The Three-Body Problem

Whenever I read harmony books I get ticked off at the sophomoric explanations of harmonic phenomena that are ever present. I should correct that and use the past tense, actually, because the harmony books in which I find these tend to be older, apparently before the concept of observation was developed. Hindemith, in particular, talks about combination tones and their overtones to discuss consonance, and I find that rather silly. He also says that intervals have roots.

What is the root of a given interval? For the major third, for instance, it's the bottom member; for the minor sixth, its inversion, the top member. How does he know? See, I disagree with him, because one would have to consider the interval in a vacuum to identify a root, and an interval is never in a vacuum! I hold that context is critical, and that the tonal center forms a third note around which the two notes of the interval gravitate. When trying to figure out the "meaning" of an interval, the (local) key is an inseparable part of the problem. Hence we have a three-body problem, which complicates the simplicity of a two-note interval with necessary ambiguity.

My favorite example is the major sixth, because either note can be the "root". What's worse, if the major sixth is G E and the key of C is well-understood, the root is the C, a note not even in the interval! If an E minor harmony is implied, E is the root; if a dominant function in the key of C is implied, G is the root. If the interval is present by itself, without any context -- or, rather, with itself as its context -- a trick of the ear can change the root, like the spinning dancer or the cube that looks like it's either coming out of the page or into the page. The beautiful simplicity of the analysis of only two tones is, sadly, not to be.

I hope that this helps dispel the notion that the overtone series has much to do with harmony beyond providing the fifth. That notion needs dispelling, and any little bit counts.

Interval of the Moment

Diminished octave. In particular, in Villa-Lobos's Suite Popular Brasileira, V - Chorinho, where there's a held low E in the bass, struck D G# B in the middle, and struck G natural in the melody. It's obviously a dominant 7th chord to A minor, even though it doesn't actually resolve that way; the G natural goes down to F then E. It's the clash of the two natures of "traditional" melodic minor that sounds so great.

Another great interval is the diminished third, especially between the raised 7th and lowered 2nd, as used melodically in Tarrega's Recuerdos de Alhambra (which, unlike the Villa-Lobos, I have not yet attempted to play; the right hand figuration is HARD). One phrase ends on the G#, the 3rd of the dominant 7th of A minor, and the next one begins on Bb, the b9th of the secondary dominant to D minor. The melody: C B A B A G#; Bb A G A G F... The first few times I heard it, I couldn't identify the interval. It's just so remote -- a diminished 3rd -- and it was THAT interval that led me to realize that a diminished 3rd is NOT the same as a major 2nd. Ah, context.

The Value of Planning

Every year I participate in a great competition that requires a composition for brass ensemble of varying size (this year, a septet) of around 15 minutes. It's a great chance to write something with a deadline, since it's due February 1st, and I do something different every year. I've been working on this year's entry lately, and I realized something everyone already knows: planning is GOOD. Editing is GOOD. Showering is GOOD.

The problem is that it takes a lot longer to write something than to sing something or think about something, so sections end up being too short. I get bored writing even short segments because it takes so much longer than the segments themselves, so my writing ends up all over the place because my ideas change much more quickly than the music. I'm finding, then, that it's a good idea to think about how things will develop in the shower, try to remember them, and write them in. Things sound much better in my head than they do once I've written them, but also, once I've written them, I can't really think of them any other way, so this is hard to do.

One thing that I used to not understand until very recently was how composers could write music that doesn't sound great throughout, with some boring moments. I think I understand now that it's for pacing reasons, because otherwise the piece isn't balanced. There needs to be time with nothing important happening so that important things are more important. Filler material, if you will, that serves to continue the piece until what needs to happen can happen. It's also a great time to introduce new motifs, or to quote old ones. There's an art to writing "boring" music as well.

Everyone already knows this, but that's what I figured out today. (: I'll hold off on details of the piece until I hear back from the competition to maintain the anonymity of my piece.