Lesson 03: Measuring the distance: intervals

Lesson objectives:

• Define an interval as the distance between two notes.
• Count an interval's number by counting letter names inclusively (both notes included).
• Name common intervals — second, third, fifth, octave — from two note names.

Prerequisites: Lessons 01-02 (note names, half and whole steps) | Previous << 02 | Next 04 >>

"It's a fifth" — a fifth of what?

Musicians throw around "that's a third" or "jump up a fifth" as if everyone counts the same way. The confusion is that these numbers are not counted the way you would count the gaps between notes — they count the letter names touched, including both ends. Miss that "count both ends" rule and every interval comes out one too small. This lesson pins down the counting so "it's a fifth" becomes something you can verify, not just repeat.

Explanation

An interval is a distance with a name

An interval is the difference in pitch between two notes¹. Every interval has a number — second, third, fourth, fifth, and so on — and that number answers "how many letter names does this distance span?"

Here is the rule that trips people up: you count inclusively, starting the lower note as 1¹. You do not count the steps between; you count the letter positions, both notes included.

Counting an interval's number

To find the number of the interval from a lower note up to a higher note, say the musical alphabet out loud from the lower note, counting it as 1, until you reach the higher note¹²:

• C up to D: C(1), D(2) → a second.
• C up to E: C(1), D(2), E(3) → a third.
• C up to G: C(1), D(2), E(3), F(4), G(5) → a fifth.
• C up to the next C: C(1), D(2), E(3), F(4), G(5), A(6), B(7), C(8) → an octave (eight).

Notice you always include the starting note in the count. That is why an octave — which feels like "the same note again" — is called an eighth: eight letter names from C up to C. If you had counted the gaps instead, you would have said seven, and been wrong by one every time.

Read the count below and predict the interval's name.

The number is only half the story (a heads-up)

You may have noticed two "thirds" can feel different — cheerful versus sad. That is because intervals also have a quality (major, minor, perfect) layered on top of the number, which comes from how many half steps the interval actually contains. This course keeps the spotlight on the number, because the number is what you count first and what scales and chords are built from. The quality words will show up naturally in Lesson 06 when major and minor chords appear — you do not need to master them here.

Worked example (follow along)

Question: what interval is E up to B?

1. Start on the lower note, E, and count it as 1.
2. Say the alphabet up to B, including both ends: E(1), F(2), G(3), A(4), B(5).
3. Five letter names → a fifth. E up to B is a fifth.

The distance in half steps (which we could also count) would tell us its quality, but the number comes straight from the letters: five names, a fifth.

Your turn (faded example)

Name the interval from D up to F. Fill in the blanks (count first, then check):

• Start the lower note as 1: D(1), then ______(2), then ______(3).
• That is ______ letter names, so D up to F is a ______.

Answer: D(1), E(2), F(3) — three letter names, so D up to F is a third. The common slip is to say "second" by counting only the one gap from D to F's neighborhood; counting inclusively from D as 1 gives three, a third.

Summary + what's next

An interval is the distance between two notes, and its number is just the count of letter names from the lower note (counted as 1) up to the higher — a second, a third, a fifth, an octave. Count inclusively and you will never be off by one.

Now we put intervals and steps together into the most important pattern in all of tonal music: the major scale. It is built from a fixed recipe of whole and half steps, and once you know the recipe you can build it starting on any note. That is Lesson 04.