The first is a version of Eduard's galop "Über Feld und Wiese" (Over Field and Meadow) published as a polka (schnell) by Herzberg & Greenburgh (New York, 1876). Link to this entry on the LOC site. The tempo of a polka schnell was probably not much less than that of a galop, and therefore one could dance a polka to it, but the musical figures are not at all like those of a polka. (A "slow polka," btw, was called polka française.) Link to this piece published as a galop.
In general, Eduard's music tends to be more conservative in its treatment of musical materials than the contemporaneous waltzes of the other Strausses. The first strain here uses quite conventional harmonic progressions, except to end the first phrase (boxed), where a characteristic figure draws ^7 over V down to ^6, and the resulting V9 resolves directly to ^5 over I.
The trio is similar. Here, a "throwaway" ^6 over I (first circle) becomes the ninth in a V9 that again resolves directly (second circle).
The second strain of the Trio is more adventurous in its cadence, finally taking up the implication of the stolid initial motive (first box) and sending the line up to ^8 in a PAC that is far more emphatic than the quick V-I that follows it.
The second example is "Mein Lebenslauf ist Lieb und Lust," a set of waltzes by Josef Strauss, as published in
Philadelphia by Louis Meyer (1870). Link to this entry on the LOC site.
In the second strain of the first waltz touches on both ^5 and ^6 over I and over V7.
The second waltz makes the play of ^5 and ^6 its main motif.
The third waltz, however, goes all out as ^5 and ^6 permeate the melody, disappearing only with approach of the final cadence (but note the reference to ^5 and ^6 over V7/V -- not marked in the score).
The second strain of waltz 3 uses ^6 and ^5 over I as the melodic answer to ^5 and ^4 over V7, quite common in legato strains. (More common though is ^5 and ^6 over I answering ^7 and ^6 over V7, a favorite gambit of Johann Strauss, jr.)
