After mid-century, the galop (see previous post) was displaced by the faster-tempo polka (the slower-tempo polka was the original type that had become very popular by about 1840). The dance was slightly different from the galop but the music was the same. (The can-can, btw, evolved the same way and at the same time.) The slower-tempo polka became known in Vienna as the polka française, the faster one as the schnell-polka.
Johann Strauss, jr., wrote polkas of both types (though not nearly so prolifically as he did waltzes) and also gave them prominent placement in his stage works. The Schnell-Polka (Galopp) "So ängstlich sind wir nicht, Op.413" uses motives from the comic operetta "Eine Nacht in Venedig."
The second strain of the trio, below, gives yet another of Strauss's manifold plays on the upper tetrachord of the major key, and on the functions and relationships of ^5, ^6, and ^7. At (a), ^5 is the traditional consonance; at (b), ^6 is possibly the ninth of a V9 but doesn't resolve directly--in fact it doesn't resolve at all as the ^6-inflection is repeated in bar 4. At (c), the string of sixths, rising, lends strength to a focus on ^5 as G4. A crucial moment is in bar 8, where the ^6-inflection occurs over the tonic resolution (arrow). Bars 1-8 are repeated and the ^6-inflection disappears in the cadence, clarifying a straightforward rising fourth line. (Note that this line is confirmed by the strong position of ^5 at (a) and strong-beat placements of each member of the line in the ascent.)