Why 34" scale?

[Oscar Stern]

The very 1st Fretless Bass was a Scaled Down Electrified Upright Bass shaped like a Guitar w/ a 34 inch scale length. 1/4 Size Double Basses have a 34 inch scale length too.

 

[TrevorG]

According to Jim Roberts book, "How the Fender Bass Changed the World", it was a combination of information from a physics book owned by Leo's secretary and/or trial and error - George Fullerton said they tried 30" - 32" and possibly 36", but chose 34".

Read the same so I guess Leo went for a certain sound. Can't get the same fatness out of my 35" bass and less than 34" gets you a very different kind of fat to my ear. Guess no one really argued with him as alternatives aren't as readily in supply.