I think that's a cornet, partly because it seems too small to be a trumpet but also because it's being held by the great Del Staigers, one of the greatest cornetists ever.

I am by no means an expert on musical instruments, but I think the "Tuba player" is actually playing a Sousaphone for the band's "signature 14 minute tuba solo".

A Tuba in use has its bell pointing upward which works great in an indoor environment. The Sousaphone on the other hand projects its sound forward which would be better for the last row of an outdoor John Phillip Sousa marching band.

The Sousaphone is also easier to carry while marching since it wraps around the body and over the shoulders. The Tuba on the other hand requires the musician to not only play the instrument but also manage its weight and size.

Wiki links here....
http://en.wikipedia.org/wiki/Sousaphone
http://en.wikipedia.org/wiki/Tuba

Ol' Nat looks like he's been doing way too many nighttime recording sessions...but seriously, as the musical director of several "house bands" at Victor, he racked up a pretty impressive list of hits, often as Nat Shilkret and the Victor Orchestra.

Through his various orchestras passed numerous young musicians who would become mega-stars in their own right some years later--Benny Goodman, Tommy Dorsey, and Gene Krupa, to name just a few.

His popularity at Victor was reportedly why Paul Whiteman, Victor's biggest recording artist for most of the decade, left the company for Columbia Records in the spring of 1928. Whiteman saw Shilkret as a potential rival and figured there wasn't enough room in Nipperland for the two of them.

The rest of the band seems to be taking 5, but the tuba player is hard at work. Perhaps this was their signature 14 minute tuba solo that happened just before intermission.

Took up the suggestion by tterrace to Google Nathaniel Shilkret, and was astonished by his history. The man was a music giant. What a career! I’m a big fan of the Fred Astaire/Ginger Rogers (and Ellie Powell, too) films and was delighted to discover Shilkret was music director for two of them, “Swing Time,” and “Shall we Dance.” Had never heard of the man before. (Yes, I know, that’s what film credits are for. Go ahead and give me a few lashes and I’ll pay closer attention.)

As an aside, may I say a great big “thanks” to everyone who makes Shorpy work, including those who comment. It’s almost like I’ve earned a history doctorate since first visiting the site.

Recordings were generally made with condenser mikes, but this one is a double-button carbon. Condenser mikes were big bulky affairs, as they contained a preamplifier tube. Google on Western Electric 47 to see some examples. The carbon mike was probably chosen for this photo session because it was less obtrusive. It's a great photo, and many thanks to Mike for identifying the players.

These guys sure knew how to put on the Ritz. Professional musicians today could take a lesson. I have seen musicians wearing the most appallingly sloppy, ill fitting and just plain wrong excuses for tuxedos over the years. That's something they should teach them in music school. Really.

the two keys to success: B sharp and B natural.

My grandfather Jack Shilkret, a band leader and composer in his own right, is on piano. Great-uncle Nat is in the center, with baton.

A picture of Jack as a child, with his and Nat's father, Wulf, is also on Shorpy.com at https://www.shorpy.com/node/7208

A later update from my mother:

The violin player next to Uncle Nat(on his left, next to the cello player) is Peter Eisenberg, who changed his name to Ellis when he moved to California. [We called him Uncle Pete, and his wife, Aunt Mae. I think he was in Grandpa Jack's orchestra, which is why we knew them so well. Grandma kept in touch with them after they moved.]

Must be a condenser mic.

Front row center, holding baton, Nathaniel Shilkret, a man worth Googling.