Tr : OPERATOR SYNTHESIS

----------
De�: Sarn Richard Ursell <thcdelta@ihug.co.nz>
� : wim.hoogewerf@fnac.net
Objet�: OPERATOR SYNTHESIS
Date�: Lun 20 d�c 1999 3:40

Thankyou very much Mr.Wim Hoogewerf,

I want you to mention that these were origionally from me!

Anyhow, here they are:

Here's one for the list:

Dearest Members of the alternative tuning digest,

I have a question:

Why does the music industry use ADDITIVE SYNTHESIS?

I mean, I realise fully that it is possible, and is conventionally used for
us to add two waveforms, with repect to time, to give us a more complex
waveform, but I got to woundering, why not MULTIPLY them?

We could tehn take the square root of this, giving a GEOMETRICAL AVERAGE,
and I have conventiently called this "MULTIPLICATIVE SYNTHESIS".

Of course, we can, and will end up with imaginary numbers, but then I got to
thinking, why not just reverse these waveforms and make them negative?

And why stop there?

We could go on to EXPONENTIONAL SYNTHESIS, and take the "QUIGGLE ROOT", or
"SUPER-ROOT".

Of course, things get interesting here, as, I now know that there are:

(2n)!
----------------
(n-1)!*n!

Ways to place brackets, called "Catalan's number", but we can use
SUPER-DUPERPOWERS (superpowers on top of superpowers on top of superpowers)
etc......, and higher and higher operations.

I am a trifle embarrased to admit that I had jumped to the conclusion that
the legal bracket placements would be permutations, originally,-but I can
now see that I was wrong.

I am severely regretful if this is boreing any of you on the tuning list,
but during my breif absence, I have been doing some research on the
superpower, and I have found some things out.

I must ask, "Why hasn't music been composed with this before"?

I mean, we, as microtonal music lovers should take an interest in the
alternative, the exotic, and the crazy,-from this truely beautiful things
can emerge,-I's sure professor Moog didn't say to himself "A "synthesizer",
too crazy to be true, I can't even be bothered".

As of this time of writeing, I have been gathering a large, healthy pile of
mathematical notes, indeed, it is not uncommon for me to come home after a
night out on Wellington, with pockets bulgeing to the brim with table
napkins, asprin packets, beer mats, etc.....all scribbeld on with barely
indecipherable, ledgeable-only-to-Sarn notes for ideas.

Anyway, down to business.

I have talked to the ROCK SHOP boys, nice guys, who barely put up with me,
and humour me every time I visit the store, and I will be purchaseing
Cakewalk, Sound forge and the Akai S2000 sampler, total cost $3000 New
Zealand, about the origional price of my computer, and hopefully, in the
coming time, I will, with another gentleman, be doing a talk on
"Radioactive" a student public radio about Xentonality, so a modicum of
study is in order.

The sampler, in my humble opinion is a "big bang-for-the-buck" little box,
altho I have liked the Morpheus 2E by E-Mu and am interested to experiment
with physical modeling.

I was origioanally going to experiment with David Cope's SARA and i have
given his books "EXPERIMENTS IN MUSICAL INTELLIGENCE", and "COMPUTERS AND
MUSICAL SYTYLE" to a friend, with a hope that he will purchase a powerMac.

Should Moore's law hold, (and I still have to read Ray Kurtzweil's "AGE OF
SPIRITUAL MACHINES"), we may have music composed in any style we so desire,
whatsoever.

I long for the day in which we can change the ACTUAL MATHEMATICS involved in
a physical modeling system,-you will, no doubt make some sort of parallel
with this and my hypothesis on "The Polyverse".

Also, as of the year 2000, I will be studying Psychology, Philosophy and
Computers more in depth at Victoria Univserity.

As a final word, I have often thought that IF New Zealand music mougils were
to REALLY AGRESSIVELY MARKET microtonal music, it would take off like a
rocket.

I beleive that Mr.Carl Lumma said once when i put this to him that he
wouldn't want to see this happen-that is, Xentonality to become mainstream
public knowledge.

I can see his point of view, and another part of me WOULD like to see a
public figure/rock band make this more commonly available to the sometimes
childish public.

Your thoughts ladies and gentlemen.

Sarn.

P.S.

Finally, could we not do ADDITIVE SYNTHESIS, GEOMETRICAL SYNTHESIS,
EXPONENTIONAL SUYNTHESIS, SUPER-EXPONENTIONAL SYNTHESIS,
SUPER-DUPER-EXPONENTIONAL SYNTHESIS on guitar strings?

We could experiment with a feedback type system of recording, and useing
these different orders of operations to average the playing guitar strings,
and I feel that somehow, with REALLY high operators, where we can hace
c(cc), and (cc)c, where "c"=Catalan, we may get some really beautiful
sounds.

----------
De�: Sarn Richard Ursell <thcdelta@ihug.co.nz>
� : wim.hoogewerf@fnac.net
Objet�: OPERATOR SYNTHESIS
Date�: Lun 20 d�c 1999 3:40

Thankyou very much Mr.Wim Hoogewerf,

I want you to mention that these were origionally from me!

Anyhow, here they are:

Here's one for the list:

Dearest Members of the alternative tuning digest,

I have a question:

Why does the music industry use ADDITIVE SYNTHESIS?

I mean, I realise fully that it is possible, and is conventionally used for
us to add two waveforms, with repect to time, to give us a more complex
waveform, but I got to woundering, why not MULTIPLY them?

We could tehn take the square root of this, giving a GEOMETRICAL AVERAGE,
and I have conventiently called this "MULTIPLICATIVE SYNTHESIS".

Of course, we can, and will end up with imaginary numbers, but then I got to
thinking, why not just reverse these waveforms and make them negative?

And why stop there?

We could go on to EXPONENTIONAL SYNTHESIS, and take the "QUIGGLE ROOT", or
"SUPER-ROOT".

Of course, things get interesting here, as, I now know that there are:

(2n)!
----------------
(n-1)!*n!

Ways to place brackets, called "Catalan's number", but we can use
SUPER-DUPERPOWERS (superpowers on top of superpowers on top of superpowers)
etc......, and higher and higher operations.

I am a trifle embarrased to admit that I had jumped to the conclusion that
the legal bracket placements would be permutations, originally,-but I can
now see that I was wrong.

I am severely regretful if this is boreing any of you on the tuning list,
but during my breif absence, I have been doing some research on the
superpower, and I have found some things out.

I must ask, "Why hasn't music been composed with this before"?

I mean, we, as microtonal music lovers should take an interest in the
alternative, the exotic, and the crazy,-from this truely beautiful things
can emerge,-I's sure professor Moog didn't say to himself "A "synthesizer",
too crazy to be true, I can't even be bothered".

As of this time of writeing, I have been gathering a large, healthy pile of
mathematical notes, indeed, it is not uncommon for me to come home after a
night out on Wellington, with pockets bulgeing to the brim with table
napkins, asprin packets, beer mats, etc.....all scribbeld on with barely
indecipherable, ledgeable-only-to-Sarn notes for ideas.

Anyway, down to business.

I have talked to the ROCK SHOP boys, nice guys, who barely put up with me,
and humour me every time I visit the store, and I will be purchaseing
Cakewalk, Sound forge and the Akai S2000 sampler, total cost $3000 New
Zealand, about the origional price of my computer, and hopefully, in the
coming time, I will, with another gentleman, be doing a talk on
"Radioactive" a student public radio about Xentonality, so a modicum of
study is in order.

The sampler, in my humble opinion is a "big bang-for-the-buck" little box,
altho I have liked the Morpheus 2E by E-Mu and am interested to experiment
with physical modeling.

I was origioanally going to experiment with David Cope's SARA and i have
given his books "EXPERIMENTS IN MUSICAL INTELLIGENCE", and "COMPUTERS AND
MUSICAL SYTYLE" to a friend, with a hope that he will purchase a powerMac.

Should Moore's law hold, (and I still have to read Ray Kurtzweil's "AGE OF
SPIRITUAL MACHINES"), we may have music composed in any style we so desire,
whatsoever.

I long for the day in which we can change the ACTUAL MATHEMATICS involved in
a physical modeling system,-you will, no doubt make some sort of parallel
with this and my hypothesis on "The Polyverse".

Also, as of the year 2000, I will be studying Psychology, Philosophy and
Computers more in depth at Victoria Univserity.

As a final word, I have often thought that IF New Zealand music mougils were
to REALLY AGRESSIVELY MARKET microtonal music, it would take off like a
rocket.

I beleive that Mr.Carl Lumma said once when i put this to him that he
wouldn't want to see this happen-that is, Xentonality to become mainstream
public knowledge.

I can see his point of view, and another part of me WOULD like to see a
public figure/rock band make this more commonly available to the sometimes
childish public.

Your thoughts ladies and gentlemen.

Sarn.

P.S.

Finally, could we not do ADDITIVE SYNTHESIS, GEOMETRICAL SYNTHESIS,
EXPONENTIONAL SUYNTHESIS, SUPER-EXPONENTIONAL SYNTHESIS,
SUPER-DUPER-EXPONENTIONAL SYNTHESIS on guitar strings?

We could experiment with a feedback type system of recording, and useing
these different orders of operations to average the playing guitar strings,
and I feel that somehow, with REALLY high operators, where we can hace
c(cc), and (cc)c, where "c"=Catalan, we may get some really beautiful
sounds.

>De : Sarn Richard Ursell <thcdelta@ihug.co.nz>

>Why does the music industry use ADDITIVE SYNTHESIS?

No commercial synthesizers I am aware of use additive synthesis in its most
basic form -- that is, each partial of a desired wave being represented by
an independent envelope and sine wave oscillator. Despite the obvious power
of such an approach, it suffers from two disadvantages that commercial
companies have been reluctant to tackle: first that it is very expensive,
second that people usually don't know these details about a sound they want
to produce. Additive synthesis is sometimes used by computer music
composers (notably Jean Claude Risset) and can be easily implemented in
languages such as Csound.
>
>I mean, I realise fully that it is possible, and is conventionally used for
>us to add two waveforms, with repect to time, to give us a more complex
>waveform, but I got to woundering, why not MULTIPLY them?

Multiplying two wave forms is called ring modulation. It was a standard way
of achieving non-harmonic timbres such as bells in analog days and
cross-synthesis as in many works of Stockhausen. It results in sum and
difference tones between the carrier and modulator, though the frequency of
the carrier disappears.
>
>We could tehn take the square root of this, giving a GEOMETRICAL AVERAGE,
>and I have conventiently called this "MULTIPLICATIVE SYNTHESIS".

Taking the root or exponentiating a wave results in what is called
waveshaping or non-linear distortion synthesis. The Casio CZ/VZ
synthesizers were based on this, though one can implement it in other
synths today, such as the Kurzweil K2x00 series. Its disadvantages include
the inability to generate non-harmonic partials and the difficulty of
predicting the spectrum of other amplitude inputs to a given system.
>
>Of course, we can, and will end up with imaginary numbers, but then I got to
>thinking, why not just reverse these waveforms and make them negative?
>
This means inverting the phase. Essentially, ring modulation is a form of
amplitude modulation in which this happens, since the carrier is multiplied
by the negative part of the modulator half the time.

>We could go on to EXPONENTIONAL SYNTHESIS, and take the "QUIGGLE ROOT", or
>"SUPER-ROOT".

I'm not sure what these mean, but they appear to be forms of distortion
synthesis, which have been well researched in the literature, beginning
with radio theory in the 1920s. While the computer music community would
welcome new synthesis methods, most research comes from the standpoint of
trying to find ways to efficiently create a desired waveform and its
changes, less often "what would happen if..." sorts of experiments.

>I long for the day in which we can change the ACTUAL MATHEMATICS involved in
>a physical modeling system,-you will, no doubt make some sort of parallel
>with this and my hypothesis on "The Polyverse".

I'm not sure what you mean, but physical modeling is a hot topic in
computer music and PM synths are widely available. They are most flexible
in Csound and like languages, and, of course, there is nothing preventing
you from implementing new PM mathematics from scratch in such a language.
Such instruments are posted on the Csound list from time to time.

>Finally, could we not do ADDITIVE SYNTHESIS, GEOMETRICAL SYNTHESIS,
>EXPONENTIONAL SUYNTHESIS, SUPER-EXPONENTIONAL SYNTHESIS,
>SUPER-DUPER-EXPONENTIONAL SYNTHESIS on guitar strings?

If you mean distort guitar sounds in various ways, sure.
>
>We could experiment with a feedback type system of recording, and useing
>these different orders of operations to average the playing guitar strings,
>and I feel that somehow, with REALLY high operators, where we can hace
>c(cc), and (cc)c, where "c"=Catalan, we may get some really beautiful
>sounds.

If by "beautiful sounds" you mean distorted to amplify upper partials (in
the case of waveshaping), bell-like non-harmonic sounds (in the case of
ring modulation), or mixing with some other source (which is I assume what
you mean by "additive synthesis" in this context) then sure. By all means
go for it.

To find out more about ring modulation, waveshaping, and other forms of
distortion synthesis and physical modeling, I would recommend a good
computer music text. I use Dodge and Jerse _Computer Music_ (2nd edition,
Schirmer), but there are other good ones. By the way, the MIT press book on
Csound is due out in January. In it I have a chapter on implementing
alternate tunings.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
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