JTM-45

Above: The front and bottom of the sixth prototype (aka #1) of the first Marshall amplifier (the JTM-45)

Pete Townshend (The Who) among other guitarists told Jim Marshall that the problem with the other amplifiers on the market, was that they were too clean. The type of music these new British bands were playing required a the sound to be heavier, grittier, louder, and more aggressive.
Jim Marshall knew straight away that they were going to build the world’s first Rock amplifier.

Jim Marshall would recruit Dudley Craven to oversee the project as the chief designing engineer; (into a workforce consisting of Jim Marshall who would make the chassis, Ken Bran who would select and install the components, and Ken & Fred Gallagher who would help out with all other aspects). 
Marshall realised they didn’t need to reinvent the wheel as there was already an amplifier that was sonically close to Townshend’s requirements – The Fender Bassman.
Fender were a company who felt that a good guitar amplifier was one that sounded clean and did not distort. The Bassman did not embody this characteristic as it was a amplifier for bass guitars, but found popularity amongst guitarists, hence the reason why it was the exception to Fender’s line.
Marshall realised that all they had to do was modify the Bassman and make it’s distorted characteristic more prominent.
Although Marshall was not the engineer on the amplifier, he was the boss and he knew what was needed. He knew that Townshend did not simply want a amplifier that sounded distorted and gritty; What was needed was an amplifier whose distortion and grit was filled with harmonics and sounded musical. This is important as today, many consider great distortion to be valve driven. Marshall was and are valve kings in the amplifier market.

Marshall would build six prototypes until they found the right one. Reportedly it was Townshend who tested the sixth and remarked “That’s it! That’s going to be the Marshall sound from now on!”.
On September 1962, The JTM-45 was born. Today the sixth prototype (nicknamed #1) is on display at the Marshall HQ.

Above: The production JTM-45. It sits on top of a speaker cabinet which houses four 12″ speakers -  a standard for Marshall.

For those interested in Jim Marshall and the company he created, I highly recommend you buy:
Maloof, R. (2004) “Jim Marshall: The Father Of Loud”, San Francisco: Backbeat Books.