Mondestrunken

Just watched Moonlight, and, happily, it’s great. Need to watch it again on short order. Don’t know if composer Nicholas Britell truly had Vaughan Williams’ Fantasia on a Theme by Thomas Tallis in his ear as he wrote the score, but I had to listen to that piece right away on finishing the film. It fit right in.

Drop-2 Chord Fun Facts

FF#1: Outer Limits

We’re going to talk a bit about seventh chord and four-part harmony here, so to keep things consistent, I’m going to refer to SATB for voicing, and keep pitch and string sets ordered from higher pitch to lower pitch.

Drop-2 seventh chords are formed by starting with a close position seventh chord and dropping the second note from the top (in SATB, the A) one octave. In the original close position chord, S and A are adjacent chord members. Now, however, S and B are adjacent chord members. So, we end up with SB pairs of {R,7}, {3,R}, {5,3}, {7,5}. In other words, between the outer voices of a drop-2 seventh chord, you always have some type of 10th or 9th.

Interesting. So, if that is going on between the outer voices, SB, what is going on between the inner voices, AT?

FF#2: Dyad Pairs

Now that we know what is always going on between the outer voices, what else can we say about how these chords are constructed? In the original close position voicing, adjacent voices, e.g., {T,B} are always adjacent chord memebers, e.g., {3,R}. But in drop-2, because of that octave displacement, adjacent voices are adjacent chord members + 1, e.g., {T,B} is now {5,R}. That means that {S,A} must be {3,7}. Well, with the knowledge of this FF and also FF#1 up above, these chords are now very easy to spell. In all four inversions, they are:
{R,5} {3,7}
{3,7} {5,R}
{5,R} {7,3}
{7,3} {R,5}

In drop-2 chords, root and fifth always go together, third and seventh always go together. This is worth memorizing.

FF#3: A Chain of Double Appogiaturas

Occasionally in jazz and popular music, we see harmonic motion by descending diatonic 5th, e.g., ii-V-I, or vi-ii-V-I, or I-IV-vii-iii-vi-ii-V-I. In four-part harmony with seventh chords, between adjacent chords we can say the following: two notes are common, the other two notes will descend a diatonic second. In fact, you can think of each of these chord pairs as double 4-3, 2-1 appogiaturas on the resolving chord. Think of the ii-V progression in Satin Doll for a good example of this.

To see how this plays out with drop-2 chords, let’s do the following. We’re going to play I-IV-vii-iii-vi-ii-V-I in F major, on the {2,3,4,5} string set, starting with the {3,7} {5,R} dyad pair. In the first progression, the common tones are between the outer voices SB, and the appogiatura happens on the inner voices AT. Next progression, the inner voices AT have the common tones and the outer voices SB have the appogiatura. From there, the cycle repeats.

FF#4: Those Dyads Again!

Let’s think about what just happened. We started with a I chord with the R member in the B voice. When we moved to the IV chord, the B voice became 5. The we moved to vii and B became R again. Wait, {R,5}, where have we seen this before?

What if we play the same sequence, I-IV-vii-iii-vi-ii-V-I, this time in Db major, same string set, but this time starting with {5,R} {7,3}. So we start with the I chord with 3 in the B voice, and next chord, the B voice becomes 7 of the IV chord. Wow, really? so now the B notes will alternate on the {3,7} dyad.

So, it looks like in a progression between any drop-2 seventh chords descending by diatonic 5th on the same string set, we have the following transformation R->5, 5->R, 7->3, 3->7. If you want to keep in simple, just remember that in the bass, {R,5} will alternate and {3,7} will alternate, depending on where you start.

FF Bonus Round:

Take any drop-2 seventh chord on the string set {1,2,3,4}. Drop the S on 1 two octaves, so that it becomes the B on 6, on the resulting string set {2,3,4,6}. What have we here?

Claude Vivier’s Zipangu

I just put up an old paper on Claude Vivier’s piece Zipangu. I think I wrote it in Carl Morey’s Music in Canada seminar back at U of T. I’m posting it (it’s in the “Writing” section of the web site) for a couple of reasons. Vivier’s life and career were both cut short in 1983, and he’s not terribly well-know outside of Canada. Which is a shame, because he wrote some really amazing music. This piece in particular, really struck me, and stuck with me. If you don’t know his music, it’s a great place to start. The paper isn’t an exhaustive analysis, but it does shed light on how the piece is put together. When I dug into the piece, I was startled at formalist it actually was. Would love to hear your comments on both the piece and the paper.

Site cleanup

As you can see, I’ve done some simplifying, standardizing, and general cleanup. A nice clean look for the fall! Please let me know what you think.

fun with time’s arrow

I had an epiphany this week. I’m sure it’s not an original idea, but it’s the first time it dawned on me. We all have an intuitive grasp that the future can play out in multiple ways. We can imagine that, staring from an arbitrary point in time, say April 25, 12:00 pm ET–let’s call that the origin–time will unfold in a certain way, dependent on an unfathomable number of contingencies. It makes sense that if we return to the origin and run time forward again, time will play out differently, owing to the randomness of the contingencies.

Here’s the epiphany: what if we return to the origin and play time backwards? The intuitive instinct which I suspect most people have is that time would play back the same way always, because, after all, it already happened that way. But in fact, wouldn’t time play out differently every time we start at the origin and go backward from there? Wouldn’t the contingencies and randomness come into play? Wouldn’t there be an infinite number of possible pasts, just as there are an infinite number of futures?

lifecycles

On the day that JD Salinger died, NAM finished draft #1 of the novel.