Interval Quality: Perfect, Major, Minor, Diminished, Augmented

The last lesson handed you a table of interval names and one rule for using it: count the semitones. That rule is a good place to start and it is not the whole truth, and the table itself shows you where it runs out.

Look at it again. It goes 5 semitones, then 7. There is no row for 6.

That gap is not an oversight. It is the shape of something the counting rule cannot express, and this lesson is about what fills it.

Two families, not one

Read the names in that table and you will notice they do not all work the same way.

Seconds, thirds, sixths and sevenths come in pairs — major and minor, one semitone apart. Every one of them has both.

Unisons, fourths, fifths and octaves have no such pair. There is no minor fifth. There is no major fourth. These four are called perfect, and the word is doing real work: it marks the intervals that were never sorted into a bright one and a dark one, because they only ever had one form to begin with.

The reason goes back to a lesson you have already read. The harmonic series produces the octave first, then the fifth, then the fourth — the simplest relationships a vibrating string can make, arriving before anything else. Those are the perfect intervals. The thirds and sixths, which show up later in the series and in smaller ratios, are the ones that split into two moods.

That is why a fifth sounds hollow rather than happy or sad. It has no opposite to be measured against.

Making one bigger or smaller

Both families can be pushed a semitone in either direction, and the names for the result are the same two words.

One semitone larger than major or perfect: augmented.
One semitone smaller than minor or perfect: diminished.

So the full chain for a third — an interval with a major and a minor form — runs:

diminished third → minor third → major third → augmented third

And for a fifth, which has only the perfect form in the middle:

diminished fifth → perfect fifth → augmented fifth

Notice what this means: a fifth made one semitone smaller does not become “minor”. Minor is not a size available to a fifth. It becomes diminished, and that is the whole difference between the two families in practice.

Now the missing row: six semitones

Six semitones is the distance between the perfect fourth and the perfect fifth — one step above the first, one step below the second. Which makes it, depending on how you arrive at it, an augmented fourth or a diminished fifth.

It has no plain name, and that is exactly why the table skipped it. Every other row in that table could be labelled with a single unaltered word. This one cannot: it is always an alteration of something else.

Musicians call it the tritone — three whole tones — and it is the most distinctive sound in the twelve. It cuts the octave exactly in half, which is why it is the one interval that sounds the same upside down: invert a tritone and you get another tritone.

Common mistakes to avoid

Saying “minor fifth”. It does not exist. A fifth one semitone short is diminished.
Assuming augmented and minor are the same because the count matches. An augmented second and a minor third are both three semitones and they are different intervals with different jobs — which is the subject of a lesson two ahead.
Treating the tritone as a mistake. It is unstable on purpose, and half the music you like uses it deliberately to create the pull that a resolution then satisfies.

Now play

The drill below plays four distances: the major third, the perfect fourth, the tritone and the perfect fifth. Three of them have plain names and one does not, and they sit within two semitones of each other, so the only way through is to hear the quality rather than count.

Listen for the tritone first. Once you can pick out the unstable one, the two perfect intervals on either side of it stop sounding alike.