Thursday, October 05, 2006

An Introduction to My Musical Language: Part 2

In yesterday’s post, I rambled about some of the basic details of the theory behind my musical style, what we usually describe as “language” though perhaps “dialect” would be more appropriate. Today, I wanted to get into a little bit about how this applies to the Theme & Variations I’ve just completed for the set of pieces for violin and piano which I’m composing for John Clare (he's all excited about it) and myself to perform some time next Spring.

Since Allen Forte lists 50 different hexachords, it’s difficult to limit yourself to just 2, so for this piece I decided to look at another pair and see what other kinds of possibilities I could find.

The first thing that came to mind would be something that would contain the notes and intervals of the open strings of the violin – G-D-A-E. I don’t use a lot of open 5ths or 4ths in my typical “language,” so I thought this would add a challenge for me. Part of the issue, basically, was my being attracted to the minor 2nd and its inversion, the major 7th, with whole steps, minor thirds and tritones next in frequency. In standard tonal language, the primary melodic intervals would be the perfect 5th, its inversion the perfect 4th, plus major and minor thirds since that also form the building blocks for the harmony, filled in by passing tones like major and minor 2nds as needed. So my melodic language also reflects the intervals used to build my harmonies as well, following the same logic. Now, with a lot of P4s and P5s (P4 = Perfect 4th), that will change my sound – subtly, to some listeners; hugely, to others.

So I found what Forte labels 6-Z25 and 6-Z47 (without explaining what the Z stands for, which marks other structural components that relate the two). The first one I tried has the open strings (Ex.1a) plus a major 7th (Ex.1b) (okay, let’s call that M7 - upper-case ‘M’ means “major”) which could also be inverted to a minor 2nd (m2 – small-case ‘m’ means “minor”). If I put that into an “abstract form like a scale,” you have the collection of pitches which I can now transpose to any other starting pitch (just like any scale) or create its inversion (but let's save that for another time).

Since I can put these in any order (just like the pitches of any scale), I can come up with a number of melodic possibilities: see Example 2. In (a), I’ve changed the open-strings motive to a series of P4s (same pitches, different order) and tagged it with (b), a descending M7 – it will sound different from the Ex.1a+b but they are the same pitches. This gives me a sense of unity but already some strikingly different variety. If I “mix up” the intervals (see c+d) or insert the M7 “tag” INTO the “open-strings motive” (see notes marked *), it’s still the same pitches but a different ordering and so it’s going to sound different. These can be transposed to other pitches just like any melodic idea could’ve been in 1800.

(By the way, don’t confuse “melody” with “melodic idea” or motive – Beethoven’s 5th starts with that famous “knock-at-the-door” motive but only after two statements of it does he actually build a melody out of it. Likewise, do not confuse “melody” with “tune” though we tend to think of them as synonyms these days.)

Now, if I form the “complement hexachord” from the other six pitches, I come up with Example 3a which still contains the open-strings motive (Ex.3b, now transposed to A-flat) but instead of the m2-M7 tag, it’s a P4-P5 (Ex.3c). This subtlety can come in handy later on. These two hexachords then become my basic “building blocks” just like a scale of a classical era piece, only here, rather than dealing with all the notes of the scale, I can focus on the attributes and potentiality of each half. In that sense, everything (more or less) grows out of six notes, not twelve (since the second half is really a different form of the first half).

If I haven’t lost you yet (and congratulations if you can follow this, whether you’re fluent in Classical Music Theory or not), let’s move on to Harmony.

If a “melody” is the linear aspect of the music, a “harmony” basically is a collection of pitches that form a vertical sonority. We’ve come to think of “harmony” or “harmonic” as meaning restful or pretty. Harmony is more, though, than just a chord: it’s really the language of how these different chords relate to one another, particularly to the tonal center of the piece (whether it’s in D Major or G Minor).

That was one of the things where people started getting lost even before the 20th Century: by weakening our awareness of that tonic center, we lose the element of resolution and so the other chords tend to become vaguer in what they’re “doing” there. Schoenberg did not invent this: in fact, the tonic centers in Wagner’s “Tristan und Isolde” move so flexibly when one resolution becomes a modulation to something else, people thought not only was the music “unhinged,” the composer was, too. But not even Wagner invented this: Mozart did it in the last movement of his Symphony No. 40 (I have read articles where authors discussed whether or not Mozart invented atonality) and Bach did it in something like his “Chromatic Fantasy & Fugue in D Minor” – in both cases, this being thrown out to sea (rather than to C Major) is an example of “extreme tension” which only strengthens the resolution finally to the home key.

So, if I group my six “abstract” pitches into “vertical aggregates” or chords, you will see or hear some that sound pretty gnarly and some which sound pretty familiar: in Ex.4, I list just six possibilities (and some of them the same with just the pitches relocated to create different “voicings” of the same chords), some of which can resolve to an A Major triad and others to a C Major triad. Or a chord built on P4s or another one all on M7s! But they’re all from the same six pitches, just different sounds.

In an earlier piece, I got the idea to start by focusing on the m2/M7-type sonorities but then, without changing the basic hexachord (or six-note scale, loosely speaking), refocusing it into more traditional sounding major and minor triads. In that way, the dramatic climax of my still un-named piece for violin and orchestra (originally inspired by the opening scene of Tolkien’s “Silmarillion” where the world is sung into existence) actually was a big loud C Major Chord – and then from there, the piece progressed back to the opening focus on the m2/M7s. That’s the idea, anyway.

Example 5 does the same thing with the complement hexachord, where something that could work like a Dominant 7th chord in E-flat actually resolves to a B Major triad in the last example. The next to last one is interesting, too: the G-flat-to-F M7 would be an “active-sounding harmony” depending on how it’s used, but with whole-step motion in the outer voices, it resolves to an A-flat Minor triad: thus giving the G-flat-to-F chord an element of tension it might not have on its own, fulfilling itself into a “tonal-sounding” resolution.

Dissonance, after all, is in the ear of the beholder but just as “Harmony” doesn’t originally mean “pretty,” “dissonance” doesn’t originally mean “ugly” – played by itself, the major 7th could actually sound fairly resolved by comparison to what else might come before. That’s the point in the study of “Harmony” – the context is more important than the individual “harmony” or chord.

At the end of my previous post, I explained how I could create “harmonic progressions” out of cadences built out of all 12 notes, using one hexachord and its complement. Here, if I take the one resolution from the end of Ex.5 and follow it with either the C Major or the A Major resolution, I get two very different sounding cadences (see Example 6). Take particular notice of the next-to-last chord in each of them, marked with the (*). In (a), there’s a strong minor 2nd between the top note and the one directly beneath it: this makes it “more dissonant” or gives it “more tension” than the (*)-chord in (b) where it’s a MAJOR 2nd which gives it a less dissonant or active sound and makes (b) sound more final by comparison to (a).

Yet they’re the same pitches, just rearranged: and out of that I have the equivalent of either a half-cadence in the tonal sense (an A Major tonality with a cadence that doesn’t end on A, usually an E chord, its dominant) or a “Deceptive Cadence” where you expect it to end on A but suddenly it diverts to something unexpectedly foreign to A Major like an F Major Chord. That then strengthens my (b) cadence here as a more stable “tonic.” Depending on how I set up the context, of course, but out of an isolated example, you’re not going to sense that context (isn’t that what sound-bytes or examples are: taken “out-of-context”? And you know where THAT can lead you...).

Near the end of an earlier post, “Getting it to Work,” I mentioned one passage where I wanted that open-strings motive (melodic idea) played by the violin as harmonics on the open strings, supported by intervals underneath it (harmonic idea) played by the piano. So what I worked out was Example 7a. Later, I wanted to reverse the instruments’ roles, have the piano play the motive (in widely spaced octaves) with the violin playing double-stops in between. I also wanted the double-stops to include at least one open-string just to be kind to the violinist. What I came up with is Example 7b.

(By the way, if you’ve already noticed that the pitches of these six-notes do NOT form the same hexachord I was using in Examples 1 & 3, it’s actually a closely related one which is allowed as a kind of lateral-move, just as one could modulate to a particular key, but to explain that now would create more bamboozlement than it’s worth: suffice it to say, move to the Head of the Class, Geek, or, if you already know Allen Forte’s book “The Structure of Atonal Music” intimately, please keep in mind I’m not writing this blog for you...)

What I hadn’t noticed until the next day was the linear aspect of each strand of that passage in Ex.7b. Refreshing the “open-strings motive” in Example 8 and reducing it to an “abstract set” starting on D where the notes form a nicely symmetrical chain of intervals – M2, m3, M2 – then notice that the upper voice in the piano becomes the same chain transposed to F, the upper part of the violin’s intervals forms the same chain transposed to C-sharp, and the lower part of the violin is the same chain transposed to A.

Yeah, I know no one listening to it is going to go “oh wow, did you hear THAT?” That’s not the point: there are millions of comparable subtleties in music but it just means to me that the logic is much tighter than if I just arbitrarily chose a bunch of pitches to slam in there. Oh wait, basically that’s what I did: but it came out working logically as well as aesthetically and that, for me, is an important aspect of what strengthens it MUSICALLY.

Well, now I need to get started on the next piece, and I’ve already got some sketches started on that which I’ll save for a later post. As they say in radio, “stay tuned.”

(Or was it the conductor who said to the violinist, “stay tuned”?)

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