# Intervals

Intervals are distances between pitches. Developing fluidity with intervals can help us build chords, appreciate the nuances of melodic lines, and train our ears.

As we learned in Chapter 1, an interval is the distance between two pitches. Half steps and whole steps are examples of intervals. In this chapter, we’ll explore intervals that span greater distances.

Intervals are important for several reasons. Chords, which we’ll discuss in Chapter 3, consist of various interval relationships, and studying intervals gives us a foolproof way to build chords. Also, we’ll discuss melodies later in terms of “steps,” “skips” and “leaps,” which are all types of intervals.

The idea of pairs of pitches having different “distances” from one another can be tricky, so let’s see what an interval of a small distance sounds like when compared to one of a greater distance. Pick up an instrument and play a C. Now play the closest chromatic note above it, a Db.

Notice how close in pitch the two notes sound.

Now play the C again, but this time follow it with a much higher note, like an A.

Notice how different the second pair of notes sounds as compared to the first pair. The “distance” between C and A sounds bigger, or wider, than that of the first pair. That difference can be explained in terms of intervals.

## Interval Names

The technical name of a given interval will have two parts. The first is a description, like “major” or “minor.” The second is a number, like “third” or “sixth.” Here are some interval names:

minor seventh
perfect fourth
major third

So what do these names mean?

Let’s start with the number part first – that part is easy. We’ll simply count letter names beginning with the lower of the two notes up to the higher note (including both of the notes themselves in our counting). Here’s an example.

We want to calculate the distance between the lower note (C) and the higher note (A). We begin with the bottom note, C, and count up until we hit the A (looping back to the top of the alphabet after G). C is 1, D is 2, E is 3, F is 4, G is 5, and A is 6. So C up to A is a sixth. Also, when determining the number part of the interval name, it doesn’t matter whether either note is sharp or flat.

Here are some examples.

That’s easy enough, right? All we have to do is count the letters. And when we’re working within a key, just saying something is a “sixth” or a “third” is often good enough. An F up to a B is a fourth, and so is an F# to a Bb, even though the two intervals sound different.

 Quick Quiz 2.1 Give the numerical interval name (“second,” “fifth,” etc.) for the following intervals. A (lower note) up to C (higher note) C# up to G G up to C# F up to Db

## Major And Perfect Intervals

Often, we want to give an interval a name that’s more specific than just a number, and that’s where words like “major,” “minor” and “perfect” come in.

Let’s go back to our C major scale, and we’ll compare each note of the scale to C, our tonic. The intervals produced are listed below, with the capital “M” standing for “major” and “P” standing for “perfect.”

Once we’ve figured out which number an interval receives (“third,” “sixth,” etc.), our next step is to pretend we are in the major key of the lowest note (even if we are actually in a different key) and see if the higher note would be in that major key. If it would, and the interval is a second, third, sixth or seventh, then the interval is called “major.” It’s called “perfect” if it’s a unison (“P1”), fourth, fifth or octave (“P8,” or “perfect octave”). There is no such thing as a “perfect third” or “major fifth”; interval numbers that can be perfect are never major, and vice versa.

Intervals that can be major: Seconds, thirds, sixths, sevenths

Intervals that can be perfect: Unisons, fourths, fifths, octaves

Here are a couple examples.

First, we count letters from the bottom note (E) to the top note (B) to determine this interval is a fifth (E, F, G, A, B). Next, we check to see whether B is in the key of E major. It is, and a fifth is perfect rather than major, so this interval is a perfect fifth.

Counting letter names tells us this interval is a sixth (A, B, C, D, E, F#). F# is in the key of A major, and sixths are called major rather than perfect, so this interval is a major sixth.

## Minor, Augmented And Diminished Intervals

Other types of intervals are trickier. What if we see the following?

Our first step will be to count note names – C, D, Eb. So we have some type of third. What type of third do we have, though? We’ll use our usual technique of imagining that we’re in the major key of the lower note. Eb is not in the key of C, though, so we don’t have a major third. Instead, the interval is a half step smaller than a major third (C to E natural), so we’ll call this a minor third. An interval a half step smaller than any major interval is called minor.

An interval a half step smaller than any perfect or minor interval is called diminished. Here’s an example.

First, we count letter names from the bottom note to the top – C, D, E, F, Gb. So we have a fifth. The fifth scale degree in our C major scale will be G natural, however, not Gb, and the interval formed between C and Gb is a half step smaller than the interval from C to G. So we’ll call it a diminished fifth.

A half step larger than any major or perfect interval is called augmented.

Counting C, D, E and F# gives us a fourth. But our fourth scale degree in C major is F, so the interval formed from C to F# is a half step larger than a perfect fourth. We will therefore call this interval an augmented fourth.

Notice that the intervals in the two previous examples are enharmonically equivalent – F# is the same note on the piano as Gb.

Technically, though, the names of these two intervals are different (“augmented fourth” for the first one, “diminished fifth” for the second). We know this because the first step we should take whenever we’re determining the name of an interval is to count letter names from the lowest note to the highest. However …

## The Tritone

Both augmented fourths and diminished fifths are colloquially called tritones. The tritone, which is a distance of six half steps, is a dissonant interval that is usually used to generate tension. The theme song to The Simpsons, which we will discuss again in the chapter on modes, shows us what the tritone sounds like. Listen to the very beginning.

In general, when we encounter an augmented fourth or diminished fifth, we can simply call it a tritone, although it sometimes helps to be able to tell the difference between an augmented fourth and a diminished fifth. The example above is an augmented fourth and not a fifth because of how we count the letters (C, D, E, F#).

## Interval Examples

To this point, this has been a tricky chapter, so now might be a good time to reread it from the beginning. If you feel ready to go on, here are a few examples.

D up to A. As always, our first step in determining the interval will be to count letter names. D, E, F, G, A is five letters, so we have some type of fifth. Next we’ll ask ourselves whether A is in the key of D major. It is. For fifths, when the bottom note is in the major key of the top note, we say it’s a perfect interval. So D up to A is a perfect fifth.

F up to E. First we count letter names – F, G, A, B, C, D and E are seven letters, so we have some type of seventh. E is in the key of F major, and we use “major” rather than “perfect” for sevenths, so F up to E is a major seventh.

G up to F. G, A, B, C, D, E and F is seven letters, so we have a seventh again. This time, though, the higher note, F, is not in the major key of the higher note, G, since G major contains F# rather than F natural. G up to F is therefore a half step smaller than a major seventh, so we call it a minor seventh.

Bb to Gb. We’ll count letter names (Bb, C, D, E, F, and Gb) to determine it’s a sixth. Gb is not in the key of Bb major, which instead contains G natural. So Bb to Gb is a half step smaller than a major sixth, so it’s a minor sixth.

G# up to E. This is another sixth (G#, A, B, C, D, E). Now, normally, we’d ask whether the higher note, E, is in the major key of the lower note, G#. In this case, though, that’s an annoying problem, because G# major would be a highly unusual key. So an easier way to solve this problem might be to lower both notes by a half step, to G and Eb. G to E natural would form a major sixth, and G to Eb is a half step smaller, making it a minor sixth. So G# to E natural is also a minor sixth.

 Quick Quiz 2.2 Give the complete name for each of the following intervals (major second, perfect fourth, etc.). A (lower note) up to C (higher note) C# up to G G up to C# F up to Db

## Consonance Vs. Dissonance

Okay, so now we know how to identify intervals. But what do different intervals actually sound like?

Traditionally in classical music, major and minor thirds, major and minor sixths, perfect fifths, perfect unisons and perfect octaves are consonances, which basically means they sound pleasing together. Meanwhile, seconds, perfect fourths, tritones and sevenths are dissonances, which means they sound harsh. Your mileage may vary, since any interval can sound pleasant in the right context. In general, though, these definitions are a good starting point – thirds, for example, usually sound pleasant, while minor seconds nearly always sound discordant.

 The Millennial Whoop Critics have begun to identify a particular interval pattern called the “Millennial Whoop” that occurs repeatedly in contemporary pop songs. The Millennial Whoop occurs in a wide variety of recent pop songs. It typically appears when the melody alternates between the fifth and third degrees of the scale. Here, we’re in the key of C major, and we bounce back and forth between G, the fifth degree of the scale, and E, the third degree. What interval is the Millennial Whoop? It’s strongly associated with major keys, but the interval is actually a minor third. (E to G# would be a major third, so E to G is a minor third.) See if you can identify the Millennial Whoop in a song that doesn’t appear in the video above. Figure out what key it’s in, and what notes the Whoop uses.

## Ear Training

College music majors learn to identify the various intervals by ear. It’s an extremely useful skill – it can help a musician write songs more fluidly, and it also helps with improvisation and with understanding what’s going on in rehearsal. Unfortunately, it takes a lot of practice, and a music major might take two years of ear training courses.

Even if you can’t take such classes yourself, though, you can benefit from trying to teach yourself what each interval sounds like. One way you can get started thinking about the sounds of intervals is by familiarizing yourself with examples of each. Here’s a list, and you can find more, along with YouTube videos of each song, at the wonderfully helpful Interval Song Chart Generator.

Minor second: Jaws theme
Major second: Beginning of a scale (“Do, re”)
Minor third: Beverly Hills Cop theme, “Greensleeves”
Major third: “Kumbaya,” “When the Saints Go Marching In”
Perfect fourth: “Here Comes the Bride”
Tritone: The Simpsons theme
Perfect fifth: “Twinkle Twinkle Little Star”
Minor sixth: Love Story theme (descending)
Major sixth: “My Bonnie Lies Over the Ocean,” NBC theme
Minor seventh: “Somewhere” (line that says “There’s a place for us”)
Major seventh:
“Take On Me” (beginning of chorus)

It takes time to learn to identify these intervals, but it can be extremely rewarding to do so. Practice on an ear training program like MacGamut or Auralia can be very helpful if you want to study the topic further. As of 2020, websites like MusicTheory.net and Toned Ear also offer ear training drills for free.

Next Chapter: Chords In Major Keys

## Quick Quiz Answers

2.1
A (lower note) up to C (higher note): third (A, B, C)
C# up to G: fifth (C# D E F G)
G up to C#: fourth (G A B C#)
F up to Db: sixth (F G A B C Db)

2.2
A (lower note) up to C (higher note): minor third
C# up to G: diminished fifth (or tritone)
G up to C#: augmented fourth (or tritone)
F up to Db: minor sixth