[sdiy] Generating acyclic waveforms?
cheater cheater
cheater00 at gmail.com
Tue Mar 23 10:56:26 CET 2010
Hi guys,
this is a digest of the emails in this thread. This is because the
archives were broken when it started and the messages will get lost
otherwise. You can safely ignore this message, it is for archival
purposes only.
D.
---------- Forwarded message ----------
From: cheater cheater
Date: Sun, Mar 21, 2010 at 17:58
Subject: Generating acyclic waveforms?
To: synth-diy
Hi guys,
I was lately considering acyclic waveforms for use in music synthesis,
and I'm wondering about techniques of realizing them in synthesizers.
Acyclic waveforms are interesting for the purpose of making the sound
less static. An acyclic waveform will interact with nonlinearities in
such a manner that the timbre will change ever so slightly over time.
It is also good for making certain harmonic tricks easier or possible
at all: an acyclic waveform hides problems in pitch articulation; on
the other hand, something like a stretched-harmonic waveform could be
used to play music compatible with the piano.
Most people here know that in piano timbre the partials are sine waves
that are not spaced like in synth waveforms. That is, in the
synthesizer, if the note's fundamental frequency is F, then harmonics
will be at 1F, 2F, 3F, 4F etc. In a stretched-harmonic waveform, the
frequencies will for example be of the form 1sF, 2sF, 3sF, 4sF, and so
on, where s is the stretching factor. For s=1 we have the usual
harmonic series. For s which is not an integer and not a specially
chosen rational number, we have a probability of 100% of generating an
acyclic waveform. Of course, the spacing of harmonics in the piano is
more complex than that, but this is the first approximation.
Here's what researchers had to say about acyclic waveforms:
> Inharmonicity is not necessarily unpleasant. In 1962, research
> by Harvey Fletcher and his collaborators indicated that the spectral
> inharmonicity is important for tones to sound piano-like. They
> proposed that inharmonicity is responsible for the "warmth" property
> common to real piano tones.[2] According to their research
> synthesized piano tones sounded more natural when some
> inharmonicity was introduced.[3] In general, electronic instruments
> that duplicate acoustic instruments must duplicate both the
> inharmonicity and the resulting stretched tuning of the original
> instruments.
>
> 2. Acoustical Society of America - Large grand and small upright
> pianos by Alexander Galembo and Lola L. Cuddy]
> http://www.acoustics.org/press/134th/galembo.htm
> 3. Matti Karjalainen (1999). "Audibility of Inharmonicity in String
> Instrument Sounds, and Implications to Digital Sound Systems"
> http://www.acoustics.hut.fi/~hjarvela/publications/icmc99.pdf
(taken from http://en.wikipedia.org/wiki/Inharmonicity )
Of course we've since learnt better than to try and immitate the piano
timbre with synths. It's a stupid want and will never happen; if you
want a piano, buy a piano. But I think it is a very worthwhile
consideration which can be used to greatly enhance the timbre of
synthesizers, and can also make synthesizers musically compatible with
accoustic instruments which, in my opinion, differ most from what we
can timbrally do with synthesizers because of their stretched-harmonic
nature.
What are some ways of generating acyclic waveforms - either in
stretched-harmonic spectra, or just generally acyclic?
Of course, trivially enough, noise is an acyclic waveform. (Unless
you're using a certain 80s synth that I forgot the name of...)
Additive approaches are one way of doing this. Pros are that
absolutely everything can be controlled about the waveform. Cons are
that these approaches are computationally intensive, the functionality
difficult to expose to the user easily, and generally this is a
digital technique, which is not always desirable. Of course, doing an
additive engine that only transforms between waveforms (by using the
harmonic levels from cyclic oscillators, i.e.
One way of generating an acyclic waveform is - I think - taking a
usual oscillator core and adding a small amount of noise to the reset
comparator's reference voltage. This is only a theory, I haven't been
able to try it. What should happen is that the waveform will still
look like the normal waveform (for triangle and ramp), and the
segments will still be linear, but the peaks will happen either sooner
or later than they should. Think of it as something similar to hard
sync, except because of the balanced nature of noise statistically the
pitch doesn't change: this means that segments will be shorter or
longer (effectively being higher or lower in pitch), but as we measure
more and more cycles the oscillator is more and more in-tune. The pros
of this approach are that it could be easy to implement in most
existing designs; that it is well behaved enough to let people
understand it; that it animates the waveform while not really altering
it that much. The cons are that it does not go very far from where we
started out, leaving a lot of space for exploration via other
techniques. Of course, it does not generate stretched tuning.
One way to generate stretched tuning in the analogue domain is to use
a frequency shifter on a normal oscillator. I anticipate this is going
to be expensive to do and failure prone: the process might not be that
well behaved. However, I'm not sure what's involved in this. Are there
good precision frequency shifters that you guys could recommend? The
frequency would only need to be shifted by a few hz, much less than
one semitone. I will leave out the pros and cons for now because I
simply don't know much about frequency shifters, so I'll leave this up
to people more knowledgable like me.
Chorus and (large, as in more than 5) oscillator stacks are some more
or less valid way of making acyclic waveforms. In this approach - as I
understand it - the power of the harmonics of the oscillator(s) is
centered around the frequencies F, 2F, 3F, ... and the further we move
away from the exact frequency nF the less power there is in the
spectrum of the resultant waveform.
But the lingering question is: is there a way to generate an acyclic
waveform algorithmically in the digital domain without using additive
approaches, and more importantly, is it possible to create an
inherently acyclic oscillator in the analogue domain, without
resorting to secondary processing such as frequency shifting,
chorusing, or stacking?
And as a follow up question: is it possible to create an inherently
stretched-harmonic oscillator in analog? Is there a specialized
algorithm in digital that can do this? We are either talking about
something that generates waveforms with partials on frequencies n*a*F,
n*a^b*F, or some other thing similar to that.
Thanks
D.
---------- Forwarded message ----------
From: cheater cheater
Date: Sun, Mar 21, 2010 at 20:44
Subject: Re: Generating acyclic waveforms?
To: synth-diy
BTW,
here are some interesting reads on wikipedia that are to the topic if
anyone's interested:
http://en.wikipedia.org/wiki/Harmonic_series_(music)
http://en.wikipedia.org/wiki/Inharmonicity
http://en.wikipedia.org/wiki/Otonality_and_Utonality
http://en.wikipedia.org/wiki/Anharmonicity
http://en.wikipedia.org/wiki/Pseudo-octave
http://en.wikipedia.org/wiki/String_resonance_(music)
http://en.wikipedia.org/wiki/Nonlinear_resonance
http://en.wikipedia.org/wiki/Duffing_equation
http://en.wikipedia.org/wiki/Anharmonicity#Examples_in_Physics
The last link might have a clue or two:
> In fact, virtually all oscillators become anharmonic when
> their pump amplitude increases beyond some threshold,
> and as a result it is necessary to use nonlinear
> equations of motion to describe their behavior.
How does this apply to the typical synth VCO?
Also the well known fact is mentioned that a pendulum, for big
displacements, starts becoming an anharmonic oscillator. I assume this
bread-and-butter experiment must have been simulated in analog
electronics during the analog computing era. Has anyone come across a
simulation like this?
This could be of use:
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V0T-4H3SBWH-5&_user=10&_coverDate=07%2F31%2F1972&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1260157201&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=23a5de9589a6c05ff330c181061795fc
(Has anyone got access to this whitepaper?)
Cheers
D.
---------- Forwarded message ----------
From: Tom Wiltshire
Date: Sun, Mar 21, 2010 at 22:12
Subject: Re: [sdiy] Generating acyclic waveforms?
To: cheater cheater
Cheater,
A very interesting post. This is something I've often wondered about
because I've spent quite a bit of time working on wavetable
oscillators. Wavetables are a fantastically versatile way of producing
timbre changes, but *inharmonic* sounds are something that you just
can't do with a simple wavetable. Stretched harmonics are right out.
So this question has puzzled me a time or two or more. I shall watch
the thread with interest!
Thanks,
Tom
---------- Forwarded message ----------
From: Tom Wiltshire
Date: Sun, Mar 21, 2010 at 22:19
Subject: Re: [sdiy] Generating acyclic waveforms?
To: cheater cheater
Cc: synth-diy
Does anyone (physicists?) on the list know whether this harmonic
stretching occurs only with strings, or do similar things happen in
wind instruments? reeds?
What I'm really asking is whether this is a 'string' effect or an
'acoustic' effect.
Thanks,
Tom
---------- Forwarded message ----------
From: cheater cheater
Date: Sun, Mar 21, 2010 at 22:23
Subject: Re: [sdiy] Generating acyclic waveforms?
To: Tom Wiltshire
Cc: synth-diy
It happens in all accoustic instruments to some degree. No accoustic
instrument adheres to the ideal string and generally ideal resonator
equations. Even wind instruments have that, because even if the air
can generate a perfect resonator, the instrument's body will have that
effect and, by leeching the accoustic power from the resonator, will
generate even more anharmonic content.
D.
---------- Forwarded message ----------
From: cheater cheater
Date: Sun, Mar 21, 2010 at 23:09
Subject: Re: [sdiy] Generating acyclic waveforms?
To: Tom Wiltshire
Cc: synth-diy
I consulted a fellow composer and he says that pretty much all western
instruments have different tuning starting the 6th harmonic of their
central pitch. So the harmonic series looks like this:
C C G C E G (Bb) C...
but the Bb is out of tune with the ieal equal temperatment tuning (and
I assume the following C too, but not sure). I didn't get to know
which way it's out of tune (sharp or flat), because he's busy dumping
MIDI. Those composers, sheesh.. ;-)
Also according to Wikipedia the Gamelan has a very stretched harmonic series.
I think it might be the same situation that causes gongs and other
such stuff to have such a very inharmonic sound, but I'm very far out
of my expertise here.
D.
---------- Forwarded message ----------
From: Ian Fritz
Date: Sun, Mar 21, 2010 at 23:33
Subject: Re: [sdiy] Generating acyclic waveforms?
To: Tom Wiltshire, cheater cheater
Cc: synth-diy
At 03:19 PM 3/21/2010, Tom Wiltshire wrote:
>
> Does anyone (physicists?) on the list know whether this harmonic
> stretching occurs only with strings, or do similar things happen in
> wind instruments? reeds?
>
> What I'm really asking is whether this is a 'string' effect or an
> 'acoustic' effect.
It's a string effect. The higher harmonics require a sharper bending
radius and therefore they see a stiffer elastic constant. Since the
string is vibrating freely, the higher frequencies run back and forth
faster than the lower ones.
You wouldn't see a significant effect like this in winds because the
waves are longitudinal waves in air and therefore have negligible
dispersion. Additionally, driven systems such as winds excite
coherent waves, so there can be no speeding up of specific harmonics
over many cycles.
Other percussive instruments such as stricken bars are just an extreme
extension of the string phenomenon, although more complicated because
of the qualitatively different kinds of modes that can be excited.
Ian
---------- Forwarded message ----------
From: Veronica Merryfield
Date: Mon, Mar 22, 2010 at 00:42
Subject: Re: [sdiy] Generating acyclic waveforms?
To: synth DIY
The effect is called harmonic sharpening and happens in all materials
used for instruments.
The process goes something like this. Imagine a taught string. It has
length and tension. When plucked, it vibrates. Looking only at the
fundamental, the string lengthens at the extremes of the excursion as
does the tension. The next harmonic is therefore subject to higher
tension and longer length. And so on. The amount of sharpening peaks
at the note start and then decays away. The effect is the same in
woodwind and brass but tends to be less so since the material moves a
lot less than a string. However, it is this subtle effect that gives
say a trumpet it's characteristic sound that a simple oscillator synth
can not reproduce.
This is one of the reasons I started looking at additive synthesis and
the Synergy. I have tried to do this in the analogue world with
several sine VCOs but it wasn't easy. Each one had an envelope
generator for pitch and amplitude. It is not as computationally
expensive to do in software or FPGA as it might seem - a few adds and
a couple of table look ups for each sine osc. The other thing to
realise is that you only need a few harmonics to make the sound seem
real. Many of the Synergy patches use 3 to 5 oscillators per voices to
sound very realistic.
Adding noise to the reset level in a VCO is not going to modulate the
harmonic content over the duration of a note to mimic harmonic
sharpening.
Veronica, currently working on a Synergy based AU
---------- Forwarded message ----------
From: Scott Nordlund
Date: Mon, Mar 22, 2010 at 01:33
Subject: Re: [sdiy] Generating acyclic waveforms?
To:
Cc: sdiy
> I consulted a fellow composer and he says that pretty much all western
> instruments have different tuning starting the 6th harmonic of their
> central pitch. So the harmonic series looks like this:
>
> C C G C E G (Bb) C...
>
> but the Bb is out of tune with the ieal equal temperatment tuning (and
> I assume the following C too, but not sure). I didn't get to know
> which way it's out of tune (sharp or flat), because he's busy dumping
> MIDI. Those composers, sheesh.. ;-)
That's just the 12 tone equal tempered scale, it has nothing to do with
inharmonicity or aperiodic waveforms. The Bb isn't the only one out of
tune either.
---------- Forwarded message ----------
From: Magnus Danielson
Date: Mon, Mar 22, 2010 at 02:06
Subject: Re: [sdiy] Generating acyclic waveforms?
To: Ian Fritz
Cc: Tom Wiltshire, cheater cheater, synth-diy
Ian Fritz wrote:
>
> At 03:19 PM 3/21/2010, Tom Wiltshire wrote:
>>
>> Does anyone (physicists?) on the list know whether this harmonic
>> stretching occurs only with strings, or do similar things happen in
>> wind instruments? reeds?
>>
>> What I'm really asking is whether this is a 'string' effect or an
>> 'acoustic' effect.
>
> It's a string effect. The higher harmonics require a sharper bending radius and therefore they see a stiffer elastic constant. Since the string is vibrating freely, the higher frequencies run back and forth faster than the lower ones.
>
> You wouldn't see a significant effect like this in winds because the waves are longitudinal waves in air and therefore have negligible dispersion. Additionally, driven systems such as winds excite coherent waves, so there can be no speeding up of specific harmonics over many cycles.
However, the end-impedance would allow for a similar effect, such that
the resonance frequency of the overtones would not match up exactly
with the integer multiples frequency-wise form the base frequency. To
illustrate the impedance effect on a wind instrument... learn how to
bend the tone by fractional opening or closing the holes. With a
little training to get it.
>
> Other percussive instruments such as stricken bars are just an extreme extension of the string phenomenon, although more complicated because of the qualitatively different kinds of modes that can be excited.
The long elevator wires of Mimer laven comes to mind. Very cool sound.
Cheers,
Magnus
---------- Forwarded message ----------
From: Eric Brombaugh
Date: Mon, Mar 22, 2010 at 19:52
Subject: Re: [sdiy] Generating acyclic waveforms?
To: sdiy
On 03/22/2010 11:27 AM, Ian Fritz wrote:
> But the original question was whether wind instruments have stretched
> harmonic spectra, and the answer is still emphatically no, because they
> are practically always in the phase locked regime, as widely discussed
> in the many books and publications on the subject.
This agrees with my experience too - I spent several summers during
high-school & college doing R&D on an electronic tuner that my father
used for tuning pipe organs. Many hours spent staring at waveforms
from different organ stops, and while the waveform shape changes
slightly from one pipe to the next, a single pipe playing has a fairly
static waveform. Hard to imagine how that could be without the
harmonics being related by exact integer ratios to the fundamental.
Eric
---------- Forwarded message ----------
From: Jerry Gray-Eskue
Date: Mon, Mar 22, 2010 at 20:00
Subject: Re: [sdiy] Generating acyclic waveforms?
To: sdiy
<<"Sustained tones from real musical instruments do, however, have precisely
repeating waveforms, and so their their individual modes must be somehow
locked into precise frequency and phase relationships despite the
inharmonicities of the natural resonances.">>
<<But the original question was whether wind instruments have stretched
harmonic spectra, and the answer is still emphatically no, because they are
practically always in the phase locked regime, as widely discussed in the
many books and publications on the subject.>>
I may be misunderstanding what "stretched harmonic spectra" actually means,
but if we take a sine wave fundamental frequency and a set of harmonics, and
use the fundamental sine wave to frequency shift (+- around zero) the
harmonics we would get a "precisely repeating waveform" with "inharmonics".
Will this class as "stretched harmonic spectra"?
---------- Forwarded message ----------
From: Ian Fritz
Date: Mon, Mar 22, 2010 at 20:51
Subject: Re: [sdiy] Generating acyclic waveforms?
To: Jerry Gray-Eskue, sdiy
At 01:00 PM 3/22/2010, Jerry Gray-Eskue wrote:
> I may be misunderstanding what "stretched harmonic spectra" actually means,
> but if we take a sine wave fundamental frequency and a set of harmonics, and
> use the fundamental sine wave to frequency shift (+- around zero) the
> harmonics we would get a "precisely repeating waveform" with "inharmonics".
I may not understand correctly what you are saying. But if you add together
Sin ((w+eps)t) + Sin (2wt)
You do not get a steady repeating waveform.
Ian
---------- Forwarded message ----------
From: Jerry Gray-Eskue
Date: Mon, Mar 22, 2010 at 22:01
Subject: Re: [sdiy] Generating acyclic waveforms?
To: sdiy
I am not quite sure how to express this properly but here is a shot at it:
A signal v(t) is periodic with period T if
v(t) = v(t+T) for all t
In other words the waveform is precisely repeating over the period T.
The Fundamental sine wave v(t)= Vo cos(wt+ phase angle). ( or is that a
cosine wave? )
v(t) is +- around zero and the Sum of (v(t) over the period T) = 0.
Now if we take the first harmonic its value is vh(t)= Vo cos(wt+ (phase
angle * 2)).
So if we vary the Harmonic thus vh(t)= Vo cos(wt+ ((phase angle +
SomeFunctionOf(v(t))* 2)).
That is the harmonic is frequency shifted using the fundamental sine's v(t)
as the control.
Assuming this is a sine not cosine wave, we have the phase angel accelerated
during the first T/2 and decelerated during the second half with a net
acceleration of zero.
So the waveform repeats each T and
Vo cos(wt+ ((phase angle + SomeFunctionOf(v(t))* 2)) = Vo cos(w(t+T)+
((phase angle + SomeFunctionOf(v(t+T))* 2)).
Clear as mud???
- Jerry
---------- Forwarded message ----------
From: cheater cheater
Date: Mon, Mar 22, 2010 at 22:23
Subject: Re: [sdiy] Generating acyclic waveforms?
To: Eric Brombaugh
Cc: sdiy
Eric,
bear in mind that in stretched harmonic timbre, there will be
noticeable shift in the frequency of a partial from where it should
ideally be - but only starting with fairly high harmonics; those high
harmonics are usually of very small amplitude. We don't see them that
well on the scope (especially since the dot is 'fat'), but we do hear
them, because our ear can hear things you'd have to zoom into many
times to see them on a wave editor.
Cheers
D.
---------- Forwarded message ----------
From: Ian Fritz
Date: Mon, Mar 22, 2010 at 22:27
Subject: Re: [sdiy] Generating acyclic waveforms?
To: Jerry Gray-Eskue, sdiy
At 03:01 PM 3/22/2010, Jerry Gray-Eskue wrote:
> I am not quite sure how to express this properly but here is a shot at it:
>
> A signal v(t) is periodic with period T if
>
> v(t) = v(t+T) for all t
> In other words the waveform is precisely repeating over the period T.
>
> The Fundamental sine wave v(t)= Vo cos(wt+ phase angle). ( or is that a
> cosine wave? )
> v(t) is +- around zero and the Sum of (v(t) over the period T) = 0.
>
>
> Now if we take the first harmonic its value is vh(t)= Vo cos(wt+ (phase
> angle * 2)).
> So if we vary the Harmonic thus vh(t)= Vo cos(wt+ ((phase angle +
> SomeFunctionOf(v(t))* 2)).
> That is the harmonic is frequency shifted using the fundamental sine's v(t)
> as the control.
> Assuming this is a sine not cosine wave, we have the phase angel accelerated
> during the first T/2 and decelerated during the second half with a net
> acceleration of zero.
>
> So the waveform repeats each T and
>
> Vo cos(wt+ ((phase angle + SomeFunctionOf(v(t))* 2)) = Vo cos(w(t+T)+
> ((phase angle + SomeFunctionOf(v(t+T))* 2)).
>
>
> Clear as mud???
Right. Sorry, but it doesn't make any sense to me. I don't see any
harmonics (2w, 3w, etc), so how is this relevant to the discussion at
all? Why are you multiplying the "phase angle" (which it is not) by
2? I think you need to back up and study the fundamentals of waves
and signals.
Ian
---------- Forwarded message ----------
From: Jerry Gray-Eskue
Date: Mon, Mar 22, 2010 at 23:07
Subject: Re: [sdiy] Generating acyclic waveforms?
To: sdiy
Theta - the "phase angle"
Schaum's Outlines Electric Circuits 4th edition pg 103 6.3
a sinusoidal voltage v(t) is given by
v(t)= Vo cos(wt+ phase angle)
----------
*2 to double the frequency. 2w I expect is a more standard representation.
---------- Forwarded message ----------
From: Ian Fritz
Date: Tue, Mar 23, 2010 at 01:00
Subject: Re: [sdiy] Generating acyclic waveforms?
To: Jerry Gray-Eskue, sdiy
At 04:07 PM 3/22/2010, Jerry Gray-Eskue wrote:
>
> Theta - the "phase angle"
> Schaum's Outlines Electric Circuits 4th edition pg 103 6.3
>
> a sinusoidal voltage v(t) is given by
>
> v(t)= Vo cos(wt+ phase angle)
Oh dear, that's too very sloppy. The phase angle of the wave is the
total argument of the sinusoid:
phase angle = wt + const,
in this case.
What they call " the phase angle" is really a phase shift angle. You
can call it "a" phase angle if you like, but it is not "the" phase
angle of the wave.
> *2 to double the frequency. 2w I expect is a more standard representation.
Uh, yeah. You can't just throw mathematical factors around
willy-nilly like that!
Ian
---------- Forwarded message ----------
From: David G. Dixon
Date: Tue, Mar 23, 2010 at 02:26
Subject: Re: [sdiy] Generating acyclic waveforms?
To: Ian Fritz, Jerry Gray-Eskue, sdiy
What's with all these acrylic waveforms? Today's music sound too much like
plastic already!
Oh, aCYClic waveforms!
Nevermind.
-- Emily Latella
---------- Forwarded message ----------
From: Dave Manley
Date: Tue, Mar 23, 2010 at 07:29
Subject: Re: [sdiy] Generating acyclic waveforms?
To:
Cc: sdiy
Ian Fritz wrote:
>
> [...] if you add together
>
> Sin ((w+eps)t) + Sin (2wt)
>
> You do not get a steady repeating waveform.
I'm probably missing the big picture here because I haven't been
paying attention since these long-winded discussions often devolve
into a lesson in logic and pointless point-counterpoint style
argument, or perhaps the thread has veered off topic as they are want
to do, or perhaps I'm on a waffle rotating around your pancake, but
isn't the whole point of the OP to not generate a steady repeating
waveform, at least not on a cycle-to-cycle basis? I assume the reason
to try to create an acyclic waveform is to remove the sterile nature
of a integer related harmonic structure, and produce a sound with,
hopefully, interesting timbre and "movement".
It's not apparent to me how this can be done except through additive
synthesis. Jittering the reset time of a vco (or more simply adding
modulation via a CV) on a per-cycle basis alters the period of the
fundamental not the relationship of the partials, so that isn't a
viable approach.
Did any of the classic additive synths allow the paritial frequencies
to be non-integer multiples of the fundamental? Did they allow the
partial multipliers to vary over time?
-Dave
---------- Forwarded message ----------
From: Scott Nordlund
Date: Tue, Mar 23, 2010 at 08:58
Subject: Re: [sdiy] Generating acyclic waveforms?
To:
Cc: sdiy
> Did any of the classic additive synths allow the paritial frequencies to
> be non-integer multiples of the fundamental? Did they allow the partial
> multipliers to vary over time?
>
> -Dave
The Kawai synths are strictly limited to the standard harmonic series,
though multiple sources can be stacked and detuned. The Kurzweil K150
permits inharmonic tuning, but I think the relative frequencies are fixed.
As far as I know, only the Synergy permits truly independent pitch
modulation per partial.
I think FM is sorta easier to deal with for that sort of thing. I think
the TG77 (hmmm, I've been looking for one) has one pitch envelope per
voice but has adjustable depth per operator. Seems like a reasonable
compromise. And of course with FM it's quite easy to make everything
subtly aperiodic/inharmonic.
---------- Forwarded message ----------
From: Simon Brouwer
Date: Tue, Mar 23, 2010 at 09:29
Subject: Re: [sdiy] Generating acyclic waveforms?
To: sdiy
Dave Manley schreef:
> Ian Fritz wrote:
>> [...] if you add together
>>
>> Sin ((w+eps)t) + Sin (2wt)
>>
>> You do not get a steady repeating waveform.
> I'm probably missing the big picture here because I haven't been paying
> attention since these long-winded discussions often devolve into a
> lesson in logic and pointless point-counterpoint style argument, or
> perhaps the thread has veered off topic as they are want to do, or
> perhaps I'm on a waffle rotating around your pancake, but isn't the
> whole point of the OP to not generate a steady repeating waveform, at
> least not on a cycle-to-cycle basis? I assume the reason to try to
> create an acyclic waveform is to remove the sterile nature of a integer
> related harmonic structure, and produce a sound with, hopefully,
> interesting timbre and "movement".
>
> It's not apparent to me how this can be done except through additive
> synthesis.
I see two other ways:
- using wavetables (very long ones)
- feeding a cyclic waveform through a barberpole phaser of some kind
--
Vriendelijke groet,
Simon Brouwer
-*- nl.openoffice.org -*- http://www.opentaal.org -*-
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