Hi,
I am aware that humans generally can't hear differences in phase; however, something of the form sin(w1*t+theta1)+sin(w2*t+theta2), fed through a nonlinear system, will have a different frequency spectrum in the output depending on the choice of phase, due to intermodulation.
Has anyone studied the audible effects of phase changes on distortion? Is it worth thinking about the phase response of tone controls (does a bessel filter sound better than a butterworth filter in front of a gain stage?), or will it sound almost the same regardless?
Is there any practical application? I imagine it's possible to for example move phases around until a certain note played through certain pickups has minimal or maximal peak amplitude (at the same volume), to change how and by how much it distorts. But maybe this doesn't translate into general utility.
Another thing I was thinking about is a "broken" phaser pedal, which is just an LFO-controlled allpass stage (without summing the original signal). Has anyone done this? Does it sound cool?
Possibly related, I noticed the DOD250 shows remarkably clear articulation and note boundaries, even when medium-high gain is involved (example). Experimenting with different instruments, signal chains, etc. led me to believe that this is almost certainly an intrinsic property of the DOD250 circuit. But looking at the circuit, everything seems extremely ordinary. I could say that a delta function that undergoes some phase distortion due to the feedback network will spread out in the time domain and get clipped a lot less by the diodes than one who doesn't, but I can't see a reason why the DOD250 would be special in this regard... (and I guess delta functions are a questionable model of note boundaries). Does anyone know an explanation for its properties?
I am aware that humans generally can't hear differences in phase; however, something of the form sin(w1*t+theta1)+sin(w2*t+theta2), fed through a nonlinear system, will have a different frequency spectrum in the output depending on the choice of phase, due to intermodulation.
Has anyone studied the audible effects of phase changes on distortion? Is it worth thinking about the phase response of tone controls (does a bessel filter sound better than a butterworth filter in front of a gain stage?), or will it sound almost the same regardless?
Is there any practical application? I imagine it's possible to for example move phases around until a certain note played through certain pickups has minimal or maximal peak amplitude (at the same volume), to change how and by how much it distorts. But maybe this doesn't translate into general utility.
Another thing I was thinking about is a "broken" phaser pedal, which is just an LFO-controlled allpass stage (without summing the original signal). Has anyone done this? Does it sound cool?
Possibly related, I noticed the DOD250 shows remarkably clear articulation and note boundaries, even when medium-high gain is involved (example). Experimenting with different instruments, signal chains, etc. led me to believe that this is almost certainly an intrinsic property of the DOD250 circuit. But looking at the circuit, everything seems extremely ordinary. I could say that a delta function that undergoes some phase distortion due to the feedback network will spread out in the time domain and get clipped a lot less by the diodes than one who doesn't, but I can't see a reason why the DOD250 would be special in this regard... (and I guess delta functions are a questionable model of note boundaries). Does anyone know an explanation for its properties?
This sort of interaction, I am told, actually matters in the exhaust manifolds of internal combustion engines. The individual exhaust gas pulses from (some) cylinders meet and mix in the exhaust manifold, and SPL (pressure fluctuation) is so high that this is heavily nonlinear mixing.
Some of the exhaust systems that have evolved for high performance vehicles - tuned header exhausts, dual exhausts vs single exhaust systems on V8 engines, et cetera - do take these nonlinear interactions into account. These days, engine performance prediction and modelling software include such effects.
For audio? The only major application I can think of is the very same phaser and flanger pedals you mentioned. Unwanted phase mixing effects are, unfortunately, much more common than wanted ones.
-Gnobuddy
Phase tuning in the exhaust systems of modern engines has more to do with maintaining an even exhaust gas flow across all cylinders than it does sound, but it definitely affects sound.
Those of us who raced cars in the 80's will remember that the "5.0" Mustangs that appeared in the 80's had a unique exhaust tone. I could hear the cars street racing from my house in Florida and could pick out a 5.0 Mustang from a mile away by the unique sound that they made. Why was it unique?
Throughout the 50's and 60's all American V8 engines used the same cylinder firing order, 18436572. Ford published a different numbered order, but they used a different cylinder numbering scheme then GM or Chrysler. The actual firing order was identical. Tuned exhaust and intake systems were not common (except on some high performance vehicles), and most V8 powered cars sounded similar.
Sometime in the 80's Ford upgraded the venerable 302 cubic inch V8 and renamed it the "5.0" The main upgrades were improved cylinder heads and a "roller" camshaft. In the process, they changed the firing order to solve a vibration problem. This changed the exhaust "phasing" also improving exhaust gas flow, and resulted in the 5.0's unique sound.
What does this have to do with the sound of a stack of guitar amps?.... Ever been to a big outdoor concert where there is a wall or several stacks of speakers behind the band (real speakers, not the fake empty cabinets used today). If most of the crowd is sitting down, or otherwise below the line from your ears to the speakers, walk along parallel to the stage 50 feet out or so and notice how the sound changes. A pair of 8 X 12 inch stacks separated by a few feet is worse case. There is a noticeable and sometimes obvious pattern of alternating "bright" and "muddy" sound. This is where the two speaker stacks exhibit alternating phase cancellation or reinforcement of the higher frequencies. This is also why those big stacks are now fake, the single guitar cabinets are miked and everything goes through the house PA, or professional sound system which can be controlled and optimized for the venue.
Ever play chords through a cranked distorted guitar amp and wonder why some sound gross, some just sound bad, while others are OK? It's because the InterModulation Distortion (IMD) created generates new notes some of which are dissonant with the existing notes. "Power chords" are designed such that the major IMD tones are consonant.
Years ago I got the brilliant idea that this could be avoided by using 6 separate amplifiers, one for each string, fed to 6 separate speakers. Each amp could be cranked to its melting point, but since each amp and speaker was processing only one note at a time, all the distortion would be harmonic. There would be no IMD. Possibly a great idea, but it sounded terrible, even when played clean. Why? I don't exactly know, but I'm guessing that my DIY pickups and the hodge podge collection of amps and speakers I used destroyed the phase relationship between the 6 individual notes. Each individual string sounded OK. Lead runs consisting of a single note at a time sounded OK, but chords sounded off, almost as if the guitar was not properly tuned. I have planned to return to this experiment. I wanted to try identical amps through identical speakers, but never have.....some day.
I suppose some experiments are in order with the digital music synth that I am designing. I have the ability to operate individual VCO's with exact frequency relationships and vary their phase with respect to each other. I would assume that some of the existing soft synths out there today that run in a PC have this ability, bit I never tried it.
Those of us who raced cars in the 80's will remember that the "5.0" Mustangs that appeared in the 80's had a unique exhaust tone. I could hear the cars street racing from my house in Florida and could pick out a 5.0 Mustang from a mile away by the unique sound that they made. Why was it unique?
Throughout the 50's and 60's all American V8 engines used the same cylinder firing order, 18436572. Ford published a different numbered order, but they used a different cylinder numbering scheme then GM or Chrysler. The actual firing order was identical. Tuned exhaust and intake systems were not common (except on some high performance vehicles), and most V8 powered cars sounded similar.
Sometime in the 80's Ford upgraded the venerable 302 cubic inch V8 and renamed it the "5.0" The main upgrades were improved cylinder heads and a "roller" camshaft. In the process, they changed the firing order to solve a vibration problem. This changed the exhaust "phasing" also improving exhaust gas flow, and resulted in the 5.0's unique sound.
What does this have to do with the sound of a stack of guitar amps?.... Ever been to a big outdoor concert where there is a wall or several stacks of speakers behind the band (real speakers, not the fake empty cabinets used today). If most of the crowd is sitting down, or otherwise below the line from your ears to the speakers, walk along parallel to the stage 50 feet out or so and notice how the sound changes. A pair of 8 X 12 inch stacks separated by a few feet is worse case. There is a noticeable and sometimes obvious pattern of alternating "bright" and "muddy" sound. This is where the two speaker stacks exhibit alternating phase cancellation or reinforcement of the higher frequencies. This is also why those big stacks are now fake, the single guitar cabinets are miked and everything goes through the house PA, or professional sound system which can be controlled and optimized for the venue.
Ever play chords through a cranked distorted guitar amp and wonder why some sound gross, some just sound bad, while others are OK? It's because the InterModulation Distortion (IMD) created generates new notes some of which are dissonant with the existing notes. "Power chords" are designed such that the major IMD tones are consonant.
Years ago I got the brilliant idea that this could be avoided by using 6 separate amplifiers, one for each string, fed to 6 separate speakers. Each amp could be cranked to its melting point, but since each amp and speaker was processing only one note at a time, all the distortion would be harmonic. There would be no IMD. Possibly a great idea, but it sounded terrible, even when played clean. Why? I don't exactly know, but I'm guessing that my DIY pickups and the hodge podge collection of amps and speakers I used destroyed the phase relationship between the 6 individual notes. Each individual string sounded OK. Lead runs consisting of a single note at a time sounded OK, but chords sounded off, almost as if the guitar was not properly tuned. I have planned to return to this experiment. I wanted to try identical amps through identical speakers, but never have.....some day.
I suppose some experiments are in order with the digital music synth that I am designing. I have the ability to operate individual VCO's with exact frequency relationships and vary their phase with respect to each other. I would assume that some of the existing soft synths out there today that run in a PC have this ability, bit I never tried it.
Hmm, I'm not bothered by IMD so long as the chord is really in tune (I could rant about equal temperament but won't). On electric violin, if a chord sounds bad, it's always my fault. When I play guitar, if it doesn't sound good at first, bending the strings a bit seems to make it better.
I've heard an example of someone doing the 6 channel guitar thing in a way they were happy with and on the chords I sort of had the feeling of "oh, that's all?".
I wonder exactly how important the IMD itself is to my ears. Would I still feel the same if each channel was amplitude-modulated by the average volume of the channels, so that chords at least distort more than single notes, but not differently?
Well, I also think it sounds really cool when one of the notes in a chord is a bend, specifically because it distorts so harshly at first during the dissonance.
But maybe that's just me.
I recently tried this type of experiment, and there was definitely an audible difference between atan(g*(sin(w1*t)+sin(w2*t))) and atan(g*(sin(w1*t)+sin(w2*t + theta))) where w2 was the 1st or 2nd harmonic or something. But it was hard to say whether it would be a musically useful effect with a real amplified instrument, and whether or not it would sound particularly more interesting than modulating the amplitude of the input signal, which would also produce varying distortion in much easier way.
I only hardcoded the input function to have varying phase, and haven't written generic phase equalizer code, so I can't easily test what it would sound like on a real signal.
I will probably try out the hardware allpass filter sometime and see what it's like.
You may find this of interest!! Or maybe NOT. My post #39
Intermodulation difference frequencies and symmetrical distortion - Page 2
Cheers,
Ian
Intermodulation difference frequencies and symmetrical distortion - Page 2
Cheers,
Ian
From that material:
This is a big part of an amps sound. Ever get an old Fender Champ to growl. Under the right conditions lead guitar cranked into distortion, but not to extremes will tax the wimpy power supply enough to cause some pretty serious 60 Hz, 120 Hz and 180 Hz ripple. The wimpy OPT and smallish speaker doesn't reproduce the 60 Hz, and the 120 Hz is masked by the cranked guitar, but the IMD created by the power supply and guitar notes create a growling lead sound. Many clones use larger values electrolytics in the power supply, and thus don't growl.
Here are the FFT's from two amplifiers that I built about 12 years ago. Both are SE designs, one, a TSE with 45's makes 2 WPC, the other an 845 SE makes 40 WPC. Both amps are DHT's with DC heating. The 845 amp actually uses a duplicate of the 45 amp as a driver, with a 3rd stage added.
The power supply in the 40 WPC amp is taxed to produce 1100 volts at 200 mA using a voltage doubler made with Sovtek 5AR4's. The power supply IMD products are about 10 db larger than the 2 WPC amp. The big amp is awaiting a power supply redesign. The little guy still gets used quite a bit, but the CRC power supply became a CLC bower supply with better caps about 10 years ago.
The 845 SE amp sounded nice, but listener fatigue sets in after an hour or so, as you stated it's worse with complex music.
Attachments
I constructed this circuit to experiment with:
I am not sure exactly what R6 and C4 are doing (filtering out the radio?), but they are in someone else's phaser design and it doesn't make an audible difference whether they are in or not, so I just left them in.
"nc" and "nc" are not actually connected as they are in the screenshot.
Any comments on the circuit design would be appreciated. If it's not doing what it's supposed to be doing, I have no way of knowing, since I don't know what it's supposed to sound like fed through any given source of distortion.
According to my math, for each of the two stages:
H(s) = (R - 1/sC)/(R + 1/sC)
Phase lag: atan2(2x, x^2-1) where x = 2*pi*f*R*C
Phase lag ranges from 0 to pi and the midpoint of pi/2 can occur anywhere from around 160Hz (max rotation) to 34kHz (min rotation) depending on the pot setting, which is to say that probably the interesting things happen when at least one pot is set somewhere in the middle, so that different harmonics of a note can be separated out more.
An experiment done today involved looping a recording of a guitar's high E into the phase-shifter, and then through op-amp clipping (DOD250 with the gain way too high), while messing with the pots. The audible effects were subtle at most. At less offensive gain settings, I heard them as "likely placebo", and with unreasonable gain I heard them as "probably not placebo, but who knows". I guess with 2 bandpass stages, this is pretty much expected. For example, maximum phase difference between fundamental and 1st harmonic of the E string should occur around R=40k, and the difference is only around pi/5 per phase. I want to say there is more aggressive distortion at medium rotation, sharper articulation at lower rotation, and nothing interesting at max rotation. I am most surprised that min rotation sounds different than max rotation, but I guess transients are where I would expect to hear a difference if anywhere.
I am curious what would happen with more stages, which would increase both the maximum possible phase lag and the difference in phase lag between relatively close harmonics.
I am not sure exactly what R6 and C4 are doing (filtering out the radio?), but they are in someone else's phaser design and it doesn't make an audible difference whether they are in or not, so I just left them in.
"nc" and "nc" are not actually connected as they are in the screenshot.
Any comments on the circuit design would be appreciated. If it's not doing what it's supposed to be doing, I have no way of knowing, since I don't know what it's supposed to sound like fed through any given source of distortion.
According to my math, for each of the two stages:
H(s) = (R - 1/sC)/(R + 1/sC)
Phase lag: atan2(2x, x^2-1) where x = 2*pi*f*R*C
Phase lag ranges from 0 to pi and the midpoint of pi/2 can occur anywhere from around 160Hz (max rotation) to 34kHz (min rotation) depending on the pot setting, which is to say that probably the interesting things happen when at least one pot is set somewhere in the middle, so that different harmonics of a note can be separated out more.
An experiment done today involved looping a recording of a guitar's high E into the phase-shifter, and then through op-amp clipping (DOD250 with the gain way too high), while messing with the pots. The audible effects were subtle at most. At less offensive gain settings, I heard them as "likely placebo", and with unreasonable gain I heard them as "probably not placebo, but who knows". I guess with 2 bandpass stages, this is pretty much expected. For example, maximum phase difference between fundamental and 1st harmonic of the E string should occur around R=40k, and the difference is only around pi/5 per phase. I want to say there is more aggressive distortion at medium rotation, sharper articulation at lower rotation, and nothing interesting at max rotation. I am most surprised that min rotation sounds different than max rotation, but I guess transients are where I would expect to hear a difference if anywhere.
I am curious what would happen with more stages, which would increase both the maximum possible phase lag and the difference in phase lag between relatively close harmonics.
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Interesting thread.
I played around with phase shifting (via allpass stages) that is implemented between two clipping stages (each with gain), and there it can make a lot of difference.
The last last stage clips first and doesn't matter much when preceding stages start to clip because a clipped square wave clipped further still is a simple square. But if you have phase distortion between stages, when earlier stages clip the resulting sharp edges may move to a position in the waveform where they are still inside the headroom limits of the last stage and you get a lot more overtones and frequency multiplying effects (doubling, tripling).
I played around with phase shifting (via allpass stages) that is implemented between two clipping stages (each with gain), and there it can make a lot of difference.
The last last stage clips first and doesn't matter much when preceding stages start to clip because a clipped square wave clipped further still is a simple square. But if you have phase distortion between stages, when earlier stages clip the resulting sharp edges may move to a position in the waveform where they are still inside the headroom limits of the last stage and you get a lot more overtones and frequency multiplying effects (doubling, tripling).
I was thinking about this and I plan to try it too! I'm guessing this is a much stronger effect, considering there are more harmonics available to move around after the first clip than in the source material.
I wonder how much of the character of well-known amplifiers is determined by the phase response of its intermediate tone controls.
The character of "well known amps" is dominated by frequency response and gain structure of the cascading clipping stages - note that guitar amplifiers rarely utilise symmetric hard clipping (per KSTR's post). Rather the clipping is asymmetric. The next most important effects are compression (from bias shifts and power rail sag) and, the one new kid on the block, power-supply-ripple driven IMD*.
If this is news, first read Rob Robinettes work; an analysis of a Soldano (hi gain) amp or the Amptone pages (start here)
Certainly, fiddling with phase will create different waveforms (with the same frequency response) which will get modulated differently by all the non-linearities in the "system". It might be interesting to look at the leading edge of a "power chord" but I'd wager it'd be subtle compared to the above.
*Tubelab_com posted something on this recently, but I've lost the URL. There's a What-the? moment caused by this reported here
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