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guitarists did not want distortion. Rock and Roll was invented ... 3rd harmonic ... only needed two fingers instead of three
There is some truth in that.
Many old-school players did not want the amp to go BLATTT when hit too hard. Of course that did become "the" sound. And a long long time ago. I just found an early Les Paul where he uses clipping for emphasis (not as his sole trick).
No, what I'm saying is a gentle rise with signal level, before you hit "max" and go to clipping.
There is musical justification. What is the difference between a yell, a shout, and a scream? There may be little difference in acoustic power. The difference is the singer (or yeller) pushes up the harmonic overtones. Common speech and mild singing drops above 800Hz, a good holler or operatic climax brings up the 2KHz band on the same nominal pitch.
Most orchestral instruments also have a rise of harmonics at high level. (In the extreme, a flute will "jump" to a harmonic at high drive level, which is both a way to extend the instrument's range and a royal pain if you want to play a low note loud.)
The string/pickup combination for a solid guitar also changes harmonic balance at high plucking level but in a different way. I suspect that a "good" set-up aims to minimize this, and let the amplifier add the scream.
Against this interpretation: some very soulful players use very souless amps. A lot of it is in the touch.
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listen to some late '40s/early '50s Bob Wills and His Texas Playboys
"Noel Boggs ...In 1946 he met Leo Fender while working with Spade Cooley at the Santa Monica Ballroom. He became the proud owner of Fender's first steel guitar and an important endorser and promoter of Fender's equipment. The friendship between Noel Boggs and Leo Fender was such that Leo Fender was the godfather of Noel's daughter Sandy."