sidebands

[uneumann]

I'm puzzled by something and maybe someone can help straighten me out on this. A plucked string produces a signal containing various freq's that are mostly harmonically related. I get that. There is an envelope however. It is the amplitude (shape) of the total signal energy over time (attack, decay), and as recent posts show, the envelope may differ for each component of the signal.

So my question is in several parts but it starts with a crucial question of how to model the string signal... Is it reasonable to model the string signal as an envelope function modulating the fundamental and harmonic signals produced by a string? Synth's actually do this, but perhaps actual strings are different in some way I'm not grasping. String pluck attacks can be quite fast, meaning high freq's are involved, while decays are often slow. That means the envelope function is broadband in nature.
If this model is reasonable, doesn't the envelope modulation produce sidebands? Theory says so, (I think) or am I missing something?

If there are sidebands, the spectrum of the overall signal should include them as sum and difference components of the fundamental and harmonics. We (me included) tend to describe a guitar signal as only a fundamental with higher harmonics. Doesn't that ignore the sideband components below the fundamental? This never seems to be considered or mentioned in terms of how an amp stage's response affects a note.

If true, there seem to be many implications of this that impact EQ and freq response in an amp. Mainly, it means that wide-band response (above and below the fundamental) is needed to reproduce any given plucked string's full signal.

Since the sidebands are envelope related, aren't they then related to the dynamics of pick sharpness and string muting? Does this seem plausible?

I'll stop here since I can see many implications that relate to amp freq response - especially at the low end. But before I get carried away, I hope to confirm or dispel my reasoning. Maybe this is all true and fine in theory, but the effects are barely audible. I don't know. Maybe I'm just the last person to get the memo and people already know about this. Has anyone seen anything written about this at all? In my lit searches, the only place I've seen mention of the spectral impacts of an envelope is in mechanical vibration analysis, and I really can't claim to understand exactly what they're doing there.

Lastly, and maybe most important - is there a way to measure sidebands to prove or disprove sideband existence and assess their significance in terms of perceived tone?

[Malcolm Irving]

Once at a band rehearsal, I was the only one to turn up on time (not all that unusual). Just messing about, I took the DI output from a Marshall and plugged it into the sub-woofer channel of a big PA. The channel had a low-pass filter which cut off somewhere around 100 Hz, so I wasn’t expecting much (if anything) to come out of the sub. I was amazed how much there was. It was all to do with the pick attack and gave out various interesting ‘thunks’ and ‘clunks’. With palm muting, the sound was amazingly.
I don’t think this helps much with the theoretical question, but I thought I would mention the experience.

[darkfenriz]

I'm puzzled by something and maybe someone can help straighten me out on this. A plucked string produces a signal containing various freq's that are mostly harmonically related. I get that. There is an envelope however. It is the amplitude (shape) of the total signal energy over time (attack, decay), and as recent posts show, the envelope may differ for each component of the signal.

So my question is in several parts but it starts with a crucial question of how to model the string signal... Is it reasonable to model the string signal as an envelope function modulating the fundamental and harmonic signals produced by a string? Synth's actually do this, but perhaps actual strings are different in some way I'm not grasping. String pluck attacks can be quite fast, meaning high freq's are involved, while decays are often slow. That means the envelope function is broadband in nature.
If this model is reasonable, doesn't the envelope modulation produce sidebands? Theory says so, (I think) or am I missing something?

If there are sidebands, the spectrum of the overall signal should include them as sum and difference components of the fundamental and harmonics. We (me included) tend to describe a guitar signal as only a fundamental with higher harmonics. Doesn't that ignore the sideband components below the fundamental? This never seems to be considered or mentioned in terms of how an amp stage's response affects a note.

If true, there seem to be many implications of this that impact EQ and freq response in an amp. Mainly, it means that wide-band response (above and below the fundamental) is needed to reproduce any given plucked string's full signal.

Since the sidebands are envelope related, aren't they then related to the dynamics of pick sharpness and string muting? Does this seem plausible?

I'll stop here since I can see many implications that relate to amp freq response - especially at the low end. But before I get carried away, I hope to confirm or dispel my reasoning. Maybe this is all true and fine in theory, but the effects are barely audible. I don't know. Maybe I'm just the last person to get the memo and people already know about this. Has anyone seen anything written about this at all? In my lit searches, the only place I've seen mention of the spectral impacts of an envelope is in mechanical vibration analysis, and I really can't claim to understand exactly what they're doing there.

Lastly, and maybe most important - is there a way to measure sidebands to prove or disprove sideband existence and assess their significance in terms of perceived tone?

Your theory is intact, but that all seems like secondary issues.
Time constants of the envelope are in order of several seconds for the fundamental and low harmonics, so the frequency 'side-banding' effect due to this is in the milliHertz area. Maybe a couple of hertz for very high harmonics.

This is buried by a couple of facts:
- guitar signal overtones are not exactly perfect harmonics, due to physics of the plucked string vibrating. That's unlike perfect harmonics in reeds or brass
- plucked string starts a little sharp due to increased string tension but decays a bit flat. It is obvious the moment you first used a good chromatic tuner. That broadens the spectrum of the fundamental and overtones
- there's more sidebanding involved in amplification, due to dynamically changing bias, sag, 50/60Hz sidebanding (ghost-notes) etc.

You may use any sort of analysis tools including fft, windowed time-spectrum analyses, kryptonite-based wavelets analysis, but I suspect it will be buried in the above.

However good point about the flaws of the typical and ubiquitous 'steady-state sine analysis' of guitar signal, which 1) isn't steady state and 2) isn't sine

Edit, more thoughts:
- there's a lot of spectrum content below 82Hz if you play two non-overtone notes (not fifth, not forth, not octave) through distortion
- palm muted notes are more inharmonic than non-muted. these further-from-perfect-overtones don't fit the handy theory...

[Malcolm Irving]

...
Time constants of the envelope are in order of several seconds for the fundamental and low harmonics, so the frequency 'side-banding' effect due to this is in the milliHertz area. Maybe a couple of hertz for very high harmonics.
...

That's the 'decay' part of the envelope, but the 'attack' part must be just a few milliseconds?

[Enzo]

reproduce any given plucked string's full signal.

I think you are overlooking one fundamental fact, guitar amps are not made to reproduce sound, they are made as basic producers of sound. In other words the amp is part of the instrument and adds its own character. If you want reproduction, then plug into a PA system. It isn't the job of a guitar amp to reproduce every thump and snort of the picking.

Individuals may want more or less of the outside waveforms, but that is a matter of taste.

[uneumann]

Thanks all - you've calmed and reassured me. It's good to know that I'm not completely off on the theory.
But the main takeaway is - it doesn't get talked about (or written about) because it doesn't make any perceivable difference. I can accept that. I've spent some time this afternoon trying to measure it with a simple FFT package. I can't measure it, but I'm also sure my experiment and measurement could be much improved with time and better tools - maybe some of those kryptonite-based wavelets will help... :-)

Thanks for your time

[Mike Sulzer]

To illustrate what darkfenriz wrote, here is the spectrum of a single harmonic (quite shifted from its nominal location). It is about 2.5 Hz wide at the half power points.

[uneumann]

To illustrate what darkfenriz wrote, here is the spectrum of a single harmonic (quite shifted from its nominal location). It is about 2.5 Hz wide at the half power points.
[ATTACH=CONFIG]44258[/ATTACH]

Thanks - but for a baseline comparison ... can you also show the spectrum of a pure sine wave (no envelope) at that frequency using the same analysis/display tools?

[Mike Sulzer]

Thanks - but for a baseline comparison ... can you also show the spectrum of a pure sine wave (no envelope) at that frequency using the same analysis/display tools?

Easier to show the fundamental from the same measurement. About .19 Hz wide (and a bit out of tune.

[uneumann]

Easier to show the fundamental from the same measurement. About .19 Hz wide (and a bit out of tune.

[ATTACH=CONFIG]44259[/ATTACH]

Mike, your measurement tools are far better than mine.
It appears that there is measurable widening of the spectrum. More in the high harmonic, yet the fundamental shows very little. Maybe the variation has to do with the envelope shape. Maybe its other factors - like string stretch. Regardless, neither effect is likely to be audible. Thanks for the data.