Of all the things I’m good at in piano class (attending, counting out loud, making my classmates laugh), playing the piano is not one of them. I do OK after a week of serious practice, but show me a new piece, say “OK, everybody, let’s try it with two hands,” and I freeze up. Translating symbols into motor skills in real time? Right. That feels suspiciously like reading a map in a moving car.
My fellow student, Mike, was no doubt trying to make me feel better last week when, after class, he asked me to explain to him again what a harmonic minor scale was. Gratefully, I accepted the task. “I’ll write something,” I said. “Then I’ll understand it.”
Honestly I’ve been trying to understand music theory ever since one of my boys said to his brother, “I’m pretty sure that’s a D-flat diminished 7th” and I thought to myself, “I’m pretty sure they’re smarter than I.” The problem is that people who teach music tend to be people who learned music as children. They learned by doing and figured out why later. They don’t know how to start from the beginning, with the big picture—which is what grownup beginners need. At least grownups like me with an insufferable need to understand.
So what follows is a bit of music theory—just the octave and scales—from someone who didn’t understand any of it until very recently. (I was helped tremendously by David Harp’s Music Theory Made Easy.) Tell me if you’re interested, and I’ll bravely move on to chords.
It all starts with the octave, an interval between two pitches that’s a actual law of nature. The tone we call a middle A, for example, has a frequency of 440 Hz (vibrations per second); double that frequency to 880 Hz and you get a sound that’s somehow the same but different—high A. Double that and you get another same-but-different sound. The same-but-different quality of two tones at each end of an octave (aka octave equivalence) is recognized across all human cultures.
So, when developing their musical languages, all human cultures begin with same-but-different pitches and the need to identify all the pitches in between them. Every culture divides the octave distance into steps (“scala” is Italian for “step,” so that’s where “scale” comes from). The Chinese divide it into 5; the Indians divide it into 22.
The Chromatic Scale
Western culture, starting with Pythagoras, divided that space into 12 steps, known as the chromatic scale. In other words, to get from middle A to high A, you take 12 evenly spaced steps: A, A#, B, C, C#, D, D#, E, F, F#, G, G#, A.
This is where it starts to be confusing, because this is where the language of music totally misleads. First of all, there’s no conceptual difference between sharps/flats and regular notes (and yes, every sharp is also a flat: it’s “sharp” relative to the note below it and “flat” relative to the note above it. I could have written the above 12 notes as A, Bb, B, C, Db, D, Eb, E, F, Gb, G, Ab). In other words, between black keys and white ones. I always assumed sharps/flats were assistant notes, not the big bosses. They simply do not seem equal—a Bb seems subsidiary to a B. But it’s not. It’s just one of twelve tones, which should simply be represented by 12 different letters of the alphabet—A through L.
OR, if we have to use in-between letters, then why isn’t it A, A#, B, B#, C, C#, D, D#, E, E#, F, F#? Why is there just one step between E and F and between B and C, although there are two between C and D, D and E, F and G, G and A, and A and B? This is either sadistic or irresponsible. (And graphical notation–printed music–carries on the farce, as the on-paper distance of B from C on the scale is represented as the same as the physical distance of C from D, even though the pitch distance is half as far. And this is supposed to be the mathematical art!)
Major & Minor Scales
But what are you going to do? We can’t change it now, any more than we can make through rhyme with cough.
So to recap, we have the chromatic scale—12 steps evenly dividing up the space of an octave. From that scale, we as a culture derived lots of other scales or patterns, the most common ones being the major and minor scales. “Major” and “minor” simply identify certain patterns of tones selected from the chromatic scale.
Both of those patterns, by the way, include eight notes, beginning with a root note and ending with the “same” note an octave above. Hence the term octave, which means eighth.
To get to those eight, though—again—we start with 12. Tragically, we must start calling those 12 steps “half steps” since (because of the crazy notation) we’re accustomed to the interval between A and B being referred to as a “whole step”—although they are actually two tones apart on the chromatic scale (A—Bb—B). From now on, we’ll refer to one tone up or down as a “half step”; two tones up or down is a “whole step.” Sorry.
If we pick a note on the chromatic scale and call it “1”, then major scales use the half steps 1, 3, 5, 6, 8, 10, 12, 1 (back to beginning). It skips 2, 4, 7, 9, and 11. Another way to put this is, beginning with the first note, major scales follow the pattern whole step, whole step, half step, whole step, whole step, whole step, half step.
Steps between: W W H W W W H
In other words, beginning with C:
W W H W W W H
That, my friends, is a C Major scale. Each scale is named for the first note in the pattern—the “root” note—followed by the kind of pattern it is. An F# Major scale is a scale that begins on F# and follows the major pattern.
You can figure out any major scale by starting with the root note—you can use any of the 12 (A, A#, B, C, C#, D, D#, E, F, F#, G, G#)—and following the major pattern. Here’s G Major, another popular beginner scale:
W W H W W W H
Of the 12 tones of the chromatic scale, the minor scale uses tones 1, 3, 4, 6, 8, 9, 11, 1 (back to beginning). So this pattern is whole step, half step, whole step, whole step, half step, whole step, whole step.
In other words, as we see in A minor:
W H W W H W W
You can figure out every minor scale, from A through G#, simply by following the minor pattern.
As to Mike’s question, a harmonic minor scale is simply another pattern derived from the original chromatic scale; it’s the same as a (natural) minor scale, with the seventh note raised one half step. In other words, the harmonic minor tone pattern is 1, 3, 4, 6, 8, 9, 12, 1, and the step pattern would be whole step, half step, whole step, whole step, half step, whole-and-a-half step, half step.
Here’s D natural minor:
W H W W H W W
And here’s D harmonic minor:
W H W W H WH W
A nice way to remember “WH” in this case is the expression “What the Hell?”