Two blog posts — one recent, the other less so — that have me jumping up and down in excited agreement:
- You’re Calling *Who* a Cult Leader? — in which Eliezer Yudkowsky (one of my favorite bloggers) points out that that it’s okay to be really enthusiastic about something:
Behold the following, which is my true opinion:
“Gödel, Escher, Bach” by Douglas R. Hofstadter is the most awesome book that I have ever read. If there is one book that emphasizes the tragedy of Death, it is this book, because it’s terrible that so many people have died without reading it.
I know people who would never say anything like that, or even think it: admiring anything that much would mean they’d joined a cult (note: Hofstadter does not have a cult)[…]
But I’m having trouble understanding this phenomenon, because I myself feel no barrier against admiring Gödel, Escher, Bach that highly.
You know, there might be some other things that I admire highly besides Gödel, Escher, Bach, and I might or might not disagree with some things Douglas Hofstadter once said, but I’m not even going to list them, because GEB doesn’t need that kind of moderation. It is okay for GEB to be awesome. In this world there are people who have created awesome things and it is okay to admire them highly! Let this Earth have at least a little of its pride!
Yes! As I have noted before, there is an inhibition in our culture against expressing strong feelings. Away with this!
I’m embarrassed to admit that I still haven’t read GEB, even though everybody raves about it and it’s got both a mathematician and a composer in the title. Well, it’s now (higher) on my to-do list. But anyone who has ever visited this blog will know that I harbor a similar level of enthusiasm for Westergaard’s ITT. And that does not make me some kind of crazed fanatic.
- What’s in a number? — in which a member of the Texas Tech music theory faculty correctly explains the meaning of figured-bass symbols (link added by me):
I often tell my students that figured bass evolved as a shorthand notation for species counterpoint.That is, figured bass actually suggests lines, not chords. Consider the example below:
If you look at those examples without worrying about vertical sonorities, the figured bass makes quite a lot of sense. Once you begin trying to assign Roman numerals, the task becomes a bit muddier. In the first example, we can easily understand the E-F motion in the soprano as some kind of neighbor motion or perhaps as the beginning of a passing motion. I prefer that interpretation to one which says the first chord is a root-position tonic and the second chord is a first-inversion submediant.
And rightfully so. In fact even to speak of this measure as being composed of two “chords” is a misleading distortion. If there are two entities into which this measure is divisible, they are a second-species line on the one hand, and a complex of three first-species lines on the other. (As a minor quibble, I will point out that “worrying about vertical sonorities”, which species counterpoint does just fine, is not to be confused with “assigning Roman numerals”, the discredited province of harmonic theory.)
In short: figured bass tells us diatonic intervals above the bass and nothing else. If notes are to be altered, the accidentals will appear in the figured bass. Figured bass is simply a shorthand for linear motion.
So true! Whether or not it is technically accurate that figured bass evolved in connection with species counterpoint per se, this is much closer to the truth than to suppose, as many still do, that it indicates some sort of preexisting awareness of Rameauvian “harmonic” concepts on the part of Baroque-era musicians. (Of course anyone who thinks that hasn’t read Schenker, but that’s for another time…)
(Not too long ago it finally occurred to me why this confusion exists. The reason for it is that people mistake figured basses, which are a form of musical notation, for some sort of analysis of the music. When you look in a treatise and see a figured bass at the top of a page, say, followed by a realization below, perhaps it’s natural to suppose that the figured bass on top is in some sense a “more primitive” structure, from which the realization is derived. But this is a misunderstanding. Figured bass was a performance practice; it was not the purposes of such treatises to engage in music theory as we know it, of the sort practiced by Westergaard — the subject had not yet come into existence as an explicit discipline. So one is by no means obliged to think of a passage in terms of some underlying figured bass. Quite the contrary, in fact: the figured bass is but a shorthand for the realization, and thus if anything the latter “explains” the former, rather than the other way around.)