of 72-tET that is everything that blackjack is *not*..... the
opposite pole. *That* is what would be needed for a suitable WTC
requiem...

I would say if we could keep it in the range of about 21 notes or
fewer that would work best...

I know I already had been discussing some of these possibilities with
Paul Erlich and others on this list... some time ago we were
bantering around the idea of a "dissonant" 72-tET scale, but never
came up with anything.

Now's the time. Any suggestions?? This is a dissonant and mournful
time if ever there was one!

Any help or suggestions would be *greatly* appreciated!

Thanks!

________ _______ _______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

> I need a scale that is expansive, resonant and pretty dissonant. I
> thought at first of possibly a non-octave scale, but really they
are
> much too difficult to notate, if I decide to include a live
> performer...

With 72 notes to an octave, you can certainly cook up a lot of
dissonances if you want to, but the whole idea seems a little
perverse--you choose a division, 72, specifically because it has so
many consonances, and then ask for dissonaces. Why not try a
suggestion of Paul, and play the 22-et with an emphasis on the 11-et
subscale? The 11-et has a lot of dissonaces, and if it is too much
you can moderate it a bit by bringing in some 22-et notes. If you
want to go all out with dissonance I would suggest a nonoctave scale
tuned by a zero of the Riemann Zeta function, which I would be happy
to supply on request.

When you are ready for a bright, cheery 21/72 scale with lots of
triads and other consonances, you can try the one I mentioned here
recently.

Why we mistake a dissonances with out of tunning
sounds ?! It's horrible :))

Dimitrov

--- genewardsmith@juno.com a �crit�: > --- In
tuning@y..., jpehrson@r... wrote:
>
> > I need a scale that is expansive, resonant and
> pretty dissonant. I
> > thought at first of possibly a non-octave scale,
> but really they
> are
> > much too difficult to notate, if I decide to
> include a live
> > performer...
>
> With 72 notes to an octave, you can certainly cook
> up a lot of
> dissonances if you want to, but the whole idea seems
> a little
> perverse--you choose a division, 72, specifically
> because it has so
> many consonances, and then ask for dissonaces. Why
> not try a
> suggestion of Paul, and play the 22-et with an
> emphasis on the 11-et
> subscale? The 11-et has a lot of dissonaces, and if
> it is too much
> you can moderate it a bit by bringing in some 22-et
> notes. If you
> want to go all out with dissonance I would suggest a
> nonoctave scale
> tuned by a zero of the Riemann Zeta function, which
> I would be happy
> to supply on request.
>
> When you are ready for a bright, cheery 21/72 scale
> with lots of
> triads and other consonances, you can try the one I
> mentioned here
> recently.
>
>
>

___________________________________________________________
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--- In tuning@y..., genewardsmith@j... wrote:

/tuning/topicId_28599.html#28600

> --- In tuning@y..., jpehrson@r... wrote:
>
> > I need a scale that is expansive, resonant and pretty dissonant.
I thought at first of possibly a non-octave scale, but really they
> are much too difficult to notate, if I decide to include a live
> > performer...
>
> With 72 notes to an octave, you can certainly cook up a lot of
> dissonances if you want to, but the whole idea seems a little
> perverse--you choose a division, 72, specifically because it has so
> many consonances, and then ask for dissonaces.

Hello Gene!

Actually, that's not entirely the case... My choice for 72-tET is
simply due to the convenience of the performer and the ease of the
notation... since 12-tET can be used as the basis for it.

In fact, I would *love* to have *many* different 72-tET based scales
ranging from the *most* consonant, such as the Miracle family, to
actively dissonant ones...

If there is a way to calculate that, mathematically, and present it
as a gradual "range" of overall, I guess, averaged concordance, that
would be what I'm looking for...

Kind of similar to where Paul used calculus to average the
dissonances present for various Miracle generator candidates. But
what do *I* know about this...?? Not much. That's why I need help
from the "scalemeisters...."

The fact that 72-tET can *also* give very consonant scales is an
added plus, an extremely important one, but it's not really the
reason I want to use 72...

I'm hoping to replace 12-tET with 72-tET for *all* my subsequent
compositions.... I think it will work for me....

best,

________ ________ _______
Joseph Pehrson

--- In tuning@y..., genewardsmith@j... wrote:

/tuning/topicId_28599.html#28600

If you want to go all out with dissonance I would suggest a nonoctave
scale tuned by a zero of the Riemann Zeta function, which I would be
happy to supply on request.
>

Whoopsie... I missed this the first time around. Well, maybe this
would be great for a totally electronic piece that didn't require
live performers. What is the Riemann Zeta function, again?? To me,
anyway, it sounds impressive, but we'll have to hear what it sounds
like... :)

Sure, please post this in cents, and I'll cook up SCALA and MIDI
RELAY to try it out.

Thanks, Gene!

> When you are ready for a bright, cheery 21/72 scale with lots of
> triads and other consonances, you can try the one I mentioned here
> recently.

I'm sorry to say it's going to be some time before I want to listen
to *anything* "cheery..."

Brahms Requiem and Mozart Mass in C Minor are about as "happy" as I
care to get at the moment...

best,

________ ________ __________
Joseph Pehrson

--- In tuning@y..., Latchezar Dimitrov <latchezar_d@y...> wrote:

/tuning/topicId_28599.html#28604

> Why we mistake a dissonances with out of tunning
> sounds ?! It's horrible :))
>
> Dimitrov
>

I like out of tunning sounds...

_______ ______ ________
Joseph Pehrson

Hi Joseph . . .

Personally, I think you can find all the dissonance you need already
in the Blackjack scale, by avoiding the consonant intervals. Play
random chords with it. What do you think?

But if you want a more conceptually dissonant scale, we've come up
with some suggestions in the recent past . . . one possibility
(though not "optimal" in any sense) is to use the "most irrational"
interval, the Golden Ratio (Phi), as your generator . . . Phi is
833.0903, approximated very well by an interval of 50 steps in 72-
tET, or 25 steps in 36-tET . . . the 23-tone MOS of this generator
would probably satisfy you most in terms of the number of notes it
contains, unless you want to go down to 13 notes . . .

Keep in mind that any scale with this many notes is going to contain
a lot of dissonances, and at least a few consonances
fortuitously . . .

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_28599.html#28619

> Hi Joseph . . .
>
> Personally, I think you can find all the dissonance you need
already in the Blackjack scale, by avoiding the consonant intervals.
Play random chords with it. What do you think?

Well, my impression of blackjack is that it is a rather "sunny" scale
on the overall... Of course, generally I have been trying to feature
consonant use of it. I might like to try something a bit
more "conceptually dissonant" as you suggest for this particular
project...

>
> But if you want a more conceptually dissonant scale, we've come up
> with some suggestions in the recent past . . . one possibility
> (though not "optimal" in any sense) is to use the "most irrational"
> interval, the Golden Ratio (Phi), as your generator . . . Phi is
> 833.0903, approximated very well by an interval of 50 steps in 72-
> tET, or 25 steps in 36-tET . . . the 23-tone MOS of this generator
> would probably satisfy you most in terms of the number of notes it
> contains, unless you want to go down to 13 notes . . .
>

Paul, would you mind "boiling out" the subsets of 72-tET in cents for
me, so I can hear what they sound like??

Didn't we also have some 19-tone subsets with various levels of
dissonance?? That would be about the right number of notes...

Thanks!

_________ ______ ______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

> Well, my impression of blackjack is that it is a rather "sunny"
scale
> on the overall...

Pick a midi file at random, use Scala to retune it to Blackjack, and
then see what you think.

--- In tuning@y..., jpehrson@r... wrote:

> Paul, would you mind "boiling out" the subsets of 72-tET in cents
for
> me, so I can hear what they sound like??

They also are subsets of 36-tET . . .

Here's the 13-tone one:

0
100
200
266.667
366.667
466.667
566.667
633.333
733.333
833.333
933.333
1000
1100

And here's the 23-tone one:

0
66.667
100
166.667
200
266.667
300
366.667
433.333
466.667
533.333
566.667
633.333
666.667
733.333
766.667
833.333
900
933.333
1000
1033.333
1100
1133.333

>
> Didn't we also have some 19-tone subsets with various levels of
> dissonance??

Well, the ones that came from the original PB studies would be
rather "conceptually consonant" . . . but I think Gene may have
mentioned some others more recently . . .

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., jpehrson@r... wrote:
>
> > Well, my impression of blackjack is that it is a rather "sunny"
> scale
> > on the overall...
>
> Pick a midi file at random, use Scala to retune it to Blackjack,
and
> then see what you think.

Well, if you're retuning keyboard key by keyboard key, this test will
actually be too biased toward making Blackjack seem "sunny", since
the common consonant intervals -- octaves, fifths, fourths, major
sixths -- happen to usually map to consonant intervals on the
Blackjack keyboard!

Also, Joseph, don't forget to try 18-tET . . . it's a subset of 72
and rife with dissonance, but may be easier to use than some of the
unequal scales . . .

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_28599.html#28626

> --- In tuning@y..., jpehrson@r... wrote:
>
> > Paul, would you mind "boiling out" the subsets of 72-tET in cents
> for
> > me, so I can hear what they sound like??
>
> They also are subsets of 36-tET . . .
>
> Here's the 13-tone one:
>
> 0
> 100
> 200
> 266.667
> 366.667
> 466.667
> 566.667
> 633.333
> 733.333
> 833.333
> 933.333
> 1000
> 1100
>
> And here's the 23-tone one:
>
> 0
> 66.667
> 100
> 166.667
> 200
> 266.667
> 300
> 366.667
> 433.333
> 466.667
> 533.333
> 566.667
> 633.333
> 666.667
> 733.333
> 766.667
> 833.333
> 900
> 933.333
> 1000
> 1033.333
> 1100
> 1133.333
>

Thanks, Paul. I appreciate this. I will try these. The way you
drew them out, they look a little like two buildings... I'm spooked...

_________ _______ ______
Joseph Pehrson

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_28599.html#28628

> Also, Joseph, don't forget to try 18-tET . . . it's a subset of 72
> and rife with dissonance, but may be easier to use than some of the
> unequal scales . . .

Great idea... I will try this as well. I have plenty to work with
here...

I thought I would be able to use blackjack for *everything* but I'll
stick with my overall contention that blackjack is, on the overall,
a "sunny" scale... and that includes the more or less "random"...
well, by "ear" but not theoretically systematic, use of the
dissonances in it...

__________ _______ ________
Joseph Pehrson