Major and minor modes

What's the difference between major and minor?  Well, I think if you asked most people, they'd say something like this:

If it's in major, that means it sounds happy.  It's upbeat.  Fun.  Something you'd want to dance to.  Songs in a minor key sound sad and gloomy.  Like a funeral dirge, or a haunted house or something.

That sounds clear enough.  Based on that description, it ought to be easy to tell the difference between a song that's in a major key, and one that's in a minor key.  Listen to these two songs and see if you can figure out which one is which:

Gloria Gaynor - I Will Survive

The Beatles - Yesterday

Obviously, I Will Survive is the one that's in the major key, and Yesterday is the one in the minor key.

Wrong.  It's actually the other way around.  I Will Survive is in A minor.  Yesterday?  F major.

So what is the difference?

Prior to the Renaissance, the distinction between major and minor didn't exist, as such.  What we refer to as major and minor scales simply weren't in common use.  During the Renaissance, Europe experienced a renewed fascination with Greco-Roman art, architecture, and civilization.   Renaissance scholars looked back to the Greeks for inspiration, and noted their fascination with music.  If music is something so powerful that it can move the gods, surely the music we create today ought to be just as powerful and moving!

The major and minor scales came about as a result of a re-examination of Pythagorean tuning during the Renaissance era.  During the Renaissance, they took Pythagoras' ideas and stretched them even further.  We already know that a 2:1 ratio in vibrational frequency will give two notes exactly one octave apart.  A 3:2 ratio ratio will give two notes that are a fifth apart - the relationship between C and G.  By extension, that means that a 3:1 ratio will give two notes that are a fifth apart, but separated by an additional octave - the difference between a bass C and an alto G.

What happens if we extend the sequence?  Start with 2:1, then 3:1, then go all the way up to 6:1?  It turns out we get something like this:
When you put all six notes together, it sounds pretty good, doesn't it?  All six notes blend into each other.  The last three notes are particularly important.  When you put a C, an E, and a G together, what you get is a major triad.  Triad, because there are three notes, and major, because the three notes have frequencies in the ratio of 4:5:6.

What happens if we pick a starting note, and then go to frequencies that are 1/2, 1/3, and so on?  I'll start on a soprano C here and see what we get.

As the bass goes down, we get the notes F, A♭, and C, which are related by a ratio of 1/6 : 1/5 : 1/4 (or 10:12:15, if you don't like fractions).  This is called a minor triad.  

Isn't that interesting?  We usually think of major and minor as being opposite to each other.  But, in fact, they're actually closely related.  More like brother and sister!

We've already got a scale to go with the major (C-E-G type) triad: it's the major scale.  C D E F G A B C.  Now we need a scale to go with the minor triad.  The scale that we need has the same notes as the C major scale, but starts on A instead.  Let's compare the two scales.  I've taken the liberty of labeling the notes that form the major and minor triads.

Like the major scale, the minor scale is defined by a pattern of intervals:

• Major scale: W W H W W W H
• Minor scale: W H W W H W W

where H is a half step, and W is a whole step.

Let's take what we've learned and build a pair of scales.  Let's build the scales for D major, and D minor.  To build these two scales, we'll need the patterns listed above, plus one rule: in any scale, each of the lettered notes has to be used exactly once.  You can add a sharp or a flat as necessary, but you have to use each letter exactly once.

So let's start with D major.  We'll write down the letters of the scale: D E F G A B C D.

Two notes require fixing.  D to E is a whole step, which is good.  E to F, though, is only a half step, and we need a whole step.  So we raise the F to F#.  For the next note in the scale, we need a half step.  F# to G fits the bill.

G to A... whole step.  Check.  A to B... whole step.  Check.  But that C is out of place.  We need a whole step for the next note up from B, but C is only a half step.  So we raise the C to C#.  B to C# is a whole step... check.  C# to D is a half step... check.  We're done!

What about D minor?  Same process.  Write down the letters of the scale: D E F 

G A B C D.  Let's see which ones we need to adjust.

D to E is good.  E to F is a half step, that's good.  F to G, G to A, those are both whole steps, good.  A to B? We need a half step here - lower the B to a B♭.  B♭ to C is a whole step, as is C to D.  So we're done.

Let's try another one.  Let's do B♭major, and B♭ minor.  Write down the letters of the scale first: B C D E F G A B.

For the B♭major scale, you should end up with the B and the E flatted.  For the B♭ minor scale, you have to flat the B, D, E, G, and A.  You get to use all the black keys!  Cool!

I love the key of B♭minor.  It's so strange, so mysterious, so spooky.  When played slow, it has a deep, mournful feel.  Listen to this gem in B♭minor by Chopin:

Frederic Chopin - Piano Sonata #2 in B-flat minor, Op 35.  III: Marche funebre

One more.  This one will be tricky.  Let's do D♭ major and minor.  D E F G A B C D.

Major scale: Obviously the D is flatted.  D♭ to E♭ is a whole step, E♭ to F is another whole step.  F to G♭, a half step.  A♭, B♭, C, D♭.  We're done!

Notice that D♭ major has five flats, just like B♭ minor.  And it's the same five notes in both scales that are flatted.  We have a word in music for this kind of relationship: enharmonic.  The keys of D♭ major and B♭ minor are enharmonic to each other because the two scales share all the same notes.  Another use of the word enharmonic is to describe two different notes that have the same pitch.  For example, the notes C# and D♭ are enharmonic to each other.  So are F♭ and E. 

Now the minor scale.  D♭, E♭, F♭...  Wait a minute.  F♭???  Sure.  F♭ and E are enharmonic - two different names, but the same note.  This looks mighty strange, though. Usually we try to avoid referring to E as F♭, because it's confusing.

G♭, A♭, and now a half step...  what now?  A half step up from A♭ is A, but we've already used the A in our scale.  So what do we do?  Call the next note B-double-flat?

We could if we wanted to.  There do exist signs for double-sharp and double-flat, and they are used with some frequency.  But there's a much easier solution to the problem.  Since writing out a scale for D♭ minor is difficult, why not instead call it C# minor and see if the problem goes away?

There we go.  Much better!

We've covered an awful lot today, so I think it's time to wind things down and recap.  Here's what you need to remember about the major and minor modes.

• Major and minor have nothing to do with the mood of a piece.  A happy piece can be in a minor key, and a sad piece can be in a major one.  It happens.
• Both the major and the minor scales are formed by a specific sequence of whole and half steps.
• Every major key has an enharmonic minor, and vice versa.  When we're talking about enharmonic scales, what we mean is that the scales share all the same notes, but start and end on different pitches.

Whew!  A little bit of music next time, and then we'll continue on to meter and rhythm.