MIDI comparison: JI/ET/Other

Hello, there, everyone, and in response to some recent discussions on
just intonation, equal temperaments, and other types of tuning
systems, I'd like to make available three MIDI versions of a
composition I wrote in 1985.

Version A:
<http://www.calweb.com/~mschulter/librarya.mid>

Version B:
<http://www.calweb.com/~mschulter/libraryb.mid>

Version C:
<http://www.calweb.com/~mschulter/libraryc.mid>

These examples are each in a different tuning system, and I'd be
curious as to how people might describe what they hear in each system,
or the "mood" of each system as applied to this piece.

Why don't I give people a chance to respond before adding a bit of
commentary on the question of "mood" in a tuning system.

Most appreciatively,

Margo Schulter
mschulter@...

For the life of me I can't tell the difference between these three. Anyone else?

Jacob

--- In MakeMicroMusic@yahoogroups.com, Margo Schulter <mschulter@c...> wrote:
> Hello, there, everyone, and in response to some recent discussions on
> just intonation, equal temperaments, and other types of tuning
> systems, I'd like to make available three MIDI versions of a
> composition I wrote in 1985.
>
> Version A:
> <http://www.calweb.com/~mschulter/librarya.mid>
>
> Version B:
> <http://www.calweb.com/~mschulter/libraryb.mid>
>
> Version C:
> <http://www.calweb.com/~mschulter/libraryc.mid>
>
> These examples are each in a different tuning system, and I'd be
> curious as to how people might describe what they hear in each system,
> or the "mood" of each system as applied to this piece.
>
> Why don't I give people a chance to respond before adding a bit of
> commentary on the question of "mood" in a tuning system.
>
> Most appreciatively,
>
> Margo Schulter
> mschulter@c...

> Message: 4
> Date: Tue, 08 Jun 2004 23:52:13 -0000
> From: "Jacob" <jbarton@...>
> Subject: Re: MIDI comparison: JI/ET/Other
>
> For the life of me I can't tell the difference between these three. Anyone else?
>
> Jacob

I also plead lack of any ear-ability whatsoever . . . . . .

I've only tried it on Quick time, maybe my synth at home would do more?

:(

Yes, whatever difference is extremely subtle to me. I thought I might guess at
the 'b' example being a bit more towards just, but on relistening, I'm not so
sure......

Margo, can you enlighten us ?

I think this is potentially a brilliant example of the blurryness sometimes
between JI and the appropriate ET/temperament, but maybe you had a different
agenda?

-Aaron

On Tuesday 08 June 2004 06:52 pm, Jacob wrote:
> For the life of me I can't tell the difference between these three. Anyone
> else?
>
> Jacob
>
> --- In MakeMicroMusic@yahoogroups.com, Margo Schulter <mschulter@c...>
wrote:
> > Hello, there, everyone, and in response to some recent discussions on
> > just intonation, equal temperaments, and other types of tuning
> > systems, I'd like to make available three MIDI versions of a
> > composition I wrote in 1985.
> >
> > Version A:
> > <http://www.calweb.com/~mschulter/librarya.mid>
> >
> > Version B:
> > <http://www.calweb.com/~mschulter/libraryb.mid>
> >
> > Version C:
> > <http://www.calweb.com/~mschulter/libraryc.mid>
> >
> > These examples are each in a different tuning system, and I'd be
> > curious as to how people might describe what they hear in each system,
> > or the "mood" of each system as applied to this piece.
> >
> > Why don't I give people a chance to respond before adding a bit of
> > commentary on the question of "mood" in a tuning system.
> >
> > Most appreciatively,
> >
> > Margo Schulter
> > mschulter@c...
>
>
> [MMM info]------------------------------------------------------
> More MMM music files are at http://www.microtonal.org/music.html
> ------------------------------------------------------[MMM info]
> Yahoo! Groups Links
>
>
>

--
Aaron Krister Johnson
http://www.dividebypi.com
http://www.akjmusic.com

Margo,
I listened to the a-b-c MIDI comparison files referred to in your
post. I find them all equally valid and interesting, but that's only
after listening to them for 3-4 times. Someone with access to the
tuning information with an opportunity to explore the tunings in more
depth would make a more complete response to the differences. They are
just too subtle for my ears to assess a mood or feeling.

I would like to understand the differences though. To do that, I would
recommend a single piece that highlights the differences. In other
words, create a piece that makes the differences into musically
interesting material. Make it more obvious to the casual listener that
there is something going on here.

If one of the thirds, fifths, seconds is lower/higher than the other,
make a piece that showcases the difference between them, so even a
classically trained ear could hear it.

Just an idea.

Prent Rodgers

P.S. if pressed, I prefer C, since it seems more complex during the
first 3-4 seconds. Less stark to my untrained ears.

--- In MakeMicroMusic@yahoogroups.com, Margo Schulter <mschulter@c...>
wrote:
> Hello, there, everyone, and in response to some recent discussions
on
> just intonation, equal temperaments, and other types of tuning
> systems, I'd like to make available three MIDI versions of a
> composition I wrote in 1985.
>
> Version A:
> <http://www.calweb.com/~mschulter/librarya.mid>
>
> Version B:
> <http://www.calweb.com/~mschulter/libraryb.mid>
>
> Version C:
> <http://www.calweb.com/~mschulter/libraryc.mid>
>

Margo,
I ran the files through a more complete comparison utility and they
are inded different. I think I can hear something, but not enough to
talk about.

Prent Rodgers

<mschulter@c...>
> wrote:
> > Hello, there, everyone, and in response to some recent discussions
> on
> > just intonation, equal temperaments, and other types of tuning
> > systems, I'd like to make available three MIDI versions of a
> > composition I wrote in 1985.
> >
> > Version A:
> > <http://www.calweb.com/~mschulter/librarya.mid>
> >
> > Version B:
> > <http://www.calweb.com/~mschulter/libraryb.mid>
> >
> > Version C:
> > <http://www.calweb.com/~mschulter/libraryc.mid>
> >

>Yes, whatever difference is extremely subtle to me. I thought I might
>guess at the 'b' example being a bit more towards just, but on
>relistening, I'm not so sure......

I had the same thing happen to me. I rerelistened just now, and
A and C sound exactly the same, but B smoother.

Then, I recorded the performances to a wave file. I'm going lo-fi
here -- my laptop's built-in synth recorded into Cool Edit through
the Windows mixer. Then I cut out the same triad from all three
files and pasted them into a new file, for direct comparison. Again,
A and C sound the same, and B noticeably smoother...

http://lumma.org/tuning/ABC3.wav

Did another triad, and B sounds different, more "open", though not
necc. smoother...

http://lumma.org/tuning/ABC2.wav

[The excerpts are in order in time, A-B-C.]

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Yes, whatever difference is extremely subtle to me. I thought I might
> >guess at the 'b' example being a bit more towards just, but on
> >relistening, I'm not so sure......
>
> I had the same thing happen to me. I rerelistened just now, and
> A and C sound exactly the same, but B smoother.

I'd propose a side-by-side of JI with atomic, but unfortunately this
would require me to sharpen fifths and major thirds by 1/96 of an atom
, which is approximately 1/38 of a mu. Brave souls who want to hear
this difference could try 440 Hz vs 440.00004 Hz in Csound. After six
hours and 50 minutes you've gone through a beat. So is it JI, or still
a temperament?

>>>Yes, whatever difference is extremely subtle to me. I thought
>>>I might guess at the 'b' example being a bit more towards just,
>>>but on relistening, I'm not so sure......
>>
>>I had the same thing happen to me. I rerelistened just now,
>>and A and C sound exactly the same, but B smoother.
>
>I'd propose a side-by-side of JI with atomic, but unfortunately
>this would require me to sharpen fifths and major thirds by 1/96
>of an atom, which is approximately 1/38 of a mu. Brave souls who
>want to hear this difference could try 440 Hz vs 440.00004 Hz in
>Csound. After six hours and 50 minutes you've gone through a
>beat. So is it JI, or still a temperament?

My relativistic definition of JI should handle for this....

http://lumma.org/tuning/CarlDefiningJI.txt

Compare to Dave K.'s definition...

http://lumma.org/tuning/DaveDefiningJI.txt

See also the thread starting here...

/tuning/topicId_26876.html#27220

Though I do wish folks would stop referring to 'JI vs. ET',
per my recent message...

/makemicromusic/topicId_6784.html#6796

Though the whole thing seems off-topic for this list!

-Carl

Hello, everyone, and thanks for the responses to my post with three
versions of the same piece, which I'm also making available as a score
in PostScript format (conversions to PDF or bitmap formats warmly
welcomed).

<http://www.calweb.com/~mschulter/library1.ps>

Please let me first give information as to the three tunings,
confirming Aaron's suggestion that my main intention was to suggest
the similarities, and then respond to some specific comments which
lead me to consider another experiment which I hope to try within the
next few days.

The three tuning systems are as follows:

a. <http://www.calweb.com/~mschulter/librarya.mid>
99-tET (fifth ~703.030 cents, ~1.075 cents wide)

b. <http://www.calweb.com/~mschulter/libraryb.mid>
Pythagorean JI (pure 3:2 fifths, ~701.955 cents)

c. <http://www.calweb.com/~mschulter/libraryc.mid>
George Secor's HTT-29, a "high tolerance temperament"
(fifths ~703.579 cents, ~1.624 cents wide)

The first system is an equal temperament, the second a JI tuning, and
the third a "near-just" temperament which, as a 29-note set, uses
multiple chains of the mildly tempered fifths to offer a great variety
of pure or near-pure ratios.

One point I wanted to make with these examples is that "mood" might
reflect the style of a given piece at least as much as fine points
about the structure of a given tuning system.

Here, for example, I composed in more or less of a 13th-century
European kind of style using diatonic Pythagorean or near-Pythagorean
intervals. For example, major thirds, relatively concordant but
unstable in this kind of style, range from a rounded 408 cents in
Pythagorean JI to 412 cents in 99-tET and 414 cents in HTT-29.

As it happens, 99-tET and HTT-29 also have available major thirds at
or near 5:4 (~386.31 cents), as does Pythagorean if carried to enough
notes, for example a 53-note circulating tuning almost identical to
53-tET. If such thirds were used as the norm in a piece in any of
these tunings, I suspect that the mood might be quite different than
in my piece.

There would, as with my piece, be small differences between the
tunings: pure 5:4 thirds in HTT-29; slightly narrow approximations of
this ratio in Pythagorean (~384 cents), and slightly wide
approximations in 99-tET (~388 cents).

Yet the contrast between a 384-388 cent range and a 408-414 cent range
might affect the "mood" more than the small distinctions within each
range.

Now for some comments which reflect this agenda and also suggest
another kind of example which, as mentioned above, I hope to post
soon.

Jacob:

> For the life of me I can't tell the difference between these three.
> Anyone else?

Christopher:

> I also plead lack of any ear-ability whatsoever . . . . . . I've
> only tried it on Quick time, maybe my synth at home would do more?
> :(

Aaron:

> Yes, whatever difference is extremely subtle to me. I thought I
> might guess at the 'b' example being a bit more towards just, but
> on relistening, I'm not so sure......

> Margo, can you enlighten us ?

Please let me confirm, as discussed above, that 'b' is indeed
Pythagorean JI. Your remarks, like those of Jacob and Cristopher,
might support the view that fifths tempered by up to at least around
1.62 cents, as in HTT-29, can sound "not so obviously different from
just."

As you propose, my agenda was indeed an "example of the blurryness
sometimes between JI and the appropriate ET/temperament." Here 99-tET
represents the ET side of the question, while HTT-29 in this
seven-note diatonic context where only a single chain of fifths is
used can represent a regular temperament other than an equal division
of a 2:1 octave.

Prent:

> I listened to the a-b-c MIDI comparison files referred to in your
> post. I find them all equally valid and interesting, but that's only
> after listening to them for 3-4 times. Someone with access to the
> tuning information with an opportunity to explore the tunings in
> more depth would make a more complete response to the differences.
> They are just too subtle for my ears to assess a mood or feeling.

Thank you for this response which not only fits what others have said,
but leads to your very interesting proposal that I would like to try
here soon.

> I would like to understand the differences though. To do that, I
> would recommend a single piece that highlights the differences. In
> other words, create a piece that makes the differences into
> musically interesting material. Make it more obvious to the casual
> listener that there is something going on here.

Actually, this gives me an idea for a piece that highlights the
difference between two tuning systems with often similar interval
sizes, but in different arrangements, so that applying them to the
same piece might result in some notable contrast.

> If one of the thirds, fifths, seconds is lower/higher than the other,
> make a piece that showcases the difference between them, so even a
> classically trained ear could hear it.

> Just an idea.

With the three tunings in these examples, one way to carry out this
idea might be to use what I might describe as augmented or diminished
intervals with longer chains of fifths, where the sizes vary more than
with regular diatonic intervals -- and I'd like to try this idea also.

> P.S. if pressed, I prefer C, since it seems more complex during the
> first 3-4 seconds. Less stark to my untrained ears.

Please let me respond to your composerly words: "Would that my ears
were similarly `untrained.'" By the way, I'm very interested in trying
CSound for Linux, and look to your music as one outstanding source in
this process.

George might score this remark about a "more complex" quality as
support for his approach in a tuning such as HTT-29: often temper
intervals just a bit to make them "less stark" -- or subtly less
simple, at any rate.

Carl (quoting Aaron's remark about `b' as sounding nearer to just):

> I had the same thing happen to me. I rerelistened just now, and
> A and C sound exactly the same, but B smoother.

Indeed for regular diatonic intervals like those used in my piece,
99-tET and HTT-29 are very similar. For example, major thirds are
around 412.12 cents and 414.13 cents respectively; and minor seconds
around 84.85 and 82.11 cents.

Gene:

> I'd propose a side-by-side of JI with atomic, but unfortunately this
> would require me to sharpen fifths and major thirds by 1/96 of an
> atom, which is approximately 1/38 of a mu. Brave souls who want to
> hear this difference could try 440 Hz vs 440.00004 Hz in
> Csound. After six hours and 50 minutes you've gone through a
> beat. So is it JI, or still a temperament?

While I'm not acquainted with the "atomic" tuning system you discuss,
the overall effect (as with pure Pythagorean, likely much less
accurate in practice than this "tempered" tuning, of course!) might
illustrate my point about mood and style.

In the style of my piece, fifths would be virtually pure, and major
thirds quite active -- here a minute quantity larger than a just 81:64
(~407.82 cents).

By the way, as to 99-tET or HTT-29, I now realize that while my
harpsichord timbre was intended to be "bright" (which can often
highlight certain distinctions), a more sustained timbre might better
bring out small nuances in the tempering of fifths, for example.

Most appreciatively,

Margo
mschulter@...

Thank you, Margo, for sharing this musical example with us.

>By the way, as to 99-tET or HTT-29, I now realize that while my
>harpsichord timbre was intended to be "bright" (which can often
>highlight certain distinctions), a more sustained timbre might better
>bring out small nuances in the tempering of fifths, for example.

I usually find harpsichord timbres pretty good for comparing tunings
despite the quick decay, but in my case the particular synth I used
could definitely stand improvement.

-Carl

--- In MakeMicroMusic@yahoogroups.com, Margo Schulter
<mschulter@c...> wrote:
> Hello, everyone, and thanks for the responses to my post with three
> versions of the same piece, which I'm also making available as a
score
> in PostScript format (conversions to PDF or bitmap formats warmly
> welcomed).
>
> <http://www.calweb.com/~mschulter/library1.ps>
>
> Please let me first give information as to the three tunings,
> confirming Aaron's suggestion that my main intention was to suggest
> the similarities, and then respond to some specific comments which
> lead me to consider another experiment which I hope to try within
the
> next few days.
>
> The three tuning systems are as follows:
>
> a. <http://www.calweb.com/~mschulter/librarya.mid>
> 99-tET (fifth ~703.030 cents, ~1.075 cents wide)
>
> b. <http://www.calweb.com/~mschulter/libraryb.mid>
> Pythagorean JI (pure 3:2 fifths, ~701.955 cents)
>
> c. <http://www.calweb.com/~mschulter/libraryc.mid>
> George Secor's HTT-29, a "high tolerance temperament"
> (fifths ~703.579 cents, ~1.624 cents wide)
>
> The first system is an equal temperament, the second a JI tuning,
and
> the third a "near-just" temperament which, as a 29-note set, uses
> multiple chains of the mildly tempered fifths to offer a great
variety
> of pure or near-pure ratios.

If anyone is interested in a *very* economical (29-tone), low-error
13-limit tuning, a Scala listing for c. is given here:

/tuning-math/message/7574

Go about halfway thru the message to "secor29htt.scl". This tuning
gives near-just 15-limit otonalities on each tone in a chain of
fifths from Bb to A. Some of the 15-limit consonances are exact
(5/4, 7/4, 7/5, and 13/9), and 11/9 and 13/11 are so close (~0.05c)
that you'll never be able to hear that they're not exact.

I hesitate to call a this a temperament, because it has *very* low
error at the 7-limit, which makes it extremely difficult to tell that
it is, strictly speaking, a temperament. To approximate the 15-limit
consonances in its 6 best keys with an ET more accurately, you have
to go over 100 tones (to 130-ET). If you want to try it in Scala,
then I strongly recommend reading the top part of the message for
advice on how to set the notation for this tuning.

Better yet, maybe I should make available an mp3 file of a recording
of a live performance I gave in San Diego in 1975, an improvisation
on the Scalatron in 29-HTT. Then you can all judge for yourselves
whether it sounds like JI or a temperament. (I should add that it
wasn't hard to come up with Scaltron timbres that are highly
effective in revealing the subtle differences between tunings.)

> One point I wanted to make with these examples is that "mood" might
> reflect the style of a given piece at least as much as fine points
> about the structure of a given tuning system.
>
> Here, for example, I composed in more or less of a 13th-century
> European kind of style using diatonic Pythagorean or near-
Pythagorean
> intervals. For example, major thirds, relatively concordant but
> unstable in this kind of style, range from a rounded 408 cents in
> Pythagorean JI to 412 cents in 99-tET and 414 cents in HTT-29.

In 29-HTT the thirds and sixths come much closer to simple ratios
than in the other tunings. The major thirds are ~14/11 and the minor
thirds are ~13/11. The net result is that, paradoxically, these
intervals are close to points of local maximum harmonic *dissonance*,
which (in conjunction with their excellent melodic effect) makes them
very suitable for Margo's neo-medieval style of composition. This is
not what I had in mind when I devised this tuning, but I'm delighted
that it has worked so well for her and am grateful that I have been
able to learn a thing or two about the relationships between melody
and harmony from her music.

> Prent:
>
> > I listened to the a-b-c MIDI comparison files referred to in your
> > post. I find them all equally valid and interesting, but that's
only
> > after listening to them for 3-4 times. Someone with access to the
> > tuning information with an opportunity to explore the tunings in
> > more depth would make a more complete response to the differences.
> > They are just too subtle for my ears to assess a mood or feeling.
>
> Thank you for this response which not only fits what others have
said,
> but leads to your very interesting proposal that I would like to try
> here soon.
> ...
> > P.S. if pressed, I prefer C, since it seems more complex during
the
> > first 3-4 seconds. Less stark to my untrained ears.
> ...
> George might score this remark about a "more complex" quality as
> support for his approach in a tuning such as HTT-29: often temper
> intervals just a bit to make them "less stark" -- or subtly less
> simple, at any rate.

Yes, and it seems to me that I said something very recently about
departing very slightly from exact mathematical relationships for
artistic effect:

/makemicromusic/topicId_6784.html#6833

BTW, hi Prent! It's been quite a few years since we've seen each
other. Good to see and hear that you're composing some very nice
things. Keep on!

> ...
> By the way, as to 99-tET or HTT-29, I now realize that while my
> harpsichord timbre was intended to be "bright" (which can often
> highlight certain distinctions), a more sustained timbre might
better
> bring out small nuances in the tempering of fifths, for example.

The problem with making tuning comparisons using sustained timbres on
synths is that the tone is almost always modulated in some way
(vibrato, chorus effects, phase shifting, etc.). While this makes 12-
ET more tolerable by covering up the rapid beating of the 3rds and
6ths, it also makes it difficult to hear subtle differences between
tunings. I suggest trying the "overdriven guitar" patch on your
synth to get relatively straight tones that are still rich in
harmonics, yet more sustained. I've already prepared some midi files
using this patch that clearly reveal subtle differences in a lot of
different tunings (JI, ETs, and middle-path), which I hope to make
available soon for all to hear.

--George

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:

> The problem with making tuning comparisons using sustained timbres
on
> synths is that the tone is almost always modulated in some way
> (vibrato, chorus effects, phase shifting, etc.).

Additive synthesis in Csound will do the job nicely.

George,

I still remember a magnificent Scalatron performance you gave at The
Center for Music Experiment in San Diego at UCSD sometime between 1975
and 1980. It thoroughly knocked my socks off and I deeply enjoyed it.

If you have a recording of that concert, I think everyone here would
really gain by listening to it. If you need assistance in getting an
MP3 of that online, let me know.

Your performance was the first time I heard someone do more with
tuning than our naive experiments on home-made metalophones, flower
pots, and finger piano instruments. The Scalatron at UCSD had a
12-tone keyboard, which limited its usefulness in many ways.

Prent Rodgers
Mercer Island, WA

p.s. Thanks for the kind words about my recent work.

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:

Better yet, maybe I should make available an mp3 file of a recording
of a live performance I gave in San Diego in 1975, an improvisation
on the Scalatron in 29-HTT. Then you can all judge for yourselves
whether it sounds like JI or a temperament. (I should add that it
wasn't hard to come up with Scaltron timbres that are highly
effective in revealing the subtle differences between tunings.)
> --George

George/Prent,

{you wrote...}
>If you have a recording of that concert, I think everyone here would >really gain by listening to it. If you need assistance in getting an MP3 >of that online, let me know.

I'll second Prent's entreaty - I've often wondered what "Secor Music" sounds like! I know Prent is in the upper left corner of the country, if you are closer to the lower left corner I'd be happy to help with the mp3 stuff as well (if you need).

Cheers,
Jon

Hi George,

For quite a few years on these lists, the term "middle path" has been
used by Margo Schulter, Dave Keenan, and myself, in discussions with
Jacky Ligon and others, to refer to a tuning concept or philosophy
that is between those of JI and the various ETs.

Some posts mentioning the concept include:

/tuning/topicId_29348.html#29348
/tuning/topicId_28984.html#29212

The idea is that, while ETs (not EDOs) take JI and simplify it
by "regularly" (or uniformly) tempering out a sufficient number of
independent commas, the "middle path" tunings regularly temper out a
smaller number of independent commas. The most famous example is
meantone temperament, whose various varieties are solutions to the
problem of best tempering out the syntonic comma (81:80) without
regard to any other commas vanishing. Schismic (or schismatic)
temperament is another classic example (q.v. Helmholtz, Groven, and
Sabat-Garibaldi), while recently we have seen the discovery and
rediscovery of quite a few other such schemes, such as Miracle,
Hanson, and the "Pajara" system which forms the underpinning for my
paper on the decatonic scales.

Like JI and ETs, middle path tunings are "regular" -- a given
consonance is represented the same way no matter where it appears in
the tuning system. It seems to me that if a property such
as "regularity" is possessed by both JI and the ETs, then it ought to
be possessed by any "middle path" between them.

My XH18 paper is a complete survey of 5- and 7-limit, two-dimensional
(like those mentioned above) "middle path" systems within a certain
boundary on error and complexity. In fact, the title of the paper is
_The Middle Path. Part 1: Fifty Floragrams_.

It seems that you are now putting forth a different definition
of "middle path", similar to the "well-temperament" concept, which
refers to closed systems (while mine refers to open systems) and
irregular systems (while mine refers to closed systems). I can
certainly see how a JI periodicity block might be created, then
tempered first near the edges, and finally tempered uniformly
everywhere to yield an ET, such that the middle step would be a well-
temperament. However, I feel this unfairly omits the whole universe
of possibilities where fewer of the periodicity blocks' unison
vectors are tempered out, and which are thus also in the "middle"
between JI and ETs.

While I certainly respect your thinking process, and the musical
value of well-tempered systems is unquestionable, I wonder if we're
heading toward a terminological nightmare here.

Cheers,
Paul

Hello, there, Prent and everyone.

Thank you warmly for converting my PostScript score to a PDF file,
Prent, making the score easily available to many more users of the
Internet.

Also, having posted these examples, I should note with due humility
that my exercise of having Scala produce MIDI versions of a piece in
three similar tunings doesn't imply that I could tell these tunings
apart by ear better than those of you who responded.

The idea of trying to select or compose a piece where there's a
distinction between the realization in two generally more or less
"similar" tuning systems that _does_ make a substantial musical
difference is engaging because it makes me ask, "What do I consider a
musically significant difference -- or what might I try to see if
people might consider the difference a `significant' one?"

Well, Prent, I am planning an example now, also an opportunity to get
a piece I have on paper into MIDI format and post it here.

This discussion could also tie into other questions, like what does it
mean to "compose a piece for a given tuning"?

Most appreciatively,

Margo
mschulter@...

On Friday 11 June 2004 08:04 pm, Margo Schulter wrote:

> This discussion could also tie into other questions, like what does it
> mean to "compose a piece for a given tuning"?

Speaking for myself, this would mean that consonance and dissonance is not
accidental--one is actually tying in compositional structure to scale
structure. For example, what chords or intervals are 'in tune' or relatively
beatless, and which are not.....

It would also mean using xentonal chord progressions, where the root motion
of the chord progression is xentonal while its consonances are not
neccessarily so.

Aaron Krister Johnson
http://www.dividebypi.com
http://www.akjmusic.com

--- In MakeMicroMusic@yahoogroups.com, "Aaron K. Johnson"
<akjmicro@c...> wrote:
> On Friday 11 June 2004 08:04 pm, Margo Schulter wrote:
>
> > This discussion could also tie into other questions, like what does it
> > mean to "compose a piece for a given tuning"?
>
> Speaking for myself, this would mean that consonance and dissonance
is not
> accidental--one is actually tying in compositional structure to scale
> structure. For example, what chords or intervals are 'in tune' or
relatively
> beatless, and which are not.....
>
> It would also mean using xentonal chord progressions, where the root
motion
> of the chord progression is xentonal while its consonances are not
> neccessarily so.

I would say that chord progressions which make use of a comma of the
tuning are clear examples of composition reflecive of tuning; the
classic example being the I-IV-ii-V-I progression in meantone/diatonic.

> > It would also mean using xentonal chord progressions,
where the root
> motion
> > of the chord progression is xentonal while its consonances
are not
> > neccessarily so.
>
cool idea.

for me, it means that the consequences of my normal actions
(chromaticism, tonality, sequencing, reharmonization) lead me
to expressively different tonal areas. I'm getting more gutsy with
my explorations in 19. i know that gets a big yawn from some
around here, but i really like my D7 chords (jazzer, ya know).

On Sunday 13 June 2004 12:22 am, tentothe99 wrote:
> > > It would also mean using xentonal chord progressions,
>
> where the root
>
> > motion
> >
> > > of the chord progression is xentonal while its consonances
>
> are not
>
> > > neccessarily so.
>
> cool idea.
>
> for me, it means that the consequences of my normal actions
> (chromaticism, tonality, sequencing, reharmonization) lead me
> to expressively different tonal areas. I'm getting more gutsy with
> my explorations in 19. i know that gets a big yawn from some
> around here, but i really like my D7 chords (jazzer, ya know).

You won't see me yawn at 19 !!!! I'm so sold on it, I could spend my life on
it. It really has some riches, for sure.

Best,
Aaron Krister Johnson
http://www.dividebypi.com
http://www.akjmusic.com

--- In MakeMicroMusic@yahoogroups.com, "Aaron K. Johnson"
<akjmicro@c...> wrote:
> On Sunday 13 June 2004 12:22 am, tentothe99 wrote:
> > > > It would also mean using xentonal chord progressions,
> >
> > where the root
> >
> > > motion
> > >
> > > > of the chord progression is xentonal while its
consonances
> >
> > are not
> >
> > > > neccessarily so.
> >
> > cool idea.
> >
> > for me, it means that the consequences of my normal
actions
> > (chromaticism, tonality, sequencing, reharmonization) lead
me
> > to expressively different tonal areas. I'm getting more gutsy
with
> > my explorations in 19. i know that gets a big yawn from
some
> > around here, but i really like my D7 chords (jazzer, ya know).
>
> You won't see me yawn at 19 !!!! I'm so sold on it, I could spend
my life on
> it. It really has some riches, for sure.
>
> Best,
> Aaron Krister Johnson
> http://www.dividebypi.com
> http://www.akjmusic.com

i'm ever tempted to delve into 31. see, for me, it's gotta have the
big consonant tones (i mean, as a reductionist, i could never
ignore the harmonic series), it's gotta be equally tempered
(because I love symmetrical modulation-i'm actually kind of lost
without it).

this is interesting. i think i'm actually just following the sound in
my head of a broader tonal system. Didn't realize that until right
now. wow. just like a druggie jazzer-always blowing his own
mind. lol

On Sunday 13 June 2004 02:08 am, tentothe99 wrote:
> I'm getting more gutsy
>
> with
>
> > > my explorations in 19. i know that gets a big yawn from
>
> some
>
> > > around here, but i really like my D7 chords (jazzer, ya know).

> > Aaron wrote:
> > You won't see me yawn at 19 !!!! I'm so sold on it, I could spend
>
> my life on
>
> > it. It really has some riches, for sure.
> >
> > Best,
> > Aaron Krister Johnson
> > http://www.dividebypi.com
> > http://www.akjmusic.com

> tentothe99 wrote:
> i'm ever tempted to delve into 31. see, for me, it's gotta have the
> big consonant tones (i mean, as a reductionist, i could never
> ignore the harmonic series), it's gotta be equally tempered
> (because I love symmetrical modulation-i'm actually kind of lost
> without it).

31 is very nice I think. As for having to have the harmonic series, I can go
either way. I love it, I also think the the universe *outside* of it is
infinitely larger, considering that by what most people mean when they say
'harmonic series' is mostly harmonics 1-16. Beyond that, the individual tones
are usually percieved as close to some ET tunings' interval, or very
xentoanlly 'out-of-tune' that I think it's worthless to squabble about JI vs.
anything else anymore.

Just my take on things.

Also, don't forget that if you are looking for a boundary between JI and ET,
19-tet kind of blurs that, in that it's pretty damn close to a chain of 19
pure minor thirds. (I know that's not what most people mean by JI--they
usually mean 5-limit duodene type stuff, or various 7-limit tunings, etc.
where the interval numbers stay 'low' (whatever that means I guess depends on
who you talk to))

Anyway I'm convinced that the boundaries become so fuzzy between JI and non-JI
that I think it's clearly a religious issue to draw a line in the sand, and
well, I don't think to fondly of religion ;)

Aaron Krister Johnson
http://www.dividebypi.com
http://www.akjmusic.com

Statements like this is what keeps the argument going. When the issue of it being
religious is brought into the picture, what follows is a witchunt. ( as usual ,
there are no witches)

as a point of reference 19 sounds absolutely terrible to my ear. i have already
stated how i have actually used instruments in 31.

"Aaron K. Johnson" wrote:

>
>
> Anyway I'm convinced that the boundaries become so fuzzy between JI and non-JI
> that I think it's clearly a religious issue to draw a line in the sand, and
> well, I don't think to fondly of religion ;)
>
> Aaron Krister Johnson
> http://www.dividebypi.com
> http://www.akjmusic.com
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In MakeMicroMusic@yahoogroups.com, "tentothe99" <tentothe99@y...>
wrote:

> i'm ever tempted to delve into 31. see, for me, it's gotta have the
> big consonant tones (i mean, as a reductionist, i could never
> ignore the harmonic series), it's gotta be equally tempered
> (because I love symmetrical modulation-i'm actually kind of lost
> without it).

Don't ignore 22 on the way to 31, though.

--- In MakeMicroMusic@yahoogroups.com, kraig grady <kraiggrady@a...>
wrote:

> Statements like this is what keeps the argument going. When the
issue of it being
> religious is brought into the picture, what follows is a witchunt. (
as usual ,
> there are no witches)

Replied to on metatuning.

>> i'm ever tempted to delve into 31. see, for me, it's gotta have the
>> big consonant tones (i mean, as a reductionist, i could never
>> ignore the harmonic series), it's gotta be equally tempered
>> (because I love symmetrical modulation-i'm actually kind of lost
>> without it).
>
>31 is very nice I think. As for having to have the harmonic series,
>I can go either way. I love it, I also think the the universe *outside*
>of it is infinitely larger, considering that by what most people mean
>when they say 'harmonic series' is mostly harmonics 1-16. Beyond that,
>the individual tones are usually percieved as close to some ET tunings'
>interval, or very xentoanlly 'out-of-tune' that I think it's worthless
>to squabble about JI vs. anything else anymore.

I'm confused. 31 approximates the harmonic series better than 19.
Part of the problem may be that I can't tell whether tentothe99 meant
"ever" or "never" there -- I'd been assuming "never".

-Carl

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "tentothe99"
<tentothe99@y...>
> wrote:
>
> > i'm ever tempted to delve into 31. see, for me, it's gotta have
the
> > big consonant tones (i mean, as a reductionist, i could never
> > ignore the harmonic series), it's gotta be equally tempered
> > (because I love symmetrical modulation-i'm actually kind of
lost
> > without it).
>
> Don't ignore 22 on the way to 31, though.

ooh that 22 has a nice P5, huh? and the thirds look good, too.
and a tritone? i'm totally sold.

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma
<ekin@l...> wrote:
> >> i'm ever tempted to delve into 31. see, for me, it's gotta have
the
> >> big consonant tones (i mean, as a reductionist, i could
never
> >> ignore the harmonic series), it's gotta be equally tempered
> >> (because I love symmetrical modulation-i'm actually kind of
lost
> >> without it).
> >
> >31 is very nice I think. As for having to have the harmonic
series,
> >I can go either way. I love it, I also think the the universe
*outside*
> >of it is infinitely larger, considering that by what most people
mean
> >when they say 'harmonic series' is mostly harmonics 1-16.
Beyond that,
> >the individual tones are usually percieved as close to some
ET tunings'
> >interval, or very xentoanlly 'out-of-tune' that I think it's worthless
> >to squabble about JI vs. anything else anymore.
>
> I'm confused. 31 approximates the harmonic series better
than 19.
> Part of the problem may be that I can't tell whether tentothe99
meant
> "ever" or "never" there -- I'd been assuming "never".
>
> -Carl

i meant that I'm tempted to delve into 31. i should have said
"ever more" tempted. i heard an ezra sims piece and a henk
badings string piece, both of which really spoke to me. sorry
about the confusion. I'm more comfortable in 19 now, have
sequence, chord, and scale charts to point out the tonal stuff.
guess I should start doing that for 22 or 31.

On Sunday 13 June 2004 08:58 am, kraig grady wrote:
> Statements like this is what keeps the argument going. When the issue of it
> being religious is brought into the picture, what follows is a witchunt. (
> as usual , there are no witches)

I dont follow. Who's doing a witchunt?

> as a point of reference 19 sounds absolutely terrible to my ear. i have
> already stated how i have actually used instruments in 31.

You are certainly entitled to your opinion !

> "Aaron K. Johnson" wrote:
> > Anyway I'm convinced that the boundaries become so fuzzy between JI and
> > non-JI that I think it's clearly a religious issue to draw a line in the
> > sand, and well, I don't think to fondly of religion ;)

Aaron Krister Johnson
http://www.dividebypi.com
http://www.akjmusic.com

>i meant that I'm tempted to delve into 31. i should have said
>"ever more" tempted. i heard an ezra sims piece and a henk
>badings string piece, both of which really spoke to me. sorry
>about the confusion. I'm more comfortable in 19 now, have
>sequence, chord, and scale charts to point out the tonal stuff.
>guess I should start doing that for 22 or 31.

Oh, cool, it makes total sense now.

-Carl

--- In MakeMicroMusic@yahoogroups.com, "Prent Rodgers"
<prentrodgers@c...> wrote:
> George,
>
> I still remember a magnificent Scalatron performance you gave at The
> Center for Music Experiment in San Diego at UCSD sometime between
1975
> and 1980. It thoroughly knocked my socks off and I deeply enjoyed
it.

I believe it was around February 1980.

> If you have a recording of that concert, I think everyone here would
> really gain by listening to it.

Sorry, I don't. However, one of the pieces that I did at that
concert was a not-completely-successful attempt to recreate a JI
improvisation that I put on tape a couple years earlier. The
recording is 12.5 minutes in length, and I consider it the best thing
I produced during the 1970s. I'll make that available, in addition
to the other improv in 29-HTT that I mentioned.

> If you need assistance in getting an
> MP3 of that online, let me know.

I now have software to produce mp3 files, and I've already done one
for the JI piece, although I think that I need to try redoing it with
a higher volume level (since I notice that the onset of distortion
does not seem to occur gradually, as with analog recording, where I
have been accustomed to leaving some headroom).

Now as far as finding a *place* to put those files goes, I haven't
given that much thought, since I am already much too busy even to
think about maintaining a website. I suppose I could use the files
section for this group if I left them there for no more than a couple
of weeks.

<JSZANTO@A...> wrote:
> George/Prent,
>
> I'll second Prent's entreaty - I've often wondered what "Secor
Music"
> sounds like!

Virtually everything I performed last century was either composed by
someone else or an improvisation. Only recently have I begun to do
any actual composing in alternate tunings, and that has been only
slow and sporadic (since I tend to be a perfectionist, and also
because the Sagittal notation project has been taking up a lot of my
discretionary time). But I expect to be putting some things out in
the near future.

> I know Prent is in the upper left corner of the country, if
> you are closer to the lower left corner I'd be happy to help with
the mp3
> stuff as well (if you need).

I left southern California in 1987 (too dry, too crowded, too noisy,
cost of living too expensive, and weather too boring -- I missed the
seasons) and am now back in middle America, where microtonalists are
fewer and farther between, but relatives are much closer.

--George

--- In MakeMicroMusic@yahoogroups.com, "tentothe99" <tentothe99@y...>
wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
> <gwsmith@s...> wrote:
> > --- In MakeMicroMusic@yahoogroups.com, "tentothe99"
> <tentothe99@y...>
> > wrote:
> >
> > > i'm ever tempted to delve into 31. see, for me, it's gotta
have
> the
> > > big consonant tones (i mean, as a reductionist, i could never
> > > ignore the harmonic series), it's gotta be equally tempered
> > > (because I love symmetrical modulation-i'm actually kind of
> lost
> > > without it).
> >
> > Don't ignore 22 on the way to 31, though.
>
> ooh that 22 has a nice P5, huh? and the thirds look good, too.
> and a tritone? i'm totally sold.

Don't expect to use any characteristic diatonic chord progressions in
22 -- they won't work (you'll end up with 55-cent pitch drift or
shifts, at best)! In fact, trying to label 22 with common practice
interval names will leave you hopelessly tied up in knots. 19 and 31
are easier for beginners because they do fit the common-practice
interval framework, where stacking four fifths gives you the
consonant major third, etc.

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich"
<perlich@a...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "tentothe99"
<tentothe99@y...>
> wrote:
> > --- In MakeMicroMusic@yahoogroups.com, "Gene Ward
Smith"
> > <gwsmith@s...> wrote:
> > > --- In MakeMicroMusic@yahoogroups.com, "tentothe99"
> > <tentothe99@y...>
> > > wrote:
> > >
> > > > i'm ever tempted to delve into 31. see, for me, it's gotta
> have
> > the
> > > > big consonant tones (i mean, as a reductionist, i could
never
> > > > ignore the harmonic series), it's gotta be equally
tempered
> > > > (because I love symmetrical modulation-i'm actually kind
of
> > lost
> > > > without it).
> > >
> > > Don't ignore 22 on the way to 31, though.
> >
> > ooh that 22 has a nice P5, huh? and the thirds look good,
too.
> > and a tritone? i'm totally sold.
>
> Don't expect to use any characteristic diatonic chord
progressions in
> 22 -- they won't work (you'll end up with 55-cent pitch drift or
> shifts, at best)! In fact, trying to label 22 with common practice
> interval names will leave you hopelessly tied up in knots. 19
and 31
> are easier for beginners because they do fit the
common-practice
> interval framework, where stacking four fifths gives you the
> consonant major third, etc.

i only use numbers anyway. that 55 cent drift would be exactly
what i'm looking for. 22 gives a nice little 2*11 symmetry, too, so
there'd be a class like "whole tone" scales with what looks like
two scales close to chromatic scales. i'd bet they'd shimmer if
you stacked 'em.

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> ...
> While I certainly respect your thinking process, and the musical
> value of well-tempered systems is unquestionable, I wonder if we're
> heading toward a terminological nightmare here.
>
> Cheers,
> Paul

Paul, I have replied on the main list:

/tuning/topicId_53587.html#53587

>Sorry, I don't. However, one of the pieces that I did at that
>concert was a not-completely-successful attempt to recreate a JI
>improvisation that I put on tape a couple years earlier. The
>recording is 12.5 minutes in length, and I consider it the best
>thing I produced during the 1970s. I'll make that available, in
>addition to the other improv in 29-HTT that I mentioned.

Oh yes, "bring it"! :)

>> If you need assistance in getting an
>> MP3 of that online, let me know.
>
>I now have software to produce mp3 files, and I've already done
>one for the JI piece, although I think that I need to try redoing
>it with a higher volume level (since I notice that the onset of
>distortion does not seem to occur gradually, as with analog
>recording, where I have been accustomed to leaving some headroom).
>
>Now as far as finding a *place* to put those files goes, I
>haven't given that much thought, since I am already much too
>busy even to think about maintaining a website. I suppose I
>could use the files section for this group if I left them
>there for no more than a couple of weeks.

I'm happy to host 'em, or try SoundClick.

-Carl

--- In MakeMicroMusic@yahoogroups.com, "tentothe99" <tentothe99@y...>
wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Paul Erlich"
> <perlich@a...> wrote:
> > --- In MakeMicroMusic@yahoogroups.com, "tentothe99"
> <tentothe99@y...>
> > wrote:
> > > --- In MakeMicroMusic@yahoogroups.com, "Gene Ward
> Smith"
> > > <gwsmith@s...> wrote:
> > > > --- In MakeMicroMusic@yahoogroups.com, "tentothe99"
> > > <tentothe99@y...>
> > > > wrote:
> > > >
> > > > > i'm ever tempted to delve into 31. see, for me, it's gotta
> > have
> > > the
> > > > > big consonant tones (i mean, as a reductionist, i could
> never
> > > > > ignore the harmonic series), it's gotta be equally
> tempered
> > > > > (because I love symmetrical modulation-i'm actually kind
> of
> > > lost
> > > > > without it).
> > > >
> > > > Don't ignore 22 on the way to 31, though.
> > >
> > > ooh that 22 has a nice P5, huh? and the thirds look good,
> too.
> > > and a tritone? i'm totally sold.
> >
> > Don't expect to use any characteristic diatonic chord
> progressions in
> > 22 -- they won't work (you'll end up with 55-cent pitch drift or
> > shifts, at best)! In fact, trying to label 22 with common
practice
> > interval names will leave you hopelessly tied up in knots. 19
> and 31
> > are easier for beginners because they do fit the
> common-practice
> > interval framework, where stacking four fifths gives you the
> > consonant major third, etc.
>
> i only use numbers anyway. that 55 cent drift would be exactly
> what i'm looking for. 22 gives a nice little 2*11 symmetry, too,
so
> there'd be a class like "whole tone" scales with what looks like
> two scales close to chromatic scales.

I mention these as a possible resource for atonalists in my paper on
22:

http://www.lumma.org/tuning/erlich/erlich-decatonic.pdf

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich"
<perlich@a...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "tentothe99"
<tentothe99@y...>
> wrote:
> > --- In MakeMicroMusic@yahoogroups.com, "Paul Erlich"
> > <perlich@a...> wrote:
> > > --- In MakeMicroMusic@yahoogroups.com, "tentothe99"
> > <tentothe99@y...>
> > > wrote:
> > > > --- In MakeMicroMusic@yahoogroups.com, "Gene Ward
> > Smith"
> > > > <gwsmith@s...> wrote:
> > > > > --- In MakeMicroMusic@yahoogroups.com, "tentothe99"
> > > > <tentothe99@y...>
> > > > > wrote:
> > > > >
> > > > > > i'm ever tempted to delve into 31. see, for me, it's
gotta
> > > have
> > > > the
> > > > > > big consonant tones (i mean, as a reductionist, i
could
> > never
> > > > > > ignore the harmonic series), it's gotta be equally
> > tempered
> > > > > > (because I love symmetrical modulation-i'm actually
kind
> > of
> > > > lost
> > > > > > without it).
> > > > >
> > > > > Don't ignore 22 on the way to 31, though.
> > > >
> > > > ooh that 22 has a nice P5, huh? and the thirds look
good,
> > too.
> > > > and a tritone? i'm totally sold.
> > >
> > > Don't expect to use any characteristic diatonic chord
> > progressions in
> > > 22 -- they won't work (you'll end up with 55-cent pitch drift or
> > > shifts, at best)! In fact, trying to label 22 with common
> practice
> > > interval names will leave you hopelessly tied up in knots.
19
> > and 31
> > > are easier for beginners because they do fit the
> > common-practice
> > > interval framework, where stacking four fifths gives you the
> > > consonant major third, etc.
> >
> > i only use numbers anyway. that 55 cent drift would be
exactly
> > what i'm looking for. 22 gives a nice little 2*11 symmetry, too,
> so
> > there'd be a class like "whole tone" scales with what looks
like
> > two scales close to chromatic scales.
>
> I mention these as a possible resource for atonalists in my
paper on
> 22:
>
> http://www.lumma.org/tuning/erlich/erlich-decatonic.pdf

great paper! thanks for posting this. smart folks here

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:
>
> If anyone is interested in a *very* economical (29-tone), low-error
> 13-limit tuning, a Scala listing for c. is given here:
>
> /tuning-math/message/7574
>
> Go about halfway thru the message to "secor29htt.scl". This tuning
> gives near-just 15-limit otonalities on each tone in a chain of
> fifths from Bb to A. Some of the 15-limit consonances are exact
> (5/4, 7/4, 7/5, and 13/9), and 11/9 and 13/11 are so close (~0.05c)
> that you'll never be able to hear that they're not exact.
>
> I hesitate to call a this a temperament, because it has *very* low
> error at the 7-limit, which makes it extremely difficult to tell
that
> it is, strictly speaking, a temperament. To approximate the 15-
limit
> consonances in its 6 best keys with an ET more accurately, you have
> to go over 100 tones (to 130-ET). If you want to try it in Scala,
> then I strongly recommend reading the top part of the message for
> advice on how to set the notation for this tuning.
>
> Better yet, maybe I should make available an mp3 file of a
recording
> of a live performance I gave in San Diego in 1975, an improvisation
> on the Scalatron in 29-HTT. Then you can all judge for yourselves
> whether it sounds like JI or a temperament. (I should add that it
> wasn't hard to come up with Scaltron timbres that are highly
> effective in revealing the subtle differences between tunings.)

Here's the file, as promised:

/makemicromusic/files/secor/improv29.mp3

I'll leave it there for only a few days, since there is not much
space.

I had been working with the Scalatron only for a few months when I
did this, so I didn't have years of experience playing the
generalized keyboard. Also, I had devised the tuning only about 6
months before and was only beginning to figure out how to use its
resources. So this is not a polished performance by a seasoned
composer -- just the best I could do at the time to present an
example of 15-limit harmony in a live performance on a polyphonic
synthesizer at a time when Ben Johnston was writing 5-limit JI and
hardly anyone was performing live with a polyphonic synthesizer in 12-
ET.

The concert, sponsored by the Motorola Scalatron Company, was given
in San Diego in November 1975 at the convention of the National
Association of Schools of Music (NASM). Half of it consisted of
pieces which I performed on the Scalatron, both solo and as
accompanist for soprano Barbara Dalheim, who sang several pieces by
Ben Johnston (who was also present). The other half was performed by
the Partch Ensemble, directed by Danlee Mitchell. Need I say that
not a single piece was in 12-ET?

--- In MakeMicroMusic@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
>
> >> If you need assistance in getting an
> >> MP3 of that online, let me know.
> >...
> >Now as far as finding a *place* to put those files goes, I
> >haven't given that much thought, since I am already much too
> >busy even to think about maintaining a website. I suppose I
> >could use the files section for this group if I left them
> >there for no more than a couple of weeks.
>
> I'm happy to host 'em, or try SoundClick.

Thanks, Carl. I think that this file would be mostly of historical
interest, so if you want to put this on your website (with some of
the preceding paragraphs as program notes), you're welcome to do so.

--George

>Here's the file, as promised:
>
>/makemicromusic/files/secor/improv29.mp3
>
>I'll leave it there for only a few days, since there is not much
>space.
>
>I had been working with the Scalatron only for a few months when I
>did this, so I didn't have years of experience playing the
>generalized keyboard. Also, I had devised the tuning only about 6
>months before and was only beginning to figure out how to use its
>resources. So this is not a polished performance by a seasoned
>composer -- just the best I could do at the time to present an
>example of 15-limit harmony in a live performance on a polyphonic
>synthesizer at a time when Ben Johnston was writing 5-limit JI and
>hardly anyone was performing live with a polyphonic synthesizer in
>12-ET.
>
>The concert, sponsored by the Motorola Scalatron Company, was given
>in San Diego in November 1975 at the convention of the National
>Association of Schools of Music (NASM). Half of it consisted of
>pieces which I performed on the Scalatron, both solo and as
>accompanist for soprano Barbara Dalheim, who sang several pieces by
>Ben Johnston (who was also present). The other half was performed
>by the Partch Ensemble, directed by Danlee Mitchell. Need I say
>that not a single piece was in 12-ET?

Awesome awesome awesome. George, may I suggest you cross-post this
to tuning? Just give this url instead, so everyone can listen...

http://lumma.org/tuning/secor/improv29.mp3

-Carl

Hi George,

Thank you for sharing. This sounds surprisingly good!

Kalle

George,
This is a great improvisation. There is one very interesting point towards the end (2:43-2:50) when you play a melody in clusters of very small intervals. Where these tuning puns, or were you going for non-just to show contrast. Neat stuff regardless.

Prent Rodgers

> From: "George D. Secor" <gdsecor@...>
> Subject: 29-HTT Improvisation
> > --- In MakeMicroMusic@yahoogroups.com, "George D. Secor" > <gdsecor@y...> wrote:
> >>If anyone is interested in a *very* economical (29-tone), low-error >>13-limit tuning, a Scala listing for c. is given here:
>>
>>/tuning-math/message/7574
>>

just beautiful. love the timbre, too.

i love the grinding when real tonal chords are played.
-that's probably my favorite part of tunings that get very close to JI.

--- In MakeMicroMusic@yahoogroups.com, Prent Rodgers
<prentrodgers@c...> wrote:
> George,
> This is a great improvisation. There is one very interesting point
> towards the end (2:43-2:50) when you play a melody in clusters of
very
> small intervals.

I've deleted this from the original (temporary) link. But, thanks to
Carl Lumma, it is now at:

http://lumma.org/tuning/secor/improv29.mp3

I wasn't able to identify the passage from your description without
using the timer, since I didn't remember using any small-interval
clusters anywhere. I thought you might have been referring to the
pairs of tones a comma apart from 1:29-2:04, but I was pretty sure
that would have been too early.

The only interval anywhere around the time range you mentioned that I
would call "non-just" is the one at 2:42, where the lower note is a
*wrong note* (drat!!!) -- you'll hear the intended interval, a 5:6,
two dyads later. The smallest intentional interval in this passage
is a repeated 13:15 (~289 cents) at 2:46-2:48. Except for the wrong-
note interval (~240 cents, or a little wider than 7:8), the entire
passage from 2:36-3:00 is nothing more than noodling on a single
harmonic series on F, with the two upper voices two harmonics apart
in the range of 7 to 15, i.e., 7:9, 8:10, 9:11, ... 13:15 above a
drone fifth, 4:6 (F:C).

Anyway, I agree that the wrong note definitely makes the passage much
more interesting -- the smaller wrong-note interval seems to
anticipate the effect of the 13:15, which doesn't come across as a
consonance, at least in this context.

> Where these tuning puns, or were you going for non-just
> to show contrast.

There was a section (2:21-2:31) where I did intentionally use three
somewhat dissonant triads with 11:14 (~major) and 11:13 (~minor)
thirds (intervals that Margo often uses diatonically) for contrast,
with the last 11:14 expanding into even more dissonant thirds, which
shows that, like JI, this tuning can deliver a high consonance-
dissonance contrast. (BTW, I hope you haven't forgotten that I said
that this tuning is actually a *temperament* that I claimed would
sound like JI. From your last comment I have gotten the impression
that I succeeded.)

> Neat stuff regardless.

Thanks for the brief critique. I will now be much less hesitant to
introduce notes that are foreign to the particular scale I'm using
(as a subset of the tuning) or that don't readily fit into my
theoretical paradigm.

--George

P.S. - Please don't get the impression that I'm averse to using JI.
While I prefer temperaments for a 13 prime limit (the lowest limit I
care to use), I feel that JI really starts to shine at higher prime
limits, where I would say that it outclasses all temperaments. There
I find that I am inclined to take a somewhat different approach to
how I derive sets of JI tones and scale subsets.

George D. Secor wrote:

>P.S. - Please don't get the impression that I'm averse to using JI. >While I prefer temperaments for a 13 prime limit (the lowest limit I >care to use), I feel that JI really starts to shine at higher prime >limits, where I would say that it outclasses all temperaments. >

How high of a Prime Limit?

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:

> P.S. - Please don't get the impression that I'm averse to using JI.
> While I prefer temperaments for a 13 prime limit (the lowest limit I
> care to use), I feel that JI really starts to shine at higher prime
> limits, where I would say that it outclasses all temperaments.

This is funny--13 is the highest prime limit I care to use. My basic
focus is 7. As for outclassing all temperaments, as n-->oo n-et-->JI.

--- In MakeMicroMusic@yahoogroups.com, David Beardsley <db@b...>
wrote:
> George D. Secor wrote:
>
> >P.S. - Please don't get the impression that I'm averse to using
JI.
> >While I prefer temperaments for a 13 prime limit (the lowest limit
I
> >care to use), I feel that JI really starts to shine at higher
prime
> >limits, where I would say that it outclasses all temperaments.
>
> How high of a Prime Limit?

Generally 19, but I have some applications that go at least as high
as 41.

--George

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:
>
> > P.S. - Please don't get the impression that I'm averse to using
JI.
> > While I prefer temperaments for a 13 prime limit (the lowest
limit I
> > care to use), I feel that JI really starts to shine at higher
prime
> > limits, where I would say that it outclasses all temperaments.
>
> This is funny--13 is the highest prime limit I care to use. My basic
> focus is 7.

At least we agree on using 13. :-)

> As for outclassing all temperaments, as n-->oo n-et-->JI.

But what is the purpose of a temperament, if not to *reduce* the
number of tones required, as well as to create bridges between
primes, thus making it possible to all tones to assume multiple prime-
identities? And how would anyone play a very large-numbered ET on a
keyboard or refretted guitar or a metallophone?

If you're going to confine yourself to electronics, then n-->oo might
be your thing, but I think acoustic instruments outclass electronics.

--George

On Thursday 17 June 2004 05:37 pm, tentothe99 wrote:
> just beautiful. love the timbre, too.
>
> i love the grinding when real tonal chords are played.
> -that's probably my favorite part of tunings that get very close to JI.

Amen to that !!!!!

I think I prefer quasi-just to true just for that reason. I enjoy the
tension !

Best,
Aaron Krister Johnson
http://www.dividebypi.com
http://www.akjmusic.com

--- In MakeMicroMusic@yahoogroups.com, "Aaron K. Johnson"
<akjmicro@c...> wrote:
> On Thursday 17 June 2004 05:37 pm, tentothe99 wrote:
> > just beautiful. love the timbre, too.
> >
> > i love the grinding when real tonal chords are played.
> > -that's probably my favorite part of tunings that get very close
to JI.
>
> Amen to that !!!!!
>
> I think I prefer quasi-just to true just for that reason. I enjoy the
> tension !

So where do "very close to JI" and "quasi-just" fall in terms of cents?

On Friday 25 June 2004 12:09 am, Gene Ward Smith wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Aaron K. Johnson"
>
> <akjmicro@c...> wrote:
> > On Thursday 17 June 2004 05:37 pm, tentothe99 wrote:
> > > just beautiful. love the timbre, too.
> > >
> > > i love the grinding when real tonal chords are played.
> > > -that's probably my favorite part of tunings that get very close
>
> to JI.
>
> > Amen to that !!!!!
> >
> > I think I prefer quasi-just to true just for that reason. I enjoy the
> > tension !
>
> So where do "very close to JI" and "quasi-just" fall in terms of cents?

Probably somewhere around 3.1415927 cents for me.....

Cheers,
Aaron Krister Johnson
http://www.dividebypi.com
http://www.akjmusic.com

--- In MakeMicroMusic@yahoogroups.com, "Aaron K. Johnson"
<akjmicro@c...> wrote:

> > So where do "very close to JI" and "quasi-just" fall in terms of
cents?
>
> Probably somewhere around 3.1415927 cents for me.....

You might consider joining the many fans of 72-equal. It is the first
et with errors under pi cents up to the 7 limit, and only the 4 cents
flat of the 9 is over up to the 11 limit. If the 5-limit suffices,
then good old 53 will do it for you. 99 gets you up to the 9-limit,
118 up to the 11-limit, and 130 up to the 13-limit. All of these, of
course, are important systems anyway.

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Aaron K. Johnson"
> <akjmicro@c...> wrote:
>
> > > So where do "very close to JI" and "quasi-just" fall in terms of
> cents?
> >
> > Probably somewhere around 3.1415927 cents for me.....
>
> You might consider joining the many fans of 72-equal. It is the
first
> et with errors under pi cents up to the 7 limit, and only the 4
cents
> flat of the 9 is over up to the 11 limit. If the 5-limit suffices,
> then good old 53 will do it for you. 99 gets you up to the 9-limit,
> 118 up to the 11-limit, and 130 up to the 13-limit. All of these, of
> course, are important systems anyway.

For 29-HTT (the tuning in the subject line) the max error is ~1.6237c
at the 7 limit and ~3.2474 at the 15 limit, with the error of each
consonance being either zero or one of those two figures (or very
close).

A listening test will show that 72-ET can't touch it, either at the 7-
limit or the 11-limit (and I have midi files to prove it). 72-ET
clearly sounds like a low-error temperament, while 29-HTT sounds like
JI without phase-locking, very similar to 130-ET. Beating that
occurs with approximated 7-limit consonances is much more noticeable
than at higher limits, so you had better cut your allowable error in
half at the 7 limit.

Gene, for your enlightenment: 29-HTT consists (except for one filler
tone) of 3 chains of fifths of ~703.5787c, or exactly (504/13)^
(1/9). The 3 chains of fifths contain tones 1/1, 5/4, and 7/4,
respectively, and the tones in each chain are taken to as many places
as are required to result in otonal ogdoads on roots Bb, F, C, G, D,
and A. This also gives very-near-just diatonic (5-limit) scales in 5
different keys.

The greatest advantage: the total number of tones/octave is small
enough to make acoustic instruments practical (the smallest intervals
being ~24 cents).

--George

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
> <gwsmith@s...> wrote:
> > --- In MakeMicroMusic@yahoogroups.com, "Aaron K. Johnson"
> > <akjmicro@c...> wrote:
> >
> > > > So where do "very close to JI" and "quasi-just" fall in terms
of
> > cents?
> > >
> > > Probably somewhere around 3.1415927 cents for me.....
> >
> > You might consider joining the many fans of 72-equal. It is the
> first
> > et with errors under pi cents up to the 7 limit, and only the 4
> cents
> > flat of the 9 is over up to the 11 limit. If the 5-limit suffices,
> > then good old 53 will do it for you. 99 gets you up to the 9-
limit,
> > 118 up to the 11-limit, and 130 up to the 13-limit. All of these,
of
> > course, are important systems anyway.
>
> For 29-HTT (the tuning in the subject line) the max error is
~1.6237c
> at the 7 limit and ~3.2474 at the 15 limit, with the error of each
> consonance being either zero or one of those two figures (or very
> close).
>
> A listening test will show that 72-ET can't touch it,

Hmm . . . since Aaron said he *wants* 'errors' of at least 3 cents or
so, isn't this a bit presumptuous of you to say in this context? At
least make the listening tests available to Aaron (and the rest of
us) so he can decide for himself . . .

> Beating that
> occurs with approximated 7-limit consonances is much more
noticeable
> than at higher limits, so you had better cut your allowable error
in
> half at the 7 limit.

I'm not sure exactly what you mean but if you mean that a
given 'error' is less noticeable for more complex ratios and more
noticeable for simpler ratios, this seems to support the 'TOP' idea
for tuning temperaments over the straight minimax-within-an-odd-limit
you seem to have advocated in the past.

> Gene, for your enlightenment: 29-HTT consists (except for one
filler
> tone) of 3 chains of fifths of ~703.5787c, or exactly (504/13)^
> (1/9). The 3 chains of fifths contain tones 1/1, 5/4, and 7/4,
> respectively, and the tones in each chain are taken to as many
places
> as are required to result in otonal ogdoads on roots Bb, F, C, G,
D,
> and A. This also gives very-near-just diatonic (5-limit) scales in
5
> different keys.
>
> The greatest advantage: the total number of tones/octave is small
> enough to make acoustic instruments practical (the smallest
intervals
> being ~24 cents).

I suggest that further analysis, and discussion of the details, of
this temperament (and of temperament tuning schemes in general) occur
on the tuning or tuning-math lists, in light of what we all know
about this list.

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:

> For 29-HTT (the tuning in the subject line) the max error is ~1.6237c
> at the 7 limit and ~3.2474 at the 15 limit, with the error of each
> consonance being either zero or one of those two figures (or very
> close).
>
> A listening test will show that 72-ET can't touch it, either at the 7-
> limit or the 11-limit (and I have midi files to prove it).

The same could be said other tempered scales around the size of 29
notes to the octave, of course; among DE scales, Hemiwuerschmidt[25]
or Hemiwuerschmidt[31], for instance. Ennealimmal[27] is pretty
cheesy, but Ennealimmal[36] or Ennealimmal[45] are not, and they are
vastly more accurate. Tertiaseptal[31] is low on tetrads, but
Tertiaseptal[47] has plenty, and Hemififths[41] does also, but does
very well for the 9-limit as well.

This discussion is interesting because Paul has been claiming that
there is not much interest in these temperaments in the 99-171 et
range, so I am gratified to hear that other people find something of
value in errors under 1.5 cents.

72-ET
> clearly sounds like a low-error temperament, while 29-HTT sounds like
> JI without phase-locking, very similar to 130-ET.

What I described here recently as "JI with a sparkle". I agree; I
think there is something attractive about the tuning in the area of
99, 118, 130, and 140. When we get up to 171, whatever it is starts to
go away and we get a sound more like true JI.

Beating that
> occurs with approximated 7-limit consonances is much more noticeable
> than at higher limits, so you had better cut your allowable error in
> half at the 7 limit.

Or use something like TOP error. I find TOP error together with Graham
complexity useful in evaluating temperaments from the point of view of
my own notions of usefulness.

> Gene, for your enlightenment: 29-HTT consists (except for one filler
> tone) of 3 chains of fifths of ~703.5787c, or exactly (504/13)^
> (1/9). The 3 chains of fifths contain tones 1/1, 5/4, and 7/4,
> respectively, and the tones in each chain are taken to as many places
> as are required to result in otonal ogdoads on roots Bb, F, C, G, D,
> and A. This also gives very-near-just diatonic (5-limit) scales in 5
> different keys.

Thanks, I'll look at this, though the results if any will probably go
up on tuning-math.

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> --- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
gdsecor@y...> wrote:
> >
> > For 29-HTT (the tuning in the subject line) the max error is
~1.6237c
> > at the 7 limit and ~3.2474 at the 15 limit, with the error of
each
> > consonance being either zero or one of those two figures (or very
> > close).
> >
> > A listening test will show that 72-ET can't touch it,
>
> Hmm . . . since Aaron said he *wants* 'errors' of at least 3 cents
or
> so,

I interpreted it to mean *no more* than 3.14 cents or so.

> isn't this a bit presumptuous of you to say in this context?

What I said about the 7 limit is in line with Dave Keenan's views
regarding what sounds like JI, but as you suggest:

> At
> least make the listening tests available to Aaron (and the rest of
> us) so he can decide for himself . . .

Okay, listen here:
/makemicromusic/files/secor/
for the same example in 17 different tunings, including JI, 72-ET,
and 29-HTT. The score is also there, at the bottom. The only
significant difference between the 72-ET and Miracle (Stud-loco)
examples is in how the two ratios of 13 are approximated.

Paul, you may be interested to compare 22-ET with 152-ET (linear
temperament using wide fifths). I was surprised to find that the
latter sounds noticeably better (at least to me), even though the
fifths have a greater error.

> > Beating that
> > occurs with approximated 7-limit consonances is much more
noticeable
> > than at higher limits, so you had better cut your allowable error
in
> > half at the 7 limit.
>
> I'm not sure exactly what you mean but if you mean that a
> given 'error' is less noticeable for more complex ratios and more
> noticeable for simpler ratios,

Yes.

> this seems to support the 'TOP' idea
> for tuning temperaments over the straight minimax-within-an-odd-
limit
> you seem to have advocated in the past.
>
> > Gene, for your enlightenment: 29-HTT consists (except for one
filler
> > tone) of 3 chains of fifths of ~703.5787c, or exactly (504/13)^
> > (1/9). The 3 chains of fifths contain tones 1/1, 5/4, and 7/4,
> > respectively, and the tones in each chain are taken to as many
places
> > as are required to result in otonal ogdoads on roots Bb, F, C, G,
D,
> > and A. This also gives very-near-just diatonic (5-limit) scales
in 5
> > different keys.
> >
> > The greatest advantage: the total number of tones/octave is
small
> > enough to make acoustic instruments practical (the smallest
intervals
> > being ~24 cents).
>
> I suggest that further analysis, and discussion of the details, of
> this temperament (and of temperament tuning schemes in general)
occur
> on the tuning or tuning-math lists, in light of what we all know
> about this list.

Okay, if anyone want to continue, then please take this to the main
list.

--George

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <perlich@a...>
> wrote:
> > --- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
> gdsecor@y...> wrote:
> > >
> > > For 29-HTT (the tuning in the subject line) the max error is
> ~1.6237c
> > > at the 7 limit and ~3.2474 at the 15 limit, with the error of
> each
> > > consonance being either zero or one of those two figures (or
very
> > > close).
> > >
> > > A listening test will show that 72-ET can't touch it,
> >
> > Hmm . . . since Aaron said he *wants* 'errors' of at least 3
cents
> or
> > so,
>
> I interpreted it to mean *no more* than 3.14 cents or so.

Aaron's words were:

"I think I prefer quasi-just to true just for that reason."

and then he threw out the figure of pi cents when asked what "quasi-
just" meant to him.

I'll reply to the rest on the tuning list.

> Okay, listen here:
> /makemicromusic/files/secor/

Whoa dude: rad!

> for the same example in 17 different tunings, including JI,
> 72-ET, and 29-HTT.

Say, what's the difference between Exmp152w.mid
and Exmp152.mid?

Ditto Exmp19p3.mid and Exmp19.mid -- does the former
have 21 notes?

Maybe you could expositate these scales on tuning.

-Carl

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:

> Gene, for your enlightenment: 29-HTT consists (except for one filler
> tone) of 3 chains of fifths of ~703.5787c, or exactly (504/13)^
> (1/9). The 3 chains of fifths contain tones 1/1, 5/4, and 7/4,
> respectively, and the tones in each chain are taken to as many places
> as are required to result in otonal ogdoads on roots Bb, F, C, G, D,
> and A. This also gives very-near-just diatonic (5-limit) scales in 5
> different keys.

Followed up by

/tuning-math/message/10549