Diapason Press

Some readers will be aware that some years ago, Dr. Rudolf Rasch of the
University of Utrecht started Diapason Press to publish three kinds of
material:

a tuning and temperament library, consisting of treatises dealing with
microtonal matters, often with translations and always with extensive
commentary.

a general series of music, consisting of works historically significant to
the history of tuning, even though not always microtonal in an explicit
sense.

Corpus microtonale, a series of microtonal compositions, mostly from this
century.

I subscribed to all three series and am glad I did because of their high
quality. However, Rudolf has been busy with other things in recent years
and hasn't issued much material, also due to some expenses involved.

The good news is that he will soon resume publication, probably within the
next year in all three series. I have been his assistant editor since
1988: that is my chief connection with Diapason Press. I encourage list
members to become acquainted with the series, perhaps by visiting a
library which has some (I know, this is impossible for many people), and
supporting them with purchases, either directly or indirectly via a
library. There is truly valuable material available here.

Because there is no web site for Diapason yet (one is planned), I will
list what's been published if enough people are interested. (But I have
only a week to do this, because I will be going away for a bit.) Further
information on prices, etc., could come later from various sources.
American and other foreign distribution is planned.

The more material Rudolf sells, the more he can print. Meanwhile, rest
assured that I receive no monetary benefit from any of this. The only
"benefit" to me is more work, which in this cause I will gladly take on
when I can.

I spent a pleasant few days with Rudolf two weeks ago in which he
explained his plans to me. I think they are very much worth supporting.
Any opinions out there?


Dr. Paul Rapoport e-mail: rapoport@mcmaster.ca
SADM (Music) tel: (+1) 905 529 7070, ext. 2 4217
McMaster University fax: (+1) 905 527 6793




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> No, harmonics from physical sources such as flutes and oboes and
> bells are not integrally separated. Generally one solves families
> of solutions to Bessel or Legendre type equations, and these are not
> simple integer multiples.

"Sources such as flutes and oboes and bells", eh?

That's kind of like saying "numbers like 2, 3, and 3738239.7564108".

Bells are a totally different matter entirely from flutes, oboes, or
other woodwinds and strings. True, none of them have mathematically exact
integer multiple partials, but bells are many many times further from
harmonic than woodwinds and strings.

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----------begin crosspost from alt.sci.physics.acoustics----------

Subject:
Re: Proof of Harmonic Series?
Date:
16 Feb 1997 22:25:51 GMT
From:
J.Wolfe@unsw.edu.au (JW)
Organization:
University of New South Wales
Newsgroups:
alt.sci.physics.acoustics
References:
1 , 2


In article , clucy@cix.compulink.co.uk
("Charles Lucy") says:

>Can anyone point me to conclusive physical proof that harmonics
>(i,e, the sounds that you hear) are only to be found at
>integer frequency ratios.
>I am seriously questioning this "hallowed" rule, and would
>appreciate pointers from the acousticians.
>(My experience and intuition tells me that harmonics beat)
>Does anyone have firm experimental data to validate the
>integer ratio mapping of harmonics on vibrating strings?

Vibrating strings:
The overtones of plucked strings are in general not harmonically
related. For very long, thin strings they come close, but normally the
higher partials are slightly sharper than the harmonic ratios. This is
due (mainly) to the finite bending stiffness of the string at the ends.
This is particularly noticeable in small pianos. In such pianos the
'octaves' are usually tuned a little sharp so that the first overtone
of one string does not beat with the string that is (approximately) one
octave higher. People say that the effect is smaller on grand pianos,
because the strings are much longer, but I have never done any
experiments. On the few harpsichords I have looked at, the overtones
were very close to being harmonic.

Bowed strings are quite different. The stick-slip action of the bow is
usually (very close to) periodic, and as Fourier's theorem tells you,
the components of a periodic function are harmonic. One can take a very
inharmonic string (e.g. attach a small weight to it) and then bow it
carefully and produce a spectrum whose components are as harmonic as
you can measure.

In wind instruments, the reed, the player's lips or the air-jet take
the role of the bow and produce a periodic function. So in steady state
the components of these instruments are harmonic, even though the
resonances of the instrument may not be. Ask a beginning flute player
to play two notes an octave apart, and you'll be surprised at the
interval that results. But look at or listen to the components of the
lower note, and you'll find that they are as harmonic as you can
measure.

Note the point about steady state: only a periodic wave that is of
infinite duration has exactly periodic components. In practice, most
string and wind instruments only play notes for say 10s or so, so you
cannot measure the frequencies more accurately than 0-.1 Hz. And
usually the players will add some vibrato as well. So, as in every
other branch of science, you can never say that the results accord
exactly with the theory, because you can never make measurements with
infinite accuracy.

But, to the accuracy of your ears, or of a spectrum analyser running
over a few seconds, the components of a steadily bowed string or
steadily blown wind instrument are harmonic.

Plucked strings are not harmonic, and noticeably so in many cases such
as pianos. Percussion instruments (you mention bells) have components
that depart even further from harmonic ratios.

Joe Wolfe, Physics, UNSW, Sydney

------------end crosspost from alt.sci.physics.acoustics----------

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> Plucked strings are not harmonic, and noticeably so in many cases such
> as pianos. Percussion instruments (you mention bells) have components
> that depart even further from harmonic ratios.

Uhmmm... Well, that may perhaps be true of SOME plucked strings, maybe
perhaps violin or viola pizzicato. But I don't think the same can be said
for many, and possibly the majority, of plucked strings, including 'cello
and bass viol pizzicato and guitar.

I say that because I personally have decomposed and then additively
resynthesized those tones with partials forced to be strictly harmonic.
What ever would posess me to do that? Because for a long time that's all
my program would do (analyze down to the nearest strict harmonic). I had a
regular test suite of about two hundred woodwind, brass, orchestral and
plucked-string, bell, piano, pipe organ, wood-bar, and metal-bar
instruments, and timpani. I ran those sounds through the program
frequently as I developed it.

It's very easy to hear that, in being forced to strict harmonics, the
strings (excluding the high register of the piano), woodwinds, and brass
suffered only slightly, whereas the characters of the those percussion
instruments, were vastly altered.

The enormity of the difference for the strings (including the plucked
strings), woodwinds and brasses I would characterize as slightly greater
than the sort of thing that distinguishes a bad guitar (for example) from a
good guitar.

Another way to characterize the difference is that the unaltered and
pure-harmonic tones were nearly indistinguishable from each other on the
Mac's built-in speaker, although the strictly harmonic timbres had a
crusty, buzzy, robotic quality when played back over big speakers in
44.1KHz 16-bit stereo.

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