Theory Thursday: Unisons and Octaves

Intervals: Unisons and Octaves

If you've been following my blog, we've been talking a whole lot about intervals for the last several weeks. Today's lesson is the final lesson about intervals (at least for a while).

So from last week, we learned that sevenths are the intervals created by skipping over 5 tones in the scale. This week, we're going to talk about two special intervals: the unison and the octave.

Unison

A unison interval is a special interval that happens when you play more than one instance of the same tone at the same time. There are not a lot of instruments that can even do this, but by virtue of the guitar having multiple strings, we can play the same tone on more than one string simultaneously.

Try it! If you play your open A string along with your low E string on fret 5, these are the same tone. It's easiest to play unisons on adjacent strings on the guitar. Why would you ever play a unison? There are a number of reasons, but mostly what you'll find is that by having two (or more) instances of the same tone played simultaneously, that tone is intensified and accentuated.

Octave

The other interval we're talking about today is the octave. The octave interval is when you skip over all the tones in the scale until get to the same tone (just 12 half-steps higher).

With both unisons and octaves, there are no major, minor, diminished, or augmented variations. The only unison for an A is another A that is 0 half-steps above. The only octave for an A is the A exactly 12 half-steps above.

Discussion

Octaves and unisons play an important role in music. When we want to "thicken" or emphasize musical ideas, we can double the important parts using unisons (this can be done by simply recording the same ideas more than once, or by having a fellow musician play the same part on their instrument).

A similar effect can be had using octaves. Adding a part that is an octave higher can give the part more drama and brilliance. Adding a part that is an octave lower can add power and depth.

Summary

So here's a round-up of all the "harmonic" or "musical" intervals we've learned about and their corresponding half-step "raw" intervals:

Interval       : half-steps
---------------------------
unison         :  0
minor 2nd      :  1
major 2nd      :  2
minor 3rd      :  3
major 3rd      :  4
perfect 4th    :  5
augmented 4th  :  6
diminished 5th :  6
perfect 5th    :  7
minor 6th      :  8
major 6th      :  9
minor 7th      : 10
major 7th      : 11
octave         : 12

Looking Ahead

Next week we are going to start dipping our toes into the water of "chords". If you're not clear on any of the intervals, go back through the past weeks and reread the lessons, and if you're still not getting it, drop me a line. Intervals are the fundamental building blocks for chords, so I want to make sure you're got them down before we go any further.

Reminder

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

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).

Theory Thursday: Sixths

Intervals: The Sixth

For the last several weeks we've been learning about a variety of intervals, starting with seconds up through fifths last week. Today, we're moving right along to the next interval, the sixth.

So from last week, we learned that fifths are the intervals created by skipping over 3 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 4 scale tones. Using the A minor scale, here's a look at the sixth (6th) intervals:

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

You got this, right? Sixths 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 sixth, if we start on A, we simply leap-frog over the B, C, D, and E to get to F. As you've guessed, for the rest of the tones in the scale, it's the same pattern of skipping over 4 tones to get to the sixth.

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 6th interval in the A minor scale. We do this by adding all the intervals between our two tones. So for example, A to F is W + H + W + W + H (using the pattern above), the B to G is H + W + W + H + W, and so on. So all together, this looks like:

A -> F : W+H+W+W+H = 8 half-steps
B -> G : H+W+W+H+W = 8 half-steps
C -> A : W+W+H+W+W = 9 half-steps
D -> B : W+H+W+W+W = 9 half-steps
E -> C : H+W+W+W+H = 8 half-steps
F -> D : W+W+W+H+W = 9 half-steps
G -> E : W+W+H+W+W = 9 half-steps

As you can see from the diagram above, most of the sixths are made up of 9 half-steps, and a few of them are 8 half-steps. Going back to our 2nds and 3rds, a larger 6th made up of 9 half steps is a major 6th (M6), while a smaller 6th made up of just 8 half steps is a minor 6th (m6).

Inversions, Revisited

Recall from last week, in addition to learning about fifths, we also learned the concept of interval inversions. We learned that 4ths and 5ths are inversions of each other, and we also learned that if we add the number of half steps from a 4th and its 5th inversion, the sum is always 12.

Just as the 4ths and 5ths have an inversion relationship, 6ths and 3rds share that same type of relationship. For example, A->C is a 3rd (a m3 to be precise), while C->A is a 6th (a M6 to be precise). So unlike 4ths & 5ths, where the inversions are both "perfect" (as in P4 inverts to P5), with 3rds and 6ths, the inversion takes on the opposite quality, i.e., major inverts to minor, and minor inverts to major. Here's an illustration:

6th         3rd
=====================
A->F = m6 : F->A = M3
B->G = m6 : G->B = M3
C->A = M6 : A->C = m3
D->B = M6 : B->D = m3
E->C = m6 : C->E = M3
F->D = M6 : D->F = m3
G->E = M6 : E->G = m3 

Just as the sum of the half steps of a 4th and its 5th inversion equals 12, the same is true for 3rds and 6ths. From the chart above, a M6 is 9 half steps, and its inversion would be a m3 which from a few lessons back is 3 half steps, so 9 + 3 = 12. And also a m6 (8 half steps) and its inversion M3 (4 half steps) is the same: 8 + 4 = 12.

Summary

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

• A sixth is the interval that results from skipping 4 scale tones
• A major 6th (M6) is 9 half-steps
• A minor 6th (m6) is 8 half-steps
• The inversion of a M6 is a m3
• The inversion of a m6 is a M3
• 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?
• What is the inversion of a P4 interval?
• What is the inversion of a m3 interval?
• What is the inversion of a d5 interval?
• What is the inversion of a m6 interval?

Reminder

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