4 Feb
2005
4 Feb
'05
6:45 p.m.
...a simple, but powerfull paradigm that helps to make
simple algorithms that produces very beautiful sounds.
Hi.
I want to open a topic about what I call "bandwidth of
each harmonic", to say some ideas that helped me to
make beautifull sounds. I am Paul, the author of
ZynAddSubFX software synthsizer (
http://zynaddsubfx.sourceforge.net ) and I wish to
share some ideas ;)
Referring to musical sounds,usually the harmonics are
considered simple sine function. Of course, the
reality shows different thing, and so, the harmonics
was started to be considered as sine functions
modulated by a lower frequencies (I saw some time ago
a link that describes that the choir sound is
beautifull because of the "micromodulations",etc...).
A very good thing is to "have a look" in a frequency
domains. Let's take for example a choir that sing same
note (like A=440Hz). Because all are human, even they
are very well trained singer, they will not sing
exactely the same note; for example one will sing at
435 Hz or other, at 443 Hz, and so on. Now, the first
harmonic (the fundamental note) is not longer a sine
of 440 Hz, but a narrow band signal that has a certain
bandwith. For example, let's take a very simple case:
if all sing at same loudness, and they sing from 435
Hz and the 445 Hz. In this case, the bandwidth will be
10 Hz. Of course, in real choir the frequency
distribution of the harmonic will be not flat, but
usually will be a curve that looks like a normal
(gaussian) curve(found this after I did some research=
very fine frequency analysis with very long FFTs).
Now, let's go to the second harmonic: if you multiply
435 and 445 with 2, the difference will be 20 Hz. So,
the bandwidth of the second harmonic is 20 Hz. So here
a important rule of real instruments (esp. ensembles):
the bandwith of each harmonic is proportional to the
it's frequency; so in this example the first harmonic
has bandwidth 10Hz, the second 20Hz, the third 30Hz,
and so on.
Here I made a very fine frequency analisys of a
synthsized sound(a real orchestra sound will give
similar results):
[img]http://zynaddsubfx.sourceforge.net/doc/paul1.png[/img]
You see, that the harmonic's bandwith increase
according to their frequency. If you don't increase
the bandwidth of higher harmonics, the resulting sound
will be unpleasant especially on higher bandwiths of
the first harmonic. So, not all quasi-periodic sounds
are good, usually only if you increase the bandwidth
of the harmonics.
Now, what's happens if there are a lot of harmonics or
the pitch of the sound is enough low?
Let's see:
[img]http://zynaddsubfx.sourceforge.net/doc/paul2.png[/img]
The upper harmonics will merge to a single frequency
band that will sound like a hiss, that is pleasent to
the ear(eg. choir).
I found that bandwidth of each harmonics can go even
greater than 50 cents (quater of a tone) and still
sound musical - I can give you some example wavs.
Please note that this a different situation than 2
notes detuned by 50 cents (that sound very dissonand).
Also, the best is that the phases are random. In real
life this is ensured by the reverberation of the hall,
for example if a instrument plays with a vibratto (a
flute).
Perhaps you noticed that always if more instruments
plays the same note(as a enseble), the sound is very
pleasant. I consider that this is the cause: the
bandwidth of each harmonic.
Unfortunately, there is very little on the internet
about this stuff, because, I think, that are used more
complicated paradigms (like some statistics on how
sine harmonics modulates, or so).
Now I want to give examples on how you can synthesize
sounds, using this ideea.
You can use zynaddsubfx or another synthesizer in most
cases. Of course: I don't claim that I invented the
bandwidth of each harmonic (or frequency distribution
of each harmonic), because the ensembles, the choirs,
the reverberations, exists since thousands of years
(or more :) ). I just consider this a very important
fact on how sounds are beautifull and it helped me to
synthsize good sounds even since I was on highschool
:D.
You can make bandwidth of each harmonics by:
1) make more oscillators and detune them a bit (and a
slight vibratto helps alot). Most synth use this and
allows this, and perhaps it is known by you. This is
one of the simplest method. This is implemented in
ZynAddSubFX as "ADDsynth" module
2) generate white noise and filter each harmonics with
a bandpass filter and mix the results. Be carefull to
make higher harmonics to have higher bandwidth. This
is implememnted in zynaddsubfx as "SUBsynth" module.
3) You see that above graphs. You can represent them
as numbers in the frequency domain that represent the
amplitudes of the frequencies, add random phases and
do a SINGLE IFFT and voila! A very beautifull sound
will "born". This new ideea is implemented in
ZynAddSubFX as "PADsynth"
4) you can do other things, like a vibratto on a
periodic oscillator and do a FFT to all sound, put
random phases, and do a IFFT.
For more information, I made few years ago a page that
describes above things at:
http://zynaddsubfx.sourceforge.net/doc_0.html
Good luck.
Paul
__________________________________
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![img]http://zynaddsubfx.sourceforge.net/doc/paul1.png[/img](http://img]http://zynaddsubfx.sourceforge.net/doc/paul1.png[/img){kind=link}
![img]http://zynaddsubfx.sourceforge.net/doc/paul2.png[/img](http://img]http://zynaddsubfx.sourceforge.net/doc/paul2.png[/img){kind=link}
4 Feb
4 Feb
9:05 p.m.
On Fri, Feb 04, 2005 at 02:45:24PM -0800, Paul wrote:
(snip)
Interesting read, a novel perspective to me.
Just wanted to note that AFAICT a chorus effect
(basically a modulating small delay line)
will produce some of this effect because the modulation
causes slight pitch shifts which apply proportially
to all the harmonics.
--
Paul Winkler
http://www.slinkp.com
5 Feb
5 Feb
12:03 a.m.
On Fri, 4 Feb 2005 14:45:24 -0800 (PST)
Paul <paulgfx(a)yahoo.com> wrote:
...a simple, but powerfull paradigm that helps to
make
simple algorithms that produces very beautiful sounds.
What you are describing is basically extensions to the
technique of additive synthesis.
However, many of these same results can be achived at what
may be a reduced computation cost using extensions to FM
synthesis where both the carriers and the modulator are
complex sinusiods rather than real valued sines.
There was an AES Journal article (somewhere around 1998)
describing Complex FM
HTH,
Erik
--
+-----------------------------------------------------------+
Erik de Castro Lopo nospam(a)mega-nerd.com (Yes it's valid)
+-----------------------------------------------------------+
Saying Python is easier than C++ is like saying that turning a light
switch on or off is easier than operating a nuclear reactor.
12:10 p.m.
On Sat, 5 Feb 2005, Erik de Castro Lopo wrote:
On Fri, 4 Feb 2005 14:45:24 -0800 (PST)
Paul <paulgfx(a)yahoo.com> wrote:
Natural Instument's (?) FM7 DX-7 emulator allows you to use complex
waveforms as carriers and modulators in FM synthesis. These include
complex sinusoids, triangles, even noise. Great tool. (DX-7
left at parents house, far, far away).
...a simple, but powerfull paradigm that helps to
make
simple algorithms that produces very beautiful sounds.
What you are describing is basically extensions to the
technique of additive synthesis.
However, many of these same results can be achived at what
may be a reduced computation cost using extensions to FM
synthesis where both the carriers and the modulator are
complex sinusiods rather than real valued sines.
There was an AES Journal article (somewhere around 1998)
describing Complex FM
HTH,
Erik
--
+-----------------------------------------------------------+
Erik de Castro Lopo nospam(a)mega-nerd.com (Yes it's valid)
+-----------------------------------------------------------+
Saying Python is easier than C++ is like saying that turning a light
switch on or off is easier than operating a nuclear reactor.
5:24 p.m.
On Sat, 5 Feb 2005 18:09:59 +0200 (IST)
michael tewner <tewner(a)jct.ac.il> wrote:
Natural Instument's (?) FM7 DX-7 emulator allows
you to use complex
waveforms as carriers and modulators in FM synthesis. These include
complex sinusoids, triangles, even noise. Great tool. (DX-7
left at parents house, far, far away).
Sorry, not comples waveforms (ie other than sine), but complex valued
waveforms. Each sample of the waveform is of the form:
x + i y
where i is defined as sqrt (-1).
See this mathworld write up:
http://mathworld.wolfram.com/ComplexNumber.html
Erik
--
+-----------------------------------------------------------+
Erik de Castro Lopo nospam(a)mega-nerd.com (Yes it's valid)
+-----------------------------------------------------------+
"Or here's an even simpler indicator of how much C++ sucks: Print out
the C++ Public Review Document. Have someone hold it about three feet
above your head and then drop it. Thus you will be enlightened."
-- Thant Tessman
5:54 p.m.
On Sun, 6 Feb 2005, Erik de Castro Lopo wrote:
On Sat, 5 Feb 2005 18:09:59 +0200 (IST)
michael tewner <tewner(a)jct.ac.il> wrote:
my bad. I thought about that after sending the email....
-tewner
Natural Instument's (?) FM7 DX-7 emulator
allows you to use complex
waveforms as carriers and modulators in FM synthesis. These include
complex sinusoids, triangles, even noise. Great tool. (DX-7
left at parents house, far, far away).
Sorry, not comples waveforms (ie other than sine), but complex valued
waveforms. Each sample of the waveform is of the form:
x + i y
where i is defined as sqrt (-1).
See this mathworld write up:
http://mathworld.wolfram.com/ComplexNumber.html 
6 Feb
6 Feb
9:27 a.m.
Es geschah am Freitag 04 Februar 2005 23:45 als Paul schrieb:
You can make bandwidth of each harmonics by:
1) make more oscillators and detune them a bit (and a
slight vibratto helps alot). Most synth use this and
allows this, and perhaps it is known by you. This is
one of the simplest method. This is implemented in
ZynAddSubFX as "ADDsynth" module
2) generate white noise and filter each harmonics with
a bandpass filter and mix the results. Be carefull to
make higher harmonics to have higher bandwidth. This
is implememnted in zynaddsubfx as "SUBsynth" module.
3) You see that above graphs. You can represent them
as numbers in the frequency domain that represent the
amplitudes of the frequencies, add random phases and
do a SINGLE IFFT and voila! A very beautifull sound
will "born". This new ideea is implemented in
ZynAddSubFX as "PADsynth"
4) you can do other things, like a vibratto on a
periodic oscillator and do a FFT to all sound, put
random phases, and do a IFFT.
With "random phase", do you mean they _can_ be random or _should_ be random?
CU
Christian
6:07 p.m.
--- Christian Schoenebeck
<schoenebeck(a)software-engineering.org> wrote:
Es geschah am Freitag 04 Februar 2005 23:45 als Paul
schrieb:
"Should" :) Because the natural ensembles have this
tendency (the individual instruments's are very like
to be somehow uncorelated. Ex: you cannot synchronize
2 singer that plays same note to start at same phase
of the fundamental note).
So, I belive that the ensembles sounds beautifull
because the bandwidth of each harmonics as described
earlier AND the phases are random (uncorelated).
Also, another thing that adds randomness to the
harmonic phases is the reverberation. Think for
example, one singer plays a note for few seconds: of
course he cannot keep the same note, and will result a
slight vibratto, that is a the simplest way to make
the bandwidth of each harmonic as described before. Or
good singers know how to add vibratto to their voices.
The problem is that there is a certain relationship
between the frequencies of a certain harmonic (in
order to result a "frequency modulated" sound by a
very low frequency). But if you pass this sound into a
reverbation, the phase relationship will be
"destroyed" and will result random phases on the
frequencies contained in the frequency band. I noticed
that the better is the reverberation, the more
randomness is added to the phases of the wet reverb
signal. To intuitively demonstrate this (that a good
reverb makes the phases more random), let's consider a
very ugly reverb: a simple comb echo with little
delay(say 50 ms) with a very high feedback. This
"reverb" sounds awful, in most cases. If you draw the
phase response of this, you'll see that this filter
changes the phases of the incoming signal by a not
random (or pseudo-random) matter. Of course, if you
add 2 or more comb filters, and the delay are
uncorelated, will be more likely to add a random phase
to the signal and this makes that the phases of the
incoming signal to be more likely to be random.
I attached 2 files (for zynaddsubfx) to explain more
about above:
1) bw_without_randomness.xmz
This makes bandwidth of each harmonic by the simplest
way: it adds a vibratto to the sound. I am reffering
as "bandwidth" and not "fast changing the pitch
according to the time", because I am consider sound
from the perspective of long FFTs. You see that is not
well sounding, because even if it has bandwidth, but
it lacks randomness of the phases.
2) bw_with_randomness.xms
I added the randomness, using a reverb and taking only
the wet signal. You see, that it sound very good, even
like a very big ensseble, but because the reverb, the
sound last few seconds more than the first.
Another way that I can convert from the first sound to
the second, is to sample few seconds from the sound,
do a long term FFT (in fact the whole sound :) ), make
the phases random and than, do a IFFT.
Another important thing that I noticed, regarding
FFT's and random phases, is the IFFT of a signal with
random phases is periodic (you know this about the
periodicity of the FFTs...), and this helped me alot
to design PADsynth algorithm; because I know that the
IFFT is smoothly periodic,so I can easily loop the
sample w/o any clicks or artifacts regarding loops.
Paul
http://zynaddsubfx.sourceforge.net
__________________________________
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You can make bandwidth of each harmonics by:
1) make more oscillators and detune them a bit
(and a
slight vibratto helps alot). Most synth use this
and
allows this, and perhaps it is known by you. This
is
one of the simplest method. This is implemented
in
ZynAddSubFX as "ADDsynth" module
2) generate white noise and filter each harmonics
with
a bandpass filter and mix the results. Be
carefull
to
make higher harmonics to have higher bandwidth.
This
is implememnted in zynaddsubfx as
"SUBsynth"
module.
3) You see that above graphs. You can represent
them
as numbers in the frequency domain that represent
the
amplitudes of the frequencies, add random phases
and
do a SINGLE IFFT and voila! A very beautifull
sound
will "born". This new ideea is
implemented in
ZynAddSubFX as "PADsynth"
4) you can do other things, like a vibratto on a
periodic oscillator and do a FFT to all sound, put
random phases, and do a IFFT.
With "random phase", do you mean they _can_ be
random or _should_ be random?
7225
days inactive
7227
days old
linux-audio-dev@lists.linuxaudio.org
7 comments
5 participants
participants (5)
-
Christian Schoenebeck -
Erik de Castro Lopo -
michael tewner -
Paul -
Paul Winkler