We recently established a successful Useful Concepts Repository. It got me thinking about all the useless or actively harmful concepts I had carried around for in some cases most of my life before seeing them for what they were. Then it occurred to me that I probably still have some poisonous concepts lurking in my mind, and I thought creating this thread might be one way to discover what they are.
I'll start us off with one simple example: The Bohr model of the atom as it is taught in school is a dangerous thing to keep in your head for too long. I graduated from high school believing that it was basically a correct physical representation of atoms. (And I went to a *good* high school.) Some may say that the Bohr model serves a useful role as a lie-to-children to bridge understanding to the true physics, but if so, why do so many adults still think atoms look like concentric circular orbits of electrons around a nucleus?
There's one hallmark of truly bad concepts: they actively work against correct induction. Thinking in terms of the Bohr model actively prevents you from understanding molecular bonding and, really, everything about how an atom can serve as a functional piece of a real thing like a protein or a diamond.
Bad concepts don't have to be scientific. Religion is held to be a pretty harmful concept around here. There are certain political theories which might qualify, except I expect that one man's harmful political concept is another man's core value system, so as usual we should probably stay away from politics. But I welcome input as fuzzy as common folk advice you receive that turned out to be really costly.
At least one of us is very confused. I don't think it's me.
At the end of the toccata there is a chord containing the following notes, from bottom to top: D (in the bass, on the pedals), another D (lowest note on the manuals), F, A, D. This is a perfectly ordinary chord of D minor, of course. After that there is a semiquaver rest and then the fugue subject begins (or, perhaps better, the fugue subject begins with a semiquaver rest). At that point, as is normal in a fugue, there is only one voice sounding.
Oh, wait, you weren't talking about the fugue at all? You meant the chord a few bars into the toccata? Well, OK then, that chord contains the notes you said it does. (Though, I repeat, it isn't "the chord held at the start of Bach's Fugue in D minor"; it's in the toccata, not the fugue; in a discussion of music analysis such distinctions are really worth making.)
But there's nothing weird about that chord! It's a standard diminished-7th chord (everything at intervals of 3 semitones from some starting point; in this instance C#, E, G, Bb). If I may quote from that bastion of the avant garde, Wikipedia:
Diminished seventh, check. Rooted on the leading tone, check. Minor key, check. It's perfectly commonplace. (There are plenty of much weirder things in Bach.)
The chord is in measure 2 of the piece, and contains these notes: D, C#, E, G, Bb, C#, E.
A diminished 7th in Dm should have D, F, Ab, Bb, shouldn't it? This is a diminished 7th C#, so what's the D doing there?
Anyway, my impression is that diminished 7ths are much more common in organ music than in piano music. I think of them as "that organ-music chord". And if you look up diminished 7th in the same music database that komponisto linked to above, you'll see it has a much higher fraction of baroque entries than any of the other items on that list.... (read more)