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Single coil pickup noise at 7546 Hz

I've done a search for this issue but haven't come across it. Please point me in the right direction if this has been answered elsewhere.

I have a MIM Jazz bass that I love the sound of and it's served me well for 7 years but I'm tired of putting up with one particular flaw.

When soloing the front or rear pup and have the tone set above 1/3 there is a pronounced 6-18dB spike in noise precisely and repeatedly at 7546 Hz, about 50 Hz wide with steep shoulders as measured on my oscilloscope.

It occurs in multiple venues and occurs both direct into a DI or into an amp. It happens with different instrument cables. It happens with or without a pedal chain. I've even tried forgoing running through a tuner and using a clip-on.

The noise is nullable if I turn the bass in an inconvenient angle (i.e. if I pivot around the noise will cancel in certain orientations), and it's far worse when in proximity (within 10 feet) to a powered speaker array, but proximity to halogen spots will also set it off.

Sometimes the person mixing can notch it out if there's time, but when I'm playing through an amp I don't have that notch control so I just roll off the tone or balance the pickups.

I really like the sound of my Jazz bass (it's the sole keeper out of a churn of 12 other basses) so I don't want to change the pickups or pots. I have shielded both the control and pickup cavities and bottom of the pickguard, everything is electrically bonded, both together and back to the ground and checked for zero resistance across the shielding to ground with a meter.

It has very little noise at any other frequency, as long as my hand is on the strings, but FOH guys complain about the high pitched noise when the music goes to a low dynamic.

I haven't read other posts about this high-frequency type of noise from single coil pups except in a recording chain. It happens when either pickup is solo'd, but off course cancels out when they are set to equal volumes.

Any ideas? Is there a magic instrument cable I could try? I could try a parametric EQ but I don't want to change the tone of this bass, just get rid of the noise at that particular frequency.
 
I don't think there's any answer you're going to like. It sounds like you've troubleshot it down to the pickups, now it's a matter of what you're going to dislike the least -- living with it, putting in a parametric EQ, or changing pickups.

If it was me, I'd try swapping out the pickups. I'd do that rather than a parametric EQ, because I don't think I could dial in the parameter to a precise 50Hz band, and whatever was dialed in might have to be turned down all the way to completely get rid of the noise. And I wouldn't want to be in the position of having to decide how much noise I could live with or how much tone I'm willing to sacrifice.

I have dual-inline coil hum-canceling pickups (Fender Super 55s if you're interested) exactly because I never want to have to deal with anything like this.
 
The issue with a low pass filters is generally that they are killing everything above the filter point. I really just want to squash a very narrow range...

However, after I posted the OM, it got me stirred up to try some old tests again.

I tried instrument cables of different lengths and it turned out that my 10 foot instrument cables (that I generally use) were really aggravating the condition whereas a 15 foot cable reduces the noise tremendously. A shorter cable reduced it as well.

I believe there's an 7540Hz standing wave being generated in my pickups that's getting reflected by the high impedance at the DI or amp input at that particular length of instrument cable. Two different brands of 10 foot cables exhibited the same problem so I'm putting it down to a standing wave reflection, one was worse than the other but it was just slightly longer. I could probably cut the cable down by a foot, re-solder the plug and it would work fine.
 
If you want to remove single coil noise you are going to lose some of that top end because you have to impact your tone. You could get one of those Audere noiseless pre-amps, if you don't mind adding an active pre-amp to the bass, or you can drop in humbuckers (or a dummy coil.) Shielding address RF interference (noise that stops when you touch metal/strings/bridge), not 60hz hum (single coil noise). While they are the same issue in theory, they are treated as two different issues with two different solutions in practice.

Single coils are susceptible to noise. That does not mean you will get noise everywhere. If you can get a nice, clean environment, you will not get any real single coil noise. I am fortunate to live in a new-ish area away from any major communications towers so I rarely get single coil noise. That being said, all of my basses have humbuckers because I do not like the added noise. I also play live more than record so it is important to not buzz under stage lights.
 
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It sounds like the pickup coil itself is the main antenna here. It's catching a standard electrical system frequency wave from the air. Some combination of the coil's geometry, turns, resistance plus the circuit's resistance is ending up resonating at that particular frequency. Changing the length of the cord is affecting the circuit's capacitance, which, as you are seeing, is softening that resonance somewhat when you get it tuned right.

I would try some experiments with adding shielding around the pickup coil itself. For example, cut a strip of copper shielding tape and wrap it around the outside of the pickup, up to the top surface, but not on the top surface. Run a small lead wire over across the outside of the body and, while you are hearing the hum, touch it to the ground side of the jack nut. See if that quiets the hum down. Shielding around the outside of the coil is likely to have the least effect on the overall sound. If that works, then you can look at doing a neater permanent shield installation.
 
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I removed length from the 10-foot instrument cable creating a 9ft cable. It made a big difference in the 7540Hz noise spike. It's now as quiet as the 15ft cable. I hadn't previously considered the likelihood of a standing wave in the cable but it makes sense now. 10ft is just an unlucky length of cable with that particular bass.

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