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Understanding Push-Pull Potentiometers

It would be better and more reliable to just use a double pot with 2 shafts and stack knobs, so you have a knob for each function. For sure with a switchable function you will use the wrong position half the time.

Edit - I read your original question again. NO you cannot use a pot with switch for 2 simultaneous functions as there is only one pot element. You can choose between 2 different functions or use the switch for something else. I do this to put a MUTE switch on some basses.

I am sure that there are some special pots made for car stereos, etc. that do what you suggest - pull for one function and push for the other, and the shaft mechanically switches between 2 different pot sections, but these are usually custom made and not available to us.
 
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I'm learning electronics, and want to understand exactly how a push-pull pot works. I know it's essentially 2 pots operated by one shaft, pushed down to control one, up to control the other.

That statement is wrong. There are two separate, concentric shafts. If the center shaft, which is controlled by the smaller knob on top, can also be pulled out, it is because it is ALSO controlling a switch, which is separate from and unrelated to the fact that it is also controlling a pot when you rotate it. That switch may or may not be hooked up to perform a function. On a commercially made bass, it will most likely be doing something (for example controlling active/passive, or changing the center frequency of a midrange control, or switching a pickup between single coil and dual coil), because they wouldn't have spent the extra $ on the more expensive component if they didn't need all of its functionality.
The outer shaft, which is a sleeve around the inner shaft, is controlling a second, separate pot that lives inside the same housing. This is called "stacked pots", and is most commonly seen on basses for one of these three purposes:
  • bass on the outer, treble on the inner
  • passive tone rolloff on the outer, master volume on the inner
  • midrange center freq on the outer, midrange boost/cut on the inner

Those aren't the only configurations, but they are probably the most common, in that order.

I'm interested in using a push-pull pot for 2 independent controls (like bass/mid, or vol/balance). I do understand the resistance and taper concepts.

I don't see why you would need a push-pull pot for either of those two purposes. You just need a "stacked pot", which is two pots, each wired separately, housed within a single component. You will have to make sure you have the right resistance value (e.g. 250K, 500K, etc.), and the right type of taper (audio taper vs. linear taper) on each pot so that it works the way you want it to. Also you have to consider whether you want a center detent or not. For example, for a balance (a/k/a "pan") pot, you probably do.
 
If I just read the first post and responded without bothering to read through the existing reserpine, I would probably post this picture to explain everything:
Story_of_Dr_Dolittle_p107.jpg

(extremely relevant!)​
 
If you want a multi function pot, consider a rotary encoder with a shaft push-button, but your bass would need an array of digital electronics, but you could have the one pot (encoder) do everything in sequence to the button presses.
Confusing .. Yes,
impractical... Yes,
but it can be done, just because..
 
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I must take exception to those who disrespect gnus.
As you can see in this photograph, the drawing above depicts an incorrect anatomical configuration for the majestic two headed gnu.

gnu 2 headed.jpg


I feel better now that that is cleared up.
 

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