AHM – Gradational Modulation

This is part of an on-going series on “AHM,” a compositional approach of mine. To get up to speed, scroll down to check out the other posts on the subject, but especially Intro to AHMCharacteristic Pitches and Modal Voicings.

In a previous post I took a look at my first efforts to use all 28 AH modes in one unified system. Of course, it wasn’t much of a system at all – it was just applying these concepts to functional harmony. I still needed to find some novel ways to use chord/modes that didn’t rely so heavily on chord functions and progressive root motion. However, because modal voicings are so rich and full of static dissonance, they don’t hold up well to the same sorts of chromatic transformation and planing that simpler structures might. If you’re not staying within the same parent scale, harmony using modal voicings quickly becomes a vague blur of unrelated dissonances. My solution to this was imposing what I call “Gradational Modulation” on the harmony.

Gradational Modulation is essentially the same thing as the concept in common practice known as “closely related keys.” Closely related keys are ones whose keys signatures are just one sharp or one flat away from the home key. This concept was essential to modulation and key relationships up until the 19th century when things started getting more complex and more foreign key relationships were introduced. Gradational Modulation takes on this concept and builds on it. Instead of looking at close Major/Minor scale relationships to the parent key, we’re now going to look at ALL possible close relationships to a given parent scale from all four parent scales. Since they’re relating by all the same notes except for 1 (the note thats changing between the two of them), the ear will still hear the modes or chord/modes as being related, even if they are from different parent scales. The blur of dissonance can be avoided.

Here’s a table that illustrates what I mean by this. (I have a copy of this table printed out and on my desk at all times…it’s very convenient)

Original Parent Scale Parent Scales 1 # Away Parent Scales 1 b away
C Major A Harmonic Minor
G Major
D Melodic Minor
C Harmonic Major
C Melodic Minor
F Major
C Melodic Minor C Major
G Harmonic Major
Bb Major
C Harmonic Minor
C Harmonic Major C Major C Harmonic Minor
F Melodic Minor
C Harmonic Minor C Harmonic Major
C Melodic Minor
Eb Major

This was exactly what I was looking for. Now we don’t have to stay within one scale, we have a bunch of relationships now to choose from. For example, let’s say I have a modal voicing on D Dorian. The parent scale is C Major, so we could go to chord/modes in C Major, OR, we could go to chord/modes from the other six parent scales listed – 48 chord/modes in all. That’s a signficant number of possibilities, although, its roughly comparable to the number of options we get when we think of functions in tonal harmony (diatonic chords, modal interchange, secondary dominants, tritone substitution, etc).

Now, obviously, there will be plenty of times and reasons to break this mold – notably at cadences are any moment where a larger shift of tone color is desired. Still, it’s nice have have neatly laid out.

One of the problems here, is that so far there isn’t any real way to gauge exactly WHICH of the 48 chord/modes to shift to. Aesthetic preference of course is king, but besides that, there are three things to keep in mind when deciding, 1) Direction of Modulation (1 sharp versus 1 flat) Root Motion (progressive versus regressive) 3) Brightness/Darkness and 4) Control of Dissonance. I’ll take a look at them in order in exhausting detail that really isn’t necessary. Fun.

Direction of modulation has a very minor effect on two chords, but if prolonged in the same direction over a course of a progression, it can give a powerful, if subtle, feeling of “ascending” or “descending.” The easiest way to hear this effect without going through the legwork of figuring out voicings is to take a simple constant structure (a major 7 chord, lets say), and then cycle it in fourths. If you ascend in fourths (Cmaj7, Fmaj7, Bbmaj7 etc), the effect is one of harmonic “descent,” and if you descend in fourths (Cmaj7, Gmaj7, Dmaj7), it has a feeling of harmonic “ascent.” These labels of ascent and descent are unfortunately the best that I could come up with, since describing musical effects is so difficult, but its still wise to recognize the fact that there is an effect.

Here is an example of a progression that “descends” (difference of a flat) and one that “ascends” (difference of a sharp). Pay close attention to the ascent/descent effects. Click for a larger image, and be sure to also listen to the midi file.

(listen)

The next thing to keep in mind with creating progressions is root motion (explained in depth here). Here are a couple of examples of progressions modeled off of the first parent scale progression that examine the effects of progressive and regressive root motion on both the ascending progression and descending progression we came up with earlier. Try playing the bassline first and then playing it with the rest of the harmony to truly hear the effect of progressive/regressive root motion outside of a functional context.

(listen)

(listen)

Next, we have brightness/darkness, which I covered in this previous entry. I was considering some fancy jargon to describe the numbers that I came up with, like “Dorian Brightness Index,” but I think “brightness” should suffice. Here’s a couple progressions considering an all bright descending progression, all dark descending progression, all bright ascending progression and all dark ascending progression. Again, listen very carefully to what effect is achieved by a bright progression versus a dark one.

(listen)

(listen)

By now, you should notice most of these progressions sound very similar. This is because the parent scales we’ve set for them haven’t changed, and like we covered in a much earlier blog discussing AHM, all of the modes of a particular parent scale end up giving the impression of that scale. It’s important to examine all of these extra nuances (brightness, root motion) within a fixed context, however, because they can be easily lost without a strong grounding.

Finally we get to the one which is the hardest to define, “control of dissonance.” This is basically the fancy way of saying “use your ear to control dissonance,” because I really don’t have a simple codification that explains the intervallic dissonance found within the AH modes. In attempting to describe brightness/darkness I’ve created a different way of looking at dissonance from a theoretical standpoint, but it doesn’t quantify it the way I might like. I haven’t mentioned it so far, but a compelling “melody” in the soprano voice is key for the ear in accepting the progression dissonant structures. If the melodic countour in the lead voice doesn’t sound compelling, you’ll have a tough time making the progression work.

With all of this said, an easy way, and perhaps “cheap way, to tone down the dissonance is to make use of anti-modal voicings. Because they’re designed to be much more stable, “controlling” their level of dissonance isn’t really a tall order. Applying them to Gradational Modulation is a great way to get a non-functional sound with more traditional sounding structures, and they can be very easily translated into chord symbol notation, whereas modal voicings often can’t. After listening to all these modal voicings, these anti-modal voicings are very easy on the ear to the point of almost being bland at some points. Have a listen (I especially like the “rising” one because the root motion is falling at the same time its going up in the circle of fifths).

(listen)

With Gradational Modulation and the four parameters I subscribed, it’s very easy to think of composition schemes, like “alternating bright/dark,” or “all neutral brightness with progressive root motion,” or “alternating ascending/descending with neutral brightness,” or whatever. Ultimately, though, it comes down to aesthetic choice, and very often this will lead the ear away from what these schemes provide. All of these parameters serve to give some qualification to this method of non-functional harmony, but they aren’t “rules” by any stretch of the imagination, and are simply things to keep in mind when you’re working out progressions.

Stay tuned for more music and theory.

-Adam

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