"So, did J.S. Bach actually
assign notes to the letters of his last name and then use these to 'sign his name' to his compositions in the days before copyright?"One wonders,
but it was certainly true that many early composers "were mathematicians." (Or, if not, that they certainly recognized the very-mathematical foundations of what they were doing.) Which is part of what makes these two very-different interpretations of "essentially the same idea" so interesting in their contrasts. Each of them focuses on entirely-different, yet fundamentally joined, harmonic principles:
- The first presenter point out how some notes naturally want to "resolve" either up or down to their neighbors, and points out how a "negative" corollary exists on the other side of the Circle of Fifths. (The arrows here are bi-directional hence "two arrows.")
- Meanwhile, the next presenter observes the "difference between one note and the next, in half-steps," and points out that you can instead go in the opposite direction ... and thereby arrives at exactly the same mathematical(!) conclusion.
So, believe it or not, both presenters are arriving at exactly the same mathematical conclusion, albeit in two apparently very-different ways. Even though the approaches are different, the outcome is actually the same. [Western] music is very much about intervals,
and any interval can be inverted.
The purely-mathematical underpinnings of Western music have always interested me although I have never fully understood them. I do remember watching one video – URL long lost although I'd love to be reminded of it – where the presenter basically said: "I could wander into higher-order calculus(!) right now if I wanted to, but I won't, since I know this would scare you all off."
(Hell, "music theory class" pretty much scared me off anyway – until, many decades later, I began to appreciate what it was actually all about.)