Tuesday, July 19, 2011

Eight is Enough

"Be sure to get Seven Days."

Or so says Beff when I go to Hannaford's on summer Wednesday mornings when we are in Vermont. The fact that I put Seven Days in Italic clues you in that it is the name a publication (and not a local disease), and yes, one that does not strive for the least common denominator — if it did, it would be called One Week. Stretching the joke much too far, it's also not called One Hundred Sixty-Eight Hours, mostly because the title would have to be set in type too small to be seen from a distance.

The publication is a weekly — or a seven-daily — which serves as the local alternative weekly. I guess. It's free, it reviews stuff, and it tells you all kinds of things that are going on around town that seven three hundred sixty-fifths of one trip around the sun.

While looking through the reviews and advertisements in One Hundred Sixty-Eight Hours last summer, Beff encountered mention of a new restaurant given the silly name Chow Bella, on Main Street in St. Albans, which seemed to be geared towards foodies, especially those that love misspelled Italian food. Since it's in the very town where I grew up, we were (or I was) interested to try it at least once. And so we did.

Ooh, it was so shi-shi that it had a live pianist! But not just any live pianist — would you believe Verne Colburn, my band teacher in high school from thirty-five years ago? Woo hoo! Now that's bringing it all home — literally. And unfortunately, that meant I did more listening to the cocktail piano than is ever customary in such situations. I seriously wanted to ask Verne if he could play one of the Schönberg chamber symphonies, but I doubt there's a lead sheet available for those, even all these years later. And I did intend to digest my food.

I looked around the cavernous bare-brick, old wood of Chow Bella, and it didn't seem familiar. Before the shopping center two miles north of town drove all the commerce (and Quebec license plates) out of downtown, my mother used to take me downtown often for her various nefarious shopping purposes, and all the usual shopping places had disappeared long ago. Fishman's Department Store with a lunch counter? Gone in 1975. Rixon's Pharmacy? Actually, still there. But we didn't shop there.

Finally I realized. This is Doolin's! That is, this was Doolin's. Or more precisely, this is the building in which Doolin's was located! Verne confirmed that when I asked him.

And what was Doolin's? In my memory, it was a fairly large store where ladies who smelled of potpourri and had hats with lace on them hung out and bought stuff, mostly as gifts. It was also the coolest place ever, because it had suck pipes. At the cash registers, often a receipt and a bunch of your cash would be put into what seemed like a mini-time capsule — or a giant aspirin with a rubber band around it — a door would be opened on a length of exposed plumbing at the end of an elbow joint, and there would be a Perot-like sucking sound. A minute later, the pipe would be opened again to another, softer, sucking sound, and there, magically to a six-year-old, would appear another mini-time capsule with a certified receipt and correct change.

I loved the suck pipes. They were the coolest thing in my life until JC Penney opened in Burlington and it had escalators. Doolin's was also one of the few stores in town without a Nous Parlons Français sign in any window. I only add that detail because I think it's fun typing the "ç". Whee! (yes, it's true; in northern Vermont, the sound of a tire deflating is "Çççççççç....."

So what did Mom do inside Doolin's? Well, they sold potpourri (obviously), Wedgewood, tchotchkes (we didn't call them that), and fabric, and patterns. A large corner of the store was dedicated to fabric and pattern books, and I was frequently sat down at the pattern book table to amuse myself while Mom decided what to get.

Mostly, she got patterns. And material.

Then she brought them home, and she made stuff on the sewing machine. Using the material.

Material. Kind of a generic word when you think of it. Despite the Madonna song. Clothes are made from materials. Are cars? Buildings? Computer programs? Molecules? Symphonies?

Now is your chance to bookmark this post (as well as this one) in your folder of awkward segues.

First thing we might notice, despite how clinical it may sound, is that materials have properties. Cotton, rayon, wool, dacron — wait, dacron? — are made of different stuff, have different feels and looks to them, yield differently to the sewing machine and all, and have different effects on those wearing them. Why is this important? Mom gave me socks made from the material wool one day in third grade, and by lunch time my entire body had a rash, and I was itchy everywhere — especially around the family jewels. I was forced to miss half a day of school because it's hard to concentrate on school stuff when you can't stop scratching (insert random junior high string orchestra joke here). From then on, I wore cotton socks. Different material — different scratch coefficient.

Yes, I was allergic to wool, as tests later confirmed. So years later, forced to march in high school band and to wear wool uniforms, I was one of very few who wore long johns in June. Because it's hard to play trombone, and march, and scratch yourself in the family jewels. This also explains the bit of shirttail sloppily sticking out in this David is so cute in his band uniform! picture. I believe in the picture I was trying to channel The Fonz.

So yes, some musicians talk about the materials in a piece — not to mention, there are countless music fundamentals textbooks with "Materials of Music" in the title, or even the whole title. What is a material? A note? A bunch of notes? A scale? A rhythm? A tone color? A sixteenth note? An orchestral crescendo? A chord progression? A cadence? A theme? A structural section?

Aaaaa! Too much! Too much! The answer to all of them is Yeç. They are all materials.

And how much are we aware of — how much do we have to be aware of — the music's materials when we listen to music?

Hee hee. Depends. The word is so broad as to be fairly useless here. You might as well ask when I listen to music, am I aware of stuff?

So I scratched my head a bit — no, I was not wearing a wool cap — when, many years ago at an artist colony, a composer told me he hadn't started his piece yet, but he had all the materials. Okay, fine, I don't write that way, so it was intriguing to think of approaching a piece by inventing or collecting its materials, and then — as an act that can follow only when the first one is completed — putting the materials together. And on further thought, I stopped scratching my head. Yes, I work with materials. I just don't call them that (I call them Fred), and I don't wait to start a piece until I have all my materials. But why should I care about someone else's process, anyway, as long as the music works?

Slippery, slippery slope here.

So lemme splain. Or try to get a little more particular. I'm going to talk about scales as a musical material. Insert fish joke of your choice here.

Scales might be thought of as like (hey, a simile! Call me Simile Guy! Again) the Sieve of Eratosthenes. And, belaboring the simile, the scale(s) a composer uses is(are) like the prime numbers that make it all the way through the sieve. Thus, belaboring the metaphor even more, in a fairly substantial majority of Western music, the chromatic scale represents the entire spectrum of possibility (the counting numbers) and the scale a composer uses as musical materials is always a subset thereof (the prime numbers).

And so let's consider a sieve of the sort that fascinated us in graduate school until it stopped. The diatonic scale — major and natural minor scales — can be sieved out of the chromatic scale by using something like (another simile!) clock arithmetic. Chromatic scale: 12 notes; clock: 12 hours. Set your iPhone to sound an alarm every 3 hours, say, and, presuming you start at 12 o'clock, when will the alarms go off?

Okay, you're just humoring me. Sure. 3, 6, 9, and 12 o'clock, and then the pattern repeats. 3, 6, 9, 12 ad infinitum. If we want to be reminded to do something at 2 o'clock, this pattern isn't going to work. Unless we start at 11, 5, or 8 o'clock. Whoa, cosmic.

So every four hours? 4:00, 8:00, 12:00, repeat. Every hour? Yes, every possible hour. But also if the alarm goes off every five hours. Then the times are... 5:00, 10:00, 3:00, 8:00, 1:00, 6:00, 11:00, 4:00, 9:00, 2:00, 7:00, 12:00 .... repeat! All twelve possible hours! Just not in counting number sequence. Thus if we similize some more, turn 12 consecutive hours into 12 consecutive adjacent notes of the chromatic scale (i.e., one hour equals a half step) ... which themselves repeat after 12 iterations ... Uh oh, I sense you nodding off.

Let's isolate every seventh note. Similistically, this is what we already know as the circle of fifths (left), which experienced musicians know covers all 12 notes of the chromatic scale and then repeats. And to be totally nerdy about it, rewind back to clock arithmetic: the circle of fifths covers all the notes of the chromatic scale because seven is prime to twelve. See, this is a property.

Now take any slice of seven consecutive notes from the circle of fifths. Go ahead. You'll be glad you did.

The red-boxed notes represent such a slice, and comprise all the notes of the C major scale, or A natural minor scale. Similarly, the green slice — which we note has six notes in common with the red slice — is the G major scale. The blue slice is the D major scale. In tonal music theory, there is the concept of closely related keys and distantly related keys. Such relationships are easy to visualize here — the red box (C major) is more closely related to the green box (G major) than to the blue box (D major) because there are more notes in common in the slices. The purple box, meanwhile is as distantly related to C major as possible: F# major, which has only two notes (F and B) in common.

Note also that the notes that have been sieved out of any particular slice are two things: what are called that slice's (key's) chromatic notes; and they are a so-called pentatonic scale. Oooh, oooh, another musical material! The notes not in the red box? The black keys of the piano!

Note also that there are twelve possible slices, hence twelve possible keys. Bach already had the temperament to knew that.

Now let's talk about more properties of any of these slices. We already know that any slice has the collection of notes we call diatonic scales. Duh. But it also happens that in such a slice there are: six possible two-note combinations to make a perfect fourth or its inversion, a perfect fifth (adjacent notes in the slice!); five possible major seconds/minor sevenths (a slice note and the note two notes later); four possible minor thirds/major sixths; three possible major thirds/minor sixths; two possible minor seconds/major sevenths; and exactly one tritone. Those are all the possible chromatic intervals, and here comes a whopper of a property in the diatonic scale: it has a unique multiplicity of intervals (uh, as in, there are six of one, five of another, etc...).

Why should anyone care about the unique multiplicity thing? Wait, let's let one-sentence Italic paragraph guy ask that.

Why should anyone care about the unique multiplicity thing?

Well, for two reasons: it is the largest possible collection of notes in the chromatic scale with that property; and it has everything to do with the sound of music that uses the scale as a material. How the composer shapes the material given the possible sounds is, well, what makes the composer a composer. Well, that, and poverty.

There, are of course, more properties that can be, and have been ascribed to the diatonic scale. For instance, once all the notes are put into the same register, and ordered, the intervals between adjacent notes form a non-redundant pattern. WWHWWWH -- the pattern of whole- and half-steps between consecutive notes in the major scale. Yes, the sound, and therefore potentially something of the affect, of diatonic music comes in no small part from the properties of the diatonic scale. For one, you always know where you are in it — uh, unless the composer has done something clever to make you think elsewise.

So what?

Does anybody need to know this? Do composers know this, or have to be aware of it?

Nope. Yep. (both)

But let me get into a heavy metaphor here. I don't need to know how a car works to drive it — turn the key, vroom! and go. But an important property of what's under the hood — gasoline asplodes when burned, making it the perfect fuel for a piston-driven engine (which is the chicken, which is the egg?) — makes the car go, whether or not I care about that. And when your car stops working and you want to drive it again, somebody in the repair shop better know something about how the car is put together. I wouldn't trust my car to a guy who told me I dunno how make vroom go.

Go back to the slices a moment. The pentatonic scale — usually, the major scale with the fourth and seventh notes omitted — is also a slice of five of the circle of fifths. It has properties, too. That interval multiplicity thing — reduce the slice by two, thus reduce the multiplicity of each interval by two, and you get zero minor seconds/major sevenths and zero tritones. The sound and affect when there are neither minor seconds nor tritones is different when both of them are present. If you hate tritones and love perfect fifths, here is a material for you to use! And if you love, love, love the expressivity of minor seconds — stay away from this material!

Fine, fine, fine. The diatonic scale has special properties, and we hear lots of music that uses it without us being aware, or having to be aware, of the properties. What happens when composers want a different sound or affect than what they perceive is possible with — or more precisely, inherent in — a diatonic scale?

Facebook Relationship status: It's complicated.

First, we must presume that composers think of what we are calling scale materials here as actual scales — with steps and what "steps" mean to a musican or listener, and that's a lot more complicated than you might think. Pitch collections with big gaps — thus meaning say, a leap of a fourth between scale members — wouldn't act very scale-like or as scale-like. And that is only partly true, because it's complicated.

Presume — and it's no small presumption — that the composer wishes to be subtle about using different scale materials in tandem — because the composer wants a variety of affect — and then we start to see that there are other commonly used scales that have their own properties, and thus potentially their own perceived affects. We've already touched on one — the diatonic scale minus two, or the pentatonic scale. No half-steps. No tritones. Black keys of the piano is one of them. Fewer so-called active or dissonant intervals, making it quite pleasant to listen to. Hardly anything bad happens in pentatonic music.

Then there is the whole-tone scale. We know it's a scale because it's in the name. And there's nothing but whole-tones in it! Thus, no half-steps, minor thirds, perfect fourths, perfect fifths — but tons and tons of tritones! Given such a multiplicity of intervals, and the extreme redundancy of the scale ...

What do you mean by extreme redundancy? Well, let's compare the intervallic info you need to construct a major scale to the info you need for a whole-tone scale. Major scale, WWHWWWH. Whole-tone scale, W. Whoa. How do composers use whole-tone scales? Well, lots of ways, but one of the more common ways is a feeling of non-directionality, weightlessness, a feeling of stuckness. Even in a very active texture such as Debussy used in Voiles (right), whole-toneness feels as if it is not moving anywhere, the notes (actually, the gestures) pushing against a harmony that refuses to budge. It's a good scale to use to build an upbeat to a bigger moment — since the non-motion can be used to create tension in need of being resolved by such a big moment.

And in jazz, more than a few players use whole-tone scales over a dominant seventh sonority. I only say that because it's true. But read on. They use the next scale in the same context.

There is a very special scale, whose intervallic info is, simply, WH. Arthur Berger gave it the name octatonic scale in an article on Stravinsky, and jazzers know it simply as the diminished scale. Jazzers have a more pictorial language, but both names simply denote a property of the scale: eight notes, contains two diminished seventh chords.


Let's go back to scheduling an alarm every three hours. 12:00, 3:00, 6:00, 9:00, then it repeats. Similize three hours to three half steps, and you get diminished seventh chords. With D as 12:00, look to the right to see 3:00, 6:00 and 9:00 — F, A-flat, and C-flat representing the notes successively three half-steps higher than the last.

There are only three distinct diminished seventh chords — in those four diminished seventh chords to the right, each is a half-step higher than the one before it; the fourth is the same in pitch content as the first, assuming that D and E-double flat sound the same — which on the piano they do. Now let's get slightly more cosmic with properties.

The intervallic info of the octatonic/diminished scale repeats every minor third. Thus, there must be a whole pile of minor thirds within the scale — diminished seventh chords! Furthermore, and I am skipping a few obvious logical steps: any octatonic scale is made up of the notes of two diminished seventh chords — and the scale's sieve leaves out the notes of the other diminished seventh chord from the scale.

Wow. Why should I care? One sentence Italic paragraph guy?

Why should I care?

Wait for me to pile up more properties, then I can give a proper answer! There are three distinct diminished seventh chords, thus three possible combinations of two of them (each combination leaves a different diminished seventh chord out). Thus there are also three distinct octatonic scales. So from the scale we see above, the D scale is the same as the F scale is the same as the G# scale is the same as the B scale.

Yes — and what that means it built-in ambiguity. If you hear D as a possible tonic note of the scale, it's easy for the composer to fool you into thinking F or G# or B is the tonic. Because of the extreme redundancy of the scale. For this to be a significant property, it has to be agreed that ambiguity is something a composer or listener values.

What about the intervallic thing? Well, all the intervals are possible, but there are lots and lots of minor thirds and tritones. If you value tritones — whether you want ambiguity, or you just like the way they sound — this scale is drenched with them.

But there is yet one more property to this scale that is extremely important — and which explains why composers as long-dead as Mussorgsky and Debussy valued it. And that is that is bears a lot of similarity to the minor scale. Look at the scale up there — the first four notes could be D minor. But the A that makes the perfect fifth with the tonic — denied! The tritone, G#, is the next note! Ambiguity, maybe! Dissonance, maybe! But still so familiar-sounding, while not being familiar at all.

Plus, both major and minor triads are available within the octatonic scale. Because the scale repeats itself every minor third, the triads a minor third higher and lower, and a tritone higher or lower, are also within the scale. Familiar sonorities here, but potentially used in such unfamiliar ways.

Also because of the scale's extreme redundancy, it is possible to use it for that floating feeling, and composers can use it for restful places, as Debussy did in Nuages

So redundancy equals ... wow, many things. Lots of tritones (dissonant! scary!) lots of minor thirds (the calling motive!), floating quality (not dissonant or scary at all!), lots of strangely related triads (mommy, where am I?).

Even this little octatonic portion of Stravinsky's Les Noces below and to the right — a florid tune over an ostinato — is both floaty and rather strangely dissonant. How did Stravinsky do that?

How about — because Stravinsky was a great composer? And because there's lots of emphasis on the A to E-flat tritone harmonically?

Bartok was also a serial user of ... oh, bad word choice. Bartok ... uh, used the octatonic scale quite a lot, usually forcefully, and often in a way that sometimes called to mind Eastern European folk music. Since Bartok's music isn't in the public domain, I'm not embedding any musical examples. But listen to the string quartets especially, Music for Strings, Percussion, and Celesta, and various other pieces, and you'll hear plenty of octatonic music in dialogue with music using other scales.

In dialogue with music using other scales.

The octatonic scale has another property that's not entirely its fault (it's hard to assign fault to inanimate material). Partly because of its properties, and partly because of the sterling example of much great music by Bartok that lots of composers wish they had written, the octatonic scale is a black hole that sucks composers in.

Composing with the octatonic sieve can be very soothing, because the composer can always feel good about the sound — it always sounds so damn great! You can have triads, you can have dangerous sounding tritones, you can get all the ambiguity you want, you can be soothing, you can be dastardly, and ... after a while, the composer can forget, or simply not care, that there are other scales — even other octatonic scales — and the sound all meshes into generic octatonicnessositudinousness, and the music grows alarmingly static. Especially if the composer is writing a string quartet, the composer loves Bartok, and the composer like scales.

Trust me. I find myself being sucked in by the octatonic scale all the time, and I've had to invent a brain switch — well, not really, but I've had to learn to be extremely vigilant about noticing when the music I'm writing is getting all octatonicky, and therefore static, and therefore ... dare I say it ... I'm getting damn lazy about squeezing out the next notes. Thirteen years ago I wrote Beff a cute little piece for E-flat clarinet that is at least ninety-five percent octatonic (and zero percent perspiration), and since it's short, I almost got away with it.

Notice my value judgment here. I suppose it's okay for the piece to be so limited and limited-sounding because it is short. But contrast and motion are valued by me (as is the passive voice), and when I write music that stands still like that, I disappoint myself. Mostly because — sigh, it's my stupid value system — which when I invoke it I know that I chose, in this piece, the easier, lazier route.

Another way of saying this — or perhaps a development of the same point — is that it takes a different, perhaps, better, composer than me to make relentlessly octatonic music sound original, captivating, and not static.

And the black hole thing? It's sucked in its share of composers. How many times have I said (rather obnoxiously) to a friend after a performance "I sure do want to hear those other four notes now."? There's an actual answer: seven. I've never said that after a piece by Bartok (usually it's more like FUCK yeah).

In my coda to this rather overly long post, I bring up that I myself do not write diatonic music, despite having a nice long list of its properties. For one, there are other composers steeped in the sound who do much nicer things than I feel like I ever could. I feel more comfortable in extended-tonal chromatic don't-let-the-octatonic-bite-ville. I suppose I've just revealed a hidden buttstik.

As to my stupid value system. It's mine, and you can't have it.