Under his left hand.
The ultimate jazz instrument is the piano, as it can do it all well. The rest is ornamentation.
Hierarchy of jazz instruments...
Piano
Trumpet (probably only because of Louis & Miles, but it is enough)
Drums
Saxophone (Alto + Tenor)
Bass
Trombone
Other woodwinds
Saxophone (Baritone)
Saxophone (Soprano)
Guitar (and I say that as a guitarist - it either apes the piano or saxophone. Completely unessential but can be nice for tone).
Vibraphone (seriously, get screwed)
Order that I want to hear solos:
Trumpet
Piano
Saxophone (Baritone)
Other Saxophones
Trombone
Other woodwinds
Guitar
*daylight*
Bass
*daylight*
Drums
*daylight*
Vibraphone
Wow !!
I recently bought Swinging into the 21st which is a box set of 11 albums by Wynton Marsalis. I also bought a box set of Louis Armstrong with the Hot 5s and 7s. I have dozens of albums by Miles Davis, Lee Morgan, Freddie Hubbard, Dizzie Gillespie.... so I share the love of trumpet.
I cannot begin to think that there is a hierarchy of instruments as rigid as yours though. I imagine a it was a little tongue in cheek ?
Jazz is such an amazingly broad church that there is a place for all of these instruments.
Gerry Mulligan's playing of the baritone sax is a thing of beauty.
Coltrane's playing of the soprano sax on My Favourite Things ????? Magnificent.
Guitar ? Kenny Burrell's playing on everything is magical, but on Chet Baker's You're Mine, You. It is a thing of rare beauty.
Jazz would not be jazz without the musicians being so broadminded.