Major, minor harmony and the harmonic minor scale
Introduction and mathematical roots
The juxtaposition of expression and mathematics has been something composers have battled with for hundreds of years of western classical music. It was the Greeks who initially figured out the maths present in the harmonic series, and from here we’ve come up with many ways to define the distance between notes in an octave.
As it stands we use a system of equal temperament (where the distance between all notes is equal), but this does result in impure intervals compared to “just” intonation as our 3rds are actually a little sharp and our 5ths a little flat.
In all honesty, this is a subject that people have devoted entire careers to, so I’ll move on the subject at hand, just know that mathematicians LOVE the numbers in music.
What is the basic major scale?
In order to understand where harmonic minor comes from, and why/how we use it, we first need to talk about the major scale.
If we begin with all the notes found in an octave we have
C C# D D# E F F# G G# A A# B C
The major scale found here begins on the note C, then follows a series of tones and semitones to locate the rest of our notes in the scale. A semitone being a distance of one note in the chromatic scale (so for example C to C#, E to F, G# to A), and a tone is a distance of two semitones (C to D, E to F#, G# to A# etc).
The major scale has a tone (T) semitone (S) pattern of TTSTTTS So we take the note C, then a tone higher we have D, a tone higher we have E, a semitone higher we have F, a tone higher we have G, a tone higher we have A, a tone higher we have B, and a semitone higher we have C.
C C# D D# E F F# G G# A A# B C
T T S T T T S
C D E F G A B C
How do you harmonize the major scale?
Knowing this we can start making chords from the major scale, from which we can start building songs. The western system of tertian harmony involves stacking notes a 3rd apart, so in this instance we take the note C, skip the note D, and arrive at the 3rd note of the scale, E. So take a note, skip a note, take a note, skip a note.
C D E F G A B C – C major
We can do this starting on each note of the scale to find out what chords are in the key of C.
C D E F G A B C – D minor
C D E F G A B C – E minor
C D E F G A B C – F major
C D E F G A B C D – G major
C D E F G A B C D E – A minor
C D E F G A B C D E F – B diminished
Now we have 7 chords, one built on each degree of the scale:
C Dm Em F G Am Bdim C
This is where we get the chords you often see people referring to in roman numerals. For example, a I VI II V in C would be C Am Dm G.
Where does the minor scale come from?
The minor scale is found in the major scale, it’s just the same notes but starting on the 6th degree, so in the case of C major, the “relative minor” would start on A.
A B C D E F G A
This scale is found naturally in the major scale, so we call it the natural minor scale. And as with the major scale it contains 7 chords, but seeing as the scale contains the same notes as the C major scale, the chords will all be the same:
Am Bdim C D Em F G Am
Now on to the harmonic minor scale
It’s at this point that we have to talk about the most important chord after the I chord, and that’s the V. If we jump back to the C major scale, you’ll see that the V chord is a G major, in fact if we add another note to this chord, the G major becomes a G7 chord
C D E F G A B C D E F
This chord is extremely important in western harmony because it contains an interval of 3 tones (a tritone) between the B and F. This is a natural dissonance occurring in the chord that wants to be resolved, and it resolves perfectly back to the C chord. The B drops down to C and the F lifts up to G. G7 resolves perfectly to C. It’s this naturally occurring function found in the scale which helps to give chord progressions in a major key a sense of order. Everything we play helps to bring up back home to the I chord. The problem is that when we look at the minor scale, it doesn’t have this function. The 5th chord in the A minor scale is an E minor chord, not an E7! The harmonic minor is a scale which just solves this little problem. While the A minor scale is spelled
A B C D E F G A
The harmonic minor scale is the natural minor scale, but with the 7th degree of the scale lifted up a semitone.
A B C D E F G# A
This G# might seem insignificant, but it does something really interesting to the chords constructed from it. Most importantly the 5th chord goes from being an Em to an E7
A B C D E F G A B – E minor
A B C D E F G# A B C D – E7
So we use the harmonic minor scale because it gives us better harmonic function in a minor key. In fact, it should now be clear where it gets its name from!
Harmonic minor usage
If we take BB King’s The Thrill Is Gone as an example, we have a chord progression in the key of B minor
Bm – Em – Bm – Gmaj7 – F#7 – Bm
This is a great example of harmonic minor in action, as in the key of B minor, the 5th chord is F#m, but the progression we’re playing borrows the V chord from B harmonic minor, and thus F#7.
What you might take from this is that harmonic minor is often a sound used in conjunction with the natural minor scale rather than one that’s used in isolation.
What you’ll find when looking at this scale is that while there are examples of it being used in many genres of music (with it being extremely popular in Latin music), culturally in western music it has undeniable ties to classical music, and as such its use really does tend to add a dark classical edge (think Bach’s Toccata and Fugue in Dm)
Another great example would be in Dire Straits Sultans of Swing, a song in D minor, but using A major instead of minor for the V chord.
Where you’ll hear harmonic minor often in rock and metal music is anything with a neoclassical flavour. Think Deep Purple, Randy Rhoads work with Ozzy, and Uli John Roth. But (and you knew we were getting there!), the poster boy for this sound is undoubtedly Yngwie Malmsteen. And to be fair, it’s for good reason! There are countless examples in his discography, but I can’t think of a better place to start than the classic Trilogy Suite Op: 5!
For more examples of harmonic minor and some burning rock licks, check out my module on the subject!