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.