Friday, January 18, 2008
The Error of My Ways
First of all, special thanks to Kevin Johnson for providing the key to deciphering measure fifteen. As you no doubt read in previous posts, I was completely confused by measure fifteen of The Black Page. The big puzzle for me was, how do you have five quarter note length figures in a measure of 4/4 time and call it a triplet? I had guessed that the 7:2 septuplet on beat three was probably a clue. I then said that I would practice playing a triplet over a measure of 4/4 and hope that would give me some clue. Well, as it turns out, I was on the right track but had one serious flaw in my approach. For some reason I kept thinking my triplet was three quarter notes over the 4/4. Kevin said hey, are you sure it isn't three half notes? That would equal six quarter notes. Then the 7:2 would mean that the septuplet is spread over two quarter notes. You have two quarter notes on the first beat of the triplet, a septuplet over two quarter notes on the second beat of the triplet, and two more quarter notes on the last beat of the triplet. Voila - five quarter note length groups over a measure of 4/4 time, counted as a triplet, and the 7:2 makes sense. Thank you Kevin! For those who didn't follow that (Andy), here's a diagram that may help (it helped me):To begin with, I said I'm playing a triplet over four downbeats and I want to try and see where all those notes line up in relation to each other. The first thing I'm going to do is find a common denominator between the 3 and the 4. In this case, since I have 5(6) quarter note groups to account for in my triplet, I'm going to multiply 6x4=24. Now I'll draw twenty-four evenly spaced beats on the page. To find the quarter note downbeat, I put a note stem down on beat one. Now I'll put a note with the stem down on every sixth beat. This should give me four evenly spaced notes - stem down. Next, to find the triplet, I'll put a half note on beat one - stem up. Next, I'll put a half note on every eighth beat. This gives me three evenly spaced half notes stem up. Now, how do the notes of the phrase relate to the twenty-four beats and the quarter note downbeat? Well, the first two items are a quarter note and two eighth notes. That equals two quarter notes, or the first half note of the triplet. Now, lets imagine our twenty-four evenly spaced beats as divided into three groups of eight. Take the first eight and line up your quater and two eighths on one, five, and seven, (think 1e&a 2e&a). Now, the septuplet, it's noted as 7:2. That means it stretches evenly over two quarter notes. Think of this septuplet as 4+3=7. The first two beats of the septuplet are eighth notes, that equals four sixteenths. The second half of the figure is three sixteenths. If you spread them evenly across, the first four sixteenths will fall slightly ahead of the halfway mark and the last three sixteenths will fall just after downbeat three. Now we get to the last beat of the triplet - a group of four sixteenths and a sixteenth note quintuplet. Okay, the interesting thing to note here is that the first four sixteenths start on the last beat of the triplet and the "and" of that group falls right on downbeat number four. There a four beats left in the original twenty-four. Here you're going to whip off a quintuplet, which is easier than it sounds. It actually feels like it's coming on the last "and" of the measure. The overal effect of this phrasing is a sensation that the tempo is speeding up, but the downbeat stays constant.