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Posted by Stedman Wilson So after finishing the first of a three quarter sequence of music theory courses at my college, I now have more theory questions than I had to begin with. Funny, huh? I've played music nearly my whole life, and here's the biggest question on my mind, one that's been on my mind for a long time: Is there a simple mathematical logic behind chord progressions? It seems that the two biggest elements of tonal music theory are voice leading/counterpoint rules like avoiding parallel fifths/octaves, and then principles for which chords should follow which. What I would really, REALLY like to know is the final answer to this question: How does one generate chord progressions? To sit down and write a chord progression from scratch, what are the OPTIMAL chords to use? That is, why did JS Bach choose the chords that he did? Forget post-classical chord changes, I'm interesting in knowing exactly why tonal chord progressions progress as they do. One of the biggest questions in this ball park is: WHY do chords tend to move in fourths (ie down by fifths, V to I progressions in other words)? Why the circle of fifths? This may sound like too grand a question, but I don't think it is. Music theory has been around since the Ancient Greeks, making it at least 2000 years old. I feel like in that huge amount of time, EVERYTHING should have been worked out. :) I've been looking all over the place, reading stuff like Mark Steedman's article on recursive grammars (in the periodical "Music Perception" (1984)), not to mention Shenkerian analysis. The thing is, I just don't really buy Shenkerian analysis. Shenker talks about IV chords, for instance, as if they arise from neighboring tones to a 3rd scale degree. But Shenker already assumes that all the notes are "in a major scale". That simply doesn't have to be the case. I'm wondering: Is there some simple algorithm (like a computer program/automata/axiomatic system--call it what you will) that can generate complex (but still tonal music), and use hardly any more constraints than simply that there are 12 equal tones to the octave? In other words, an algorithm that generates chord progressions, and can basically also be used to "derive the major scale"? Steedman's grammar is very interesting, but here's the problem as I see it: You can just go in and replace any little chord you like by a new group of chords. In other words, his rules make no reference to a unified structure--they don't say: Edit this big group of chords into this, and only then go in and make tiny adjustments. I strongly feel that music is organized more like this though--there are large scale structures at work, and smaller structures which are subserviant to them. I've experimented with a lot of ideas, the most fruitful being a kind of recursive rule that takes just one chord, say C, which represents the entire song, and adding a period of tension before it (which would be the V chord G), and then going in and perhaps adding tension there, calling G a new "frame", but still respecting that the listener is hearing the C as the slightly more important tonic. In other words, adding Dm before G to release to G but still be more consonant in the key of C than Dmajor. The thing is I feel like someone must have already come up with this, Has someone? If so, it'd be quite a relief! :) As another example of my idea above, here's a question whose answer could prove VERY enlightening: Is there a way, using similar ideas, to generate a chord progression based on a kind of recursive heirarchy of chords? Ie, some chords definitely being less and more important than others? I know this post is kind of long. I apologize if it is too long. But thank you very much for any insight, advice, or good sources for further reading. Best,
on 12/28/2005, 1:44 am
24.25.61.16
Hi,
What are the basic rules behind generating tonal chord progressions?
Suppose you have the chord progression:
C-Em-Am-Dm-G7-C
Now, one could say, well the E is a fifth up from A, so Em acts like a V chord to Am (a secondary dominant), and then Am acts like a secondary dominant Dm, etc, until we reach G7, the V of I which is C. Great, we have a bunch of V-I progressions, which always sound good (strong sense of tension and release). But here's the problem. Actually, E7, not Em, is the secondary dominant of A or Am. Em seems "weaker", because the leading tone G# in the A major scale is not present in Em. We could instead have a progression of ACTUAL secondary dominants:
C-E7-A7-D7-G7-C
But this kind of progression is MUCH LESS common than the previous one. Why? My guess is that even though we want a dominant function V-I from E to A, we must still respect the overall importance of the tonic C, and thus use the chord Em instead of E7, since Em is more consonant in the key of C than E7. This is of course simply total speculation.
--Stedman
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