Never ending math equation

[This post is related to the recent, suprisingly popular "irrational" rhythm posts -- Part 1  & Part 2. Since (A) I can't sleep, and (B) apparently y'all love this stuff, here is the followup I promised.]

Maria Schneider runs in very different circles from the metametric/totalist crowd. Her music doesn't sound anything like  Michael Gordon's (he of the infamous Trance bassline), Mikel Rouse's, John Luther Adams's, or Kyle Gann's. But I think you can see, in some of her works, an interesting example of convergent evolution. Her own approach to "feelable/performable rhythmic complexity" (which, of course, has been a part of jazz since the very beginning) is informed primarily by flamenco, and South American music, but it has led her to stretch those traditions in ways that are, in some respects at least, recognizably similar to the rhythmic techniques used by the above-listed metameric composers.

Let's take a look at Maria's Bluería, Soleá y Rumba from her 2004 release Concert In The Garden -- specifically, the initial bulería section. The bulería is a 12-beat flamenco rhtyhm. It comes in a couple of varieties, but the version we're interested in is the one with accents on beats 3, 7, 8, 10 and 12:

Note that the pattern begins on beat 12, and beat 1 is a weak beat. If you're not versed in flamenco (and/or if you're a white kid from suburbia, like me), you'd probably hear the bulería pattern like this instead:

Since Maria isn't trying to write authentic, traditional flamenco, but instead to use bulería as a jumping-off point for her own personal expression, she opts to use the shifted form above (which, as you will see later, makes her subsequent rhythmic twists and turns much easier to read). When you look at the shifted bulería rhythm above, you can see it implies a 6/8 + 3/4 feel — which is, of course, also ubiquitous in a whole range of South American music:

The first thing Maria does is to subdivide the "6/8" portion of the bar into four parts instead of two parts -- which, if we go back to the 12/8 notation, looks like this:

Does that combination of dotted eighth notes and non-dotted quarter notes in 12/8 remind you of anything?

No, it's not "irrational" like the Michael Gordon bassline -- if you wrote it out in 4/4, you wouldn't have incomplete triplets -- but the rhythmic profile is similar.

Anyway, in her score, Maria chooses to augment the bulería rhythm, doubling all the rhythmic values — again, out of notational convenience:

This makes it possible for her to notate the entire bulería section without resorting to any sixteenth-note subdivisions. But you can see that the underlying pattern remains the same, only instead of 6/8 + 3/4, it's now 12/8 + 3/2.

Here's the initial theme -- check out how it sometimes reinforces and sometimes pushes against the 12/8 + 3/2 bulería foundation:

(I took the liberty of making some slight alterations to the beaming patterns in the original notation, in order to make the 12/8 + 3/2 pattern explicit.)

Here's the audio of the above, from the original recording:

MP3: Bulería, Soleá y Rumba, Maria Schneider Jazz Orchestra (excerpt) -- click to listen, right-click/control-click to download

A bit later on, Maria introduces triplets, a new rhythmic element that creates 3-against-4 and 6-against-4 relationships to the bulería pattern:

She also frequently uses this rhythm, a string of quarter notes starting on the second eighth of the bar:

There's also an incredibly striking moment beginning in m.19, where the 12/8+ 3/2 pattern is temporarily suspended in favor of an eight-quarter-eighth sequence, whose binary profile strongly implies a superimposed 2/2:

These are a lot of different, non-obvious ways of carving up the 12/8 bar! But even so, we have only just barely begun to scratch the surface.

For instance, I like what happens when you play the bulería pattern followed by its retrograde (in other words, play it forwards, then backwards):

Or, in classic metametric fashion, you could mess around with multiple simultaneous juxtapositions:

Finally, if you're interested in acquiring the score to Bluería, Soleá y Rumba -- which trust me, rewards close study -- you can buy it from Maria's site.

Comments

[g]

1.

So are the meanings of written note values changing when she changes the denominator, as with the post-classical people? 'Cause if so, you could avoid that by just writing the 3/4 as 6/8, no? Are the 12/8 eighth notes supposed to have a triplet feel, as I'm used to?

My prejudice changing denominators all the time (aside from not being used to it) is that it means players have to recalculate all the various note values from measure to measure, which makes it harder to read, if not necessarily to feel.

[DJA]

2.

g,

Relax -- this is not as complicated as you think! There is no actual time signature shifting going on -- the bulería section we are talking about is notated entirely in 12/8.

Maybe take another look at the post with fresh eyes. If you check out the noteated excerts carefully and listen along with the MP3 excerpt, and I think you'll find your questions are all answered.

For instance, the example labeled "Maria's bulería pattern -- augmented," as well as the percussion (bottom) staff in each excerpt, show you how the 12/8 is subdivided. The first measure of the pattern has 4 groups of 3 eighths (like you'd normally expect in a bar of 12/8), and the second measure of the pattern has 3 groups of 4 eighths -- but the first accent of the second bar is on the third eighth note, instead of the downbeat.

[g]

3.

No, I shan't relax. It's not like just saying it can make it happen.

Anyway, looking at the following examples (as I hadn't previously) clarifies how it should be subdivided; it just seems like that change to 3/4 is a totally (if not totalistically) unnecessary annoyance...

Now, looking at the thing with the dotted eights, I could kinda sorta see the sense of having the the 1st bar in 2/4 and the second in 3/6 or 6/12 or whatever, but I still wouldn't like it..

I could see the reason that kind of in the "What is a compound without an element?" example because it avoided that weird thing where you had a triplet group starting on an eighth note upbeat, but unless that's something that turns up in this piece, I'd rather just stick to regular old easy-to-read eighths and triplets.

I also don't like different clefs. And what's the deal with neckties?

[g]

4.

"I could see the reason that kind of in"="I could see the reason for that kind of notation in"

Also, insert some sort of smiley after the thing about shan't relaxing.

[g]

5.

...'cause it was supposed to sound charming and cute.

[DJA]

6.

g.,

We love you, man, but you have got to read the posts.

Once again, there is no change to 3/4. The bulería section of Maria's piece is notated in 12/8 throughout.

I only showed the 6/8 + 3/4 example to illustrate a more abstract point about how the shift in the middle of the bulería rhythm feels -- the first half of it has a triple subdivision (2 groups of 3 eighths), and the second half of it is has a duple subdivision (3 groups of 2 eighths).

This notation is not used in the piece. None of the first four examples in the post appear in that form in Maria's score. They are there because I am explaining how you get from the pure, traditional bulería pattern to the modified pattern that is used.

Again, this 6/8+3/4 feel -- not notation, feel -- is really, really, really, really common. "I like to be in A-mer-i-ca"? Same 6/8 + 3/4 shift. (Only difference is that in this case, the "mer" syllable would be syncopated instead of being on the downbeat.)

Maria's version is (like it says in the post) an augmented version of this pattern -- so, instead of 2x3 eighths + 3x2 eighths, it's 4x3 eighths + 3x4 eighths.

[g]

7.

OK, interest drifting to other things now, but I am sad to see that that wiki link says that evil notation is standard.

...but all this 12/8 talk did get me wondering what the name is of this rhythm that I always hear latin bands playing. Using the system on that wiki page, it goes like this:
[1] 2 [3] 4 [5] 6 [7] [8] 9 [10] 11 [12]

I also wikipediaed "clave" but couldn't find it, but I hear it all the time. Name?

[g]

8.

The inevitable oops and correction:

[1] 2 [3] 4 [5] [6] 7 [8] 9 [10] 11 [12]

[g]

9.

So apparently it's called a West African or Nigerian Bell Pattern, which isn't as romantic sounding as I'd hoped. All done now.

[g]

10.

Oh well, I've already got 7 comments here already (profuse apologies for that), so I guess one more won't do too much harm.

I just wanted to add that it was never really my intention to argue with this post as such. It was just that the 1st bit brought to mind a thought or two that I'd been having about the earlier ones, where I guess it would have been a little more appropriate to post it/them.

[Kass]

11.

I enjoyed this post. I'd be interested to see your analysis of Aires de Lando sometime. Another intricate Maria piece which I'm sure you have thoughts on :)

[DJA]

12.

Thanks Kass. I actually have not yet bought the score to Aires de Lando, although you're right, I should.

[Kass]

13.

You're welcome, I'll look forward to that. I'm also looking forward to your show on Saturday. Best!

[Juan]

14.

It´s funny you guys named the Landó rhythm after g wrote that "Nigerian Bell pattern"...that´s exactly the Peruvian Lando clave, as played by cajon and double bass most of the time (I don´t remember Maria´s piece though).
Amazing posts on "Buleria..." and irrational meters, they have given me a lot of rhythmic food to chew. Thanks for leading to Kyle Gann´s amazin essay on totalism.