On a lot of threads, I end up trying to explain to people how passive tone controls on basses work (spoiler - they don't work like you think they do). Though they are simple circuits, the reactive nature of the pickups feeding them results in behavior you wouldn't really expect - they don't just "turn down the treble". Anyway, having designed circuits and other pro audio stuff for a living, Spice simulations (they way we predict circuit behavior before building prototypes) are in my wheelhouse. I won't go into tall the details of this (you need to characterize the pickups, which is a non- trivial task, but still not rocket science). Anyway, the point is, we'll be looking at the electrical behavior of passive tone circuits, which are part of the sound of a bass (pickup location is move complex, but also something you can simulate well - that's for another day).
So, We're starting with a bass that has 2 single coil (jazz) pickups - the ones used here are Nordstrands. The output here is what ends up at the amplifier input after loading by the volume control, the tone circuit, a cable (550 pF in this case - a 15 foot DiMarzio cable), and using 1 MegOhm for the amp's input impedance. The tone circuit is a 250 K pot, and a .047uF capacitor. Whew!
OK, so we see a flat curve in the bass end and low mids (which is true for all magnetic pickups - there is no rolloff or scoop in your pickup (a topic for another day). In the upper mids, there is a peak - the pickups's inductance resonating with the cable and interwinding capacitances. So far, simple. Now, a question - what effect does the value of your tone cap have on your tone at max tone? OK, here's what you get with 3 different values of tone capacitors - the .047 we started with, a .022, and a .10 uF:
Only see one curve? That's because the frequency responses using those 3 different tone caps are right on top of each other at max tone. If you buy a different value tone capacitor (or a "better" one), and hear a difference with your tone control dimed, well, that's confirmation bias.
OK, so let's see what happens when you turn down the tone control, starting with the .047 uF in all cases:
What you' re seeing is the response at "quarters" - full tone, 3/4 tone, 1/2 tone, 1/4 tone, and minimum tone. Note that at 3/4 and 1/2 tone, what has happened is that the upper mid peak has been damped - the treble part of the curve (up at 10kHz) hasn't really moved much, even at half tone. This isn't what most people think is happening - what is actually happening is definitely counterintuitive.
OK, so let's see if different capacitor values affect tone when things are turned down. First off, 3/4 tone:
OK, still right on top of each other - no difference in the sound when you change the capacitor up or down by a factor of 2. OK, what about at half tone?:
OK, so there's a tiny bit of difference, but it isn't at high frequencies - it's much lower. Hmm
On to 1/4 tone:
There is a difference - here is where the capacitor value you use starts to actually make a difference. But.. even at "1/4 tone" the difference is in the mids - the capacitor value you use does not affect what's happening at the upper end at all - where the treble is is dependent on the resistance in the circuit at this point.
OK, on to min tone (aka "tone off"):
OK, finally - here and only here, with the tone control off, does it really all line up like you'd expect - the bigger capacitor value finally has less treble! There is a sort of abrupt change in character of things as you approach min tone, which you can hear if you pay attention.
One other note - what people think a tone control does is turn down the treble first, then a bit of the slight lower treble, etc. To get that effect, what you can do is add loading capacitance. here's a curve with added loading capacitance (1500 pF in this case), which shifts the resonant peak lower in frequency, though the height is still about the same:
If you add capacitance and turn down the tone control a bit you get the red curve - what people think is happening when they turn down their tone control is achievable, but you don't do it by just turning down your tone control - it's a bit more complicated.
So, We're starting with a bass that has 2 single coil (jazz) pickups - the ones used here are Nordstrands. The output here is what ends up at the amplifier input after loading by the volume control, the tone circuit, a cable (550 pF in this case - a 15 foot DiMarzio cable), and using 1 MegOhm for the amp's input impedance. The tone circuit is a 250 K pot, and a .047uF capacitor. Whew!
OK, so we see a flat curve in the bass end and low mids (which is true for all magnetic pickups - there is no rolloff or scoop in your pickup (a topic for another day). In the upper mids, there is a peak - the pickups's inductance resonating with the cable and interwinding capacitances. So far, simple. Now, a question - what effect does the value of your tone cap have on your tone at max tone? OK, here's what you get with 3 different values of tone capacitors - the .047 we started with, a .022, and a .10 uF:
Only see one curve? That's because the frequency responses using those 3 different tone caps are right on top of each other at max tone. If you buy a different value tone capacitor (or a "better" one), and hear a difference with your tone control dimed, well, that's confirmation bias.
OK, so let's see what happens when you turn down the tone control, starting with the .047 uF in all cases:
What you' re seeing is the response at "quarters" - full tone, 3/4 tone, 1/2 tone, 1/4 tone, and minimum tone. Note that at 3/4 and 1/2 tone, what has happened is that the upper mid peak has been damped - the treble part of the curve (up at 10kHz) hasn't really moved much, even at half tone. This isn't what most people think is happening - what is actually happening is definitely counterintuitive.
OK, so let's see if different capacitor values affect tone when things are turned down. First off, 3/4 tone:
OK, still right on top of each other - no difference in the sound when you change the capacitor up or down by a factor of 2. OK, what about at half tone?:
OK, so there's a tiny bit of difference, but it isn't at high frequencies - it's much lower. Hmm
On to 1/4 tone:
There is a difference - here is where the capacitor value you use starts to actually make a difference. But.. even at "1/4 tone" the difference is in the mids - the capacitor value you use does not affect what's happening at the upper end at all - where the treble is is dependent on the resistance in the circuit at this point.
OK, on to min tone (aka "tone off"):
OK, finally - here and only here, with the tone control off, does it really all line up like you'd expect - the bigger capacitor value finally has less treble! There is a sort of abrupt change in character of things as you approach min tone, which you can hear if you pay attention.
One other note - what people think a tone control does is turn down the treble first, then a bit of the slight lower treble, etc. To get that effect, what you can do is add loading capacitance. here's a curve with added loading capacitance (1500 pF in this case), which shifts the resonant peak lower in frequency, though the height is still about the same:
If you add capacitance and turn down the tone control a bit you get the red curve - what people think is happening when they turn down their tone control is achievable, but you don't do it by just turning down your tone control - it's a bit more complicated.
