Theory Thursday: Intervals Part 2

Intervals, part 2

The whole-step and half-step intervals we talked about last week are what I call raw intervals. They can be used to define the space between any two musical tones. If the space is bigger than a whole-step, you can refer to the space in either the number of half-steps, or the number of whole-steps + half-steps.

For example, the space between A and C is either "3 half-steps" or "a step and a half". As a guitarist, I tend to prefer using half-steps because they correspond directly to frets. For example, C is 3 half-steps above A, and likewise C is 3 frets above A.

This is all well and good, but what about intervals like A to F? It starts to get cumbersome to say "8 half-steps above A". We need a way to refer to a relationship between tones that doesn't leave us counting frets all day long.

The relationship between tones is still an interval, but we need a different type of interval that makes the relationships between tones more manageable, but still descriptive.

To accomplish this, we need to review the numbers we introduced a few weeks ago:

TONE: A B C D E F G A B C D E F G A etc.
   #: 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 etc.

Just as each tone in our A minor scale has a number, these numbers correspond with a different type of interval called a harmonic interval.

Following the numbers of the scale, the harmonic interval from A to B is a 2nd, A to C is a 3rd, A to D is a 4th, A to E is a 5th, A to F is a 6th, and A to G is a 7th. Make sense?

With these harmonic intervals, we're not as explicit about whole and half steps. What we're more focused on are the relationships between members of our scale. So as you may have guessed, these harmonic intervals exist beyond relationships with A.

The following table is a list of the interval relationships between "A" and the rest of the A minor scale: Now here's the twist... Every tone in the scale has these types of interval relationships.

START: A B C D E F G
  2nd: B C D E F G A
  3rd: C D E F G A B
  4th: D E F G A B C
  5th: E F G A B C D
  6th: F G A B C D E
  7th: G A B C D E F

For example, starting from B, B to C is a 2nd, B to D is a 3rd, etc.

Review

• What is the harmonic interval between A and E?
• What is the harmonic interval between C and D?
• What is the harmonic interval between F and B?
• What is the harmonic interval between B and F?