The Eat at Joe's Kawai K5000 Message Board Digest
Creating Basic Waveforms
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Those nonlinear rates and levels
Friday, 27-Feb-98 03:48:44
130.67.0.118 writes:
At one time I believe I saw one of you - maybe it was Kenji - post information
about the nonlinear nature of harmonics levels and how you had taken this into
account in making a sawtooth wave. I cannot find that in the digest, so maybe
the poster could point me to the right place or repeat the explanation, please?
The thing is, the envelopes we get from books or PC sound tools need to be
translated into K5000 terms, and for this purpose we need to know the precise
nature of the rates and levels. The rates of the harmonic envelopes appear
to be logarithmic. For a given level, the time needed to reach it seems to be
proportional to 2^(-Rate/8). (Anyone know this for sure?) However, the level
also needs to be part of this formula for the time, and it is obviously nonlinear.
That's why I ask for that formula posted previously.
Tore
tl001@online.no
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Re: Those nonlinear rates and levels
Friday, 27-Feb-98 04:36:09
194.172.230.108 writes:
Hi Tore!
It's here: (Let's see if the following becomes a link; otherwise, you will find
it "by hand".) Things that Should be in the Manual (Details!)
0.75 dB per step means, as formula:
amplitude = max_amplitude * 2^((level_value-127)/8)
Or:
level_value = 127 + 8 * log2(amplitude/max_amplitude)
To create a sawtooth wave, the amplitude spectrum must be inversely proportional
to the harmonic number, that is:
level_value = 127 - 8 * log2(harmonic_number)
For those who are missing the base-2 logarithm on their pocket calculator - use this:
log2(...) = ln(...) / ln(2)
Have fun with your additive sawtooth!
Jens Groh
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Pulses and Combs
Monday, 09-Mar-98 23:41:25
199.86.33.32 writes:
More of the theory discussion: The amplitude (on the K5k) of harmonic n of an
X% pulse is:
Amplitude = 127+8*log2(abs(sin(X%*Pi*n)/n))
If you switch the sin to cos, you get a comb-filtered saw, i.e. the sum of two
saws that are out of phase by X%, so that some harmonics cancel and some reinforce.
leiter@skypoint.com
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"Fat" Sawtooth
Saturday, 17-Apr-99 16:00:07
207.90.173.253 writes:
What do you think would be the best way to create a nice sawtooth sound? We can
already create a mathematically precise sawtooth, however that might not actually
be what we really want to hear.
My question is:
1. Why is the default sawtooth ADD set for the K5K (using the ADD switch feature)
not a mathematically precise sawtooth?
2. Why is the SoundDiver sawtooth not a mathematically precise sawtooth?
3. Why in the world did they use what look like truncated sine waves for the
PCM samples?
4. Do these sawtooths sound BETTER than a mathematically precise sawtooth?
5. What can we do to create a sawtooth with the best flavor for getting a nice
fat sound and really good filter/LFO effects?
Here are some relevant resources from past discussions/research:
K5000 Waveforms (graphic intensive)
http://www.geocities.com/SunsetStrip/Lounge/6766/k5kwaves.html
Creating Basic Waveforms
http://www.geocities.com/SunsetStrip/Lounge/6766/digests/sawtooth.txt
Techniques and Formulae for Creating ADD Patches
http://www.geocities.com/SunsetStrip/Lounge/6766/digests/techniqu.txt
Has anyone tried sampling unfiltered and unmodulated sawtooth wavforms from
"vintage" synths? Maybe it would be useful to start building up a library
collection of basic sawtooth/square ADD profiles to use as a basis for new
patches....would the differences between the various profiles be worth the
effort?
Kenji
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Re: "Fat" Sawtooth
Sunday, 18-Apr-99 16:13:03
199.199.158.217 writes:
The pure saw is good for some things, but it''s often too bright. On bass notes,
the cricketing is pretty loud. It can be good to filter. For saw samples, phase
differences may account for some of the quirks in the appearance of the
waveforms, so it isn''t always clear what''s going on with the harmonics.
A saw has so many audible harmonics that there''s a lot to mess with. I''m sending
three patches I think some of these count as fat, but let me know!
C Saw 20: Dark saw with HH''s 2-7 boosted and 9+ cut, falling to 0. Related to
a 2% pulse.
C Saw 10: Medium dark saw with HH''s 2-17 boosted and 20+ cut, falling to 0.
Related to a 1% pulse.
W Saw: Wavey HH profile with high fundamental and mid HH''s and cut low and
high HH''s.
leiter
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Re: "Fat" Sawtooth
Monday, 19-Apr-99 07:16:13
194.172.230.108 writes:
Do I remember right that some "vintage" synths had exponential sawtooth waves?
Aren't they said to sound fat? Anyway, if you want to have an exponential
sawtooth wave on your K5000, simply program a linear falling slope on the
harmonic level scale. (Says theory.)
Should be easiest to be done using the "All", "Dark" and "Bright" edit macros.
Jens Groh
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Re: Re: "Fat" Sawtooth
Monday, 19-Apr-99 10:38:34
192.28.2.16 writes:
>Do I remember right that some "vintage" synths had exponential sawtooth waves?
Is that where the diagonal is more like an S-curve, with the middle more
horizontal? (The two "C Saw" patches do that, plus the vertical is tipped a
little.)
leiter
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Re: Re: Re: "Fat" Sawtooth
Tuesday, 20-Apr-99 10:20:47
194.172.230.108 writes:
This is what I mean: Go to the Fourier synthesis website
(http://www.nst.ing.tu-bs.de/schaukasten/fourier/en_idx.html - Java required)
and enter these values (an approximate exponential function):
a0 = +5.0
a1 = -4.5 b1 = -4.5
a2 = -2.6 b2 = -2.6
a3 = -1.5 b3 = -1.5
a4 = -0.9 b4 = -0.9
a5 = -0.5 b5 = -0.5
a6 = -0.3 b6 = -0.3
You see an exponential sawtooth wave.
But the K5000 has only sine, no cosine components. Watch what happens when you
reset all "a" values to zero: There you are, leiter - the sawtooth wave that
you described!
Jens Groh
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Re: Re: Re: Re: "Fat" Sawtooth
Tuesday, 20-Apr-99 15:51:45
192.28.2.16 writes:
>You see an exponential sawtooth wave.
Yep-that's the "vintage" waveform I've seen.
>But the K5000 has only sine, no cosine components. Watch what happens when you
>reset all "a" values to zero: There you are, leiter - the sawtooth wave that
>you described!
Yep, it's the same! It looks like the general rule is to boost the low middle
harmonics, i.e. 2-~16, and cut the high harmonics. Boosting the low mids rounds
the points of the waveform and gives the diagonal an S-curve and cutting the
highs makes the vertical less vertical. These changes make the pure saw somewhat
closer to a thin pulse. (I'll have to try that with an analog; add a thin pulse
to a saw.)
The waveforms in the L7, L2 and L1 patches are also boosted in the low-mids
and cut in the highs. Maybe this is a general fat rule. Alternately, you could
say, cut the fundamental and the high harmonics. You'd think that cutting the
fundamental would make a weak waveform but it seems to be the opposite sometimes.
I have a good accoustic-sounding bass with no fundamental at all!
Detuning also adds lots of fat, as Leslie pointed out. Detuning makes all of
the harmonics oscillate in volume at a rate proportional to their frequency.
Since it's slowest with the fundamental, it's arguably most noticable there.
leiter
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Re: Re: Re: Re: Re: "Fat" Sawtooth
Thursday, 22-Apr-99 01:49:55
209.214.60.81 writes:
Leiter said:
"Yep, it's the same! It looks like the general rule is to boost the low middle
harmonics, i.e. 2-~16, and cut the high harmonics. Boosting the low mids rounds
the points of the waveform and gives the diagonal an S-curve and cutting
the highs makes the vertical less vertical. These changes make the pure saw
somewhat closer to a thin pulse. (I'll have to try that with an analog;
add a thin pulse to a saw.)"
If I remember correctly, the MiniMoog's most famous 'fat' sound was the
result of a combination of a Triangle wave and a Pulse wave.
Terry
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Re: Re: Re: Re: Re: Re: "Fat" Sawtooth
Thursday, 22-Apr-99 23:25:26
199.199.158.131 writes:
> If I remember correctly, the MiniMoog's most famous 'fat' sound was the result
> of a combination of a Triangle wave and a Pulse wave.
Do you know what width pulse?
leiter
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Re: Re: Re: Re: Re: Re: Re: "Fat" Sawtooth
Friday, 23-Apr-99 12:54:47
209.214.60.82 writes:
> > If I remember correctly, the MiniMoog's most famous 'fat' sound was the
> > result of a combination of a Triangle wave and a Pulse wave.
>
> Do you know what width pulse?
Sorry, I don't (though the number 16% is floating around in my brain for some
reason, still, the fact that the MiniMoog used a straight triangle wave makes
me suspect things were kept as simple with the pulse wave (ie, at 50%).
Terry
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Re: Re: Re: Re: Re: "Fat" Sawtooth
Friday, 23-Apr-99 12:08:24
192.28.2.16 writes:
>It looks like the general rule is to boost the low middle harmonics, i.e. 2-~16,
and cut the high harmonics. Boosting the low mids rounds the points of the
waveform and gives the diagonal an S-curve and cutting the highs makes the
vertical less vertical. These changes make the pure saw somewhat closer to a
thin pulse. (I'll have to try that with an analog; add a thin pulse to a saw.)
>The waveforms in the L7, L2 and L1 patches are also boosted in the low-mids and
cut in the highs. Maybe this is a general fat rule. Alternately, you could say,
cut the fundamental and the high harmonics. You'd think that cutting the
fundamental would make a weak waveform but it seems to be the opposite
sometimes. I have a good accoustic-sounding bass with no fundamental at all!
Come to think of it, this is related to what happens on a guitar (or bass) when
you combine a neck pickup out of phase with the bridge pickup. You can get a
talky, mid-rich lead tone. You couldn't do the same with a filter unless you
were tracking the pitch somehow.
leiter
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Re: "Fat" Sawtooth
Monday, 19-Apr-99 18:27:07
206.57.21.184 writes:
I'm not sure if this will answer your question, but I think what makes those
analog synths sound so fat isn't necessarily the shape of the waveforms but how
the oscillators interact. If you take two oscillators and assign a saw to both,
what will happen is that the phase of one oscillator will differ from the other.
This phase relationship seems to change each time a key is pressed. This causes
a slight difference in sound even if the same note is played over and over. I
think this is one of the things that makes analogs sound so fat.
The trick on a digital synth, like the K5000, is to simulate this type of
random phase relationships between two waveforms. One way might be to layer two
sawtooth waveforms, assign a pitch envelope to one of them, and set it so that
it cause the pitch of the waveform to go from sharp to being in tune very
quickly. This will cause the two waveforms to have different phase relationships.
You would then want to route the modulation amount of the envelope to velocity.
Since a note you play will likely have a different velocity amount from the
previous one, the notes should sound slightly different. Hopefully, this would
make a digital synth sound a little more lively.
Leslie
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