Les Paul mods: "treble bleed"

 Hi folks. Another post about Les Paul circuitry customization: this time I'll show the effect on the tone of the so-called "treble bleed", a mod that many people consider a good enhancement.
The rationale for this mod is that when you turn down the volume, you hear what many consider a loss of treble. Looking at the graph it seems that this description is inaccurate, because as you turn the volume knob, initially the resonant peak get smoothed (and here there is actually some treble loss), but then the frequency response extends a bit, with a resonant peak that is less pronounced but higher in frequency than the one at full volume. So I think the ear just get just "tricked" a bit. Or maybe the real-world components just behave different enough from the ideal ones of these simulations to arise the bad volume behavior.
Whatever the truth, the "cure" is to add a small capacitor between the pickup pin and the middle pin of the volume potentiometer to let some treble "bleed" straight to the output. Many people advocate to add a resistor in series or parallel.
The problem is that the values of the capacitor and the resistor and their configuration are pretty critical. In general the bigger the cap the more dramatic the effect, while the resistor smooths somewhat the effect.

I chose here to show a parallel configuration, with values matching ones from this forum thread. It seems, looking at the plots, to be a nice combo, with a distinct but not overkill effect on the sound.
The graphs shown are logarithmic plots of the frequency response from 20 Hz to 20 kHz between the pickup ideal signal and the output, for the standard wiring and for the one with the treble bleed, and for different positions of the volume potentiometer (I set ten values of a logarithmic sweep from 1 Ohm to 500 kOhm). The first plot is for the tone knob fully on bright (on "10"), and the second one is for the tone knob fully on dark (on "0").

 

You can clearly see the effect: with the tone on bright and partial volume, the resonant peak is lower in frequency (and, with this cap value, in a position close to the one at full volume) but more pronounced, and, with both of the tone positions, the roll-off of the high frequencies is less steep, as expected, giving a brighter tone.

Note, however, that there's no effect at full volume, where the steeper roll-off is retained; this implies a more or less pronounced timbre change as you turn the volume knob.

The effect of the volume knob is also a bit slower near the full volume and faster near the lower end.

For a more in-depth analysis, you can check this excellent thread.

Of course, this is just a circuit simulation with ideal components; if you want to know how this translates in reality just open your axe, check some different caps and resistors, and - as always - let your ears be the judge!

PS:

The software I used for the simulation is Qucs on Linux, but on the website you can find downloads for Windows and Mac OS X as well.
There's no potentiometer component in Qucs, so I just used two resistors with the values bound together by the equation Rvb=500k-Rva.
For the pickup I chose values that, combining various sources, seem to be good representatives of a standard Gibson PAF pickup.