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> Re: Request for Lesson Plan in J.I.

> Wow! It seems this topic struck a chord with a few people. Thank you
> all for your suggestions. If I wind up having to write this myself,
> I'll certainly incorporate your ideas on how to go about it. I'm
> keeping all of your replies in a folder.

Dear Robin,

Please let me thank you for giving us the opportunity to share one of
the greatest responsibilities we have: to help others form their own
artistic judgments and enjoy the vast range of world musics in JI and
other intonation systems.

I feel that it is very important, in letting students experience a
sample of this vast diversity, here with a main focus on simple or
complex just ratios, but not excluding various other styles of tuning
which may lend a bit of perspective.

This should also be a lesson in tolerance and empathy. For example,
just about _any_ world musical tradition, emphatically including the
classical composed tradition of Western Europe at any historical era,
could be viewed as "unnaturally limited."

For example, in classical Western European music from the medieval era
to the 19th century, there are the familiar whole-tone and semitone
steps. In Near Eastern traditions (Arabic, Persian, Kurdish, and
Turkish) there are likewise these familiar steps, but also neutral or
"middle" seconds and other intervals somewhere between major and
minor. These steps may often follow or approximate just ratios like
14:13, 13:12, or 12:11. Hearing and recognizing them is a bit like
learning the sounds of an unfamiliar language, if one has not grown up
in such a tradition.

Someone from one of these cultures might argue: "How is it that
someone has indoctrinated you so that you have not followed the
natural course of using these beautiful melodic intervals, which the
great lutenist Mansur Zalzal made popular in the 8th centuries.
What has held you people back 1200 years?"

We understand that each culture has developed in its own way, so that
for people in each some just (as well as tempered!) intervals may seem
familiar and "natural," others strange or less inviting. Pythagorean
intonation, favored at various times and places, is simply a system
for tuning in pure 3:2 fifths and 4:3 fourths. In Europe and also Near
Eastern traditions influenced by the Greek tradition, this is
associated with Pythagoras and his followers. In China or Japan, it
has deep roots also. It's neither a great conspiracy nor a universal
solution to all musical problems, just one kind of JI approach, and a
very easy one to tune.

For example, getting back to the Near East, many intervals such as
major or minor thirds are often played at or near Pythagorean sizes,
because fretted instruments are often tuned in pure fifths and
fourths. However, the middle or neutral intervals I mentioned have
another basis, and sometimes we have major or minor thirds at a
variety of ratios. One of the first lessons of JI is that there are
often lots of ways to tune an interval.

One thing I would urge: if a tuning system is taught, students should
have an opportunity to hear some musical pieces, or at least examples
of actual passages or progressions, where that system fits the music.
For example, with Pythagorean, you could use some Chinese or Japanese
music showing this kind of intonation; or 12th-14th century European
music performed in this style. On a keyboard, it would be good to know
at least a few simple cadences which make the available sizes of
intervals move in a musically effective way. This goes for other just
tunings also.

> I am still looking for a ready made plan to use, however. I know there
> must be an elementary school math or music teacher on this list???
> Please!!!!

> Thanks again,
> Robin

As a very amateur and uncredentialed educator, maybe I could offer to
help develop something, with feedback welcome from teachers or others
in making things comprehensible to ordinary sane people, including
younger ones <grin>. There's lots of music on the Web to supplement
whatever instruments or recordings might be available in class.

Please feel free to contact me via e-mail: this could be a great
learning experience for us all.

Most appreciatively,

Margo Schulter
mschulter@calweb.com

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:

Margo addressed her post thusly:

>
> Dear Robin,

Though I'm not so dense as to fail to realize that a lot of it is
actually a bit of finger waving at me for having spoken negatively
about Pythagorean tuning.
>
>
> I feel that it is very important, in letting students experience a
> sample of this vast diversity, here with a main focus on simple or
> complex just ratios, but not excluding various other styles of tuning
> which may lend a bit of perspective.

I agree completely, though they first have to get a grip on the basic
concept. And that means getting a handle on overtone congruence as the
arbiter of interval size, at least up to 5-limit. As far as I'm
concerned, if you want to push their conceptual envelopes, it would be
far better to carry on exploring the universe of intervals to be found
within a single tone, to 7-limit and 11-limit, than to introduce some
unnatural system like Pythagorean.
>
> This should also be a lesson in tolerance and empathy.

A sort of political correctness in intonation theory?

;-)

> For example,
> just about _any_ world musical tradition, emphatically including the
> classical composed tradition of Western Europe at any historical era,
> could be viewed as "unnaturally limited."

Of course, but it all depends on how you slice it. If the basic mode
of approach AT THE MOMENT is JI, then Pythag is a limited unnatural
system because it replaces the natural tuning of the major and minor
third (and their inversions) and sevenths and so on if you want to go
further by those dissonant intervals which only appear when one uses
the unnatural synthetic approach of an extended series of but one
natural interval to derive all the others.

>
> Someone from one of these cultures might argue: "How is it that
> someone has indoctrinated you so that you have not followed the
> natural course of using these beautiful melodic intervals

Margo errors in confusing that which is only perceived as being
natural with what is objectively natural, i.e., those intervals which
naturally occur within the lower regions of the harmonic series,
intervals which are universal and not dependent upon cultural choice.
For me, this is what JI is all about; it's not just anothe system, it
is THE only natural system. I'm not talking about various limited
forms of JI, Pythgorean or the ubiquitous "Just Scale" of the
acoustics theory books, though I admit that I did recommend that Robin
use this particular structure to expand the essential JI concept to a
selection of chords familiar to most teenagers.

> We understand that each culture has developed in its own way, so that
> for people in each some just (as well as tempered!) intervals may seem
> familiar and "natural," others strange or less inviting.

Again, I am not talking about what people THINK is natural, only that
which is indeed natural according the laws of physic, according to
those complex sounds produced by oscillating objects which manifest a
harmonic series, which happens to be a majority of musical instruments
world wide, including the human voice, bells and bars being the most
obvious exceptions.

Pythagorean
> intonation, favored at various times and places, is simply a system
> for tuning in pure 3:2 fifths and 4:3 fourths. In Europe and also Near
> Eastern traditions influenced by the Greek tradition, this is
> associated with Pythagoras and his followers. In China or Japan, it
> has deep roots also.

No matter how ancient, I view any mathematical system which
synthetically constructs a scale or a gamut by the extension of
logical structures beyond the bounds of the lower (audibly
perceivable) regions of the harmonic series as being after the fact,
and in that sense, unnatural. I strongly suspect that ancient Chinese
and Japanese intonation was like current day Mongolian intonation,
until some wise guy came along and ran the numbers and imposed a
Pythagorean cookie-cutter mentality upon it.

It's neither a great conspiracy nor a universal
> solution to all musical problems, just one kind of JI approach, and a
> very easy one to tune.

Only when you have the intellectual construct of deriving things by
making chains of other things, AND when you have the practical
construct of a musical instrument which allows you to realize the
intellectual construct. In the absence of both, a pure major third is
far more obvious and far easier to tune than a Pythag third.
>
> For example, getting back to the Near East, many intervals such as
> major or minor thirds are often played at or near Pythagorean sizes,
> because fretted instruments are often tuned in pure fifths and
> fourths.

My point exactly. Without such instruments, they'd find it rather
difficult. While we have no way of proving it, I find it preposterous
to entertain the notion that any hunter/gather or early agrarian
tribal group would hit upon something so unnatural as a Pythagorean
major third. I think it is obvious that what "ur altes" peoples did
was simply to open their mouths and make sounds which seemed pleasing
in some way, and when this involved what we would call "harmony", it
would have been combinations based on readily perceivable overtone
congruence, which is what we would call (extended) Just Intonation
(though not in the sense of any rigid extended gamut derived by an
extension of natural proportions). This is what the Mongolians do,
what the Aborigines do, what Norwegian traditional musicians do, what
lots of peoples do all over the planet, those who have been lucky
enough to escape the curse of some Mesopotamian or Chinese or G(r)eek
number cruncher coming along and telling them that what they are doing
is wrong and they should stop listening and start adhering to some
intellectual construct. They just pick up a bamboo tube and blow on
it, or stretch a string and start plucking it, or grab an ox horn and
blow on it, or pick up a tree branch hollowed out by termites and blow
on it, and Lo! and Behold! - a scale emerges, which they imitate.
Amazing! How is it possible without proceeding by a series of pure
fifths until you have synthetically determined the precise placement
of each tone? It just happens, that's how. And that is why I call
Pythagorean "unnatural". The only thing it is natural for is a fifth.
One only. One could arge that a pure ninth is also Pythagorean, but
the point is that you don't have to KNOW that it is the same thing as
a stack of two pure fifths in order to hear it, nor do yo have to
proceed by stacking fifths in order to produce it. If the tone is rich
in harmonics, it jumps out and shouts, "Hey! Listen to me!!"

> One thing I would urge: if a tuning system is taught, students should
> have an opportunity to hear some musical pieces, or at least examples
> of actual passages or progressions, where that system fits the music.

Agreed completely. Otherwise it's just a bunch of dead numbers.

Ciao,

P