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Harmonic & Subharmonic generator
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françois



Joined: Dec 23, 2006
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PostPosted: Fri Dec 21, 2007 10:52 am    Post subject: Harmonic & Subharmonic generator
Subject description: worth the hassle ?
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Hello all,

One more idea of mine, which I submit to get advice & criticism. Please do not feel anything like respectful or polite, I just want to know what you think of it.

I was thinking about waveshapers, essentially these who are driven by a sawtooth wave. Most of you certainly know how to make a sawtooth twice or half the original frequency (IIRC Rene Schlmtz has a very simple circuit for that, and many others do). Now, what about making a sawtooth three times the original frequency (one perfect fifth) ? Or three times lower ?

Well, let us look at the frequency tripler. A microsecond of thought will convince everybody that multiplying the incoming sawtooth by 3 will build another sawtooth raising 3 times as fast as the original. What we need is to reset it at the appropriate times. Just drawing the waveforms on paper, it it easily seen that (starting with a raising sawtooth from -5V to +5V, my preferred standard for all signal generators) :
-- during the first third of the perios, you shouold have Vout = 3*Vin + 10V ;
-- during the middle third of the period, Vout = 3*Vin ;
-- during the last third of the period, Vout = 3*Vin - 10V.
All these are obviously realized with a simple opamp circuit. How do we know if we are in the first, middle, or last third of the original sawtooth wave ? The very great advantage of this waveform is its perfect predictability. A window comparator will do the job, and the offset voltage (-10V / 0V / +10V) may be selected through any analog multiplexer (e.g. 4053 based).

Of course, the very same principle can be applied to have 5 times the original frequency (perfect third). Or 7 times, or 11, or 13 times... it's up to you, you'll just need more comparators & switches.

And now, the subfifth generator. Here we want to have a sawtooth one third the frequency of the original. Again, drawing the waveforms shows that we have to "glue" three consecutive periods, with appropriate offsets. Alternatively, we can algebraically reverse the above equations, to get :
-- during the 1st period, Vout = (Vin + 10V)/3 ;
-- during the 2nd period, Vout = Vin/3 ;
-- during the 3rd period, Vout = (Vin - 10V)/3.
How do we know which one is the first or second or third period ? No way. Some kind of shift register, or divide-by-three counter, will inform us of the relative positions of the original periods. Maybe some kind of sync signal would be welcome here.

Again, the very same idea may be applied with a perfect sub-third instead.

Now, which interest ? I didn't test it yet, I will draw a schemo and make some SPICE simulations. The sawtooth wave having all harmonics, adding to it a super or suboctave will certainly fatten the sound, but not necessaraily the texture. Comparatively, the square wave has only odd harmonics, so that adding a sub-octave adds all even harmonics (the Roland SH-101, of which I have two, does this very well & efficiently). But the sawtooth wave can be morphed in many ways (square, PWM, triangle, sine) so that you might envision some kind of "drawbars" à la Hammond for each of your VCOs...

Probably overkill, but IMHO a module providing x2, x3, x5, :2, :3, :5 frequency intervals (and of course fully patchable to give e.g. 3/2 or 5/4) might be a useful aid to a 2-VCO source.

è-- françois

Last edited by françois on Sat Dec 22, 2007 3:24 am; edited 1 time in total
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ian-s



Joined: Apr 01, 2004
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PostPosted: Fri Dec 21, 2007 11:29 am    Post subject: Reply with quote  Mark this post and the followings unread

I just patched up the x3 version and it works well.

I think if you combined it with a sawtooth animator you could be onto a winner.

Even just separate pwm on each sawtooth sounds quite phat. see mp3


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cbm



Joined: Oct 25, 2005
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Location: San Francisco

PostPosted: Fri Dec 21, 2007 11:33 am    Post subject:
Subject description: Salamander Frequency Transmuter
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Your post made me think of the Salamander Music Systems (SMS) Frequency Transmuter, which has some of the ideas you mention:
http://www.xfade.com/gear/Salamander/modules.html#m103

It has a frequency doubler, tripler and quadrupler. This section expects a triangle as input. It has a bank of dividers that generate square waves.
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Tim Servo



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PostPosted: Fri Dec 21, 2007 12:38 pm    Post subject: Harmonic & Subharmonic generator Reply with quote  Mark this post and the followings unread

I think such a thing is definitely worth doing, if nothing else to gain better familiarity with what works and what doesn't in waveshapers (sometimes the frequency multipliers you described will be very sensitive to timing issues at higher frequencies and not behave well across the entire audio range). What would really make such a module worthwhile would be if you could introduce a small amount of variation (preferably with voltage control) in the "trip points" for the higher (2x, 3x, etc.) frequency waves. This would introduce some phase differences and would really fatten things up. Oh, sorry, I meant "phatten." Having everything phase locked would not be as much fun, IMHO. I haven't drawn this out, but voltage control over comparator trigger levels is very simple (it's basically built in to a comparator). Also I don't know if it would be easier to use a window comparator (with a setup to change the trip levels as the input saw progressed), or just a set of 2 or 3 'standard' comparators. The window comp would allow you to choose how many times to reset on the input wave, but would also involve more circuitry to change the trip levels.

Still, could be a fun project. I've considered doing something similar with my 566 VCO, as it has tri, square and saw waves that could (potentially) all be divided and/or multiplied). Let us know how you get along with this!


Tim (divide/multiply and conquer) Servo
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frijitz



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PostPosted: Fri Dec 21, 2007 4:19 pm    Post subject: Re: Harmonic & Subharmonic generator Reply with quote  Mark this post and the followings unread

Tim Servo wrote:
I haven't drawn this out, but voltage control over comparator trigger levels is very simple (it's basically built in to a comparator). Also I don't know if it would be easier to use a window comparator (with a setup to change the trip levels as the input saw progressed), or just a set of 2 or 3 'standard' comparators. The window comp would allow you to choose how many times to reset on the input wave, but would also involve more circuitry to change the trip levels.
Laughing
You are getting very close to my 5Pulser and other pulse-based waveshapers. (Much easier to derive various pulse signals from a sawtooth than to make other sawteeth. And more variety in timbre, because you can vary both pulse width and pulse position.)

Also see Bernie Hutchens, "A Sawtooth Frequency Multiplier", Electronotes Application Note No. 190 (1980), which is the same idea as what Francois is describing.

Ian
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toppobrillo



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PostPosted: Fri Dec 21, 2007 5:39 pm    Post subject: Reply with quote  Mark this post and the followings unread

also, see ken stone's circuit here:

http://www.cgs.synth.net/modules/cgs38_saw_pitch_shift.html

josh
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Dave Kendall



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PostPosted: Fri Dec 21, 2007 6:25 pm    Post subject: Reply with quote  Mark this post and the followings unread

Quote:
also, see ken stone's circuit here:
http://www.cgs.synth.net/modules/cgs38_saw_pitch_shift.html


I second that. Smile
Have just built 2 of them. In pitch shift mode they are seriously good, although a triangle wave for the LFO is the one to use for the LFO, rather than the suggested saw (typo perhaps?) The slight glitch on the down output is not a problem IMO - with 2 of these wired up, you can't hear it at all - it simply doesn't matter any more because it sounds so fat....

I'm playing with some simple VC LFOs so as to add a slight speed incease as the key CV goes higher. A LFO rate setting that's right for bass notes is a bit too static in the higher registers - get it right up high, and the bass notes sound too chorusey, so a tracking VC LFO should fix this.

Another pleasant saw animator surprise was with the CGS65 tube VCA. With a 100K LIN feedback pot wired from OUT back to IN, as suggested on the CGS site, when increasing the FB amount, the wave form starts to become gradually squarer, with a simultaneous increase in the duty cycle. Above around 90% duty cycle, it goes crazy, halves in frequency, and other stuff, and simply stops tracking the input saw. Fun to look at on a scope...
Below this point, slowly turning the FB pot back and forth gives a glorious PWM sort of thang.... If the FB pot has IN and OUT jacks, then modulating this with a VCA, and a scaled/offset TRI or SIN LFO should be very tasty.

Definitely check out the CGS38, and CGS65 if you like saw animators/wavefolders. Smile

Cheers,
Dave
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Rykhaard



Joined: Sep 02, 2007
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PostPosted: Sat Dec 22, 2007 12:40 am    Post subject: Reply with quote  Mark this post and the followings unread

The last message reminded me of a circuit that I actually designed in my earlier days, that I'll have to bring back to life. My 1995 (mis-named) Voltage Controlled Wave Splitter.

The basic idea of V1.00, was to split the incoming audio into positive and negative voltage halves, allowing offsets to each half, including external input (The VC portion); mixed back together; split again and processed and mixed together again for final output.

I liked it, but tried modding it again. It's in the 2nd version where I added a controllable portion of the original signal into the mix (V1.41) that I ACCIDENTALLY got it into FOLDING the waves over when they reached their peaks. THAT sounded GREAT. (The 3rd version lost that ability.)

I'll see about building one again as well as posting the schematic for the 2nd, which I still have. Slightly different sounds once again. Had a nice character to it. Simple circuit. Shall get to it soon and post the schematic in my Schematics section. Smile
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françois



Joined: Dec 23, 2006
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PostPosted: Sun Dec 23, 2007 2:14 am    Post subject: Reply with quote  Mark this post and the followings unread

Thank you all ! I didn't expect that such a circuit could raise so much interest.

I tested the x3 and :3 versions in simulation (LTSpice) and they work as expected. There are indeed some glitches, but if they are audible at all, they can be filtered out with just a capacitor. Admittedly, it is not clear if the device will operate properly at higher frequencies. Only a real world implementation could tell, and I've not my gear at home, I don't know when I can do it.

Yes, the idea of adding a sawtooth phase shifter is a good one. I think I would go for a module providing x2, x3, x5, :2, :3, :5 besides the "fundamental", plus some PWM (just simple comparators) & phase shift. Now all this is a lot of signals, not all of them being used at the same time (IMHO). Having a separate level (VC preferably) would certainly be overkill, the sound won't only be phat, it will be obese.

I think there should be a VC mixer near this module where you can select & mix whatever (sub)harmonics you want.

Thank you again,

-- françois
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françois



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PostPosted: Mon Dec 24, 2007 3:33 am    Post subject: Reply with quote  Mark this post and the followings unread

I tried the sawtooth frequency tripler at higher frequencies, and the glitches (spikes) are way too important. I didn't test if they were audible, but they can reach over 12V at the end of the driving sawtooth period. This occurs mostly at frequencies over 1~2kHz, which is high-pitched, but not ultrasonic...

Moreover the peak voltages are getting farther and farther from +/-5V (even ignoring the spikes). I'm using a "standard" model for the TL08x, I mean it is not at all considered an ideal opamp. So this is what might (will) happen in reality.

Strangely enough, the frequency doubler does not exhibit such spikes. Any idea why ?

Thank you,

-- françois
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frijitz



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PostPosted: Mon Dec 24, 2007 11:29 am    Post subject: Reply with quote  Mark this post and the followings unread

françois wrote:
I tried the sawtooth frequency tripler at higher frequencies, and the glitches (spikes) are way too important. I didn't test if they were audible, but they can reach over 12V at the end of the driving sawtooth period. This occurs mostly at frequencies over 1~2kHz, which is high-pitched, but not ultrasonic...
Francois --
What seems to work best to counter the glitches is to uses fast opamps, or even comparitor chips, followed at the end by a slow opamp (741, 324, etc). Simple filtering smears them out too much.

Very Happy

Ian
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françois



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PostPosted: Tue Dec 25, 2007 4:13 am    Post subject: Reply with quote  Mark this post and the followings unread

frijitz wrote:
What seems to work best to counter the glitches is to uses fast opamps, or even comparitor chips, followed at the end by a slow opamp (741, 324, etc). Simple filtering smears them out too much.

Thank you, Ian.

Fast opamps are a bit expensive for such a thing, but it didn't come to me that slow opamps can be much better LPFs than a simple capacitor. Just their limited slew rate will probably get the glitches out. I've LTSpiced all x2, x3, x5, :2, :3 and :5 generators and they work well (with glitches, although) but a simple capacitor at the output either smears things out or introduces some "ringing".

LTSpice has several levels of modelling for opamps, including the possibility of a second pole in the frequency response. But there are so many parameters to these models, I have to delve into them to account for realistic behaviour. And uA741 models I found on the Web just have odd pinouts so... I'll try when the after effects of Christmas dinner are gone.

I also did a bit of acoustic tests with LTSpice's ".wave" directive ability, and the glitches do not seem to be audible (but with sample rate at 44.1kHz there is no room for aliasing). The sounds are indeed phat (or obhese ?) as expected, although less than I hoped. I think this is due to the driving sawtooth having already all the harmonics, odd & even). Adding phaes shift and/or (AND, definitely) PWM will turn a single VCO source into some kind of monster with dozens of jacks & switches & pots... I don't think my audio files are worth posting, but I will do so if some of you are interested.

BTW, I designed and tested a sawtooth symmetry waveshaper (from rising sawtooth to triangle to falling sawtooth, voltage controlled), very similar to Osamu Hoshuyama's design, and although there were big spikes in the simulation they were not audible in the "true" circuit...

Merry Christmas to all !

- françois
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françois



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PostPosted: Thu Dec 27, 2007 8:13 am    Post subject: Reply with quote  Mark this post and the followings unread

I tried it today with a µA741 SPICE model and the spikes have "miraculously" disappeared. Certainly due to the 741's limited slew rate, but how spectacular ! Thank you again for this advice, Ian !

-- françois
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