[David] Neumeyer has made an elegant case for the viability of a "three-part Ursatz with an "ascending Urlinie" but some questions remain. The minor mode, for example, is obviously less conducive to such a structure than the major. . . . Then there is the question of the relative hierarchical status of the two upper voices. I have assumed here, based largely on my own intuitions, that in a three-voice counterpoint of this sort the descending linear progression is hierarchically superior to the ascending one, even when the ascending progression lies above; that is why I have referred to the latter progression in such cases as a "descant." I suspect that this is consistently true in Corelli's music, and that it remains true in most music by other composers. But there are surely exceptions. To consider an extreme example, if Beethoven's C major Bagatelle Op. 119, No. 7, is not based on an ascending Urlinie, what music is?I'll answer his final question in a separate post (hint: Op. 119n7 isn't, but that just makes everything more complicated, and from a hermeneutical standpoint more interesting, doesn't it?)
To the problem of the rising line as "descant" voice, that's been an issue from the beginning in what I will call the positive style of critique of the ascending Urlinie (the negative style just rejects the rising line out of hand). In one of the essays published on Texas Scholar Works (link), I write about the "descant" voice and the process by which it overcame a subsidiary role to become a primary figure in some compositions and should be treated as such in analysis intended to be both musically and historically sensitive. Here is a link to a blog post that quotes from the essay and shows a few early examples.
Perhaps the most important point to make is that the process was largely finished by the end of the 16th century, in the last moments of the long-running change from priority to tenor to priority to bass (solidified--not invented--in the adoption of the basso continuo). Associated mainly -- though by no means exclusively (link) -- with dance-songs and music associated with improvisatory practices in the 17th and 18th centuries, ascending cadence gestures seem to have been suppressed somewhat in more formal musics by the clichéd figures of the partimento tradition. Once that tradition died out in the early 19th century, ascending cadence gestures gradually became more common.
Reference:
Rothstein, William. 2006. "Transformations of Cadential Formulae in the Music of Corelli and His Successors." In Essays from the Third International Schenker Symposium, edited by Allen Cadwallader, 245-278.
