Karl Eitz and Tonwort

I did an Altavista search for Eitz and Tonwort and found the following
as a new book at the Eda Kuhn Loeb library at Harvard. If anyone has the
time to peruse it, Nadja Schnetzler ()
would most likely be very grateful and show her gratitude with chocolate
.


47.Eitz, Carl, 1848-1924. Das Tonwort : Bausteine zur musikalischen
Volksbildung. Leipzig : Breitkopf & Hartel, 1928. -- [HOLLIS#
AIP5489]


--John

On Thu, 1 Oct 1998, bram wrote:
> My guess, without knowing exactly what those papers say, is that they are
> generally based on an algorithm for cancelling out the beats of any two
> notes. I know the beats can be essentially calculated using continued
> fractions, so I'm guessing there's a rather straightforward way of
> calculating, given a*sin(x) + b*sin(y), a and b being volumes and x and y
> being wavelengths, there's a rather straightforward way of calculating a
> bunch of other sin functions which when added will cancel out all the
> beats.

I don't think Bill is canceling out the beats in an antinoise sense;
rather, he is matching tuning and timbre so that the intervals of the
scale line up with the partials of the sound. That is, he gets rid of
the beats the old-fashioned, JI way: by making the overtones match up.

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

On Thu, 1 Oct 1998, Paul Hahn wrote:
> On Thu, 1 Oct 1998, bram wrote:
>> I know the beats can be essentially calculated using continued
>> fractions, so I'm guessing there's a rather straightforward way of
>> calculating, given a*sin(x) + b*sin(y), a and b being volumes and x and y
>> being wavelengths, there's a rather straightforward way of calculating a
>> bunch of other sin functions which when added will cancel out all the
>> beats.
>
> I don't think Bill is canceling out the beats in an antinoise sense;

Actually, thinking further on it, I don't think that would even be
possible, considering that the beats don't actually exist physically,
but arise because of nonlinearities in the auditory system.

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

On Thu, 1 Oct 1998, Paul Hahn wrote:

> On Thu, 1 Oct 1998, Paul Hahn wrote:
> > On Thu, 1 Oct 1998, bram wrote:
> >> I know the beats can be essentially calculated using continued
> >> fractions, so I'm guessing there's a rather straightforward way of
> >> calculating, given a*sin(x) + b*sin(y), a and b being volumes and x and y
> >> being wavelengths, there's a rather straightforward way of calculating a
> >> bunch of other sin functions which when added will cancel out all the
> >> beats.
> >
> > I don't think Bill is canceling out the beats in an antinoise sense;
>
> Actually, thinking further on it, I don't think that would even be
> possible, considering that the beats don't actually exist physically,
> but arise because of nonlinearities in the auditory system.

Ah, but they do :)

After thinking about it a bit more, I realize that the beats need to be
'augmented' rather than 'cancelled', since they correspond to regions of
decreased volume.

The very simplest example is sin(x/n)+sin(x/(n+1)) since that only has one
beat.

Consider the case where n=4. It starts out at about double the volume of
an individual sin wave, then the volume decreases until the two waves
exactly cancel out at x=10, then come to complement each other and x=20,
and continue to alternate.

If a sin wave is now added which becomes most angular at the place where
the other two waves cancel out, it will tend to make the volume consistent
throughout. Specifically, the function

sin(x/4) + sin(x/5) + 5*sin((x+10)/40)

should have less of a beat.

I say less instead of none because I'm fairly certain I did something
wrong with the volumes. Can someone verify for me whether sin(x) and
a*sin(x/a) are of the same volume? If they are, I know how to make it
exact.

Note that phase information is very important here - simply adding a third
sin wave of the correct wavelength but wrong phase will be unlikely to do
a good job fixing the beat.

Unfortunately, I don't have the tools handy to make neat diagrams or sound
files to illustrate the above - could anybody suggest some good free ones
which work under windows?

I'm still not sure what to do when the phases of the two waves don't line
up exactly, and haven't really looked into how to fix ratios with more
beats (like 21/17) but I think I'll be able to work that out later - it's
an *interesting* problem.

-Bram

I really doubt that it could be done as bram describes (and if it can, I
suspect it would do odd things to the timbre and/or harmony), but hey,
go for it. Let us know how it works out.

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

> Can someone verify for me whether sin(x) and
> a*sin(x/a) are of the same volume? If they are, I know how to make it
> exact.

Their volume difference (in decibels) would be 20 log a.

> As Bill Sethares shows in his recent papers on timbre and
> consonance,("Local consonance and the relationship between timbre and
> scale"1993.

I suggest you get a copy of his book/CD. It's called ... (ooo, I hope I
get these words in the right order!) ... Tuning Timbre Spectrum Scale, and
published by Springer.

Bram wrote,

>I have a somewhat better idea of what I mean by 'beats' now. If take
the
>volume of a sound wave (I forget the three letter acronym off the top
of
>my head)

RMS?

>and express it as the sum of a bunch of volumes of individual
>sine waves, (no, I don't know a simple way of doing that
transformation)

Is it unique?

>the beats are the waves in the resulting summation which weren't added
>together to get the original waveform.

Sounds like you're talking about interference, which is a much more
general phenomenon than beating.

>I think making a sound whose timbre is a bunch of pure tones is even
>easier - just take the derivative of the square root of the sum of
their
>squares, but that just seems *too* easy.

I don't understand what you mean by that, but any sound can be expressed
as a (possibly infinite) bunch of pure tones.

HI,

Sorry for the delay with my 2 cents. I haven't had access to the
internet for over a week,
and when I did yesterday I had to do it on Windows, an absurd program
called
Explorer, and an absolutely idiotic-unintuitive mail (apparently)
program called Outlook (which managed to destroy some of my mail).
Coincidentally all 3 apps are made by the same obscure North-West
American company.

I don't know much about all this yet, but might what Brad is talking
about and Sethares' approach be achieved using additive synthesis ?

It just seems the logical solution.

There's bound to be a lot of info on the mighty mighty infobahn about
additive. Greg Sandell's SHARC Timbre database also (I think) has some
info
that is of use, since there's been mention on the Sharc list about
people using
the data to build sounds in the Kawai K-5000 additive synths (I wonder
if they
have any microtuning capability) .

If you don't have access to any real-time additive synthesis system
(Kyma,
K-5000, MSP,etc.) , there's always building samples in any of the free
software
synthesis systems (Csound, Syd, etc.) and loading them
into a sampler like Vsamp
(on a PowerMac).

BTW, Kyma is now just $3300 for the base unit (four 80 MHz dsps, 96 MB
RAM
, digital i/o) and it's new and improved:
"Based on the new Motorola DSP-56309 chip running at 80 MHz, the
Capybara
320 base unit is now available for US$3300 and provides a minimum of
four DSPs
(expandable to 28) with multi-channel I/O, synchronization to external
clocks, and
96 MB of sample RAM (expandable to 672 Mb) in a low-noise,
rack-mountable package
connected to a desktop or laptop Macintosh or Windows PC."
This beaut is getting more and more
affordable (compared to many of the commercial synths and samplers
around,it's
actually cheap !) and powerful......

-Drew

----------------------------------------------------------------------------
"Out of the ash
I rise with my red hair
And I eat men like air."-Sylvia Plath

"Ricka-racka-firecracker,Sis-boom-bah.
Bugs Bunny,Bugs Bunny,Rah Rah Rah !"
----------------------------------------------------------------------------

On Wed, 21 Oct 1998, Drew Skyfyre wrote:

> I don't know much about all this yet, but might what Brad is talking
> about and Sethares' approach be achieved using additive synthesis ?

Yep.

> there's always building samples in any of the free
> software
> synthesis systems (Csound, Syd, etc.) and loading them
> into a sampler like Vsamp
> (on a PowerMac).

I should probably look into CSound, the sound capabilities for Java (my
development environment of choice) appear to not have been written yet.

I've now gotten a copy of Roederer's book, "The Physics and Psychophysics
of music" and have to say the first chapter is one of the best
philosophical tracts I have ever read.

I've also got a copy of Sethares's book on special order, but it will be a
matter of weeks or months before it arrives (grrr). Anybody have a
suggestion for how to order it other than just going through amazon.com?

I have a somewhat better idea of what I mean by 'beats' now. If take the
volume of a sound wave (I forget the three letter acronym off the top of
my head) and express it as the sum of a bunch of volumes of individual
sine waves, (no, I don't know a simple way of doing that transformation)
the beats are the waves in the resulting summation which weren't added
together to get the original waveform.

I think making a sound whose timbre is a bunch of pure tones is even
easier - just take the derivative of the square root of the sum of their
squares, but that just seems *too* easy.

Some testing is clearly called for.

I'll let you all know how it goes.

-Bram

On Wed, 21 Oct 1998, Paul H. Erlich wrote:

> Bram wrote,
>
> >the beats are the waves in the resulting summation which weren't added
> >together to get the original waveform.
>
> Sounds like you're talking about interference, which is a much more
> general phenomenon than beating.

I think you're right, although I've done some poking around and haven't
been able to find anything which describes interference much past the
usual constructive versus destructive interference. Could anyone point me
to a more in-depth explanation of it?

-Bram

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End of TUNING Digest 1569
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