But there is a parallel. The Ellington band of the 30s and 40s was a paradox. Even today, jazz critics still ask why so few of the talented musicians who produced such wonderful ensemble sounds managed successful solo careers of their own.
So it has sometimes seemed with the Saatchis alumni. There are those who managed to make names for themselves - Paul Bainsfair, TBWA's European chairman, and Adam Crozier, the Royal Mail chief executive, to name but two. Others, though, never replicated their association with the Saatchis elsewhere. Ron Leagas, once the managing director, tried, but never entirely succeeded in translating their "can do" approach into his agencies; the one-time chief executives Roy Warman and Terry Bannister never realised their ambition of forging a successful European network.
Why? Maybe because, like the Duke, the Saatchis have always played it their way, fostering a "family" atmosphere and nurturing such a fierce loyalty among their senior people that leaving can seem like letting the side down.
Now Nick Hurrell, one of the most loyal of the lot, has decided to leave home after 21 years to join the TBWA\London chairman, Neil Dawson, in a start-up. It remains to be seen whether his long immersion in the Saatchi culture will help or hinder. He and Dawson want an agency that breaks the traditional mould and is configured to meet the evolving communications demands of today's clients.
But there are some credibility hurdles to overcome. For one thing, both Hurrell and Dawson are the products of conventionally structured agencies. For another, they have yet to fully articulate how they plan to achieve their aim. One thing is certain - they will have to hire people, especially creatives, who are nothing like themselves.
As anybody who has ever worked for the brothers is told, nothing is impossible. That creed has not always been true for some who have attempted to implement it beyond Saatchiland. Watching Hurrell and Dawson as they set out to do so will be fascinating.