By the mid 1850s, when Jacques Offenbach began his prolific career as a composer of operetta and opera bouffe, rising cadence gestures were already well embedded in musical practice. (See my essay on Adolphe Adam's Le Châlet [1834]: link. The essay was based on posts to this blog; follow the labels for "Adam" or go to the first post in the series: link.)
The composition and production history of Offenbach's final work, Les contes de Hoffmann [The Tales of Hoffmann] is complicated, but there is no ambiguity about its most famous number, the Barcarolle "Belle nuit, ô nuit d'amour," number 13 in the four-act version of published French editions from the two decades after the composer's death. A duet for two sopranos, Giuletta, female lead of Act 3, and Nicklausse, Hoffmann's muse (a pants role), the soloists are joined by a chorus in the second half of the piece.
My comment in note 31: "^5 is prominent in the upper octave as a cover tone, also." Alas, here I was a bit optimistic about the status of the rising line. It is a distinctive figure to be sure--in fact, it is Giuletta's cadence line, and therefore ought to be given priority over the orchestra's plodding descent at that same place in the music. The orchestra's role in the gestures and topical expression of this particular number, however, is so strong that nowadays I have to regard the voice and orchestra as equals. That being the case, Giuletta's rising line is an inner voice, a "structural alto" to the orchestra's descending line from ^5. Details below.
I have shown just two systems from the vocal score. In the first, see the prominent A5 (^5), which of course has sounded many times before.
At (a) is the orchestra's descending line in the fifth octave (the keyboard reduction is corroborated by the full orchestral score, btw). At (b): Giuletta's ascending line, with ^6 (*) as the waltz ninth. At (c) Niklausse copies part of the orchestra's descent in the fourth octave. At (d) the curious detail of the second chorus alto repeated ^4-^3.