What's the highest corner frequency....?

[Transmogrifox]

^ TL;DR

I'm reasonably sure Mark is asking about 60Hz hum picked up by single coils.

The point being made is whether coming in through directly connected PSU's, or through the air into the coil, this isn't likely to be a pure 60 Hz sine wave.  It's most likely to be jagged pulses that repeat on 16ms or 8ms intervals.  Sounds low frequency, but filtering off the low frequency (fundamental) takes away only a small portion of what you hear.

I'm pretty sure Mark lit the fuse and now he's just sitting back watching the show with an amused grin on his face

Popcorn anybody?

[Rob Strand]

FYI: (many examples over the past 40 years or so.)

https://www.researchgate.net/publication/235388107_Power_line_interference_cancellation_in_in-vivo_neural_recording

For guitars it's much easier to get out the copper tape.  For biomed stuff you *have to* connect to the patient's body.

[Rob Strand]

I'm pretty sure Mark lit the fuse and now he's just sitting back watching the show with an amused grin on his face

Popcorn anybody?

[Mark Hammer]

Definitely not sitting back like Bugs.  I got busy the rest of the day yesterday and couldn't check back to see any responses until just now.  The discussion has been thoughtful and thought-provoking, so thanks to all.

Yes, my query was in regard to hum in single-coil pickups.  Some folks find their personal cure lies in any of the varieties of hum-cancelling pickups that approximate SC tone; maybe supplemented by forms of shielding.  Others find the tone of their SC pickup something they wish to hang onto, so they seek other sorts of cures.

Like others here, a lttle bit of hum is not always a deal-breaker.  The problem lies in the extent to which a great many players take that liveable hum and plug it into a pedal, or even succession of pedals, that amplify that hum manyfold.  And THAT's where noise-control products can start to become objectionable for many, perverting the attack and decay characteristics of the signal as the threshold gets turned up to keep out the amplified hum.

I like the idea of a steep notch filter.  The question this prompts, however, is whether what it takes to provide a serviceable degree of attenuation introduces any unwanted "humps" around the notch frequency.  The other question it prompts is whether going at 60hz in surgical fashion still leaves us with problematic content at multiples of 60hz.

[Rob Strand]

I like the idea of a steep notch filter.  The question this prompts, however, is whether what it takes to provide a serviceable degree of attenuation introduces any unwanted "humps" around the notch frequency.

If the bandwidth of the notch too wide (ie. the Q too low) then you will get a wide "suck out" region either side of the notch which is unwanted.   So a high Q notch with a pot to tweak the frequency is the best bet.   You can design high-order notch filters which produce humps each side of the notch like you see with low-pass and high-pass filters.  These Notch filters are fraught with tolerance problems.

The other question it prompts is whether going at 60hz in surgical fashion still leaves us with problematic content at multiples of 60hz.

The annoyance of the harmonics, the buzz,  will still be present I'm sure. I have my doubts the notch will be good enough for a single coil pickup.  It might stop the massive hum you get when you place the guitar close to the amp, or near a plug-pack,  but that's about it.

If you think about guitar speakers and the general tendency to cut bass on high-gain pedals  (eg. the 47nF cap on the tube screamer)  there's already some low frequency cut going on and it's not good enough.

[Edit:  The notch with do *something*  but it's probably not enough.   It seems to me that filtering at 150Hz/180Hz is far more noticeable.]

[GGBB]

The point being made is whether coming in through directly connected PSU's, or through the air into the coil, this isn't likely to be a pure 60 Hz sine wave.

Right, but no one has said otherwise, and you're the only one who has used the word "pure."

[Transmogrifox]

So a high Q notch with a pot to tweak the frequency is the best bet. 

Maybe.  You still have the transient response of the filter to deal with.  There's a chance a high-Q notch will muddle up palm mutes or other forms of percussive playing.  This might be the optimization: 
>Too high Q, long transient response, audible. 
> Too low Q, too much suck out of band.

The other question it prompts is whether going at 60hz in surgical fashion still leaves us with problematic content at multiples of 60hz.

That is the point I was trying to make however it may have come off.  I think the answer is what Rob has been saying.

Right, but no one has said otherwise, and you're the only one who has used the word "pure."

Yes, with emphasis on *not* pure.  Which means everything not 60 Hz is still audible after you notch out 60 Hz, whether it's coming from the pickup or from somewhere else.

[Rob Strand]

Maybe.  You still have the transient response of the filter to deal with.  There's a chance a high-Q notch will muddle up palm mutes or other forms of percussive playing.  This might be the optimization:
>Too high Q, long transient response, audible.
> Too low Q, too much suck out of band

Yes it crossed my mind you wouldn't want to build a drum emulator.  I suspect it would end up with a Q between 5 and 10 (roughly 1/3 to 1/6 octave equalizer). If you consider mains frequency wander and temperature effects (on the caps) you probably wouldn't want to go much higher than Q=10.

[GGBB]

Yes, with emphasis on *not* pure.  Which means everything not 60 Hz is still audible after you notch out 60 Hz, whether it's coming from the pickup or from somewhere else.

Naturally - that's how notch filters work.

[Transmogrifox]

Yes, with emphasis on *not* pure.  Which means everything not 60 Hz is still audible after you notch out 60 Hz, whether it's coming from the pickup or from somewhere else.

Naturally - that's how notch filters work.

Sorry to detract from the thread.  I think we're both saying the same thing and we don't get each other's language.

If we're saying the same thing then we all agree:
1) The original intent of the thread was a question about whether a high-pass filter can be designed to sufficiently reduce 60 Hz hum and not significantly affect the guitar tone.
2)  The overwhelming response is to the question expressed by reading between the lines.  Yes you can probably make a filter to eliminate a 60Hz sine wave and still keep it out of the way of your guitar tone, but even so this probably doesn't solve the problem implied by the original question.
3)  It doesn't matter where it comes from, whether currents in surrounding wiring couples into the guitar pickups or whether it's coming in to/from the amp, rack, lighting, or stompboxes, etc, or all of the above at the same time in different parts of the circuit.  It all has harmonic components that remain even if 60 Hz is removed, and we still call it "60 Hz hum" and the more discerning call it something like "buzz".

Something I may be unwittingly assuming to be obvious to everybody is the physics behind power line noise getting into circuits. A lot of people who frequent this forum pick up (pun intended) a lot of this stuff and show evidence of a pretty good foundation in physics and engineering (Gordon included), so it's natural to assume the general audience is on the same page regarding things left unstated. Let that be a compliment to all of you whether it's true or not)

For those of whom this assumption is wrong, here's my attempt at outlining it.  Note, this still requires a certain level of background knowledge, but there are enough buzz words (pun intended again) to google these concepts and maybe explore a bit. 

1) Direct conduction:  The circuit generating the noise is in some way connected directly to your amplifier or stompbox (PSU rectifier, wall-wart, "suicide" capacitor, etc).  In rare cases it may be a somewhat conductive floor connected to your somewhat conductive body, connected to your very conductive guitar strings which are capacitive plates coupled to your pickup coils.

2)  Electric fields:  The tendency everything attached to your guitar has for acting like the opposite plate of a capacitor.  The other terminal of this capacitor is found in the venue wiring, lights, racks, anything not grounded with some coupling to something energized. Shielding takes care of this part of the problem.

3) Magnetic fields:  A guitar pickup is an electric generator, working from a change in a magnetic field. A good primer on the physics of this: http://zerocapcable.com/?page_id=219

Further, a current in a wire generates a magnetic field https://web.pa.msu.edu/courses/1997spring/PHY232/lectures/ampereslaw/wire.html

Therefore, a wire carrying current at power line frequency generates a proportional magnetic field.  This magnetic field adds to the magnetic field within the coils of your pickup and is injected using the same principle in physics that makes your pickups work, so you can't exactly shield this with foil and good grounding.  Magnetic fields blow through grounded conductive materials as if they are air unless they are a magnetic material (like iron).

Your guitar pickup combined with surrounding powerlines and power wiring form a loosely-coupled transformer.  The primary is connected to noise you don't want, and the secondary is connected to the place you don't want the noise.

In comes the humbucking pickup and noise-cancelling wiring configurations with multiple single coil pickups.  This essentially adds another primary winding that is wound in the opposite polarity as the original, so the current in both primary windings sums to something very small in the secondary.
https://en.wikipedia.org/wiki/Humbucker#How_humbuckers_work

If humbuckers or other hum-cancelling technology is objectionable, magnetic fields can be shielded by ferrous material. You need something that will generate eddy currents when exposed to a magnetic field, then you need to ground this thing so if those eddy currents develop a voltage across the ferrous material, it will be shielded so it cannot subsequently couple capacitively (electric fields) to your guitar pickup.

The complete shield would be an iron plate covering the back of your guitar, and an iron plate in front of your guitar, spaced far enough to give you room to strum the strings and work the knobs.  The assumption is magnetic fields coming in between the plates perpendicular to the coils is not correctly polarized to generate much noise. Both iron plates are lined inside with foil (electrostatic shield), and both sides are grounded. 
> Magnetic fields generate eddy currents in the iron plate and energy is dissipated as heat.
> Electric fields are shorted to ground by foil lining.
> Any further electric fields generated by potential across the iron (ferrous) plate due to eddy currents gets shorted to the foil, to ground.
> Other magnetic materials could be substituted for iron although iron is generally cheapest and most common.
* It is obvious this type of shielding is impractical unless you play in a really weird band where people expect you to be wearing strange stuff and have strange things on your guitar.

This is all the background to my statement about playing in a shielded booth lined with ferrite plates.  The metal shield attenuates electric fields and the ferrite plates attenuate magnetic fields.  This arrangement is the composition of an anechoic chamber used for measuring RF emissions for the reasons I have stated.

*************************************************************************
So...
Whether injected by conduction or electric fields or magnetic fields it is likely to couple strong in harmonics.  So the sum of it all is that even if you perfectly notch 60 Hz, you don't get rid of power line noise.

The question of whether notching 60 Hz is effective at removing the objectionable hum all depends on how much of the total induced noise is 60 Hz fundamental and how much is "buzz".

Now finally the crux of it all is that all means of coupling are high-pass in nature.  The higher harmonics are going to couple into the wrong places at greater magnitude than low frequency stuff.  If you have harmonics, that's the part that gets coupled the strongest.

[Rob Strand]

Now finally the crux of it all is that all means of coupling are high-pass in nature.  The higher harmonics are going to couple into the wrong places at greater magnitude than low frequency stuff.  If you have harmonics, that's the part that gets coupled the strongest.

That's about it.

FYI, I did the experiment.   Took a file with junk in it and did the filtering using various equalizers/parametrics/notches available in audio software and vst plugins.   (BTW a considerable percentage of these softwares produce terrible notches, nothing like the analog model that conjures in your mind when you set the parameters.  Check the frequencies of the hum and harmonics before filtering.)

Removing 50/60Hz is audible but nowhere near as effective as removing 150/180Hz.    In my mind removing 150/180Hz takes much of the perceived hum out of the signal.  Even if you take out 50/60Hz and 150/180Hz, as expected, the annoying buzz is still present.   Moreover you start to detect the whine/whistle of the harmonics between say 200 and 800Hz.

I'd say if you wanted to remove harmonics without affecting the signal (much) you need a harmonic canceller like that paper I posted above - it has source code as well BTW.    There's apparently commercial products around that do this for audio now.