The date of the first application of the pickup on a guitar is uncertain but Loyd Loar who worked for Gibson from 1920 to 1924 (and is famous for his mandolins and arch tops) developed a pickup. The company developed a bunch of prototypes which were not accepted by the "agents" (who I believe sold to the retailers). Vivi-Tone whom you mention, was founded by Loar and two other folks from Gibson - however they were too far ahead of the curve, and there was no market.
Walter Fuller recalled that when he joined Gibson in 1933, he found some pickups that he believed were made ten years earlier under Loar's supervision. They were more like microphones than modern day pickups with a fixed anode and charged, stretched diaphragm. It was not a successful design.
Commercially successful electric instruments began to appear in the 1930s. In 1931 Rickenbacher (that's a correct spelling for the era) produced a Hawaiin guitar that came to be known as the "Frying Pan". It was the first instrument to use a modern stye electromagnetic pickup, which, in addition to ten years of market simmering, might explain its success.
Rickenbacher was not alone - Rowe-DeArmond had started producing pickups early in the decade, and Dobro produced a small number of amplified resonator guitars in 1932.
While the Hawaiian guitars were solid from the start, the electric "Spanish" guitars of the time were mostly arch tops with a pickup stuck on them. Various global events were pulling attention from guitar manufacturing.
As a result the electric guitar did not begin to become well known until the late 30's when Charlie Christian and Benny Goodman's band brought Gibson's ES-150 to the masses. (Note that "ES" stands for Electric Spanish).
The war continued to hamper development because people with manufacturing skills were pressed into service.
Les Paul (born in 1916) had experimented with his own pickups as early as 1929. He was certain that making a stiffer instrument keeping the pickup in place and allowing the strings to move was the way to go, and so started working toward solid instruments.
He had John D'Angelico put a soundpost or block inside an instrument for him to keep the top still, and in 1937 commissioned an instrument from Larson Bros.
of Chicago with a heavy solid top and no sound holes. A short while later he experimented with "The Log", essentially a railroad tie, where he stuck the bouts of the guitar to the plank which contained everything else. He built this at the Epiphone's New York factory in 1941.
At the same time in California (where Les Paul spent some time) Paul Bigsby and Leo Fender were also experimenting. In 1947 Bigsby made a now famous solid body instrument with a single pickup for Merle Travis. It's infamous for looking like a cross between a "Les Paul" but with a headstock similar to a Strat.
Obviously neither instrument existed, so that's not the case, (possibly the reverse) but is a clear indicator that cross pollinization was taking place.
In 1947 Leo formed the Fender Electric Instrument Company and in 1948 started to market the "Broadcaster" whose name was changed to the "Telecaster" in 1950. With the Broadcaster the modern solid body, two pickups, etc.
had finally begun production.
The 40's also saw the birth of the modern, amplified pedal steel. Named the "Electraharp" and produced by Gibson, it's history forks at this point because it really was no longer a guitar, but something else entirely.
The electric bass guitar was first marketed by Fender in 1951, and it was this instrument that could be said to be his unique invention. I'd have to do more research, but the combination of bass range and guitar frets is probably his in a sense. My caveat is only because many early instruments had frets tied around the neck so the idea could have essentially been in place for hundreds of years at that point, but I believe he was the first to bring together bass range, frets, and pickups into the first electric bass guitar.
As the market developed Gibson produced the Les Paul in 1952 and Fender brought out the 3 pickup Stratocaster in 1953.
Remember that up until now the single coil pickup was all that was in production. (Think P90 and "soapbar" pickups on Gibsons at this point).
The next breakthrough was the work of Seth Lover and Walter Fuller who created the humbucking pickup in 1954. (It grew out of the needs of Radio broadcast and recording where, as to this day, quieter is better.) Gibson's ES 135 was the first to sport this innovation and entered into regular production on Les Paul guitars in late 1957.
Early humbuckers have entered the mythology stamped with the now famous "patent applied for" phrase. The design of these pickups is exactly the same as is produced today.
At that point the essence of the modern electric guitar was in place.
There have been a few innovations since. The Alembic company (formed in 1968 to supply the Grateful Dead's sound systems) were the first to put transistorized preamps in guitars and basses. Arnie Lazarus produced the FRAP (flat response audio pickup) piezo transducer in '69.
Ovation may have been first to use individual tranducers under each string.
Everything else (while the art has been greatly advanced) seems like a variation on these themes. Certainly Bill Lawrence, Seymour Duncan, DiMarzio, Floyd Rose, and many others have widened the flow of this river of innovation.
But as far as I know Les Paul's pursuit of the solid body is what brought all this to the fore.
From my perspective Leo Fender did three great things. He timed the start of business just right, and he taught the world how to manufacter guitars.
Gibson had an acoustic guitar background as did almost everyone else. Leo looked at the solidbody with fresh eyes. Bolt on necks may or may not have been innovated by him (they existed on other instruments) but he pulled together the art of manufacturing guitars like no one else.
And of course, he created the electric bass.
In all this I also overlook the input of many players who helped develop various features and ideas. As an example, I believe Alan Holdsworth was one of the first folks to put a humbucker in a Strat (which was sometimes made out of lighter weight wood than a Les Paul) and started a revolution which can be seen in any music store today.
The ES-335 and its variations and knockoffs are still extremely popular. Even the modern archtop, a very different instrument today than the ones built by Gibson, Stromberg, Epiphone etc. during those times has benefitted from the humbucker and piezo pickup development.
The instrument that I've played for the longest time is an Ibanez AH-10 which is Strat like, but with a single humbucking pickup in the neck position. It didn't come that way, and various experiments show on the pickguard. It has a fairly light basswood body, a knife edge whammy which has three springs tightened down and maple neck with a rosewood fingerboard.
Its the classic story of finding an inexpensive guitar that with a little tweaking becomes something special. Yeah!
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