An interval is nothing more than the distance between two tones. It is often convenient to speak about music in terms of intervals, so it’s important that you know the terminology.
We distinguish between two kinds of intervals:
A melodic interval is the distance between two tones played after each other:
A harmonic interval is the distance between two tones played at the same time:
The rules for both types of intervals are the same.
The problem we are trying to solve is: If you have two tones, then what is the interval between them called?
There are several ways to approach this:
Count the number of half-steps between the two tones and look it up in a table.
A half-step (or “semitone”) means: go one key on the keyboard to the left or right. Suppose we start at the C key. A half-step up from C is C#, a half-step up from C# is D. Conversely, a half-step down from C is B, a half-step down from B is Bb.
In other words, a half-step is the distance between two adjacent notes. There is also something called a whole-step (or “whole tone”) which is simply two half-steps. You can also think of a whole-step as skipping a note.
Example: find the interval C to E.
We begin at C on the keyboard and count up: to C# is one half-step, to D is two half-steps, to D# is three half-steps, and finally to E is four half-steps.
Look it up in the table:
|Octave (or eight)||12|
We find that C to E is called a major third interval.
Example: find the interval G to Bb.
Again we count the half-steps: G to G# is 1, to A is 2, to Bb is 3. According to the table, 3 half-steps is a minor third interval.
Note that both intervals from the examples are called a “third”, although one is “major” and the other is “minor”. There are three other qualifiers in addition to major and minor: perfect, augmented and diminished.
Perfect applies only to unison (1), fourth (4), fifth (5) and octave (8) intervals. Major and minor apply only to second (2), third (3), sixth (6) and seventh (7). There is a reason for this distinction, but we won’t go into that here.
All intervals may be diminished or augmented. Diminished means the interval is made a half-step smaller. Augmented means the interval is made a half-step larger.
Sometimes people drop the qualifier and just say: “From C to E is a third,” without specifying exactly what kind of third it is.
As you can see in the table above, different intervals can have the same number of half-steps: an augmented fourth and a diminished fifth are both 6 half-steps apart. Which one should you choose?
Here is a more precise way to find the interval names: First, you drop the sharps and flats and just use the note names. Then you count the number of notes in that interval. Finally, you adjust for the sharps and flats that you removed.
Example: the interval C to F#.
We drop the # from F# so the interval becomes C to F.
Then we count the number of tones in this interval, starting at 1: C = 1, D = 2, E = 3, F = 4. That means the interval C to F# is some kind of fourth because we counted four tones.
However, we need to find F# and not F, so we “sharpen” (or “raise”) the interval to make it a half-step larger. After all, F# is a half-step above F. A fourth plus a half-step is called an augmented fourth.
Example: the interval C to Gb.
We drop the b from Gb and count C to G, which is 5 tones. The interval is some of kind of fifth but not a regular fifth because we want Gb instead of G, which is a half-step lower. So we “flatten” (or “lower”) the interval to make it a diminished fifth.
Note that the intervals C to F# and C to Gb sound exactly the same on the piano because F# and Gb are the same key. We call these intervals “enharmonically equivalent”.
That doesn’t mean you can simply substitute them for each other: if the top note is named F# then the interval must be a fourth; if the top note is named Gb then the interval must be a fifth. You can’t call a fourth a fifth and vice versa.
Example: the interval F to Ab.
As before, we drop the b and count F to A, which is 3 tones. That means the interval is some kind of third. Because Ab is a half-step lower than A we flatten the third to make it a minor third.
Now why is a flattened third called “minor” but a flattened fifth called “diminished”? For the same reason some intervals are called “perfect” (unison, fourth, fifth and octave) and others are not (second, third, sixth and seventh).
The rules for interval calculations are:
- Perfect intervals can be augmented or diminished.
- Major intervals may be augmented or made minor.
- Minor intervals may be diminished or made major.
You can also look it up here:
In this table, b means “flatten” or lower by a half-step, bb means lower a whole-step, # means “sharpen” or raise by a half-step.
In the above examples, we dropped the # and b from the second interval tone, but what if the first tone has a # or b?
Example: C# to E.
First, we drop the sharps and flats like before, and count: C = 1, D = 2, E = 3. The interval we are looking for will be some kind of third. However, because the first tone is C# and not C, we need to make the interval a half-step smaller (not larger!) to find a minor third.
Here is the full procedure again:
- Remove flats and sharps from the note names.
- Count the number of tones in the interval.
- If the last tone has a #, raise the interval.
- If the last tone has a b, lower the interval.
- If the first tone has a #, lower the interval.
- If the first tone has a b, raise the interval.
- Look up the interval name in the table.
It may seem complicated but once you get the hang of it, finding the names of intervals quickly becomes automatic.
Intervals can go beyond an octave, by the way. Then we simply call them a 9th, a 10th, an 11th, and so on. Such big intervals are also known as “compound intervals”. For example, a tenth is also called a compound third.
Read more articles on Piano Clues: