Major and minor

Digging into some music theory basics

This summer I am writing more music theory teaching materials for beginners. In this post, I will be explaining major thirds, minor thirds, major chords, and minor chords.

So, what are these things? The definitions are annoyingly circular.

• A major third is the interval between the first and third degrees of the major scale. And what makes it a major scale? The interval between its first and third degrees is a major third.

• A minor third is the interval between the first and third degrees of the minor scale. And what makes it a minor scale? The interval between its first and third degrees is a minor third.

Maybe it's more helpful to count piano keys, guitar frets, or spaces on the MIDI piano roll. Each of these increments is called a half-step or a semitone. Why not just call them steps? The ancient Greeks came up with whole steps/whole tones first, and the idea of splitting them in half came later. Anyway, now we can come up with more satisfying definitions:

• A major third is four semitones (piano keys, guitar frets, piano roll spaces).

• A minor third is three semitones (piano keys, guitar frets, piano roll spaces).

Here are three different visual representations of the major third between C and E, the first and third degrees of the C major scale. The left shows Western staff notation; the center is the MIDI piano roll in Ableton Live, and the right is the scale wheel developed by the NYU MusEDLab.

Here is the minor third between C and E-flat, the first and third degrees of the C minor scale.

Here is the major third between D and F-sharp, the first and third degrees of the D major scale.

Here is the minor third between D and F, the first and third degrees of the D minor scale.

Just as there are major and minor thirds, there are also major and minor chords. But now things get confusing: to make major and minor chords, you have to mix major and minor thirds together.

Here is a C major chord, the first, third and fifth degrees of the C major scale. There's a major third between C and E, and a minor third between E and G.

Here is a C minor chord, the first, third and fifth degrees of the C minor scale. There's a minor third between C and E-flat, and a major third between E-flat and G.

Here is a D major chord, the first, third and fifth degrees of the D major scale. There's a major third between D and F-sharp, and a minor third between F-sharp and A.

Here is a D minor chord, the first, third and fifth degrees of the D minor scale. There's a minor third between D and F, and a major third between F and A.

All major chords have the same intervallic structure: a major third plus a minor third. All minor chords have the same intervallic structure: a minor third plus a major third. Learning all the note names and their associated sharps and flats takes a while, but in the meantime, if you can count piano keys or guitar frets or piano roll spaces, you can make whatever chords you want.

The Online Etymology Dictionary says that the word "major" comes from the Latin maior, a version of magnus meaning "large" or "great". The word minor comes from Latin minor, meaning "less" or "smaller". A major third is wider than a minor third. That explains the names, but what is the origin of the intervals themselves? They must be incredibly ancient. This Paleolithic bone flute plays the major pentatonic scale, which includes both major and minor thirds.

The ancient Greeks made major thirds by adding whole steps together, and they made whole steps by combining fifths and octaves. Is that how Paleolithic people conceived things? My guess is that they were more likely to have been inspired by the natural harmonics, which they would have experienced from the natural resonance of their voices in caves.

• The interval between harmonics four and five is a major third.

• The interval between harmonics five and six is a minor third.

• Harmonics four, five and six produce a major triad.

So major triads are right there in the overtone series, but to make a minor triad, you have to do some abstraction. Many people believe that this explains the conventional association between major and happy, and between minor and sad. Is that true, or is it a convenient post hoc explanation? Not all of the world's people hear major as inherently happy or minor as inherently sad. Even among contemporary Americans, other musical factors can easily overwhelm the ostensible emotional qualities of major and minor. There are plenty of sad songs in major keys, and happy songs in minor keys.

I got curious as to when this trope of "major happy, minor sad" arose in the first place. According to Richard Parncutt, the trope gradually took hold in Europe between about 1400 and 1700, as the church modes gave way to the major/minor tonal system. There was not an immediate consensus among theorists. Gioseffo Zarlino described minor thirds and minor triads as sad in 1558, but in 1591, Adam Gumpelzhaimer described the pre-minor Dorian mode as "cheerful" and the pre-major Lydian mode as "harsh". Zarlino's interpretation eventually became the conventional one, but it took a few hundred years.