Docs
There is this document about fixing an Epiphone Wildkat with better wiring.

Well, as usual this is too emotional, the author for some reason insists different capacitor types are the same (wonder why they exist then?). They aren't. Cleanest/most transparent types are: polypropylene, silver mica, teflon. Barmiest are: polyester, low-quality electrolytic. Good quality tantalium is somewhere in-between polypropylene and good electrolytic, ancient tantalium might be awful because tantalium capacitors are electrolytic too (common electrolytics are based on aluminium). So they suffer from electrolytic rot. Ceramic capacitors are microphonic, so they don't take vibration too well and therefore aren't suitable for guitars.

The one bit which you must understand about all those types who insist that there is "no difference between different types of wood, capacitors, wire..." and so on is: they never play tuned down and overdriven. All they do is plink away on an electric guitar tuned to E as if it were acoustic. So they cannot notice the much subtler difference there is in "acoustic" tuning. Overdrive/distortion and tunings starting with D and lower are like magnifying glass: they bring out everything. Nut material, capacitor character, wire reactivity, neck joint, wood and metal resonance and character. Most people play electric guitars the way they are meant to: overdriven/distorted. So they do notice the differences.

Capacitance itself slows current down and changes its shape.


Izotope Trash 2, "Capacious" distortion filter.
Exaggerated compared with real-life effect,
but it sure shows what it sounds like.

Unlike direct current flow, current is depressed and slightly squashed, with a spring-like effect. Because of this it is not a good idea to insert capacitors anywhere on pickup input. Pickups ought to get the cleanest, fastest, most powerful current possible.

Another effect of capacitors is buffering: they accumulate current and later release it, so there is no underflow of current. This is used in a lot of electronic device schemes. For guitar purposes though it is best to insure said buffer is on output, not input and use a low-capacitance, low-impedance guitar->amp cable.

Polypropylene works for a guitar with a lot of body resonance. It might be too tinny for a very dampened guitar with a lot of string tone (neck-through alder with a composite neck, say). Polypropylene is clean and quick, easy to play. It's almost like it's not there. Polypropylene can transmit string shimmer, and it can give out a fancy "o-o-oi" string echo on powerful plucks when overdriven.

Polypropylene capacitor with an alnico pickup and high-cap wiring:


- this is noticeably faster than polyester. Easier to play, too.


Tantalium (small yellow) and polypropylene (orange cylinder) tone capacitors.
The polypropylene capacitor is 600V, hence its size.
Black/gray wire is silver-plated twisted pair. White is also SPC.
Red and blue are pickup cables.

Polyester, although its name sounds similar, can be anything from awful to tolerable. The worse cheap examples are tubby, slow, and compressing midrange. If your goal is a muddy ugly overdriven sound, it might work. Otherwise it's pointless. The more expensive polyester tends to be more like better electrolytics, though still a tad too tubby.

Polyester capacitor with an alnico pickup and high-cap wiring:


- this is really a very good-sounding example, in reality the guitar is duller.

Aluminium electrolytics can be anything from plain awful for the very cheap Chinese-made mass junk to near-polypropylene quality. The cheap junk is like switching a bad lowpass filter in - no treble, everything's boomy and muddy. The best electrolytics are mostly transparent, though still a bit laggy compared to polypropylene.

High-quality tantalium caps are a good choice for any guitar that'll do a lot of overdrive/distortion (that's just about any electric). Unlike aluminium electrolytics, tantalium electrolytics are more reactive and have more of a character, adding a sort of midrangey beefy sparkle when overdriven.

Tantalium/polypropylene tone capacitors with alnico and ceramic/cryogenic pickup and SPC wiring:


- Notice the punchy sparkle and speed.

Rewiring

With regards to wire, the best kind of wire is really silver-plated copper or pure silver. But there is an effect to watch out for: capacitive wire adds body! The reason Epiphone puts high-capacitive wire in their guitars is this: electric guitars do not have a resonator hole, so they don't have a natural delayed body like acoustic guitars. Capacitance though slows dynamics down and adds a subtle delay effect. A guitar with this subtly-delayed sound is easier to play, to an extent (most living beings perceive sound as a series of echoes - delays added together; what sounds like an instrument's body to us really is a lot of wood/string echoes combined). Now of course this'll make it play more "industrial", thick, and less natural, with a blurrier, less metallic tone. But then that is what most people expect out of an electric guitar.

So recabling with low-capacitance, high-conductive wire will actually kill some of this delayed body. The guitar will play more like an acoustic. More precisely, it'll play more like strings and less like wood, as laggy capacitance highlights wood resonance by slowing the overall dynamic response down.

A good idea is to avoid placing high-cap wire anywhere on pickup input. Output, maybe. Low-capacitance, fast wire combined with an output capacitor is easier to play anyway.

Smoothie Capacitor Placement

Silver-plated copper or silver recable will make the guitar more realistic ("stringey") and easier to play, but it'll also make it less powerful, to an extent. Less thick. This might make sense for recording, but sometimes it can be a shock as the result will be almost like a different guitar. If it sounds too sharp and lacking body overdriven, swapping the tone capacitor(s) for a darker value might help. Adding another small capacitor at the output might also help. 0.33 microfarad tantalium at the positive terminal/cable works to somewhat increase the tantalium beefiness effect. A value of up to 1 microfarad ought to be fine; 10 microfarad is already too thick/slow and harder to play. The trick is, it has to be at the positive terminal, not between the socket's terminal or negative terminal. This is because negative terminal is really positive (backward notation stupidity there). So what you get is, the "negative" path is really supplying pickups with current. Placing a capacitor on the current path to the pickups is daft, as it'll deform current. Good distortion requires a sparkling-clean signal to begin with. Smoothing output is smarter. So the capacitor goes long leg on the positive wire, short leg on the positive (more precisely, "positive") socket terminal. And, of course, soldering a capacitor in-between socket legs only makes sense if it's non-polarised (not electrolytic or electrolytic double-back non-polarised). But that is a daft concept anyway, as it'd mean distortion both ways.

If anyone doubts this, he can verify the theory by soldering either one of three ways. The sharpest/punchiest overdriven sound is when the capacitor is soldered as advised above.

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