I ran across this thread randomly from an internet search. As a jazz bassist who doubles on cello, is doing his master's thesis on jazz cello use, and is a big fan of Ron Carter's piccolo bass work, I figured perhaps I ought to fill in what information I can here, although much has already been answered.
Most bassists who have doubled on cello tuned it in fourths, like a bass one octave up, and played almost exclusively pizzicato. This includes Oscar Pettiford, Harry Babasin (who actually beat Oscar to it by a few years), Ray Brown, Sam Jones, Percy Heath, Eldee Young, Hal Gaylor, and Todd Coolman, and probably some others I'm forgetting. A notable exception is Ron Carter who played cello in fifths and frequently arco (he had actually started on cello as a child before switching to bass). Dave Holland is the other big exception among the bassists, as he also bows cello (ridiculously well I might add) and I suspect he probably tunes in fifths but I haven't heard enough yet to be sure.
Ray did work with Kay instruments (in the early sixties, I think?) on making a custom "jazz cello" to accomodate these bassists, and I believe they were marketed with his name. Todd Coolman knew a little about them and told me that, as best he could remember, they were slightly larger with a slightly longer string length than a normal cello, and the fingerboard was a bit wider to space the strings out a bit more, making it feel slightly more like a bass. Ray obviously used one of these, as did Percy (who picked up the instrument much later when playing with the Heath Brothers band - there's an interview online somewhere where he talks about it), and probably several other notable bassist-cellists. I'd love to get my hands on one of these myself sometime and check it out. Another bit from that Percy interview that might be useful - he says that Ray told him he'd have to "use three", and eventually figured out he meant three fingers - in other words, in order to make bass fingerings work on cello they substitute third finger for fourth finger and don't use their pinky.
Ron Carter had an instrument built for him in the seventies which he termed a piccolo bass. I believe he once described it in an interview as "three fourths the size of a three quarter bass, and tuned like a cello backwards." To be more straightfoward, it's smaller than a normal bass, tuned in fourths, and tuned a fourth higher than a regular bass (so basically just take off the E string and add a high C string). In another interview I read, Ron says he wanted an instrument he could lead a band with both sonically and visually, and play melodies on, but also still be low enough to walk behind the other bass player's solos occasionally. Ron's first piccolo bass was custom made for him, but I think I read that he later found an old three-string bass from Europe that he liked and had refitted to his specs. Ron released quite a few albums with his piccolo bass, usually backed with a full rhythm section and often set against a group of four cellos, for which he writes quite well; you can listen to his most recent such album, "Eight Plus", on his website for free:
www.roncarter.net (my favorite track by far from that album is "El Rompe Cabeza".) Buster Williams also plays a piccolo bass like Ron's now and then.
To answer your question about spacing on the piccolo bass - I haven't played one myself but I managed to get down to Merkin Concert Hall a few weeks ago to catch the Ron Carter Nonet live, so I saw Ron playing his, and I'd say that it's very close to a bass's string length and spacing - in other words, it's much more like a bass than like a cello. However, remember that it's essentially a custom instrument - I don't think there's really a "standard" per se for how acoustic piccolo basses should be made (although you could try to get ahold of whoever the luthier is who made Ron his first one).
I know less about electric piccolo basses, but apparently in the electric bass world "piccolo" usually means tuned one octave up and "tenor" means tuned a fourth higher - so I guess what Stanley Clarke calls a tenor bass would be tuned the same way as what Ron calls a piccolo bass.
While I'm posting all this information about odd tunings - Glen Moore, bassist with Oregon, uses a regular 4-string bass but tunes it with a low C, a regular A and D, and a high C.
Incidentally, there have been plenty of non-bassist cellists in the jazz world as well who are worth checking out if you're interested in the instrument. (They usually played in regular fifths tuning, of course.) Names would include, in no particular order, Fred Katz and Nate Gershman (who both played with Chico Hamilton), Akua Dixon (who plays on several of her husband Steve Turre's albums), Calo Scott, Abdul Wadud, Matt Brubeck, Fred Longberger-Holm, David Baker, Joel Friedman, and whoever that guy is who plays with the Turtle Island String Quartet (absolutely sick stuff, check out their rendition of On Green Dolphin Street). And perhaps my personal favorite: Erik Friedlander, a current player in New York whose albums with his group Topaz I would very highly reccomend. And I'm sure I forgot a few good ones.
Wow, sorry for such a long winded post. Can I get away with plugging my own cello playing while I'm at it? (If you're wondering, I play the instrument in its standard fifths tuning.) While back in Ohio for the summer I've put a little quartet together:
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I'm planning on putting a similar group together in New York this fall.
