TUNING digest 1145

>I am interested in hearing about any list members' experiences in
>writing in Just Intonation for acoustic instruments, such as orchestral
>instruments, natural brass instruments (cf. Koechlin's "Sonneries"
>for natural horns), or specially designed instruments other than
>Partch-type percussion (such as harmonic flutes, Branca-type zithers,
>etc.). What are the capabilities and drawbacks, how well do performers
>adjust, how accurate are the results with what prime limits, etc.
>Christopher J. Smith
>


Check out our web page. Look at the instruments section. Many of our
instruments are not yet posted, but you mentioned Harmonic Flutes. We have
developed an entire family of these. they started out as the long straight
Fipple pipes, which I called "Harmonic Whistles" back in the 70's, because
they play the natural harmonic series, like a bugle. Then there are the
medium sized pipes with one hole, which allow alternation between two
adjacent series and allow for composite scales between them. Finally, there
are the custom recorders, (Alto, soprano ans sopranino ranges) which have
their holes placed for segments of the subharmonic series (harmonics are
blown on these to get the higher pitches on the series). Using these
instruments we are able to navigate the entire 11 limit matrix, and also
play some other tonalities, because of the higher harmonics in some of the
pipes. In addition we have worked with violin and cello players. Personally,
I find the Cosmolyra and Theremin to be my favorites at this time.



Best wishes,

Denny Genovese
Director

Southeast Just Intonation Center sejic@afn.org
World Harmony Project Inc.
PO Box 15464 http://www.afn.org/~sejic
Gainesville, FL 32604 USA



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From: alves@orion.ac.hmc.edu
Subject: Re: Just Intonation for acoustic instruments
PostedDate: 06-08-97 19:57:26
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It seems nobody has picked up on this, so I'll offer
some comments. Most of this is pretty involved, so you have
my permission to skip to the end of this post.

James Kukula wrote:

>The sound generated by a periodic motion will have integer overtones, by some-

>classical theorem of Fourier or whoever.

The Fourier series is a way of turning a periodic signal into a
sum of sinusoidal waves of integer frequency multiples. I've
never heard of this stated as a theorem, but it is.

> Furthermore, a system with one
>degree of freedom is pretty much constrained to move in a periodic fashion,
>at least for bounded trajectories.

This would be true for autonomous systems -- that is, where the
state of the system depends entirely upon its previous state,
and not explicitly on time. The wave equation is a 2-D
autonomous equation -- it depends upon amplitude and its
derivative with respect to time. An autonomous system with 2
continuous variables can have a stable periodic motion, but
cannot have prolonged aperiodic motion. With 3 variables, chaos
can arise, and a system with 1 degree of freedom can have a 3
dimensional equation of motion. I can explain more of this
off-list.

>Ideal one-dimensional systems of coupled linear oscillators, like vibrating
>strings or columns of air, will have an integer overtone series.

I'm not at all sure what this means. To clarify, though:

A one dimensional continous autonomous system cannot have
periodic behaviour: that would mean moving in different
directions from the same state.

A perfect, infinitely thin string with perfectly clamped
endpoints _can_ have non-integer overtones. This will always
be the case where the speed of sound in the string depends
upon its frequency.

I'm sure two coupled oscillators can produce chaotic motion.


As regards this FAQ, can we have some kind of historical and
geographical coverage of standard tuning practice? When was
meantone / well / equal temperament in use is a question that
seems to come up fairly frequently.



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From: mr88cet@texas.net
Subject: Re: Natural Harmony
PostedDate: 11-08-97 20:49:19
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>The article points out that there's a more common class of seismic
>signals called harmonic tremors with a nice overtone series.

That strikes me as surprising (although I'm not suggesting that they're
lying of course). It seems surprising because of the answer to your second
question:



>Strikes me a tuning FAQ ought to address the question, are integer overtone
>series natural or artificial, where do they come from?

Harmonic partials come from vibrating systems with uniform and elastic
vibrating media bound by two immobile "nodes". The most obvious example is
a vibrating string, the two nodes being the nut (or fret) and bridge.
Those systems can set up "standing waves", which resonate strictly at
harmonically-related frequencies.

I would think that most seismic waves would not fit this model at all,
but instead would vibrate along the effectively infinite expanse of the
crust of the Earth. But getting back to musical instruments...

Systems that produce nonharmonic partials don't follow that scheme at
all, an example being a drum head. Systems that produce NEAR-harmonic
partials almost always have that essential scheme, but the perfection of
one element or another is compromised. High-register piano strings for
example, are not entirely harmonic because they are very stiff, and thus
compromise the elasticity requirement.

Most wind instruments somewhat compromise the absoluteness of the nodal
points. The vibrating medium, air itself, is an almost ideal (in this
sense of the word) vibrating medium unlike the high-register piano string.
The physical basis for this is somewhat more complicated to describe, so
bear with me here:

In wind instruments, the wave is easiest viewed as an air-pressure wave
traveling along the axis of the tube, the nodes being the points where the
air-column is exposed to the open atmosphere. At those points the air
pressure can't fluctuate very much. Why? Because, unlike within the tube
where the air molecules' movement is restricted to the confines of the
tube, any attempt to pressurize them in the open atmosphere will be
immediately thwarted by their freedom to move so as to disperse that
pressure.

The compromise to the absoluteness of the nodes occurs right at the
opening to the atmosphere. It's called an open-end effect, and it gets
even more complicated with woodwind-style toneholes. The air molecules'
movement isn't sufficiently unrestricted to form a pure node until they get
somewhat outside the tube. How far outside the tube they have to be
depends upon a great many factors including the geometry of the tube (e.g.,
its diameter and whether it's cylindrical or conical), the amplitude of the
wave moving them, and yes, the frequency of that wave as well.

For a purely cylindrical tube like you'd find on a fife, the effective
nodal point is fairly predictable, lying outside the end of the tube about
0.6 times the diameter of the tube. A flared bell like brass instruments
have tends to blur the exact placement of that nodal point much more than a
simple cut in the tube. The effective vibrating length of the air column
therefore varies a bit more between harmonics in brasses than in woodwinds
or strings.

But, as I've mentioned before on this list, I have quite a bit of direct
experience with the tones of orchestral instruments forced to exact
harmonic overtone structures, and I think it's important that these are -
in the big scheme of things - fairly subtle differences. They are of the
magnitude that distinguishes a good simulation of an instrument from a bad
one, not ANYWHERE NEAR the sort that distinguishes, say, a flute from
trumpet.



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From: Denis.Atadan@mvs.udel.edu
Subject: Tape Swap is like Soyulent Green
PostedDate: 11-08-97 20:50:23
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>> Furthermore, a system with one
>>degree of freedom is pretty much constrained to move in a periodic fashion,
>>at least for bounded trajectories.
>
>This would be true for autonomous systems -- that is, where the
>state of the system depends entirely upon its previous state,
>and not explicitly on time. The wave equation is a 2-D
>autonomous equation -- it depends upon amplitude and its
>derivative with respect to time. An autonomous system with 2
>continuous variables can have a stable periodic motion, but
>cannot have prolonged aperiodic motion.

You're right that periodicity would depend on the system being autonomous.
I suspect we're having some terminological confusion here. I studied physics
once upon a time but that was a long time ago. Somehow we need to
distinguish between ordinary differential equations and partial differential
equations for starters. What I mean by a system with one degree of freedom is
something like a simple pendulum.

Once we get into the wave equation, to me that's a partial differential
equation. That describes a system like a vibrating string, that has roughly
an infinite number of degrees of freedom - i.e. each little section of the
string can be budged up or down a smidgeon independently of how much other
little sections are budged, though of course the elastic forces acting on the
various little sections depend precisely on all those budgements.

Another factor coming into play could be the order of the various
differential equations. E.g. harmonic oscillators are second order
differential equations, because acceleration is the second time derivative of
position.

>>Ideal one-dimensional systems of coupled linear oscillators, like vibrating
>>strings or columns of air, will have an integer overtone series.
>
>I'm not at all sure what this means. To clarify, though:
>
>A one dimensional continous autonomous system cannot have
>periodic behaviour: that would mean moving in different
>directions from the same state.

So it's my turn to be confused. An ideal string can certainly have periodic
motion. Actually any vibrating body will have a whole set of modes of
oscillation, and if you get the body to vibrate in just one mode, then its
motion will be periodic. That's what modes of oscillation are, roughly
speaking. (A little more precisely, the periodic motion will be follow a nice
sinewave shape).

I suspect we're just getting caught by words like "one dimensional
continuous".

I'm not sure just how much physics is really appropriate in this forum. But
it seems worthwhile to try to clarify:

>>The article points out that there's a more common class of seismic
>>signals called harmonic tremors with a nice overtone series.
>
> That strikes me as surprising (although I'm not suggesting that they're
>lying of course). It seems surprising because of the answer to your second
>question:
>
>>Strikes me a tuning FAQ ought to address the question, are integer overtone
>>series natural or artificial, where do they come from?
>
> Harmonic partials come from vibrating systems with uniform and elastic
>vibrating media bound by two immobile "nodes".

Integer ratio overtones can come from other mechanisms besides uniform and
elastic etc.

If you take a nice clean laboratory sinewave oscillator and run it through an
amplifier and through a loud speaker and CRANK THE VOLUME WAY UP it won't be
a nice clean sinewave any more. The distortion of the loudspeak, amplifier,
etc. will generate nice integer ratio overtones! No vibrating strings around.

I'm not sure if this is related to the one-degree-of-freedom business or
not. But periodic motion necessarily generates integer-ratio overtones, and
systems with one degree of freedom are more or less forced to be periodic -
as long as they're autonomous and probably some other restrictions, this gets
over my head pretty fast.

Anyway it seems like integer-ratio overtones are important to tuning theory
so maybe not too much of a waste of bandwidth to try to get clear.

Jim



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From: Denis.Atadan@mvs.udel.edu
Subject: Great Tape Swap Deadline
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