The Eat at Joe's Kawai K5000 Message Board Digest
K5000 Harmonic Phase Problems
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The gap between theory and reality
Saturday, 07-Mar-98 15:27:58
130.67.2.99 writes:
Someone please explain to me why any attempt to translate bookish knowledge
into sound seems to backfire on this synth. For instance, I have tried to
emulate the behavior of a string plucked at 1/4 of its length. For the first
24 harmonics I have used these levels:
127, 115, 102, 0, 90, 90, 82, 0, 76, 78, 72, 0, 68, 70, 64, 0, 62, 64, 59,
0, 57, 60, 55, 0
Getting the attack right is a problem, of course. But it seems that no matter
what sort of attack I use, whether or not I let the high harmonics decay faster
than the low ones, etc., I am still miles away from the sound of a real string
being plucked.
In particular, I am worried about the murky sound I get with series of harmonics
like the one above. It reminds me of the sound you get if you play a
guitar where part of the wrapping on the wound strings is loose, if you have
ever tried such a thing. I wonder if any of you understand precisely when and
why this murkiness comes about.
Could this have any connection with the incorrect phases that result when we
enter absolute values for the levels? The series above is calculated using the
amplitude formula sin(PI/4 * n)/n^2 - where n is the harmonic number - which
is alternately positive and negative. The complete formula is:
127 + 8 * ln abs(sin(PI/4 * n)/n^2/sin(PI/4)))/ln2
Negative values do not have logarithms, so I have to use that abs() function.
But how does this affect the composite wave function? It seems to me that a
sum of positive terms and a sum of alternately positive and negative terms
ought to add up to two different waves, but I am probably wrong here since
everyone, it seems, is doing it this way. If any of you Fourier experts out
there know the deeper reason for why the abs() values can be used, I would
like to hear more about it.
In any case, the murkiness is there, and the only cure that I have found is
to avoid sustained sounds with many neighboring harmonics of comparable
amplitude. Fortunately, this cure is at least POSSIBLE on the K5000, which is
not the case with a number of other synths. But it would still be nice to get
some sort of theoretical handle on sound formation on this machine.
I hope everyone will share their thoughts and experiences with the K5000 on
this board. It would be interesting to see more people telling about their
work with sound formation, both the positive and negative aspect of it.
Tore
tl001@online.no
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Re: The gap between theory and reality
Sunday, 08-Mar-98 22:15:32
199.86.33.82 writes:
QUOTE
Negative values do not have logarithms, so I have to use that abs() function.
But how does this affect the composite wave function? It seems to me that a
sum of positive terms and a sum of alternately positive and negative terms
ought to add up to two different waves, but I am probably wrong here since
everyone, it seems, is doing it this way.
UNQUOTE
With a triangle wave, which also has a 1/n^2 amplitude profile, every other
harmonic is supposed to be negative phase. If you leave them positive phase,
the resulting wave form is like a sine that bulges out on the sides instead of
being flattened on the sides. But--it sounds the same. (At least by itself; there
are probably some subtle differences when you combine waves.)
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Re: Re: The gap between theory and reality
Tuesday, 10-Mar-98 05:43:28
130.67.66.36 writes:
Leafing through some books, I find that already Helmholtz asserted that we are
not able to hear phase, so I guess this is an established fact since it has
survived for more than a century.
But I would like to know more about those "subtle effects". Some of you may
have found that additive organ tones can be a strain on the K5000. (They
can, in fact, be a strain on humans too.) I wonder if this is a matter of
sustained amplitude only or whether the phase issue could have something to do
with it.
Tore
tl001@onlin.no
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Re: Re: Re: The gap between theory and reality
Tuesday, 10-Mar-98 11:41:15
192.28.2.19 writes:
I don't know how you could hear the phase of a single harmonic, but with two
identical harmonics the phase determines whether they cancel or reinforce.
By subtle effects I meant the way, say, two notes in an interval interact:
some pairs of harmonics cancel when others reinforce and vice versa.
As far as ear strain, BBE makes an "enhancer" box that corrects for the phase
shifts caused by electronic circuits like amplifiers. It definitely sweetens the
sound. (Some Aiwa home stereos have this curcuit now, too.) The "enhancer" in
the effects section of the K5k is supposed to be like the BBE box; I
haven't tried it much yet. (The "exciter" is different, it's supposed to add
soft distortion to the high frequency portion of the signal to generate high
frequency even harmonics.)
leiter@skypoint.com
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Importance of phase relationship between harmonics?
Monday, 09-Nov-98 20:05:23
209.207.189.184 writes:
Just how important is the phase relationship between harmonics? I've read that it
plays a somewhat minor role in the perception of timbre but is important for sounds
containing large phase shifts and/or high levels of "intensity". Does anyone know
any more about this?
It's too bad that the K5000 even numbered sources don't give you a choice between
the harmonics 65~128 and the cos series since this would allow you control over the
phase also.
jon
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Re: Importance of phase relationship between harmonics?
Wednesday, 11-Nov-98 05:30:29
209.160.126.143 writes:
According to the book "Acoustical Foundations of Music", the ear can hear changes
in phases of the harmonics of complex tones. It qualifies this by saying that the
ear can only tell the differences under certain conditions. What those
conditions are, the author wasn't sure, but it might have to do with how many
sharp dips or peaks a waveform has. In most cases, it is not a pronounced effect
(quoting from the book). My edition of the book was written in 1969. I would hope
that we have found out more conclusive evidence since then, but I don't know.
Leslie
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Re: Re: Importance of phase relationship between harmonics?
Wednesday, 11-Nov-98 21:20:16
209.83.12.170 writes:
i recently studied harmonics in a physics course i'm in. one of our labs consisted
of using one of these science-type synthesizers that allows you to adjust the
levels of the first 7 harmonics, *and* their phase. our project was to create a
waveform as close to a square wave as possible.. and in order to this, it was
necessary to tweak the phase of some of the harmonics, to get sharper edges for the
square. i didn't think to check whether the difference was audible, but if it
affects the shape of the wave, i would expect it to be. i guess this raises the
question of whether kawai could implement the ability to change phases of each
harmonic in the system 4.0 that's supposedly coming out..
-kc
kent christopher
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Re: Re: Re: Importance of phase relationship between harmonics?
Thursday, 12-Nov-98 15:25:30
153.35.108.142 writes:
Uh, Oh! I guess that you already turned in your lab report, but you should have
found that the easiest way to get the square wave was to have all sine waves of
the same phase. The only non-zero amplitudes should've been for the sine
waves whose frequency where in odd multiples of the fundamental's. The amplitude
levels should've varied as 1/N where N is the frequency multiple.
jon
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Re: Importance of phase relationship between harmonics?
Thursday, 12-Nov-98 10:26:47
194.172.230.108 writes:
Phase information is virtually irrelevant for the perception of what we call
timbre, thus, the spectral properties which show in the steady-state portion of a
sound.
But our sense of hearing does also perceive the time domain properties, which show
in transients, mainly in the attack portion of a sound. Here, the phases are
everything but arbitrary: A sine being switched on sounds different from a cosine
being switched on. But that depends on the switching speed - if you do just a slow
fade-in, it will be almost the same as the steady state!
So, what if an envelope generator turns out to be too slow to produce transients
fast enough to let us hear phase differences? Then, the phase control capability
would be a waste of computing time.
Thus, I think it is important to ask for fast, fine-grained and flexible amplitude
control first, and then to ask for phase control.
Jens Groh
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Re: Re: Importance of phase relationship between harmonics?
Thursday, 12-Nov-98 15:16:45
153.35.108.142 writes:
Thanks for the well thought out responses! This is an interesting and possibly
important subject. I can see how the phase relationship may not be important in
perception of timbre when I think about something like two flutes playing the same
notes at the same time. If these are played by "real" musicians then it is almost
impossible for it to occur that the two waveforms will be in phase. But I doubt if
any one could tell the difference between in phase flutes and out of phase flutes.
On the other hand if you consider the situation of two sine waves of equal
amplitude and frequency emananating from the same point in space then phase
obviously matters in the perception of timbre. This is so because if one sine wave
is 180 degrees out of phase then the waves will cancel one another and no timbre
will be perceptable. I would assume that the effect would be different if the
signals originated from different points in space, but it would probably still be
perceptible.
Since we don't have any control over phase with the K5000 I guess this all kind of
irrelevant. I'm definitely very happy with the superb amplitude control of the
partials the K5000 offers, since this is the most important factor, but at the same
time phase control would really make the instrument more powerful. Especially since,
with synths, we are in the scenario where the waveforms are emanating from the same
location in space(the speaker) where phasing effects would seem to
matter the most.
I'm just hoping that when Kenji persuades Kawai to build the K5,000,000 that they
will give the option of using the second source for either harmonics 64~127(of more
sine waves) or for cosine harmonics 1~64. I don't know for sure, but I suspect
that phase relationships may have a more profound effect on timbre than the
addition of 64 more harmonics.
With the cosine oscs we would have control over phase (of course the cos oscs need
to have their own amp levels and amp envs)and the engineers could avoid having to
implement computation costly phase change envelopes. Just an idea, I wonder if it
would be possible to do this with an OS upgrade!?
jon
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Re: Re: Re: Importance of phase relationship between harmonics?
Thursday, 12-Nov-98 16:53:04
209.160.126.134 writes:
This is probably irrevelant to the K5000, but with my ESI-32, I sampled some
analog waves (saw, triangle, PWM, etc.). For some of the patches I would layer the
same sample with itself (i.e. a saw wave). Then I would have the velocity
change the sample starting point of one of the waves so that it would have a
different phase relationship with the other wave depending on how hard you pressed
the key. This really livened up the sound. Also as you played a note repeatedly,
each note would have a slightly different velocity setting thus giving you
variations in sound.
Leslie
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Re: Re: Re: Re: Importance of phase relationship between harmonics?
Thursday, 12-Nov-98 18:55:17
208.213.99.41 writes:
you could also set the sample start to be modified by the lfo, that way you get a
different start point regardless of velocities.
You could also sample your K5K and delay the start and play it unison with your
esi32 and go out of phase that way. It doesn't matter how it gets to the speakers
as long as it gets there.
cheddar
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Re: Re: Re: Importance of phase relationship between harmonics?
Friday, 13-Nov-98 07:57:30
194.172.230.108 writes:
Jon, you said:
"I can see how the phase relationship may not be important in perception of
timbre when I think about something like two flutes playing the same notes at
the same time.
[...]
On the other hand if you consider the situation of two sine waves of equal
amplitude and frequency emananating from the same point in space then phase
obviously matters in the perception of timbre."
(Leslie expressed similar thoughts.)
But I was talking about the phase of single tones, not of unisono layered sounds!
Of course, when you add several tones with the same pitch but different phases, the
overall timbre will change. But this comes from in-phase respectively out-of-phase
addition of different harmonics, and thus is a matter of amplitudes again. You
could create the same timbre by appropriate amplitude control of a single tone!
(I'm not talking about stereo, that's a different case.)
Still an interesting idea of yours, Jon! Imagine, if, in addition, the harmonics'
amplitudes could be made negative, as well, and the amplitude LFOs were programmed
to generate a sine wave and a cosine wave, you could even create a frequency
shift with it, according to the formula:
sin(x) * cos(y) + cos(x) * sin(y) = sin(x + y)
You would have to use two ADD SOURCEs and to have a fine control over the
harmonics' amplitudes (finer than we are having now with DHE loops, and
with strict synchronization between SOURCEs). But each harmonic would get an
individual frequency offset!
Jens Groh
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Re: Re: Re: Re: Importance of phase relationship between harmonics?
Friday, 13-Nov-98 11:59:32
153.35.108.236 writes:
Thanks for the response, the more I think about this the more interesting this
all becomes.
The two sine waves of the same frequency and amplitudes being out of phase by 180
degrees is a degenerate case(I'm only considering strictly periodic steady state
waveforms here). But if this gives the net result of no sound wave being
produced then it seems reasonable that the first and second harmonics being out of
phase would also produce a remarkable change in timbre. The exact change in timbre
would depend on the amplitude relationships between the harmonics. I'm kind of in
the dark here, but it seems that as you move away from these simple cases by
adding more harmonics and greater and greater frequencies of differing phase content
the ear loses the ability to interpret this as a difference in timbre. What causes
the ear to not interpret the complex cases as changes in timbre? Is it high
frequencies? Is it the low amplitudes that are typical of high order harmonics?
Does it become confused due to the number of harmonics present? A combination of
all of the above?
You're pretty to close to what I was thinking about with the even numbered sources
generating Cosine instead of Sine. When you calculate the Fourier series for a
particular periodic waveform you assume that F(X)= SUM(from 0 to infinity) of
(An*SIN(X) + Bn*COS(X)). This is the Fourier series representation for one period
of the waveform(for steady state this is all that we need). Defining
Cn=Squareroot(a^2 + b^2) each term can be written as
Cn(COS(Pn)*SIN(X)+SIN(Pn)*COS(X)). We can apply your trig identity to finally get
each term represented as Cn*SIN(X + P). This is where it gets interesting, Cn is the
numbered that we have all been using to program our K5000's since it's what comes
out of the FFT (I'm sure that this is what Sounddiver is doing)if this is applied
to a waveform. But the K5000 gives you no way of specifiying P (the phase) for
each harmonic in the series. If you go back to the point where we had Sins and Coss
there is no phase factor, so if we stuck to calculating An and Bn coefficients for
our series then we really wouldn't have to worry about computationally controlling
phase relationships. I suspect that this is one reason why the import wave
procedure in Sounddiver doesn't work so well.
Sorry I know that this post is confusing to look at, I hope that it's somewhat
readable.
jon
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Frequency range stops at 10000 Hz
Tuesday, 01-Dec-98 15:23:36
130.67.68.47 writes:
Just want to hear if anyone else has a problem with poor treble sound. My own
K5000R seems to give up around 10000 Hz or slightly below. If I play a source with
only the 64th harmonic activated, there is no sound above D3 = 147 Hz, so
this means no sound above 147 Hz * 64 = 9408 Hz.
I bypass the DCF, bypass effects, and the bias of the formant filter is set to
-63. Any ideas about some other parameter that can be tweaked in order to awaken
the remaining frequencies up to 20000 Hz?
Tore
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Re: Frequency range stops at 10000 Hz
Thursday, 03-Dec-98 00:42:34
153.35.138.172 writes:
Yeah, some of my sounds with a high frequency content start to "mellow" out around
E5. I also fiddled around with various parameters to try and get my harmonics
back, but with no success so far. Are the higher order harmonics just too
highly pitched for the K5000 to generate when the fundamental is oscillating
around E5?
jon
jonwest@vcu.org
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Re: Re: Frequency range stops at 10000 Hz
Thursday, 03-Dec-98 21:12:35
209.214.60.64 writes:
Definitely yes.
Terry
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Frequency range stops at 10000 Hz & more on phase....
Thursday, 03-Dec-98 21:51:19
153.35.138.96 writes:
That's too bad. I think that the oscillators should hold up at least over the
normal range of the keyboard. It makes me wonder what the use of having oscs
65~127 is when 1~64's upper harmonics start cutting out in the upper range of the
K5000S's keyboard.
I would much, much rather have the second set of oscillators available for cos
waves (so sines and cosines were available)to get the phase relationships right
than have the ultra high harmonics that will just cut out.
Speaking of phase, some of you may remember the discussion about that subject that
took place here awhile back.
Here's an update, I went to the library and read up on the subject. I found several
texts on aural perception and here's what I found:
1. The older the text, the less the effect of phase on perception of timbre. The
really old texts are the ones that say it doesn't matter at all.
2. The newer texts (last 5~10 years) really shift the focus from examining
situations where phase does matter (this used to be considered the unusual
situation) to situations where it doesn't matter (this is now the slightly odd
situation).
This really didn't come as a surprise to me. If anyone has doubts about this I
would suggest using the additive JAVA page leiter found
(http://www.nst.ing.tu-bs.de/schaukasten/fourier/en_idx.html) to test it out.
The applet gives you control over sines and cosines (& therefore phase). If you
replicate a waveform with the proper phase relationships you get one sound and if
you use only sine waves (adjusted with the proper spectral amplitudes like
we do with the K5k) you get a second differing sound. It's true that the second
sound has some of the flavor of the first but it's sort of like sugar vs
nutrasweet. Not the same.
I don't mean to sound too down on the K5k, all synths have their limitations
(usually having something to do with shortcuts taken in the design process to
save $). It's better to focus on what a synth can do, and the K5k can do alot.
It's just not the perfect additive machine....
jon
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Harmonics 64-127
Sunday, 06-Dec-98 23:59:45
166.55.9.59 writes:
I actually think that those upper harmonics are very important. Listen to my
ADDSaw patches. I it uses two sources to get the full range of harmonics. Actually
I think there are two of each for detuning purposes (two 0-63 and two 64-127).
Play the lower half of the keyboard. Now disable the two sources that are used for
the upper harmonics. The change in the sound is dramatic. I think that low notes
sound much much better with the full range of harmonics!!!
-Kenji
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