Pitch Class Sets Part the Third

First Read: Pitch Class Sets Part the Second and Pitch Class Sets Part the First

So no we've got all these funky chords and we need to name them. Why do we want to name them? For the same reason we name traditional chords: because the sonorities all sound similar. A C major chord sounds like a C major anyway you play it as long as it has even the meaning of C-E-G behind it. With atonal chords, the aural similarities may not be readily apparent to most but the idea is that with a trained ear, you can hear it. Pitch class set theory allows you to talk about it with your music theory nerds. I mean friends.

So let's say you've got this crazy chord that goes C-D#-E-F#. In numbers, that would be 0-3-4-6. Without going into the actual details, let's call that chord "4-5". The first number denotes the cardinality of the chord you're naming (in essence, the number of distinct pitches it contains) and the second number denotes a unique identifier. Some pioneering theorists named Allen Forte looked at every possible chord combination and gave them names back in the day so now us nerds talk about how 3-7 is related to 6-18 and how it's cool that 4-Z15 and 4-Z29 are m5 or m7 related and such. Again, without getting into the craziness, pitch class set theory is, preliminarily, a way to abstractly equate atonal chords.

Once you get the basics of identifying chords down, then you can start analyzing relationship between them. We're trained to hear in a diatonic doe-ray-me-far-sew-la-tea-doe kind of way so hearing progression from C Major to G Major is easy for us. Hearing the change between a a4-Z15 and 4-Z29 chord is pretty much impossible for most of us. Pitch class set theory gives us an edifice, albeit mostly an academic rather than aural one, with which to grapple with atonal music (of the Schoenbergian variety).

That's enough pitch class set theory for now. Perhaps I'll come back later and explain some of the mechanics of it in detail. I know you're just dying to hear that!

Spinning Advice

Some advice on practicing spinning poi:

Make your own practice poi. Small bags of rice in socks will do. And in a pinch, you can smack your opponent with your dirty sock-poi and demand satisfaction. Much more humiliating than a glove and if you're lucky, he'll get an infection and die from that nasty sock poi you've been swinging around everywhere before you'll have to avoid confronting him at the appointed time because you're a pansy and never really wanted a duel in the first place but goddamit you can't retract a satisfaction demand.

For the guys: watch out for your groin. You're going to be working on that forward 5-beat weave and you're going to think you're the (somewhat effeminate) man when you start getting it down when all of a sudden, *fwap*, a rice bag nails you in the groin. Then it's an emphatic *ooph*, a bit of doubling over, some embarassed laughter, and no kids for Johnny. Don't let poi ruin your chances to propagate your seed. Let your social awkwardness and that nervous tick do it instead. It's what they're there for.

For the girls: secretly watch your boyfriend practice poi. Sooner or later he'll smack himself in the groin and it'll be hilarious. No children for you guys but it's not like you wanted to poop out a mankind propagator anytime soon or anything and besides, you were thinking about ditching him in a month or two anyway. I mean seriously, what is UP with that hair???

Where do you get it?

Ever notice how there are things which you know exist and which you know are used by a lot of people but have absolutely no idea how to get? An item which everybody knows about and perhaps some even use but you just can't find it anywhere? I've got one for you: Kerosene.

There are kerosene heaters, even kerosene lamps and I can get those at Home Depot. Great, so one would think Home Depot might have kerosene. Nope.

OK then, since kerosene is a liquid fuel that is much safer and less volatile than some other readily available fuels (like gasoline or even Coleman fuel), perhaps could conceivably use it for camping? Maybe a sporting goods store with a camping section will have it. SportsMart: Yes on the Coleman, but no on the kerosene.

Well maybe a pharamacy/general store like RiteAid will have it. Ask an attendant: yes! They have kerosene! Alright! Right down here aaaaand oh wait that's Coleman. Note to self: cheaper than SportsMart.

Alright, last ditch effort, let's go to the supermarket.
Me: "Do you know if you sell any kerosene?"
Attendant: "Sorry, what?"
Me: "Do you know if you sell any kerosene?"
Attendant: "I don't know..uh..."
Me: "Or just the section where kerosene would be in...?"
Attendant: "Oh, I uh, I don't know what that is. What did you say?"
Me: "Kerosene."
Attendant: "Clariseen? What is that?"
Me: "Oh it's a kind of liquid fuel."
Attendant: "Is it like lighter fluid? We have those in aisle 6..."
Me: "No, it's not lighter fluid actually. It's just...uhm...it's kerosene..."
Attendant: "OK, let me call somebody and ask. *dials phone* Hey do you know if we carry any claritin"
Me: "kerosene"
Attendant: "...uh...klarosene"
Me: "kerosene(!!!)"
Attendant: "oh, uh...kerosene? Yeah? OK."
Me: "Oh, and if you don't, could you please ask where I might be able to get some?"
Attendant: "Oh we have it. It's right down aisle 6."
Me: "OK thanks! *runs down aisle 6* *comes back* This...this is lighter fluid."
Attendant: "Oh...yeah, I don't know."
Me: "OBVIOUSLY"
Attendant: "Are you stepping? What do you need kerosene for anyway?"
Me: "It's none of your business! You want to take this outside?"
Attendant: "Hell yeah! I'll wait, what? what are you doing? Stop squirting lighter fluid on me! Is that a match? Get a way from me with that match you fraaagggghhhhh!!!!! I'm on fire!!!!"
Me: "That's what I needed it for but I guess lighter fluid will do."

So where was I? Oh right! Kerosene. Where does one buy kerosene? And really, I want kerosene for fire spinning purposes, not for whimsical immolation though it's not like the latter doesn't appeal to me a great deal.

Interlude: Getting Smashed

There's a ring of sites called smashourstuff.com wherein the gimmick is that they take donations from the readers, buy a coveted tech item, and smash it. Cnet just did a short article on it and talks about negative reactions to these sites. For example:

"This is not harmless fun, it is pure poison. Their enjoyment comes not from the achievement of values, but from the destruction of the values of others. Their response to the phenomenon a happy man, is to take his happiness and mangle it. This is what Ayn Rand so eloquently identified as, 'hatred of the good for being good."
From The Benjo Blog

No, cyanide is pure poison. And in case you missed it, Benjo, they're destroying an XBOX360, not the values of others. Let me make that clear again: it's only an XBOX360! And it's not somebody else's XBOX360, it's their own! How is that destroying somebody else's anything, much less their values??? In the not-so-grand scheme of things, this is less important than a speck of flour underneath your couch next to that hideous floral-pattern chair which, despite it being very comfortable and cheap, is just wrong. The problem I see with such a reaction is that it forcefully imputes meanings to an act which was neither intended as being particularly meaningful nor as something which could shoulder the burden of all these extra subtexts. And right, Ayn Rand, the practical philosopher of our times. *snort* I'm a fan of her philosophy and books but I don't ever delude myself by mistaking an interesting point of view with an applicable one. Ad hominem attacks are pointless too. For example:

"Even if these neanderthals were simply smashing an expensive object in mindless glee, I would still feel contempt."

and

"But these cretins are much worse than cave men."
From The Benjo Blog

And since when, Benjo, did you become the supreme arbiter of all that is good in the universe? What happened to free speech? Neandertals might have judged others without a second thought but surely, Benjo, we are above this? A case might be made that destroying an XBOX and deriving satisfaction from its destruction is similar in nature to a sort of societal nihilism and masochism. Rejoice in other people's pain, criticize all that is good for no other reason than to be contrary, and otherwise encourage the rotting of our morals and ethics, hoorah. But the fundamental flaw in such a comparison is the scale and impact of said act. In some far off abstract philosophical land (incidentally where Ayn Rand lived) the scale might not matter but in reality, it does.

The smashourstuff ring is nothing more than a few sites devoted to a few uninspired stunts. If we're going to talk about publicity stunts, the antics of Hollywood deserve much more attention than one broken XBox? If Benjo really believes that our society is going to hell because we're disparaging good because it is good, why not go after bigger fish? Using smashmyxbox.com as an example is like speaking about how a particular brand of butter is no longer available and then using that as an example for world poverty.

I don't think we should criticize the good just because it's good and we certainly should criticize the bad if it's bad. But I do not believe that we can criticize something and label it as bad just because it does not fit our own definitions of "good." Not good is not necessarily bad. And we certainly can not then generalize a very small example of "not good" to epic proportions. While I disagree with Benjo's point of view, I am more than happy that he can hold it without retribution. I just have a problem with his angle of attack which to me seems a bit unsound. But if you don't agree with me I will destroy my XBOX360 by hurling a kitten at it (her name is Bubbles) repeatedly until both have expired. This will in turn precipitate the total collapse of civilization as we know it, so just watch it buddy.

Pitch Class Sets Part the Second

First Read: Pitch Class Sets Part the First

How does one assign numbers to pitches? Easy. There are twelve chromatic pitches to cover: A, A#, B, C, C#, D, C#, E, F, F#, G, and G#. We could get all silly and assign 1 to A, 18 to A#, and 6,655,321 to C but that's not really all that useful. Instead, we arbitrarily pick C to be 0 and go up from there. So: C=0, C#=1, D=2, D#=3, E=4, and so on and so forth until we get to B=11. Calling the pitches the numebrs through 11 is convenient because it equalizes their importance. There is no "key" of A where A is important. A will always be 9 so just live with it. The numbers also take advantage of an existing arithmetic system, namely arithmetic (har har har). Figuring out the interval between A and D# takes some thought and often involves, for many, visualizing a keyboard. With pitch numbers, it's easy once you know the numbers well. D=2 and A#= 10 so from A# to D is 10 to 2 is 4 (remember that the pitches wrap around so 2 is in essence 14) and from D to A# is 8.

The wrapping nature of pitches is the reason why they are called pitch class. For most people, hearing a C really on a cello sounds similar to hearing the same C high on a violin. They're both Cs but one sounds low and sounds high. This is the concept of octave equivalence. So the numbers stand for not a single pitch but a pitch class, regardless of the octave (this is the same as calling a note a C rather than a C3, for example).

So we've got pitch classes, now we need to get sets in there. Fundamentally, chords are bunches of notes played at the same time. Given enough importance, they become entities in their own right and retain identity through deformation, separation of its constituents, and other tranformations. A C major chord sounds like a C Major chord whether you play C, E, and G all at the same time or one after another. The sonority is the same. But after old Ahnold (the Schoenberg one) comes along, it's pointless to call something C Major because that harmony is assoicated with the old notion of a scale. Instead, we could have chords like C, C#, E, G, and Ab all played at the same time. What would you call that? A C-15 chord with a raised 15th, a flat 13th, and missing 7th, 9th, and 11th? Seems silly. Here's were the sets of pitch class set theory comes in.

Continued in the next and final installment of this exciting new series!

Pitch Class Sets Part the First

Advanced Music Theory is often compared to mathematics but the resemblance is superficial at best. Both involve systems of discrete units, true, but at that level of abstraction, mathematics is similar to far more things than music theory (like social sciences or even linguistics). And for those not in the know, I think one specific branch of modern music theory is responsible for giving lay people the impression that music theory requires math: pitch class set theory.

Most of the music that we listen to, whether classical or popular, is scalar, meaning that pitches and their functions are derived with an implicit scalar structure in the background. By far the most popular in recent memory (say from 1700 onwards for the Western World) are the major and minor scales. For people who remember the sound of music, "Homer: Doh! Marge: A deer! Lisa: A female deer!" teaches you how to sing the major scale. The scale gives the tones one sings a field with guideposts. Some tones are more important and stable, other are more tense and create interest, while others serve as signs to lead you from one tone to the next. Without a scalar structure that differentiates pitches, one could imagine a flat musical landscape which generates little or no possiblities at all for interesting music.

Pitch class set theory came about when the scale was in essence obliterated by Arnold Schoenberg and his 12-tone system. Schoenberg did flatten the musical landscape by putting all 12 chromatic tones in the Western equal-temperament system on equal footing. His music harmonic, not scalar, and focuses on pitch sonorities rather than pitch stability. Calling something C and something else C# made no sense in this context because C# was no longer an embellishment of C by rising a half step higher. C# was the same as Db, which is the same as B double sharp, and so on and so forth. So what's an analyst to do? Assign the pitches numbers!

Part II in the next post...

Cathartic Repetition

I'm becoming more and more convinced that a rote repetition is the key to cathartic events. For me anyway, a reptitious sequence of events is a great antidote to the free form academic thinking that makes up the rest of my life. Of course, montonous actions are no fun either. Licking and sealing 1,000 envelopes is hardly cathartic. But skills which can be improved upon by repetition (like fire spinning, the recent obsession) can be wonderful for the spirit. There is a sense of accomplishment and of certainty which lends much stability to one's mental outlook. There is also the ease of being able to focus on one act, facilitating an ignorance of worldly worries and stress. Note to self: next time I need to procrastinate, don't do anything creative. Instead, practice fire spinning or some other skill. Much better for the soul.

Unseen Work

So long without an update! I've been a bad boy. Oh yes. I need a spank. Oh yeah. Right ther...oh hi. Sorry.

It's ultimately a good thing but I hate it when a chunk of my work goes unseen. First the down side. Let's say I'm working on a piece of code (as I have been) and I continually find different ways to perform the task/process I want. So after a week of exploring different options, I'll come upon a solution that takes fewer lines and is more stable than all the pasghetti code I've written. Why is this bad? It's not, but for purposes of vanity, if anybody were ever to look at the code, they might "wow, this isn't so hard. It's just invoking these couple of functions." But see, it IS hard. Don't you see, dammit, that it took me an entire week to find those functions!

On the other hand, it is good in the end. A generalization of Occam's razor does work in most cases: simpler is better. Why do

int i = 0;
while (i < 5) {
DO_SOMETHING();
i++;
}

when you can do

for (i = 0; i < 5; i++) {
DO_SOMETHING;
}

right? So in the end, the simpler and more logical solution is better but it doesn't show the sweat and toil that it cost you to get there. But perhaps this is the case for a lot of people and the next time I see elegant code, I shouldn't think "That wasn't so hard" and instead "I wonder how much knowledge and research it took to find such a simple way of doing things."

Unequal

Bush Contends Partisan Critics Hurt War Effort

OK, but don't Partisan Critics Contend War Effort Hurts America? So which is more important, Bush or America? Hmmm...

What's on the radio?

Being a specialist in classical music makes one sensitive to the kind of incongruous information hollywood tries to pass off as intelligent conversation. The same applies to a specialist in any field I suppose but classical music is a field that fewer and fewer people know well. Most people would laugh at a mechanic considering listening to an engine and wondering if it's the rear differential that's leaking or the steering wheel that needs new leather. The difference between Debussy and Scriabin, on the other hand, is in essence non-existent for most people. To me though, one is a french "impressionsitic" composer hopped up on mythical creatures and the other a Russian mystic hoping to bring you to close to that brilliant distant star until you burn up in its flames and experience some kind of spiritual ecstasy. Oh, and their music sounds absolutely nothing alike too.

Chromatic Saturation

I've always thought that the best classical music academic would be someone who knows pretty much all of classical music. Somebody who is as familiar with David Del Tredici as he is with Wolfgang Amadeus Mozart. Obviously, this is impossible because almost nobody has such a tremendous musical memory and even if somebody did, he/she would not have the time to consume all available music. So, instead, us musical academics do what we can with the music that we have in our heads, eclectic though it may be.

But what seems like even the most odd connections should not be dismissed as random coincidence. On the other hand, such connections need to be carefully examined for what they are. Some sonic connections may lead to deeper analyses and others may just be nothing more than a superficial coincidence. On that note (pun intended):

The first "theme" of Prokofiev's Toccata is a "12-tone" melody compound melody. It starts from the mid-range and expands to an A octave over a d minor arpeggio. It systematically and tonally saturates the chromatic octave. The theme from the fugue from Musica Ricercata XI by Ligeti is very similar. It is also a compound melody that branches out from the middle of an octave and chromatically expands to fill an octave (also starts on A, incidentally). What is more interesting than the superificial resemblance is how these similar structures act in similar ways despite their chronological separation. Both melodies are an exaggeration, almost an exploration, of the limits of certain aspects of tonality.