Question: I have a question about intervals. My assignment is to write the full name of each interval:

• D to C-sharp?
• F to E-flat?
• B to G-sharp?

I’m very confused. Can you help me?

– Beibei (Singapore)

Albert’s reply: While initially they can be among the more confusing elements of music theory, intervals are actually pretty basic once you learn a few techniques.

First, it’s important to know all of your piano scales. We’ll use all the major scales as references.

Second, you’ll need to know how to read sheet music – at least the basics. The reason is that you can determine the interval visually, just by counting lines and spaces.

For instance, the following interval is a third, since the notes are on adjacent lines, with a single space in between:

We don’t actually know which notes they are or what kind of third (major, minor, diminished, augmented), since there’s no clef.

While there’s a more technical, algorithmic way to determine intervals (which involves separating them into diatonic and chromatic intervals and mapping them in a matrix), I’ll give you a practical shortcut. First, use the major scale as a reference. The interval between the first and second notes of a major scale (scale degrees 1 and 2) is a second; between the first and third notes is a third; between the first and fourth is a fourth, and so on.

Next, we need to look at the kind or quality of each interval. The interval between scale degrees 1 and 2 in a major scale is a major second, between scale degrees 1 and 3 is a major third, 1 and 4 is a perfect fourth, 1 and 5 is a perfect fifth, 1 and 6 is a major sixth, 1 and 7 is a major seventh, and 1 and 8 is a perfect octave.

Fourths, fifths, and octaves can’t be major or minor – they’re called perfect intervals for acoustic reasons.

Now let’s take a look at your questions:

If we play a major scale starting on the bottom note, D, we’ll discover that C-sharp is indeed in the scale. Therefore, this interval is a major seventh.

Now for your second question, F to E-flat:

If we play an F major scale, we’ll discover that E-flat is not in the scale. Instead, E natural is scale degree 7. Since E-flat is one half step below E natural, instead of a major seventh we have a minor seventh. (If it were E double flat – two half-steps removed from scale degree 7 – we’d have a diminished seventh.)

Finally, let’s look at B to G-sharp:

Here, G-sharp is the sixth note in the B major scale. This interval is therefore a major sixth, according to my above description of intervals within the major scale.

If you join key-notes as a member, you’ll find an entire course dedicated to intervals, as this is the foundation for chords.