The Circle of Melodic Dissonance, part 1
May 21st, 2009
Disclaimer: this post is about music theory. It will be somewhat dry. A reasonable understanding of basic musical scales and notation is presupposed.
Most popular music is written in either a major scale or a minor scale. Major scales sound happy and jubilant; minor scales are dark, stratospheric, melancholy. It is instructive to understand, however, that minor is simply a mode of major; for instance, C major and A minor both consist of the white notes on a piano. No flats, no sharps. Even though the keys used are identical, if the all-white-keys song is played with C as “home base”, it will sound happy, whereas if A is used as the “base”, it will sound sad.
In this way I can say that minor, or Aeolian (the original Greek term), is the sixth mode of the major scale. The major mode (Ionian in Greek) is the first mode of the major scale. And by the major scale I mean this specific sequence of seven notes, selected from the Western idiom of twelve possible notes:
C (C#) D (D#) E F (F#) G (G#) A (A#) B
The bolded notes represent the scale of C major. The notes in parentheses are the black notes on a piano; the notes that are not in the C major scale. Note that the major scale follows the pattern of two steps from C to D (skipping C#), two steps from D to E (skipping D#), one step from E to F, two steps from F to G (skipping F#), and so on. [Aside: I don’t mean to be needlessly confusing, but traditionally a single step is referred to in most music notation as a “half step”, and two steps as a “whole step”, so I will use this terminology as I continue. Quick e.g.: C to D is a whole step. E to F is a half step.] Written out in this way, the major scale is simply whole-whole-half-whole-whole-whole-half, or WWHWWWH for shorthand. This pattern is consistent regardless of the note one begins on: G major is simply G A B C D E F# G, for example, and E major is E F# G# A B C# D# E. It is left as an exercise to the reader to verify these scales’ patterns.
Now if I keep the scale the same, but start my step-counting on A, I get the universal pattern of the minor mode (Aeolian): WHWWHWW. It is a mode of the major scale because the beginning point of the scale is simply shifted over, but the underlying pattern is the same. The astute reader will wonder: “what about the other modes? Doesn’t the major scale theoretically have seven beginning-points, and thus seven modes?” This is exactly the case. In order, the seven modes of the major scale are called: Ionian (major), Dorian, Phyrgian, Lydian, Mixolydian, Aeolian (minor), and Locrian. They are all distinctly different in mood; some are darker, some are light and airy. They are related laterally, in that their step patterns are all derived from the major scale; for example, in a given melody, I could shift from C Ionian (C D E F G A B C) up to D Dorian (D E F G A B C D), and then to G Mixolydian (G A B C D E F G), and so forth and so on. This requires changing the home base of my song, though. The listener will clearly note the song “moving” from a home base of C, to D, to G. What about shifting around within a given tonal center? What if I want to add color and flavor to a melody, but keep it strictly in C?
There is a second way that the modes are related; it is a melodic relationship, in that the underlying “home base” does not change. For example, I can shift from C Ionian (WWHWWWH) to C Mixolydian (WWHWWHW). The step-patterns make it less clear as to what is going on, so I will write it out:
C Ionian (C D E F G A B C) —-> C Mixolydian (C D E F G A Bb C)
I would recommend mapping the step-patterns to the actual piano notes as a useful exercise. What’s the difference between Phrygian and Locrian, for example? What notes change? What notes stay the same?
Also, note that the shift from C Ionian to C Mixolydian is quite subtle; only a single note changes, and only by a half-step at that. It is the smallest possible melodic change. This is a useful concept; it provides color without the listener consciously pulling away from the song and thinking “well, that was obvious.” For those taught in traditional harmonic counterpoint, it is like shifting from C major to G major; only one tiny thing is changing. Here on out I will refer to this concept as SPMC (Smallest Possible Melodic Change). All of the modes of major are related by SPMC, which is spelled out in exhaustive detail below.
C Lydian (C D E F# G A B C) <—-> C Ionian [major] (C D E F G A B C)
C Ionian [major] (C D E F G A B C) <—-> C Mixolydian (C D E F G A Bb C)
C Mixolydian (C D E F G A Bb C) <—-> C Dorian (C D Eb F G A Bb C)
C Dorian (C D Eb F G A Bb C) <—-> C Aeolian [minor] (C D Eb F G Ab Bb C)
C Aeolian [minor] (C D Eb F G Ab Bb C) <—-> C Phrygian (C Db Eb F G Ab Bb C)
C Phrygian (C Db Eb F G Ab Bb C) <—-> C Locrian (C Db Eb F Gb Ab Bb C)
There are a few interesting epiphenomena that arise out of SPMC. Lydian is the “lightest” of the seven modes of major; it is very airy and carefree-sounding. Locrian, on the other hand, is the “darkest”, very sinister and primordial. The closer a mode is to Lydian, the lighter in mood; the closer a mode to Locrian, the darker the mood. (Dorian is centralized and is neutral in color.) Also note that when “traveling” from Lydian to Locrian via SPMC, the note that changes always descends, never ascends.
Additionally, every note of the scale descends by one half-step at some point in this system, except for home base, the C. While it is technically possible to “move” from C Locrian to B Lydian, the note that changes in this shift is the tonic itself (C moves down a half step to B). By SPMC rules, this isn’t allowed, as moving the tonic has a jarring effect on the listener, and is not considered to be a melodic shift, but rather a harmonic one. And we have to draw the line somewhere, otherwise bestiality and pedophilia will become commonplace. And we don’t want that, do we?
See if you can follow me a little further. The sharp/flat system has been primarily designed for use in the major/minor system; when speaking modally, it’s a lotta look, to quote a famous fashion designer. All the flats and sharps tend to obscure the simplicity of SPMC. If C is assigned the number 0, C# the number 1, all the way up to B = 11, we can study the system numerically, and also universally, as any home base can be assumed. 0 can just as easily be G#, or E. Also, since the home base can never change by definition, it’s not necessary to include it. Here’s an example to show what I’m talking about.
C Mixolydian is C D E F G A Bb C. If we assume that C = 0, and continue from there, then C Mixolydian can also be described as 0 2 4 5 7 9 10 12. Then simply note that by SPMC rules, the note C will never change, so the numbers 0 and 12 can be omitted, which leaves us with a nice universal way to describe all Mixolydian modes. Mixolydian is (2 4 5 7 9 10). Reread this paragraph, then prove to yourself that Aeolian (minor) is represented by (2 3 5 7 8 10).
Here’s the SPMC major mode order, in this new easier-to-look-at (hopefully) format:
( 2 4 6 7 9 11) Lydian
(2 4 5 7 9 11) Ionian (major)
(2 4 5 7 9 10) Mixolydian
(2 3 5 7 9 10) Dorian
(2 3 5 7 8 10) Aeolian (minor)
(1 3 5 7 8 10) Phrygian
(1 3 5 6 8 10) Locrian
Look at how only one number changes between each set of modes. Think about this for a little while, shifting from mode to mode. The really fun stuff is just around the bend.