Theory Thursday: Sevenths

Intervals: The Seventh

For the last several weeks we've been learning about a variety of intervals. Today, we're moving right along to the next interval, the seventh. While it might seem like this can go on forever, I've got some good news: next week will be the last lesson on new intervals, at least for a while.

So from last week, we learned that sixths are the intervals created by skipping over 4 tones in the scale. This week, as you've probably guessed, we're going to talk about the interval relationship that happens if you skip 5 scale tones. Using the A minor scale, here's a look at the seventh (7th) intervals:

A -> G
B -> A
C -> B
D -> C
E -> D
F -> E
G -> F

I'm betting you already guessed these, right? Sevenths are really just the next increment in the pattern we've been exploring for the last several weeks, and again the only thing new here is that the interval is getting bigger. So to build a seventh, if we start on A, we simply leap-frog over the B, C, D, E and F to get to G. As you've guessed, for the rest of the tones in the scale, it's the same pattern of skipping over 5 tones to get to the seventh.

Counting the Half-Steps

Let's now take another look back at our pattern of whole and half steps that make up our A minor scale (I included the scale on top and the interval between each tone below...):

A B C D E F G A B C D E F G A ... etc
 W H W W H W W W H W W H W W  ... etc

Again, remember, every W is 2 half-steps.

So let's now take a look at the raw intervals that make up each 7th interval in the A minor scale. We do this by adding all the intervals between our two tones. So for example, A to G is W + H + W + W + H + W (using the pattern above), the B to A is H + W + W + H + W + W, and so on. So all together, this looks like:

A -> G : W+H+W+W+H+W = 10 half-steps
B -> A : H+W+W+H+W+W = 10 half-steps
C -> B : W+W+H+W+W+W = 11 half-steps
D -> C : W+H+W+W+W+H = 10 half-steps
E -> D : H+W+W+W+H+W = 10 half-steps
F -> E : W+W+W+H+W+W = 11 half-steps
G -> F : W+W+H+W+W+H = 10 half-steps

As you can see from the diagram above, most of the sevenths are made up of 10 half-steps, and a couple of them are 11 half-steps. The 7ths come in major and minor variations, just like with 2nds, 3rds, and 6ths. A larger 7th made up of 11 half steps is a major 7th (M7), while a smaller 7th made up of 10 half steps is a minor 7th (m7).

Inversions, Revisited

Just as the 4ths & 5ths are inversions, and 6ths & 3rds are inversions, 7ths and 2nds share that same type of relationship. For example, A->B is a 2nd (a M2 to be precise), while B->A is a 7th (a m7 to be precise). So just like with 3rds and 6ths, the 2nd & 7th inversion takes on the opposite quality, i.e., major inverts to minor, and minor inverts to major. Here's an illustration:

7th         2nd
=====================
A->G = m7 : G->A = M2
B->A = m7 : A->B = M2
C->B = M7 : B->C = m2
D->C = m7 : C->D = M2
E->D = m7 : D->E = M2
F->E = M7 : E->F = m2
G->F = m7 : F->G = M2

Just as the sum of the half steps of a 4th + 5th inversion equals 12, the same is true for 2nds and 7ths. From the chart above, a M7 is 11 half steps, and its inversion would be a m2 which from a few lessons back is 1 half step, so 11 + 1 = 12. And also a m7 (10 half steps) and its inversion M2 (2 half steps) is the same: 10 + 2 = 12.

Summary

So the important things to remember from today's lesson are:

• A seventh is the interval that results from skipping 5 scale tones
• A major 7th (M7) is 11 half-steps
• A minor 7th (m7) is 10 half-steps
• The inversion of a M7 is a m2
• The inversion of a m7 is a M2
• The sum of the half steps between an interval and its inversion is always 12

Review

• How many half-steps in a minor 2nd interval?
• How many half-steps in a major 2nd interval?
• How many half-steps in a minor 3rd interval?
• How many half-steps in a major 3rd interval?
• How many half-steps in a perfect 4th interval?
• How many half-steps in an augmented 4th interval?
• How many half-steps in an diminished 5th interval?
• How many half-steps in a perfect 5th interval?
• How many half-steps in a minor 6th interval?
• How many half-steps in a major 6th interval?
• How many half-steps in a minor 7th interval?
• How many half-steps in a major 7th interval?
• What is the inversion of a P5 interval?
• What is the inversion of a m2 interval?
• What is the inversion of a M7 interval?
• What is the inversion of a m3 interval?

Reminder

If you have ANY questions or comments, please leave a comment here, on my Facebook page, or tweet at me (@chrisstarkgtr).