Okay - here is a quick brain dump before I dig into work:
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A 1-knob electric got popular with Eddie Van Halen - 1950’s Les Paul Juniors had a single pickup with a volume and tone control.
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Eddie was, in a lot of ways, really playing his amp, a hot-rodded Marshall - he stripped down his setup to the bare minimum, only using the Volume knob for swell effects (dialing down the Vknob, striking the strings, then dialing up the volume to get a swell with no initial attack)
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Having a capacitor in the circuit by including a Tone knob will affect the overall tone even with the Tone knob on 10, so yeah, most guitar circuits don’t have true bypass. I believe some Esquire (Telecasters with just a bridge pickup) have a true bypass setting that does bypass the Tone circuit completely. And by the way - it is like having the Tone control all they way up to 10/full on - except just a tad less; as I mention above, introducing a capacitor via a Tone Circuit is typically not true bypass, so a bit of latent capacitance is introduced.
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FWIW and slight hijack - but Esquires have a cult around them when it comes to “simple.” Folks talk endlessly about “that unique Esquire tone” and how the lack of a neck pickup reduces magnetic pull on the strings so they vibrate more freely / differently, giving the Esqy a beefier tone.
IM-not-so-humble-O, not having a Tone circuit is a Bad Thing, as is the habit most playings have of simply diming their Tone control (i.e., leaving it at 10 and forgetting it). Eddie Van Halen is and always will be differently than you and I - sure, I suppose I am referring to technique (duh), but I really mean playing situation: super-high-volumes, driving more air than I will breathe in a lifetime through a bazillion cabs and a bunch of 100watt amps with their tubes glowing. Oh, and changing those tubes regularly because Eddie runs them so hot they burn out. That’s one of his tone things - and it takes the edge off of a bypassed Tone control. Restated: he can run his guitar with a bright Tone/no control because the highs get rounded off via his over-driven amps - that Eddie’s Brown Sound.
Your average Joe doesn’t play in those circumstances - where he/she can simply use Volume to sculpt the tone. As I have said a bunch on this board, when you play with an overdriven tube amp, the Volume control on the guitar is really functioning as a Master Voicing control: You set your amp to just be veering into crunchy tone, more than you want for cleans, and then back off your on-board Volume so that at about 5-6, you get a decent, usable, sellable clean tone. Then head up to 7-8 - you should have a working, solid, chunky classic rock crunch rhythm tone. Then open it up all the way - a big, thick, overdriven lead tone. Your Volume control settings enable you to dial up the clean-to-crunchy, rhythm-to-lead voicing you want.
Within that context, the Tone is a fine-tuner for the Voicing you are after. When clean, if you go with a 8 - 10 Tone, you get a bright, maybe brittle tone - a lot of room for twang if you pick near the bridge. But if you roll it off to 4-5, especially if you dial up the Volume to 7-8, you get a thick rhythm tone. When I am playing with a crunchy tone, I dial the Tone know while I am letting a knob ring out and there’s this little, slow “wah” - like you are slowly stepping on a wah pedal - that I listen for and use to dial up the Tone setting. Very cool.
By the way - I am speaking from the experience mainly on a Tele - the Volkwagon Bug of electrics; the best starting place I can think of. With Gibson layouts with separate V’s and T’s you can find cool combinations along the way when you blend.
It’s such a great tool - took me a while to get past my EVH-idolizing beginnings but I am so glad I did…