Stretching Exercises from a Microtonal Contortionist

Stretching Exercises

Working with Non-Octave Tunings has led me to devise a couple of
Stretch Tuning techniques that I'd like to share with friends here
(will be in installments).

Let's take a simple 5 Limit JI scale, and look at how one of these
stretching schemes will change the structure. Our first goal here
will be a linear stretch which will leave the symmetry of the scale
intact.

Nine Tone, 5 Limit, Inversionally Symmetrical JI Scale
Ratio Cents Consecutive
1/1 0.000 0
9/8 203.910 203.910
6/5 315.641 111.731
5/4 386.314 70.672
4/3 498.045 111.731
3/2 701.955 203.910
8/5 813.686 111.731
5/3 884.359 70.672
16/9 996.090 111.731
2/1 1200.000 203.910

Let's stretch the above familiar JI scale by .428 cents, to slightly
augment each degree proportionally. We can do this by creating a
stretch table, where we simply multiply .428 cents by numbers 1-9,
then add these values to each successive scale degree. The table
looks like this:

Cents
1.000 0.428
2.000 0.856
3.000 1.284
4.000 1.712
5.000 2.14
6.000 2.568
7.000 2.996
8.000 3.424
9.000 3.852

So we'll add these values to our 5 Limit scale to obtain:

Cents Consecutive
0
204.338 204.338
316.497 112.159
387.598 71.100
499.757 112.159
704.095 204.338
816.254 112.159
887.355 71.100
999.514 112.159
1203.852 204.338

One can see that the stretched scale maintains its original symmetry,
and remains with 3 step sizes, but is wider by 3.852 cents at the
2/1. This is a nice scale too, and I invite folks to try it out to
let me know what you think. Hopefully my JI friends out there won't
banish me to the wastelands for the blasphemy of stretching our
beloved 5 Limit JI. I think you may be surprised at how nice it
sounds though. My interest here parallels my love of Gamelan, and
these are attempts to transform a tuning to include subtle beating,
like that found in a Gamelan scale.

Now for fun, let's look at a more severe stretch, using the same
method, but this time with a 1.67 cents stretch:

Cents Consecutive
0
205.580 205.580
318.981 113.401
391.324 72.342
504.725 113.401
710.305 205.580
823.706 113.401
896.049 72.342
1009.450 113.401
1215.030 205.580

Here we've stretched the octave by 15.030 cents, and have more
radically altered the original scale.

Next installment: Applying a "Curved Stretch" to a scale.

Thanks, and happy stretching!

Jacky Ligon

Jacky Ligon wrote,

<<Let's stretch the above familiar JI scale by .428 cents, to slightly
augment each degree proportionally. We can do this by creating a
stretch table, where we simply multiply .428 cents by numbers 1-9,
then add these values to each successive scale degree.>>

If you wanted to start with the amount you'd want the octave (or
periodicity or "interval of equivalence", etc.) stretched or
compressed by then you could write this as (where X indicates the
periodicity in cents):

(LOG(n)-LOG(d))*(X/LOG(2))

I use this a lot as it allows you to stick whatever you wanted for
ratios into the scale and they'd have an appropriate logarithmic
stretch (or compression or whatnot).

So say you wanted to project the 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1
syntonic logarithmically into the Bohlen-Pierce 3/1. Then let X =
(LOG(3)-LOG(1))*(1200/LOG(2)) and you have (in rounded cents):

0 323 612 789 1113 1402 1725 1902
0 289 466 789 1078 1402 1579 1902
0 177 500 789 1113 1290 1613 1902
0 323 612 935 1113 1436 1725 1902
0 289 612 789 1113 1402 1579 1902
0 323 500 823 1113 1290 1613 1902
0 177 500 789 966 1290 1579 1902

Say you wanted a stretched octave scale where the overtone series 5-10
was shrunk into a 17/12 and extended out to the 4/1. Let X =
(LOG(17)-LOG(12))*(1200/LOG(2)) and you'd have a unique set of
Messiaen like "modes of limited transposability":

0 159 293 409 511 603 762 896 1012 1114 1206
0 134 250 353 444 603 737 853 956 1047 1206
0 116 219 310 469 603 719 822 913 1072 1206
0 102 194 353 487 603 705 797 956 1090 1206
0 92 250 384 501 603 695 853 987 1104 1206

I use these types of things quite a bit. The possibilities are
endless.

--Dan Stearns

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Jacky Ligon wrote,
>
> <<Let's stretch the above familiar JI scale by .428 cents, to
slightly
> augment each degree proportionally. We can do this by creating a
> stretch table, where we simply multiply .428 cents by numbers 1-9,
> then add these values to each successive scale degree.>>
>
> If you wanted to start with the amount you'd want the octave (or
> periodicity or "interval of equivalence", etc.) stretched or
> compressed by then you could write this as (where X indicates the
> periodicity in cents):
>
> (LOG(n)-LOG(d))*(X/LOG(2))
>
> I use this a lot as it allows you to stick whatever you wanted for
> ratios into the scale and they'd have an appropriate logarithmic
> stretch (or compression or whatnot).
>
> Say you wanted a stretched octave scale where the overtone series 5-
10
> was shrunk into a 17/12 and extended out to the 4/1. Let X =
> (LOG(17)-LOG(12))*(1200/LOG(2)) and you'd have a unique set of
> Messiaen like "modes of limited transposability":
>
> I use these types of things quite a bit. The possibilities are
> endless.
>
> --Dan Stearns

Dan,

Profuse thanks to you for this - it is terrific and quite beautiful
what you have shown here, and I was hoping that someone would chime
in with a more formal way of doing this than what I was showing.
Extremely cool - Dan the Man!

What a great way to instantly transform a basic scale into NJNE! I'm
loving the sound of these tunings.

Now show me how you'd apply a Fibonacci-like curve (both positive and
negative) to a tuning, and I'll sing heavenly Paeans in your name.

Infinite Thanks,

Jacky Ligon

In message:

/tuning/topicId_20388.html#20388

We looked at how we may apply a linear stretch to a JI Scale (and
masterfully expanded upon by microtonal semi-deity Dan Stearns), to
tune a few cents away from JI (ironically something advocated by
former list member, Paul Erlich); our purpose being to introduce
subtle beating - or natural "chorusing" - into a well known 5 limit
mode.

Today let's take a look at how we may use a similar logic to apply
a "Curved Stretch" to the same mode. The difference here is that we
will wish to make the scale have larger steps at the lower end of the
tuning, which grow progressively smaller toward the middle of the
scale, then in a reverse order; grow larger toward the top of the
scale. I've read about this kind of tuning in regard to Piano Stretch
Tuning, as well as Gamelan, where a similar logic may be used across
several octaves - or in the case of Gamelan metallophones - about a 2
octave range. Here we'll use our familiar 5 Limit mode over a 2
octave range as an example. As follows:

Ratio Cents Consecutive Intervals
1/1 0.000
9/8 203.910 203.910
6/5 315.641 111.731
5/4 386.314 70.672
4/3 498.045 111.731
3/2 701.955 203.910
8/5 813.686 111.731
5/3 884.359 70.672
16/9 996.090 111.731
2/1 1200.000 203.910
1403.910 203.910
1515.641 111.731
1586.314 70.672
1698.045 111.731
1901.955 203.910
2013.686 111.731
2084.359 70.672
2196.090 111.731
2400.000 203.910

Applying the stretch to this scale is a two step process, where we
first add a "curved series" to each scale degree, then secondly, we
compress the overall tuning (to be explained).

An important note is that the curve one chooses may be of many
varieties (a simple linear approach is also good). Here we'll use a
symmetrical Fibonacci Series of cents values, as a template for our
stretch tuning:

Fibo Curve
34
21
13
8
5
3
2
1
1
1
1
2
3
5
8
13
21
34

Now we'll simply add the above series to the Consecutive Intervals
column, giving the following values:

Cents Consecutive Intervals
0
237.910 237.910
370.641 132.731
454.314 83.672
574.045 119.731
782.955 208.910
897.686 114.731
970.359 72.672
1083.090 112.731
1288.000 204.910
1492.910 204.910
1605.641 112.731
1678.314 72.672
1793.045 114.731
2001.955 208.910
2121.686 119.731
2205.359 83.672
2338.090 132.731
2576.000 237.910

As one can easily see, we have over-stretched here by about a small
semitone, so it becomes necessary to compress the scale to within the
desired range, using the basic method outlined in the former article;
except here we will subtract rather than add the linear stretch,
which will "compress" the tuning to desired parameters. To do this
we'll have to use 8.1 cents multiplied by 1-18 to obtain our
compression table, looking like this:

8.1
16.2
24.3
32.4
40.5
48.6
56.7
64.8
72.9
81
89.1
97.2
105.3
113.4
121.5
129.6
137.7
145.8

So now we simply subtract these values from the above, which gives us
a stretched octave of 1215.100 cents, and our final tuning:

Cents Consecutive Intervals
0
229.810 229.810
354.441 124.631
430.014 75.572
541.645 111.631
742.455 200.810
849.086 106.631
913.659 64.572
1018.290 104.631
1215.100 196.810
1411.910 196.810
1516.541 104.631
1581.114 64.572
1687.745 106.631
1888.555 200.810
2000.186 111.631
2075.759 75.572
2200.390 124.631
2430.200 229.810

You'll notice here, that the inversional symmetry of our scale has
not been corrupted by this process, which lends itself to very
orderly behavior as one plays across the range. Of course our 5
Limit template scale, which this tuning is generated from, has been
totally transformed. Interestingly though, this takes on an
incredibly "Gamelan-like" quality, which is unbelievable sweet and
expansive. I prefer this on a metallophone timbre, and have played it
extensively on a vibraphone patch to pleasing effect. There is
something truly magical about the infinite possibilities of what one
can do with this technique. An obvious transposition of this, would
be to use an inverted curve to compress the octave, but I'll leave
that to the experimentalists out there to try (I've tried it and like
it, but somehow prefer stretched rather than compressed octaves for
this).

If Dan Stearns or Jeff Scott (or anyone for that matter) can show a
more formal method of doing this, the Paeans will issue forth
immediately.

Thanks,

Jacky Ligon

--- In tuning@y..., ligonj@n... wrote:

/tuning/topicId_20388.html#20397

> In message:
>
> /tuning/topicId_20388.html#20388
>
> We looked at how we may apply a linear stretch to a JI Scale
> (and masterfully expanded upon by microtonal semi-deity Dan
> Stearns), to tune a few cents away from JI (ironically something
> advocated by former list member, Paul Erlich); our purpose being
> to introduce subtle beating - or natural "chorusing" - into a
> well known 5 limit mode.
>
> Today let's take a look at how we may use a similar logic to
> apply a "Curved Stretch" to the same mode. The difference here
> is that we will wish to make the scale have larger steps at
> the lower end of the tuning, which grow progressively smaller
> toward the middle of the scale, then in a reverse order; grow
> larger toward the top of the scale. <etc. - snip>

Hi Jacky,

I mentioned something almost identical to this a few months
back. I think it was during the time when you got offended
and blew off the list, so you must have missed it.

The original message, with links to all the follow-up posts, is:
/tuning/topicId_13830.html#13830

The message with the Excel math formula is:
/tuning/topicId_13830.html#13895

And the graph is:
/tuning/files/monz/rhodes.jpg

(Thanks to Allan Myhara for the math help.)

After my Microfest presentation I plan to finally finish
retuning that piece and upload it to my website.

> If Dan Stearns or Jeff Scott (or anyone for that matter) can
> show a more formal method of doing this, the Paeans will
> issue forth immediately.

You may kneel and start praising now.

-monz
http://www.monz.org
"All roads lead to n^0"

Dan Stearns wrote:

> If you wanted to start with the amount you'd want the octave (or
> periodicity or "interval of equivalence", etc.) stretched or
> compressed by then you could write this as (where X indicates the
> periodicity in cents):
>
> (LOG(n)-LOG(d))*(X/LOG(2))
>
> I use this a lot as it allows you to stick whatever you wanted for
> ratios into the scale and they'd have an appropriate logarithmic
> stretch (or compression or whatnot).

A very timely post, Dan! I was just thinking about applying the higher rings of Wilson's Golden
Horagrams of the Scale Tree to the whole range of human hearing, as opposed to the more obvious
approach of applying a lower ring to the octave. But I wasn't quite sure how to calculate it. Now
I know! :-)

Mmmm, Golden Horagrams. An important part of a tuner's complete breakfast!

Jacky Ligon wrote:

> What a great way to instantly transform a basic scale into NJNE! I'm
> loving the sound of these tunings.

What's NJNE?

--
David J. Finnamore
Nashville, TN, USA
http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html
--

David!
I have thought that since the ear hears better in certain ranges, one could start also with the
inner levels in the bass and use the outer ones in the prime hearing range, and thinning it out as you
proceed up.

Don't know if you saw this, but might spark some ideas for you or not
http://www.anaphoria.com/hora.PDF

"David J. Finnamore" wrote:

> A very timely post, Dan! I was just thinking about applying the higher rings of Wilson's Golden
> Horagrams of the Scale Tree to the whole range of human hearing, as opposed to the more obvious
> approach of applying a lower ring to the octave. But I wasn't quite sure how to calculate it. Now
> I know! :-)
>
> Mmmm, Golden Horagrams. An important part of a tuner's complete breakfast!
>
> Jacky Ligon wrote:
>
> > What a great way to instantly transform a basic scale into NJNE! I'm
> > loving the sound of these tunings.
>
> What's NJNE?
>
> --
> David J. Finnamore
> Nashville, TN, USA
> http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> David!
> I have thought that since the ear hears better in certain
ranges, one could start also with the
> inner levels in the bass and use the outer ones in the prime hearing
range, and thinning it out as you
> proceed up.

That's a cool idea.

> Don't know if you saw this, but might spark some ideas for you
or not
> http://www.anaphoria.com/hora.PDF

Yes, thanks. Really appreciate that you made it a single PDF file! I
have it on my hard disk and reference it regularly. In fact, I'm
preparing some data and observations about it to share with the list.
It's an awful lot of material, though. It might be better if I put
it in html format and just post the URLs to the Tuning List. Say,
come to think of it, maybe I should make my material into a PDF, too,
once I finish it (which will takes weeks, at least; maybe months).

David Finnamore

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

> If you wanted to start with the amount you'd want the octave (or
> periodicity or "interval of equivalence", etc.) stretched or
> compressed by then you could write this as (where X indicates the
> periodicity in cents):
>
> (LOG(n)-LOG(d))*(X/LOG(2))

It appears that it can be made even a little simpler than that:

(LOG(n/d))*(X/LOG(2))

David Finnamore

The LA Times did a Sunday feature on MicroFest today:

http://www.calendarlive.com/top/1,1419,L-LATimes-Calendar-X!ArticleDetail-26705,
00.html

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

--- In tuning@y..., Bill Alves <ALVES@O...> wrote:

/tuning/topicId_20388.html#20420

> The LA Times did a Sunday feature on MicroFest today:
>
>
http://www.calendarlive.com/top/1,1419,L-LATimes-Calendar-X!ArticleDet
ail-26705,
> 00.html
>

Hi Bill!

Actually, this link is broken... and, in fact, I can't even copy it
in Netscape. Somehow, I WAS able to copy it in Internet Explorer,
and
got the page. Since it is so short, I am reproducing it below, if
you don't mind:

Sunday, March 25, 2001

On Another Scale Altogether
MicroFest's organizers are expanding the annual event to take
advantage of growing Western interest in the alternate pitches of
microtonality.

By JOSEF WOODARD

"In the cracks" is the operative phrase for microtonal music.
This is music with notes and scales that fall between those of
conventional Western music, which assigns 12 pitches to an octave.
Tuning systems outside of that norm can strike many ears as weird,
even heretical. Never mind that a variety of musical schemes have
existed in other parts of the world since time immemorial.
Poetically enough, the culture of microtonal music too tends to
fall between the cracks of existing institutional and performance
channels. But that may be changing. Microtonality has been sneaking
into wider consciousness through world music and such rock artists as
Sonic Youth, as well as through underground scenes where
experimentalism and self-determination rule.
John Schneider--microtonal performer and composer, Pierce
College
music professor and founder-director of MicroFest, an annual
celebration of microtonality--has been in a good position to note the
widening world of unconventional tuning. "Everybody I talk to, all of
a sudden, says, 'I know about that music.' In every musical
community,
there's somebody who has gone micro," he laughs.
Fittingly, this year, MicroFest will also widen its reach. The
kickoff, April 6-8, will include concerts and an academic-style
conference, and there will be four performance events around the area
in May that will also carry MicroFest sponsorship.
The centerpiece of the April festival, organized by Harvey Mudd
College assistant music professor Bill Alves, a participant in
previous festivals, will be a tribute to Northern California composer
Lou Harrison. Harrison is arguably the best-known microtonal composer
in the world. He will give a keynote address April 7, the night
before
a concert of his music, which will include the world premiere of a
piece he wrote in 1935, at age 17. The work is scored for eight
stringed instruments in quarter tones.
MicroFest's expanding profile in Southern California is no
fluke.
Microtonal events have taken place around the country, including the
American Festival of Microtonal Music in New York, run for the last
17
years by bassoonist Johnny Reinhard. But Southern California was home
to two influential early U.S. experimenters in alternate tunings,
John
Cage and especially Harry Partch, a patron saint of this subculture.
Partch, who was born in Oakland and lived in many places around Los
Angeles and San Diego later in his life, constructed his own musical
universe out of a personalized 43-tones-to-the-octave scale and
elaborate handmade instruments to make it manifest. The May MicroFest
events include a Partch centennial celebration, in conjunction with
UCLA, and features an instrument "petting zoo," a performance, panels
and screenings of two films about Partch.
Now, says Alves, in addition to "the Harry Partch heritage,"
Southern California is home to microtonal theorist Erv Wilson and
one-time Partch collaborator Jonathan Glazier, who runs the Sonic Art
Gallery in San Diego. The delightfully eccentric microtonal prophet
and instrument-maker Ivor Darreg, who died in 1994, operated out of
his home in Glendale. Other avid microtonalists here include
players--mostly percussionists--and composers Kraig Grady, Ron George
and Rod Poole, each of whom is putting together MicroFest concerts.
Schneider sees the strength of the microtonal community in these
parts as a natural result of both the experimental tradition, on the
one hand, "and the influence of the incredible ethnic salad" here, on
the other. "The fact is that West Coast musicians have always felt
somewhat apart from East Coast tradition, which itself is beholden to
European tradition. We're about as far away as you can get from
Europe. Part of the reason people are here is that they're looking
for
another way. And because of our proximity to the Pacific Rim, that
influence, I think, is very strong."
Schneider got the festival bug after joining Reinhard for a
festival in Denver called Microstock. He says, "I got to thinking,
'Why not here?' "
In 1997, MicroFest began at Pierce College in Woodland Hills
with
just one concert. From the beginning, Schneider wanted the festival
to
showcase music from different stylistic quarters. Concerts have
included the Indonesian gamelan and Persian music, alternate-tuned
folk music and experimental composers such as Ben Johnston, who
studied with Partch in the '50s and whose music was featured in last
year's festival.
Schneider defines microtonality's appeal for musicians as "a new
toy box." "For us in the West, it's like, what are all these colors?"
says Schneider, who hosts the radio program "Global Village" on
KPFK-FM (90.7). "But a lot of Western musicians don't have a handle
on
what to do with these things, because it is new material. I always
find it instructive to turn to traditions who have had [these
tunings]
for centuries, if not millennia."
Schneider's long-range goals for MicroFest include building a
complete set of reproductions of Partch's instruments--he has created
three so far; starting a touring MicroFest ensemble; and creating a
MicroFest record label, "a focal point for the dissemination for
microtonal music."
It was Alves who pushed to add a conference to the festival this
year, and raised funds to help it happen. Most of the papers will
come
from microtonal practitioners rather than professors per se.
According
to Alves, "The academic universe, at least in the United States, as a
generalization, doesn't have very much interest in microtonal music.
I'm not sure why that is, except for the inherent conservatism of the
academy. Of course, it was much more conservative back when Harry
Partch was beating his head up against it." Among the topics: "Visual
Music: A Graphic Appreciation of Partch's Tuning," "Making the
Recorder Microtonal" and "Navigating the Infinite Web of Pitch
Space."
As a composer, Alves' own path to a belief in alternate tunings
included a passionate interest in Indonesian music. He spent time
studying the gamelan in Java, and had instruments built to his
specifications there, which he will perform with April 6.
Alves admits that the esoterica involved in microtonality can
lead to a certain cultishness. But, he says, "I certainly hope that
people look upon microtonality and alternate tunings as something
serious and something that is not just what a couple of crackpots are
doing in California."
The papers at the festival, he says, will mostly appeal to the
initiated, but the performances should make converts to the cause.
"We've been hearing this tuning system with 12 notes for so
long," he says, "it's only natural that we fit things to it. But once
you start to train yourself to listen out of that, to hear the
harmonies for what they are instead of for what they aren't, it can
make music a more wonderful experience.
"Microtonality is not a style but it certainly does lend to the
composer new avenues of exploration," he continues. "It can lead to
new ways of thinking about music and new ways of hearing music.
That's
one of the most startling things that people discover when they start
getting into this. They begin to hear [typical 12-tone tuning] as a
kind of gray, monochrome music that doesn't offer the
wonderful-sounding pure chords or very expressive nuances of pitch or
other potentials that other tuning systems can offer."

* * *

On the Schedule for MicroFest 2001 April 6-8
"Conference and Festival of Music in Alternate Tunings," at the
Claremont Colleges. Most events take place at Scripps College's Balch
Hall, 1030 Columbia Ave., Pomona, and Pomona College's Thacher Music
Building, corner of 4th Street and College Avenue, Pomona. Special
guest: Lou Harrison. All concerts are free.
http://www2.hmc.edu/~alves/microfest2001.html.
May 5-6
"Her Stirring Stone: An Anaphorian Shadow Play by Isafa, A
Mythical Journey in Search of a Lost Object," created by Kraig Grady.
10 p.m., Holly Matter Art Gallery, 710 Heliotrope Drive, L.A. (323)
666-0303.
May 12
Rod Poole and guests. 9 p.m., Holly Matter Art Gallery, 710
Heliotrope Drive, L.A. (323) 666-0303.
May 19
"Microtonal Music for Original and Traditional Instruments,"
featuring Ron George and Ringing Tambellans; Nyoman Wenten and the
CalArts Gamelan Ensemble; USC Percussion Ensemble under director Erik
Forrester; and CalArts Percussion Ensemble under director David
Johnson. Works by Ben Johnston, Ron George and James Tenney. 8 p.m.,
CalArts, 24700 McBean Parkway, Valencia, Roy O. Disney Music Hall.
(213) 623-6845. $12 at the door.
May 26
"The Partch Centennial Celebration," presented by MicroFest, the
UCLA Music Department and the UCLA School of Arts & Architecture.
Panels, lectures, exhibits, film screenings and an evening concert
performed by Just Strings. All day, starting at 10 a.m., Schoenberg
Auditorium, UCLA. (310) 396-5915. $25 for the day; $5-$15, concert
only.
- - -

Josef Woodard Is a Frequent Contributor to Calendar

Copyright 2001 Los Angeles Times

__________ __ _____ _
Joseph Pehrson

Joseph,

Welcome back!

--- In tuning@y..., jpehrson@r... wrote:
> Hi Bill!
>
> Actually, this link is broken...

No, Joe, it is just line wrapped and you didn't cut-and-paste the
entire link, all the way through the "00.html". Pretty common for
systems that feed up a site automatically from big databases.

And, as long as you posted the _entire_ article, note the last thing
you posted:

> Copyright 2001 Los Angeles Times

Since you probably didn't get permission, well, I imagine they have
better things to do than chase you, but...

Cheers,
Jon

Bill,

--- In tuning@y..., Bill Alves <ALVES@O...> wrote:
> The LA Times did a Sunday feature on MicroFest today:

Excellent coverage. I'll put a link in on the Partch site, and be
seeing you in a couple weeks...

Cheers,
Jon

--- In tuning@y..., JSZANTO@A... wrote:

/tuning/topicId_20388.html#20424

> Joseph,
>
> Welcome back!
>

Thanks, Jon, for your nice message, and also for the greeting in
response to my Moscow post. I haven't read through all the posts yet
since I've been back...

The "Internet Cafes" are quite a development and, although I knew of
course they existed in many of the larger European cities, I didn't
know one existed in Moscow until we saw it in an English-language
newspaper...

It's right in the very center of town, right near the Kremlin. Do
they perhaps "monitor" e-mail there?? Well, as Ionesco says at the
end of the "Chairs"... ummmmm, ummmm, gooooo, goooo....

> --- In tuning@y..., jpehrson@r... wrote:
> > Hi Bill!
> >
> > Actually, this link is broken...
>
> No, Joe, it is just line wrapped and you didn't cut-and-paste the
> entire link, all the way through the "00.html". Pretty common for
> systems that feed up a site automatically from big databases.
>

Hi Jon...

Actually I saw the break and tried to copy it several different ways,
but it wasn't working in Netscape for some reason. It wouldn't copy.
However, I DID get it to copy in Internet Explorer.

> And, as long as you posted the _entire_ article, note the last
thing
> you posted:
>
> > Copyright 2001 Los Angeles Times
>
> Since you probably didn't get permission, well, I imagine they have
> better things to do than chase you, but...
>
> Cheers,
> Jon

Yes, I know. Well I saw "copyright" so I thought I'd just "copy
right..."

Seriously, though, this is probably "fair usage" for our "educational
purposes" in the tuning community... and I have no intention of
"selling" the article or anything of the kind..

Anybody want to buy it?? :) (just kidding)

Now... I be bad... so nobody "tell" on me, OK??

best,

Joe
_________ ______ ______ _
Joseph Pehrson

--- In tuning@y..., "monz" <MONZ@J...> wrote:
> I mentioned something almost identical to this a few months
> back. I think it was during the time when you got offended
> and blew off the list, so you must have missed it.

Who? Little old me???

> After my Microfest presentation I plan to finally finish
> retuning that piece and upload it to my website.

I'll be awaiting this with baited ears!

>
> > If Dan Stearns or Jeff Scott (or anyone for that matter) can
> > show a more formal method of doing this, the Paeans will
> > issue forth immediately.
>
>
> You may kneel and start praising now.
>

But Master Monz, before I bring you your slippers and tea, and
assemble the Heavenly Paean Choir in your honor; how may I apply any
curve that I desire? I set up the formula in Excel, and it worked
fine, but I was unable to see how to plug in my own curves. It would
be a "stretch" to say that I can only find contentment and inner
peace, with one curve alone.

So for now, we will only do humming warm up exercises in preparation
for full blown Paeans.

Your humble servant,

Jacky Ligon

--- In tuning@y..., "David J. Finnamore" <daeron@b...> wrote:
> What's NJNE?

Non-Just, Non-Equal

Jacky Ligon

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> David!
> I have thought that since the ear hears better in certain
ranges, one could start also with the
> inner levels in the bass and use the outer ones in the prime
hearing range, and thinning it out as you
> proceed up.

There are indeed ways of doing similar things of this nature with JI
ratios.

Jacky Ligon

Hi Jacky,

<<What a great way to instantly transform a basic scale into NJNE! I'm
loving the sound of these tunings.>>

I like these tunings a lot too, but I'm not so sure that I'd even call
them NJ (non just) exactly... I see them more like a funny mirror
reflection where a set of ratios is distorted with respect to the
usual periodicity -- the almighty octave.

Slight distortions are easily recognizable as regards their original
constitution. Radical ones only questionably or dubiously so. But
still, they are (or can be) based exclusively on ratios, so NJ doesn't
seem quite right even in the extreme distortion cases... note that I
don't have any better suggestions though!

<<Now show me how you'd apply a Fibonacci-like curve (both positive
and negative) to a tuning,>>

Hmm, having already read your other post and Joe Monzo's reply I think
you must mean something different than regular stretched octaves... ?
I'll take a better look at it later and see if I can figure out what
your saying here in a generalized sense.

--Dan Stearns

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Hi Jacky,
>
> <<What a great way to instantly transform a basic scale into NJNE!
I'm
> loving the sound of these tunings.>>
>
> I like these tunings a lot too, but I'm not so sure that I'd even
call
> them NJ (non just) exactly... I see them more like a funny mirror
> reflection where a set of ratios is distorted with respect to the
> usual periodicity -- the almighty octave.

Dan,

I think it's more of a technical call. Kind of a "covert" NJNE.

: )

>
> Slight distortions are easily recognizable as regards their original
> constitution. Radical ones only questionably or dubiously so. But
> still, they are (or can be) based exclusively on ratios, so NJ
doesn't
> seem quite right even in the extreme distortion cases... note that I
> don't have any better suggestions though!

Yes, I'd totally agree here, and that is indeed one of the great,
curious and beautiful things about this. Even severely distorted
scales can be quite consonant or else compelling where they may be
harmonically challenging.

> <<Now show me how you'd apply a Fibonacci-like curve (both positive
> and negative) to a tuning,>>
>
> Hmm, having already read your other post and Joe Monzo's reply I
think
> you must mean something different than regular stretched
octaves... ?
> I'll take a better look at it later and see if I can figure out what
> your saying here in a generalized sense.
>
> --Dan Stearns

I'll be very interested in this. Of course my "crude" methods will
work, but it'd be nice to have a slick one-step method. I just can't
seem to think of a way other than what I posted (with many variations
on the theme), because I'm having to deal with a long table of cents
values, which the "shape" of the tuning is made to conform to (I have
refined this process since, but still takes a few steps - perhaps ok
if it gets the job done).

Thanks,

Jacky Ligon

--- In tuning@y..., ligonj@n... wrote:

/tuning/topicId_20388.html#20439

> --- In tuning@y..., "monz" <MONZ@J...> wrote:
>
> > I mentioned something almost identical to this a few months
> > back. I think it was during the time when you got offended
> > and blew off the list, so you must have missed it.
>
> ...
>
> But Master Monz, before I bring you your slippers and tea,
> and assemble the Heavenly Paean Choir in your honor; how may
> I apply any curve that I desire? I set up the formula in Excel,
> and it worked fine, but I was unable to see how to plug in my
> own curves. It would be a "stretch" to say that I can only
> find contentment and inner peace, with one curve alone.
>
> So for now, we will only do humming warm up exercises in
> preparation for full blown Paeans.

Darn, and I was all set to enjoy unending adulation, not to
mention the microtonal hymns in my honor. Oh well...

Seriously, I guess I didn't fully understand what you were
getting at. My mathematical abilities are hopelessly inadequate
to help you with this. Better to keep asking... eventually
one of the real math wizzes around here should speak up.

-monz

Jacky Ligon wrote,

<<I think it's more of a technical call. Kind of a "covert" NJNE.>>

Well in the (Helmholtzian) "harmonic entropy" sense these types of
ratios in a non-octave periodicity certainly would be acutely NJ... or
only just in an irrelevant or incidental way.

But in another sense, especially in the extreme cases like the 5/4 of
a 15/8 or what have you, they're almost like alternate realities...
and while I don't think this is a very useful analogy in the aural
causation sense of JI, I do think it's an appealing one in terms of
projecting and manipulating proportion.

--Dan Stearns

David Finnamore wrote,

<<It appears that it can be made even a little simpler than that:
(LOG(n/d))*(X/LOG(2))>>

Right, they're synonymous. Also, while I think it's so much more fun
to write and see these as rationals within an alternate periodicity,
unless X is a non-octave octave (i.e., a 1:4, 1:8, 1:16, etc.), then
the ratio will be an irrational in the form of

N^(X/P)
---------
D^(X/P)

where X is an alternate P and P = 1:2

--Dan Stearns