How to Find an Interval

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Chapter 3 · Lesson 04

In short

To find an interval you work in two steps: first you count the size (the note names) and then the quality (the tones). For large intervals, inversion makes the job easier.

Lesson Notes

We now know what the size, the quality and the inversion are. Time to put them all together into one simple method that works for every interval.

01Two steps, always in order

Every interval has two characteristics, so you find it in two steps. First the size, by counting the note names. Then the quality, by counting the tones and semitones.

It doesn't matter whether the notes sound together or one after the other, or whether they go up or down. The interval is measured the same way.

02Identification examples

Let's try the method on three intervals smaller than a sixth: one harmonic, one melodic ascending and one melodic descending. In all three we work the same way.

The same method, three ways of writing

Harmonic · C-G

perfect fifth P5

Melodic ascending · D-F

minor third m3

Melodic descending · A-E

perfect fourth P4

Three intervals written in different ways. The method is the same: we count names for the size, tones for the quality.

In the harmonic C-G we count five names (C-D-E-F-G) and 3½ tones, so a perfect fifth. In the ascending D-F, three names and 1½ tones, so a minor third. In the descending A-E the direction changes nothing: four names and 2½ tones, so a perfect fourth. The tones of each quality can be looked up in the table of qualities.

03Large intervals: the inversion trick

The larger the interval, the more tedious the tone counting gets. This is where inversion helps. Let's see it in three steps, with D-C, a seventh.

Invert to find it easily

The unknown · D-C

seventh ?

Inversion · C-D

major second (M2)

D-C inverts to C-D, which we easily find to be a major second (M2).

We invert. D-C becomes C-D.
We find the small one. C-D is easy to measure and it is a major second (M2).
We go back with the rule of 9. The inverted size becomes a seventh (9−2) and major becomes minor. So the original interval D-C is a minor seventh (m7).

04The reverse: how to write an interval

Other times you know the interval and you are looking for the note. The method is the same, in reverse. Say we want a major third above G.

A third above G

We count three names from G: G (1), A (2), B (3). The third note is B.

We find the name. We count three names from G, G-A-B, so the note is some B.
We adjust the quality. G-B spans 2 tones, so it is already a major third. The note we want is B.

If we wanted a minor third instead of a major one, we would have to shrink the interval by a semitone, adding a flat: B♭.

Recap

You find an interval in two steps: first the size (count names), then the quality (count tones).
Melodic or harmonic, ascending or descending, the interval is measured the same way.
For large intervals: invert, find the small one, and go back with the rule of 9.
To write an interval: first the note name (count names), then an accidental if needed for the right quality.