a harmony lesson

A few days ago, fringefaan posted this quote, from Christopher Palmer's liner notes to a recording of Benjamin Britten's opera The Turn of the Screw:

"It is perhaps scarcely an exaggeration to claim that, in this opera, the entire 'natural' musical order of things is inverted; 'inverted' being the operative (and in this case appositely loaded) word, since the result of inverting a perfect fourth is a perfect fifth, and what is the musical meaning of 'Quint' but a fifth? I am aware that this is in effect asking the reader to accept that the entire musical structure of The Turn of the Screw was motivated by a pun; and while I feel that Britten must have been aware of the musical implications of Quint's name, I think it likely that they unconsciously, rather than consciously, influenced his choice of vocabulary. Whatever the facts of this matter, we should not be chary of recognising Britten's achievement (a) in creating a sense of all-pervasive evil through the very musical formulas normally and naturally (but there is nothing 'normal' or 'natural' about The Turn of the Screw) associated with all-pervasive good, and (b) in avoiding totally the cliché of the augmented fourth/diminished fifth, the conventional, traditional diabolus in musica."

How interesting, I thought, musical symbolism, but rather technical in nature. When fringefaan said that, while he got the gist of the point, he didn't understand the technical musical points, I undertook to explain.

Having a keyboard in front of you may be handy, and if you don't have one, here's a picture of one:

Well, "inversion" means taking a chord or a sequence of notes and doing them upside down, i.e. going down the scale instead of up and vice versa. Thus, a C and the F above it would be a fourth, but if you take that C and the F below it instead, that's a fifth, as you count four steps upward (including the note you start with) from C to get F, but five steps downward to get an F.

If C and the F above it are a fourth, and C and the G above it are a fifth, then C and the black key in between F and G on the piano are the tritone, either an augmented fourth (C and F-sharp) or a diminished fifth (C and G-flat) depending on harmonic context. Perfect fourths are traditionally a consonant interval; perfect fifths without fill-in harmonies are hollow and were once avoided but became a basis of modern post-1600 harmony (if C and the G above it are a fifth, add the E in between and you have a major chord in root, i.e. uninverted, position), but the tritone in medieval harmony was a big no-no, the diabolus in musica as it was called and Palmer refers to it. It has consequently been a favorite of composers wanting to express pain or unease ever since.

That's what I wrote, but ( there's more. )