Octave Up Achieving... Ideas, Thoughts, Experience & Theory?

[Scruffie]

Hey all,

At present I am fiddling with some (Clean) Octave Up ideas (I know it's been done to death and that analogue up octaves can't be done simply and well by even the best of builders which I am certainly not and it will never be a POG, I have one already so I'm covered for that)

But i'd like to know a bit about the theory for my messing and also some particularly innovative or interesting ways that have been used to achieve an octave and why those simple 2 transistor 10component ish style octave pedals work how they do (I notice one major issue with them always seems to be a lack of gain, easily sorted though, just a thought)

I think I have to be quite strict about the cleanness of the octave a bit of fuzz is acceptable, but I don't want some uncrontrolable muck, I know you get the green ringer for modulated octave and lots of octave pedals that create a sort of octave bend if you will (info on why these pedals do these things is welcome for learning, but I don't want to build one) I'd like something where I could choose to stick the fuzz after it to get if the mood takes me any desired octave fuzz tone.

Also the theory of tracking issues would be appreciated.

I realise for a begginer builder such as myself this is asking alot and perhaps I wont understand it all, but I hope to learn from it and keep working till I get something I feel I like out of my design, feel free to discourage me if it really is just to a lost cause to get anything that hasn't been done.

Earthtonesaudio already gave me a couple of good ideas on the 'other' forum, Fundamental nulling, Achieving a smooth sine wave input but some more ideas and some ellaboration is always good.

Thanks for any help & info,
Scruff.

[Taylor]

Well, with an analog octave (the usual rectification type anyway), there is no tracking. The negative portion of the waveform is folded up into the positive area, thus doubling the frequency, which gives you a note one octave higher.

Here's a picture that shows that happening:

http://www.rfcafe.com/references/electrical/images/period5.gif

As far as I know, this kind of circuit can't give you a clean octave, but if you can settle for "clean-ish", you might be in luck. There are also some schemes for generating a synthesized note that tracks your original note, but these usually put out a pulse wave or square wave, so that's not really "clean" either. And it doesn't sound anything like your original note. For a note that sounds like your note, but is an octave higher, you need to go digital, and some people don't even feel that sounds enough like your original note.

This can be a fun subject to work on, and I'm brewing up something in this area myself, but for real pragmatism, if you want something that sounds like commercial pitch shifters, you can get it a lot better and cheaper by just buying one. If you want to come up with something new and unusual, though, go for it.

[brett]

Hi
after messing with octave quite a bit, I've found that the best octaves offer a pleasant blend of fundamental and octave.  You CAN use a multiplier (e.g. AD633) to get a pure octave, but they aren't particularly popular.  On the other hand, fuzz-octaves such as the Tycho and RM Octavia are quite popular.

One avenue that I haven't tried, but I think would work well, is to build an RM Octavia with a different front end (the front end is an RM "Axis" fuzz IIRC.  Which explains why it's so fuzzy).  I would use an "almost clean" boost at the front.  My choice would be a JFET boost, like the Stratoblaster, set for moderate gain (5 to 10x).

just my 2c
Have a great day.   

[R.G.]

...i'd like to know a bit about the theory for my messing and also some particularly innovative or interesting ways that have been used to achieve an octave and why those simple 2 transistor 10component ish style octave pedals work how they do

Theory: An octave is a frequency ratio of exactly 2:1. The human ear has some internal affinity for this, for reasons no one has explained, to my knowledge. To make and octave up from a pure tone, you simply double the frequency.

This can and has been done by using electronic multipliers. Put the same signal into both inputs and you get the square of the signal. By exercising some trigonometric theory, one can show that the square of a sine contains just the sine (or cosine, I forget) of twice the frequency. No problem.

Well, there is a problem. Electronic multipliers have errors, drift, expense, need trimming, and so on. Until recently good ones were quite expensive. But that's not the problem. The problem is that no musical instruments produce a pure tone (i.e. a sine wave). A softly blown flute probably comes closest.  But all instruments produce a note which is the sum of a fundamental, some harmonics or near-harmonics of the fundamental, and other junk which is not tonally related to the fundamental. If you do the math, a summation of weighted sine waves plus extras like this, when squared, produces the square of all the components, plus the squares of the sums and differences of each component. These sums-and-differences are one form of intermodulation distortion, where one component modulates another. Sums and differences of frequencies in the original signal are NOT musically related to the fundamental, and sound harsh.

And that *is* the problem. Even perfect squarers can't bypass the intermodulation math. DSPs can, because they can effectively manipulate time, not just the signal voltage at each instant.

I came up with a new technique for squaring that used the square-law nature of FETs to do the squaring. Works, just like multipliers, and has the same issues with intermodulation.

None of the ten-parts octave up circuits do the multiplication thing. What they do is to full-wave-rectify the signal, just like a power supply might. Used on a sine wave, this produces a full wave rectified signal that has a noticeable octave plus a slew of distortion harmonics. Used on a signal with more than just a sine wave, it produces an octave, plus a slew of harmonics, plus intermodulation distortion.

The intermodulation is inherent in the math that describes these processes and cannot be completely avoided. It can only be ameliorated and dealt with.

There is one other octave-up scheme that has the potential to do a pure-sine octave up from any waveform. That's a phase locked loop with a sine wave VCO. A PLL locks onto a frequency by comparing the phase of the signal plus the oscillator of the loop. It forces the oscillator in the (frequency) direction which minimizes phase changes and then differences between the oscillator and the signal. If a PLL's VCO has a square wave output, this can be sent through a digital divider, and the divider output used to compare to the signal. When the loop locks, the VCO is then running the inverse of the divider faster than the signal. So a PLL with a flipflop divider can generate a square wave which is exactly 2x the frequency of the signal it is tracking. (oops, I said "tracking").  It can also be multiplied many times higher than that, and the higher multiple square wave used to divide DOWN to make a digital approximation of a sine wave, which can be very pure, especially compared to the intermodulation of the other techniques.

But the PLL output has two difficulties: it must track, and it has no dynamics, as it's always the same size, not the size of the signal that made it. PLL octaves must have a lot of housekeeping circuitry to (a) determine when the loop is locked, because if it's not locked, a full output, non-signal related sound comes out, and mute when it's not locked, and (b) impress on the output in some way some amplitude changes to follow the original signal.

Notice that tracking comes in two flavors: frequency tracking and amplitude tracking. When the input signal fades out, the loop has nothing to lock to, and jumps around hunting. When the input signal fades out, the loop output doesn't, which is major annoying. "Tracking" is also a problem with rectification and multipliers because as the signal get smaller, they start rectifying or multiplying signal+noise, and if they have any dead zone around zero where nothing happens, the signal sputters in and out of tracking as the signal fades out. You also don't want a PLL tracker/octaver to lock onto a harmonic or near-but-not-quite harmonic in the signal. No multiple notes, as that forces a single-note tracker to make a decision, and it simply can't do that.

(I notice one major issue with them always seems to be a lack of gain, easily sorted though, just a thought)

Gain is easy. Intermod is hard.

I know you get the green ringer for modulated octave

No, you don't. The green ringer is a simplistic full wave rectifier. If you feed a full wave rectifier two (main) notes simultaneously, it generates an intermod product of both tones. Get the tones right and the modulation can be pleasant under certain conditions. There is no modulation happening inside a green ringer.

and lots of octave pedals that create a sort of octave bend if you will (info on why these pedals do these things is welcome for learning, but I don't want to build one)

Intermodulation.

I'd like something where I could choose to stick the fuzz after it to get if the mood takes me any desired octave fuzz tone.

So would everyone else. Welcome to the club.  

Also the theory of tracking issues would be appreciated.

See above.

I realise for a begginer builder such as myself this is asking alot and perhaps I wont understand it all, but I hope to learn from it and keep working till I get something I feel I like out of my design, feel free to discourage me if it really is just to a lost cause to get anything that hasn't been done.

I don't want to discourage you, because we need new people taking up the discipline. However some very smart people, much smarter than me, have tried to do something similar for about half a century now. Worse yet, the underlying math says that non-DSP processes have minimal chances of ever doing what you describe. Maybe zac will pop in with a pep talk about not letting anyone tell you that something can't be done and to keep easter-egging parts until you create your own beautiful reality; I guess that might even happen. But like I said, quite a number of very smart people have tried this for a long time. I personally have been digging out info on how to do clean octaves-up since at least 1972. This is one reason I know the background.

Earthtonesaudio already gave me a couple of good ideas on the 'other' forum, Fundamental nulling, Achieving a smooth sine wave input but some more ideas and some ellaboration is always good.

"Fundamental nulling" is one way of describing what I did for my FET square-law device, the FET doubler, and Mu-doubler. Since FETs are square-law devices, the distortion they generate tends to be in the form of the square of the signal, and for a sine, that's the octave up. I dreamed up a setup where you feed two FETs equal and opposite signals, tie their outputs together so the amplified signal cancels - that is, fundamental nulling. What is not nulled out is the even-order distortion products where the summing reinforces them. But even a theoretically pure squarer has to cope with the sum-and-difference intermodulation.

The math is what is going to give you problems. Learn the math.

[Cliff Schecht]

Meh. The math is easy, it's all of the theory that will get you. I've designed every type of multiplier you can name and while every one of them has intermodulation  (no escaping this!), some still sound more musical than others. The rectifier type multipliers tend to sound very nasally and gatey, both  of which are side effects of using diodes. The nasally sound comes from taking the absolute value of your signal (this is mathematically what a full-wave rectifier does) and the gate type effect is a side effect of using diodes. Germaniums gate less and Schottky's even less than Ge, but the Schottky's are leaky and don't sound that good. Ge's are my favorite for diode-based multipliers.

IC based multipliers tend to sound very bland and, well, perfect. They're great for synth stuff but tend to sound pretty lame as is with a guitar. FET based multipliers (yeah R.G., you aren't the first ) are my favorite, especially because there is more than one way to use a FET (or FETs) as a multiplier. Diff-amp octave based effects are another favorite because the distortion they produce is oh-so-musical.

[brett]

Hi

Germaniums gate less and Schottky's even less than Ge, but the Schottky's are leaky and don't sound that good. Ge's are my favorite for diode-based multipliers.

Yep.  The gating/signal decay problem can be significant.

There are, however, a couple of things that can reduce the problems.  Take the Neoctavia circuit, which is typical in that it uses a transformer as a phase splitter and Ge transistors as rectifiers. http://www.tonepad.com/project.asp?id=43

The first thing I wonder about this project is why it uses a step-down transformer (if the primary connects to the op-amp and the secondary to the diodes).  This increases the gating/decay problem.  If I were building this, I'd turn the transformer around the other way.  The op-amp will easily drive the secondary (now the primary), and the output of the primary (that was the secondary) will be larger (3x larger than the other way around).  Gating will be much less.  A transformer with a wider impedance ratio would be even better if it were also reversed (e.g. 42TM021, or even the 42TM017 which reversed gives 11.4x the standard Neoctavia output and only a fraction of the gating).

Another way to reduce gating is to apply a bias voltage to the centre tap of the transformer output.  Apply about 0.3 V to the centre tap for Ge diodes or 0.7 V for Si diodes and there will be little or no gating/decay, because the diodes will conduct even a tiny signal, because the diodes are already conducting to a small degree ((Vbias-Vf)/Output resistance, e.g. (0.3-0.28)/60 = 0.3 mA)

just my 2c...

cheers

[Scruffie]

Cheers guys for explaining all that, some very interesting stuff there that's cleared up a few of my misconceptions and has led me to research further into the theory, looks like something i'm gunna have to commit to and put all other projects on hold if I wanna end up with something that atleast is useable.

I'm alright with a bit of nice harmonic distortion on top as long as it sounds smooth and doesn't clutter the signal and i'm also okay with some synthy sounding as long as it's not messy or overly buzzy but I suppose getting a level I find acceptable for myself is gunna be part of the ride.

As you say thought R.G gunna have to learn the math of this all to apply it... shame I only got a C at GCSE... this is gunna inolve alot of learning, I can see why people just buy a POG or use a simple octave fuzz, but I shall pursue this anyway, who knows, might end up with something that doesn't exactly do what i set out to do, but doesn't something nice anyway.

I shall start working with FETs though as I haven't tried that yet and see what I can come up with, shortage of funds is clearly going to be an issue though as I don't have enough spare parts lying around to just stick them in the breadboard if and when needed...

But anyway I shall continue and thanks for all your comments, they have been very useful.

[R.G.]

... FET based multipliers (yeah R.G., you aren't the first ) are my favorite, especially because there is more than one way to use a FET (or FETs) as a multiplier.

Oh, I didn't mean I came up with FET based multipliers first at all. What I was referring to was the MOS Doubler, JFET Doubler and Mu Doubler. The central idea is that a single diffamp has as its output two signals, equal and out of phase, each a distorted replica of the input. If you maximize the input by feeding phase-split signals to the gates and cancel the amplified output by connecting the drains, the output signals cancel and what's left is an amplified even order distortion. Only incidentally related to something like the Gilbert Cell.

[Cliff Schecht]

... FET based multipliers (yeah R.G., you aren't the first ) are my favorite, especially because there is more than one way to use a FET (or FETs) as a multiplier.

Oh, I didn't mean I came up with FET based multipliers first at all. What I was referring to was the MOS Doubler, JFET Doubler and Mu Doubler. The central idea is that a single diffamp has as its output two signals, equal and out of phase, each a distorted replica of the input. If you maximize the input by feeding phase-split signals to the gates and cancel the amplified output by connecting the drains, the output signals cancel and what's left is an amplified even order distortion. Only incidentally related to something like the Gilbert Cell.

I only took a quick peek at the schematics last night and obviously didn't catch the gist of what you were doing. Very cool idea though! I suspect the output waveforms look very sawtoothy and that distortion sounding pretty synthy (FETs and BJT's in a diff-amp made some classic synth circuits). It's sort of a bummer that you have to match the FETs for your circuit. I completely understand though, FETs vary all over the map from device to device. How much cancellation do you lose if you don't match them?

[owenjames]

Like these guys have said, it is going to be close to impossible to do what you are asking with analogue. I have some tips on getting a more or less clean octave up if you use the octave fuzz approach. While lots use the transformer then full wave rectify route. I feed my signal into two op amps one inverting and one non-inverting. I set the output DC voltage of each op amp at 4.5V, I then place a forward biased diode after each output. I set the DC voltage after the diodes to be 3.8V (for Si diodes) this gets over the gating effect. You then just join both ends together. That gives you a full wave rectified ungated signal.  Put low pass filtering before the op amps with a cuttoff of about 1.2KHz, this allows all notes on the fretboard tro pass through while reducing harmonics as much as possible. put a lowpass filter with a cuttoff of 2.4KHz after the diodes, this smooths out as much of the fuzziness as possible while allowing all notes on the fret board through un affected. Somehting you could try, which i havent done but might work is having 3 or 4 of the above stages in parrallel with different filtering, which are then summed together at the end. So the bass notes get a 300Hz filter then have a 300-600Hz filter then a 600-1200Hz filter so each gets octaved seperatly, this will produce much more cleanness over the whole fretboard, but would require 7 opamps.

[R.G.]

I only took a quick peek at the schematics last night and obviously didn't catch the gist of what you were doing. Very cool idea though! I suspect the output waveforms look very sawtoothy and that distortion sounding pretty synthy (FETs and BJT's in a diff-amp made some classic synth circuits). It's sort of a bummer that you have to match the FETs for your circuit. I completely understand though, FETs vary all over the map from device to device. How much cancellation do you lose if you don't match them?

Actually, the results are very much like the output of a multiplier, very much a square of the instantaneous input. A sine, for instance, make a very pure sine wave of 2x frequency.

Matching is critical, unfortunately. That's the big problem with it. If you think about it, what this rig produces is zero times the amplified signal, and two times the distortion. The distortion in a JFET is down in the 1-2% range, so you get about 2%-4% of the amplified signal out if the main undistorted signal is cancelled perfectly. Unfortunately, MIS-cancellation by 2-4% can wipe you out, then. 

[Cliff Schecht]

I only took a quick peek at the schematics last night and obviously didn't catch the gist of what you were doing. Very cool idea though! I suspect the output waveforms look very sawtoothy and that distortion sounding pretty synthy (FETs and BJT's in a diff-amp made some classic synth circuits). It's sort of a bummer that you have to match the FETs for your circuit. I completely understand though, FETs vary all over the map from device to device. How much cancellation do you lose if you don't match them?

Actually, the results are very much like the output of a multiplier, very much a square of the instantaneous input. A sine, for instance, make a very pure sine wave of 2x frequency.

Matching is critical, unfortunately. That's the big problem with it. If you think about it, what this rig produces is zero times the amplified signal, and two times the distortion. The distortion in a JFET is down in the 1-2% range, so you get about 2%-4% of the amplified signal out if the main undistorted signal is cancelled perfectly. Unfortunately, MIS-cancellation by 2-4% can wipe you out, then. 

That's a slim margin for error.. So what if you intentionally mis-match the FETs, say a device with a high gm with a low gm unit? Does the "unbalanced" resulting distortion sound good? I would think that unbalancing the current through each FET (even if perfectly matched) will give some interesting results, especially if you cranked the gain of your diff-amp up (increase the drain resistor or decrease the source resistance?).

[soggybag]

Great discussion. The suggestion of applying .3v to the center tap of an inductor based octave (Would you say biasing the center at the diode forward voltage?), reminds me of the Bobtavia. The Bobtavia has a 100K from 9V going to center tap. It uses Si diodes. Maybe you could tune this value to improve sustain and negate splutter?

The Bobtavia is a great project makes a pretty octave, fuzzed up, but sounds great, and you can get all of the parts at RS.

[Cliff Schecht]

All you're doing with the center-tap DC trick is literally mixing in a DC component with your incoming signal. You just have to add enough DC to make sure that the lowest voltage the diodes ever see is over one diode drop (0.6-0.7 V Si, 0.3 V Ge, 0.15 Schottky). You could also add a resistive bias network (resistor from V+ to diode anode and one from anode to ground) to keep the diode turned on at all times. Or you can use a perfect rectifier (op amp with diode in the feedback path) to eliminate the diode drop problem completely.. I don't think I've seen the last one done though.

[ACS]

Like these guys have said, it is going to be close to impossible to do what you are asking with analogue. I have some tips on getting a more or less clean octave up if you use the octave fuzz approach. While lots use the transformer then full wave rectify route. I feed my signal into two op amps one inverting and one non-inverting. I set the output DC voltage of each op amp at 4.5V, I then place a forward biased diode after each output. I set the DC voltage after the diodes to be 3.8V (for Si diodes) this gets over the gating effect. You then just join both ends together. That gives you a full wave rectified ungated signal.  Put low pass filtering before the op amps with a cuttoff of about 1.2KHz, this allows all notes on the fretboard tro pass through while reducing harmonics as much as possible. put a lowpass filter with a cuttoff of 2.4KHz after the diodes, this smooths out as much of the fuzziness as possible while allowing all notes on the fret board through un affected. Somehting you could try, which i havent done but might work is having 3 or 4 of the above stages in parrallel with different filtering, which are then summed together at the end. So the bass notes get a 300Hz filter then have a 300-600Hz filter then a 600-1200Hz filter so each gets octaved seperatly, this will produce much more cleanness over the whole fretboard, but would require 7 opamps.

Interesting approach.  Do you have any clips at all?  Would be interesting to compare this to the more common approaches.  Seeing as I'm just intelligent enough to understand this, but not intelligent enough to convert this to a circuit, do you have any schem's that we can breadboard to play with?

[R.G.]

... Or you can use a perfect rectifier (op amp with diode in the feedback path) to eliminate the diode drop problem completely.. I don't think I've seen the last one done though.

Not commercially. John Hollis' Omnidrive used the two-opamp full wave rectifier and I believe that one of Anderton's circuits did too.

It works as expected.

[R.G.]

... Somehting you could try, which i havent done but might work is having 3 or 4 of the above stages in parrallel with different filtering, which are then summed together at the end. So the bass notes get a 300Hz filter then have a 300-600Hz filter then a 600-1200Hz filter so each gets octaved seperatly, this will produce much more cleanness over the whole fretboard, but would require 7 opamps.

One thing I designed but never had the time or money to build was a filter bank distortion. Three or four bandpass filters per octave for the four octaves of the fundamentals on a guitar. The filters have to be sharp enough to cut out the second harmonic from a string well. That's twelve to sixteen filters, each of which has a full wave rectifier and filter for note detect, as well as its own clipping. It's the logical extension of the Quadrafuzz. Lets you separate out each string, and use logic on the note detects to get rid of harmonics that would confuse things. As you might guess, this would have been ... big...

[Scruffie]

Hmm my circuit was slowly creeping towards what I wanted... but I have none of the funds to get into these territorys at the moment and tbh, I really think it has been decided here that just buying digital is easier (even though I already knew that and have a digital octaver) so I guess I shall forefit from what has been said and maybe just run off what i've started into something else if funds permit.

Thanks for all the comments though and keep them coming as i'd still like to hear your ideas, perhaps i'l pick it up again when I get the motivation.

[Taylor]

Even when this kind of thread doesn't result in an "aha!" I think they do provide a lot of "hmm...."s, so still pretty fruitful, IMO.

I'm going to reread this page a few times and let all that info swirl aronud in my brain for awhile, and maybe something neat will come out eventually.

One thing that's unfortunate for people like me, who were born in the 80s or later, is that we got used to digital processing before we really knew anything else. My very first effect pedal cost $150, and had 30 effects, including glitch-less pitch shifters that didn't change tone too much. As a result, I didn't really appreciate until much later how much of a "holy grail" this is.

But what's cool about that is that when I listen to imperfect solutions, those imperfections are more charming than irritating.

[brett]

Hi
RE: ideal rectifier

I don't think I've seen the last one done though.

Quite a few of us have done this and been disappointed. 

I forgot to mention above that if you use the guitar signal as the modulator in a ring modulator (especially a dodgy transformer-based one), you get interesting octave results.

You can also use the guitar signal to drive the switch in a balanced modulator.  e.g. drive a 4066 bilateral switch from A to B (and back), where A is a +ve phase signal and B is a -ve phase signal.