How John Entwistle recounted it in 1975:
I was looking for bass strings which vibrated properly, and I couldn’t find a good E and A string on any set at all, except maybe for LaBella — they weren’t too bad. But I wanted a round-wound string. I was approached by Rotosound, and they said they’d make some strings for me, exactly what I wanted. So I went to the factory, and they brought out a set of their round-wound and asked what I thought of them. The E and the A didn’t vibrate properly, and the D and the G weren’t heavy enough. So I sat there all afternoon while they made me strings with different cores, and different gauges, and different types of wire, and finally got through the E, A, D, G, and got a balanced set. And I said, “they’re fine, make me as many sets as you can.” They started making them and said, “look, we’ll put your picture in the string sets, and we’ll put these strings on the market.” So they issued them as “Swing Bass,” and they’ve been out ever since.
And again 20 years later:
It was in 1966 and I was looking for that Danelectro sound again. I tried everybody’s strings but the E and the A’s just didn’t work. It was the same with Rotosound but there was something about them that was almost there but not quite. To solve the problem I got in touch with James Howe[sic] and told him his D and G strings were great but the E and A didn’t vibrate properly. He told me to take my bass along to Rotosound and have some strings made until they got it right. After a couple of hours, we realised that the problem wasn’t in the wire winding, but in the core of the string. You could see that the strings vibrated in a big circle and that was wrong; the core needed to be thicker. We also made the overall gauges a bit heavier and they sent me away with 12 sets to use. A couple of days later they called and asked if I objected to them putting my name to the strings and selling them commercially. I told them I didn’t mind as long as they kept me supplied with free strings! But then we had to do the same with medium and short scale strings because I had loads of different basses by then. Those strings, the RS 66 sets, were the first that vibrated properly other than the Danelectros.