More Score-Turning

Last month I dabbled in a bit of score-turning, mostly just for show, as the visuals were mostly beside my point. This month the score-turning is less just for show, although mostly for fun. Below is the first cantus firmus from Johann Joseph Fux’s Gradus ad Parnassum of 1725.

An interesting thing happens when you rotate everything but the staff a little bit counterclockwise to make a new melody:

Now there are only the two different notes of D and G — octave differences aside — rather than five different notes.

When combining lines in counterpoint, Fux recommends, all things being equal, that one use more imperfect intervals (thirds, sixths, and their octave compounds) than perfect intervals (unisons, perfect fifths, and their octave compounds) between simultaneous notes. This two-tone melody makes this quite easy: one could simply place a drone of B flat or B natural under or over this two-tone melody and only thirds and sixths will sound. When you rotate these two lines the same little bit back clockwise, the old melody returns and the drone becomes a line that completely descends by step. Here it is with the added line below; only thirds and sixths sound.

Fux wouldn’t like how it begins and ends, but, as I said, this is mostly for fun.

Next month I will share a winter holiday tune that basically has this same property as Fux’s cantus firmus.