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).

Theory Thursday: Fifths

Intervals: The Fifth

In the last couple weeks we learned about 2nd, 3rd, and 4th intervals. For seconds and thirds there are major and minor varieties, and with fourths there are perfect and augmented varieties. Today, we're moving right along to the next interval, the fifth.

So from last week, we learned that fourths are the intervals created by skipping over two tones in the scale. This week, we're going to talk about the interval relationship that happens if you skip three scale tones. Using the A minor scale, here's a look at the 5th intervals:

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

Still with me? Fifths are really just the next increment in the pattern we've been exploring for the last few weeks, and again it's just that the interval is getting bigger. So to build a fifth, if we start on A, we simply leap-frog over the B, C, and D to get to E. Then of course it's the same for every subsequent tone in the A minor scale.

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

A -> E : W+H+W+W = 7 half-steps
B -> F : H+W+W+H = 6 half-steps
C -> G : W+W+H+W = 7 half-steps
D -> A : W+H+W+W = 7 half-steps
E -> B : H+W+W+W = 7 half-steps
F -> C : W+W+W+H = 7 half-steps
G -> D : W+W+H+W = 7 half-steps

As you can see from the diagram above, most of the fifths are made up of 7 half-steps, and just one of them is 6 half-steps. Similar to 4ths, 5ths that consist of 7 half-steps are called "perfect" fifths (P5) and because the fifth made up of 6 half-steps is just a little smaller, it's called a "diminished" fifth (d5).

If you look back at last week's discussion of fourths, you'll see that an augmented fourth is made of the same 6 half-steps as a diminished fifth. Uh oh! What's worse is that to our ears, there is NO difference between an augmented 4th and a diminished 5th. They sound exactly the same.

So how can we tell them apart?

The answer is actually pretty simple. If you look at the A4 interval F -> B, there are 2 tones in between (G and A). When you skip 2 tones, you have a fourth. If you look at the d5 interval B -> F, there are 3 tones in between (C, D, and E). When you skip 3 tones, you have a fifth. Not so bad, right?

New Terminology

We just learned that even though the interval of a diminished fifth and an augmented fourth sound the same (because they have the same number of half steps), they have different names. There is a special term for these intervals that have different names but the same number of half-steps: enharmonic equivalents. It's kind of a yucky term to remember, but it just means intervals that have the same raw interval but different harmonic names. In a sentence, you'd say "Augmented fourths and diminished fifths are enharmonic equivalents."

In time, we will cover several other enharmonic equivalent intervals, but for now with the A minor scale, the A4/d5 pair is the only one we will encounter.

But wait! There's More!

If you take another look at our B->F and F->B example from above, notice that both of these  intervals use the same two tones, B and F. The only difference is which tone comes first. Intervals that share the same tones but just have a different order are called inversions.

If you start with a fourth interval (C->F for example), then swap the order of the tones (F->C) it becomes a fifth. Any time you invert a fourth it becomes a fifth. Likewise, any time you invert a fifth it becomes a fourth. More specifically, if you start with a perfect fourth, the inversion is a perfect fifth (and vice versa). Likewise, if you start with an augmented fourth, the inversion is a diminished fifth (and vice versa).

Going back to the raw intervals, if you add a perfect fourth (5 half steps) and its inversion, a perfect fifth (7 half steps), the result is 12. If you add an augmented fourth (6 half steps) and its inversion, a diminished fifth (6 half steps), the result is 12 again.

The sum of the half steps of an interval and its inversion is always 12. We'll see a bit more of that when we talk about 6ths next week and 7ths the following week.

Summary

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

• A fifth is the interval that results from skipping 3 scale tones
• A perfect 5th (P5) is 7 half-steps
• A diminished 5th (d5) is 6 half-steps
• Intervals that have the same number of half-steps but different names are called enharmonic equivalents
• When you flip the order of tones in an interval, it is called an inversion
• The sum of the half steps between an interval and its inversion is always 12
• Fourths and fifths are inversions of each other 

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?
• Define the term enharmonic equivalents.
• What interval is A->E?
• What would be its inversion?
• What interval is the inversion?

Reminder

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

Theory Thursday: Fourths

Intervals: The Fourth

In the last couple weeks we learned about 2nd and 3rd intervals, and their major and minor varieties. Today, we're moving right along to the next interval, the fourth.

So from last week, we learned that thirds are the intervals created by skipping over a tone in the scale. This week, we're going to talk about the interval relationship that happens if you skip two scale tones. Using the A minor scale, here's a look at the 4th intervals:

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

None of that seems too bad so far, right? It's really a lot like everything else we've covered so far, it's just that the interval is getting bigger. So to build a fourth, if we start on A, we simply leap-frog over the B and C to get to D, and then we do the same for every tone in the A minor scale.

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 etc
 W H W W H W W W H  etc

Again, remember, every W is 2 half-steps. So let's now take a look at the raw intervals that make up each fourth interval in the A minor scale. We do this by adding all the intervals between our two tones. So for example, A to D is W + H + W (using the pattern above), the B to E is H + W + W, C to F is W + W + H, etc. So this looks like:

A -> D : W+H+W = 5 half-steps
B -> E : H+W+W = 5 half-steps
C -> F : W+W+H = 5 half-steps
D -> G : W+H+W = 5 half-steps
E -> A : H+W+W = 5 half-steps
F -> B : W+W+W = 6 half-steps
G -> C : W+W+H = 5 half-steps

Remember how there are major and minor seconds and thirds? Well things change a little for fourths. As you can see from the diagram above, most of the fourths are made up of 5 half-steps, and just one of them is 6 half-steps. Fourths that consist of 5 half-steps are called "perfect" fourths (P4) and because the fourth made up of 6 half-steps is just a little bigger, it's called an "augmented" fourth (A4).

So the important things to remember about fourths are 1) a fourth is the interval that results from skipping 2 scale tones, and 2) a perfect 4th (P4) is 5 half-steps, and 3) an augmented 4th (A4) is 6 half-steps.

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?

Reminder

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

Theory Thursday: Thirds

Intervals: The Third

Last week we learned that adjacent tones in a scale have the interval relationship of a second. And we also learned that if the second is made up of a single half-step (or one fret space on a guitar), it is called a minor second. Likewise, a second made up of two half-steps (i.e., two frets on a guitar), it is called a major second. Easy peasy, right?

This week, we're going to talk about the interval relationship that happens if you skip a tone. As you've likely guessed by today's blog title, it's called a third. So let's take a look at what the thirds look like in the A minor scale:

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

None of that seems too bad so far, right? If we start on A, we simply leap-frog over the B to C, and we do the same for every tone in the A minor scale. Let's now take a 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 etc
 W H W W H W W W H  etc

Remember, every W is 2 half-steps. So let's now take a look at the raw intervals that make up each third interval in the A minor scale. We do this by adding adjacent intervals. So for example, A to C is W + H (using the pattern above), the B to D is H + W, C to E is W + W, etc. So this looks like:

A -> C : W+H = 3 half-steps
B -> D : H+W = 3 half-steps
C -> E : W+W = 4 half-steps
D -> F : W+H = 3 half-steps
E -> G : H+W = 3 half-steps
F -> A : W+W = 4 half-steps
G -> B : W+W = 4 half-steps

Remember how there are major and minor seconds? Well the same is true for thirds. A minor third (m3) is 3 half steps and a major third (M3) is 4 half steps.

Over time, you will naturally start to remember that A+C is a minor third. Right now, I don't think it's very important for you to memorize which thirds in the A minor scale are major or minor. What IS important is that you remember that minor thirds are 3 half steps and major thirds are 4. 

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?
• Try to list out from memory the A minor scale and write the intervals between each tone.

Reminder

These lessons are really intended to help you get a grasp on music theory. Things are a little slow moving at first because I'm not assuming ANY prior knowledge of this stuff. It's going to get a lot deeper as we continue. If you have ANY questions or comments, please leave a comment here, on my Facebook page, or tweet at me (@chrisstarkgtr).

Theory Thursday: Gimme a Second

Intervals: The Second

Summing up what we've learned so far about intervals, we know that a) an interval is a relationship between two tones, b) raw intervals measure this relationship in terms of individual half-steps and whole-steps, and c) with harmonic intervals we measure the musical value of this relationship.

Today's lesson is going to focus on one of the smallest harmonic intervals: the second.

From last week, we learned that the interval between any tone in the A minor scale and its nearest neighbor is called a second. But if you play the A minor scale on your guitar (especially the A minor scale all on one string), the raw intervals between some of the tones is just a single fret -- a half-step, while the interval between the rest of the tones is two frets -- a whole-step. Remember our pattern of whole-steps (W) & half-steps (H)?

W H W W H W W

How can it be that the harmonic interval between every neighboring tone in the minor scale is a 2nd when we can see that the raw interval changes between whole and half-steps?

The answer is that both whole steps and half steps can be called seconds. But there's a catch…

When a second is made up of a half-step, it's called a minor second. Likewise, when a second is made up of a whole-step (two half-steps), it's called a major second.

NOTE: It is common to use M for major and m for minor. So if you see M2, it means major second, and m2 means minor second.

So with that in mind, let's have a look at the second intervals in the A minor scale:

A -> B : M2
B -> C : m2
C -> D : M2
D -> E : M2
E -> F : m2
F -> G : M2
G -> A : M2

The important thing for you to remember about the second interval is that it comes in a couple different varieties: major & minor. Remember that a minor second (m2) is ALWAYS a half step, and a major second (M2) is ALWAYS a whole step.

EXTRA: There is one more type of second, but we don't find it in our A minor scale, so we're going to skip it for now. It is called an augmented second, and it is made up of three half steps. We will get to augmented seconds later.

Review

• What is an interval?
• What is a raw interval?
• How is a raw interval different from a harmonic interval?
• What is the difference between a major second and a minor second?
• What are the common shorthand notations for major and minor seconds?

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?

Theory Thursday: Intervals Part 1

Intervals, part 1

Leaping way back to our chromatic scale, it's time to explore another fundamental concept of music: the interval. An interval is the space between two musical tones. We're going to start with the smallest interval, but first, here's the chromatic scale again, but I shrank the tones with two names to make it more readable:

A A#/B♭ B C C#/D♭ D D#/E♭ E F F#/G♭ G G#/A♭ A

The space between any tone and its adjacent neighbor -- either above or below -- is the smallest musical interval -- there's nothing in between. This smallest interval is called either a semitone or half-step.

NOTE: I learned half-step before I learned semitone, so I'll use the term half-step, just out of my own comfort. Just be aware that half-step is the same as semitone.

So now you know that a half-step is the space between each of the tones in the chromatic scale. The half-step is also the interval from each fret on the fretboard to the next higher or lower fret.

For example, on any of the strings, if you start on the 5th fret, the 4th fret would be a half-step LOWER and the 6th fret would be a half-step HIGHER than the 5th fret. Make sense?

So as you may have guessed, if you skip over an adjacent tone, either higher or lower, the resulting interval is a whole-step. Half + half = whole, after all. Also, just as a half-step is also a semitone, a whole-step is also a whole-tone.

So using the same example of starting on the 5th fret, a whole-step higher would be the 7th fret, and a whole-step lower would be the 3rd fret. Got it?

Now let's look both the A minor scale and chromatic scale again. I've underlined and emboldened the tones that make up the A minor scale so you can see how it is a subset of the chromatic scale.

Chromatic: A A#/B♭ B C C#/D♭ D D#/E♭ E F F#/G♭ G G#/A♭ A

A Minor: A B C D E F G A

We've already seen that the interval between EVERY adjacent tone in the chromatic scale is a half-step, but that's not the case at all with the A minor scale. If you look at the bold & underlined tones from the A minor scale, you can see that the A minor scale starts on A, then whole-step to B, half-step to C, whole-step to D, whole-step to E, half-step to F, whole-step to G, then finally another whole-step back to A. Every time you skip over a tone, that's a whole-step.

If we use W for whole-step and H for half-step, the pattern for the A minor scale looks like:

W H W W H W W

Exercise A: Review of A minor scale

Take a look at the A minor scale exercise from a couple weeks ago (listed below), and look how that pattern of whole and half steps from above corresponds to the fret positions of the scale.

Exercise B: Shifting the Minor Scale around

What do you think might happen if you were to take the pattern of fret intervals that you use for the A minor scale, and start on a different fret? For review, here's the A minor scale from a couple weeks ago, in the three tone per string pattern:

What if you were to start on the 8th fret instead of the 5th fret, but play the same pattern, just 3 frets higher?

Without necessarily knowing what tones you were just playing, you just played a C minor scale!

Wait, what?!?

That's right! EVERY minor scale uses the same pattern of intervals:

W H W W H W W

Whichever tone you choose to start from becomes "1" (the tonal center) and the rest of the scale falls into place, solely based on the pattern of intervals.

That's pretty crazy, right?

Well, let's not get too ahead of ourselves. We're going to stay focused on the A minor scale, but I just wanted to give you a quick taste of how relatively easy it will be to apply what you know about the A minor scale to the other minor scales.

Review

• What is an interval?
• What are two common names for the smallest interval?
• What are two common names for the interval you would get if you were to combine two of the intervals from the previous question?
• What is the pattern of intervals for the A minor scale?

Theory Thursday: Scales & Numbers

Scales & Numbers

You likely decided to become a musician because hearing your favorite songs causes you to uncontrollably tap your foot or wiggle some part of your body to the beat, and even if you're not ready to admit it to others, you know that the right song at the right time has even caused your eyes to well-up with tears or caused your heart to skip a beat.

So the last thing you probably want to hear is that you often have to use numbers when communicating musical ideas. Don't worry though, this focus on numbers isn't about turning an art-form that is rich with emotion into some sort of clinical and calculated science (not that there's anything wrong with science). This is about learning a universal way of putting names to the relationships that musical sounds have with one another.

In music, we use numbers in a lot of different contexts, so it can be challenging to keep things straight. To help you keep these different numeric contexts organized in your mind, I'll try to present these different contexts as clearly as possible. Just remember that a lot of concepts in music theory are a bit of a chicken & egg scenario where foundational concepts can sometimes interdepend upon each other. If you don't understand a concept at first, hang in there and try to work through it. It could be that the following concept provides the clarity you need.

As you learned in the A minor scale exercise from last week, scales repeat their pattern of tones, so the tones A through G of the A minor scale actually look more like:

A B C D E F G A B C D E F G A B C D E F G A B C D E F G A (etc.)

Not too bad so far, right?

One of the ways musicians make it easier to relate what they know about one minor scale to another is by using numbers. Because our A minor scale starts on the tone A (hence the name "A" minor), "A" gets the number "1". So following that, we get:

TONE: | A | B | C | D | E | F | G | A | B | C | D | E | F | G | A |

   #: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 |

So to clarify: using numbers and the A minor scale, the first scale degree (i.e., the tonal center) is "A", the second is "B", third is "C", etc., up to the seventh degree being "G". This type of numbering is the foundation for a lot of future concepts, so it's very important that you start to memorize the tones and their corresponding numbers.

Review

• If you were going up the A minor scale, fill in the 5 tones in this sequence:

A B C D E F _ _ _ _ _

• If you were going down the A minor scale, fill in the 5 tones in this sequence:

C B A G F E _ _ _ _ _

• In the A minor scale, which tone is represented by the number 5?
• In the A minor scale, which number represents the tone C?
• Which number represents the tonal center of the A minor scale?
• What is the corresponding tone?

Theory Thursday: The A minor scale

Chromatic Scale Recap

So you already know from the chromatic scale in the previous chapter, that a scale is just a collection of tones.

The chromatic scale is a bit of an oddball in that is really has no beginning or end; it's just EVERYTHING, and it doesn't even matter which tone you start from. Pick a tone and play every single tone up the neck until you've started repeating.

Review: Chromatic Scale

While we do need to know what the chromatic scale is, you can see it's not terribly musical or useful. Let's just agree right here and now that if you understand that the chromatic scale is all of the 12 tones, you already know enough about the chromatic scale.

Let's move on to something more interesting!

The A Natural Minor Scale

Before you get worried that this course is going to turn into a silly list of useless scales, I want to make it clear that we're going to focus on ONE single scale for quite some time. This new scale is called the A natural minor scale — for now we'll just call it the A minor scale. In time, we'll bring back the "natural", but for now it's not important.

One of the characteristics of the A minor scale that makes it quite different from the chromatic scale is the concept of the tonal center. The tonal center of a scale is the most important tone in the scale. Out of the collection of tones that make up the scale, the tonal center is the tone that our ears want to hear the most.

The tonal center for the A minor scale is "A" — hence the name. If we were to talk about any other scale, for example, D major, F♯ lydian, or G minor, the tonal centers for these scales would be D, F♯, and G, respectively. Scales are named after their tonal centers. The chromatic scale has no tonal center, thus it doesn't have a tone in its name.

Unlike the 12 tones of the chromatic scale, the A minor scale has only 7 tones. If you've ever recited the English alphabet, you already know A minor:

A B C D E F G

That's it! No sharps, no flats, no tones with more than one name, it's just a repeating set of the tones A through G. If you've got a keyboard handy, it's just the white keys.

On the guitar, we're going to learn to play the A minor scale a few different ways. Our long term goal is to be able to play the tones in the A minor scale all over the fretboard of the guitar. But for now, we're going to learn two different ways of playing the A minor scale.

Exercise A: Three tones per string A minor scale starting from 5th position

In the preceding exercise, the A minor scale repeats once, and the tonal center (A) is indicated by accent marks (>) on the note heads.



Exercise B: A minor scale laterally on each string

Exercise B is also the A minor scale, as it falls on each of the 6 strings. The diagonal slash indicates where you should slide positions. I recommend you use your pointer, ring, and pinky fingers for the two groups of 3 tones — and use your pointer finger to guide you as you glide from one position to the next — and use your pointer and ring fingers for the highest to tones on each string. So on each string it will go like: "pointer, ring, pinky — slide — pointer, ring, pinky — slide — pointer, ring".

Lesson Review

• What is a scale?
• What is a tonal center?
• How can you tell what the tonal center is of a given scale?
• What tones are in the A minor scale?

Theory Thursday: Your First Scale!

Recap

From last week, we learned that tones are the most basic unit of musical sound and there are 12 unique tones that are the building blocks for music. We also learned that the "♭" symbol is pronounced flat and it means lower than, and also that the "♯" symbol is pronounced sharp and it means higher than.

Scales

We're still just barely scratching the surface here, but we're going to dive right in to the deep end by learning our first scale. But first, what the heck is a scale?

A scale is a collection of tones.

The first scale we're going to learn is called the chromatic scale. This scale is simply the collection of all 12 tones. You don't need to memorize the individual tones in the chromatic scale (not yet anyway), but I do want you to memorize the term "chromatic scale", and that it means all 12 musical tones.

The following exercise will help you to hear what the chromatic scale sounds like. If you are unfamiliar with tablature notation, please see last week's lesson that explains how to read this notation. After you play this exercise as written, try playing the same thing on each of the strings on your instrument. Even though you're starting from different strings, you should notice that the chromatic scale sounds very similar on every string.

Exercise 1A: Play the chromatic scale (click to enlarge).

Now the reality is that the chromatic scale isn't terribly useful. It's literally the entire set of tones! Normally, a piece of music will use a smaller collection of tones -- anywhere from 5 to 8 tones. We'll start looking at more musical scales starting next week.

Review

• What is a tone?
• How do you pronounce "G♭"?
• How do you pronounce "D♯"?
• How many tones are there in total?
• What is a scale?
• What is the chromatic scale?
• How many tones are in the chromatic scale?
• Play the chromatic scale on your instrument, starting from an open string.

Theory Thursday: The Basics

What is music?

Music has been called the art of noise, and in some sense, that’s one of the best descriptions of music that we have. We all know intuitively what music is, but describing it can be tough. How does one adequately describe a phenomenon that encompasses variety as wide as Tibetan Buddhist monk overtone throat singing, garage rock, hip-hop, and dub-step? What all of these have in common is an organization of sound and silence over a defined period of time.

By this definition, our first entries into the realm of music theory will be a description of these three concepts: sound, silence, and time. We'll take them one lesson at a time.

Sound

Before we get any further in discussing sound (as it relates to music), there are a number of terms that we need to define that can unfortunately sometimes be used interchangeably. I'm going to define these terms now, but their meanings will become clearer as we progress. These terms are tone, pitch, and note.

Tone - a musical sound

Pitch - the degree of highness or lowness of a tone

Note - a single tone having a specified pitch and duration

Basically tones are our most basic unit of describing musical sounds.

Modern electric guitars have 6 or more strings and 20 or more frets, but even on a 9 string guitar with 30 frets, there are only 12 unique tones. On any of our instruments, there are just 12 tones.

Take a look at your guitar’s fretboard or the guitar in the photo. If you have fretboard inlays, often times the 12th fret has a special design — maybe something as simple as two dots instead of one — but there’s usually something that offsets fret 12 from the rest of the frets. This is no accident!

Try playing an open string on your guitar — even if you haven’t tuned the string. Now on that very same string, finger the 12th fret and play the string. It sounds the same, just a bit higher, right?

The same thing will happen if you finger the first fret, then again the 13th fret, then 2nd & 14th, and 3rd & 15th, etc.

On a guitar, every 12 frets, the cycle of tones repeats. The same thing happens on a musical keyboard: every 12 keys, the cycle of tones repeats. On a keyboard, it’s easier to visualize because there is a repeating visual pattern:

Take a look at the image of the keyboard above. Using a toothpick, fingernail, or anything else with a point, find one of the white keys just left of a grouping of two black keys. Now count 12 keys to the right, including the black keys. You should land again on a similar-shaped white key that is just left of another grouping of 2 black keys. If you have a keyboard available, try playing keys that are 12 apart. What do you notice? They should sound like the same tone, but the leftmost key will sound lower than the rightmost key. As an experiment, try separating by 24 or even 36 keys.

What all of this means in practical terms is: everything we’re going to learn about music theory uses only 12 tones. All of the music we love — and even the music we don’t — is all formed using a system of 12 tones.

The 12 Tones

The 12 musical tones have names corresponding with the English alphabet. First, there are the 7 pitches that correspond to the repeating white keys on a keyboard. These are simply:

A, B, C, D, E, F, G

If you look at the white keys on the following diagram of a musical keyboard, notice that the pattern of tones just repeats over and over.

Where things get just a bit more tricky are the “in-between” tones — the ones represented by the black keys. These still use the same letters as the white keys, but they have modifier symbols called accidentals that tell us the tone is just a nudge higher or lower than its letter name. The "♯" symbol is pronounced sharp, and the "♭" symbol is pronounced flat, so "A♭" is pronounced "A flat".

Notice that these black keys have two different names on each key. Don't worry about this just yet -- you don't need to memorize right now. Notice however that there is a pattern to the names. For example, the black key tone named C♯/D♭ is both higher than C and lower than D. Soon enough we'll learn when to use which tone name, but for now just try to see the pattern, understanding that "♭" means lower than and "♯" means higher than.

Summary

So for today's lesson, you should memorize the following:

• Tones are the most basic unit of musical sound.
• There are 12 unique tones.
• The "♭" symbol is pronounced flat and it means lower than.
• The "♯" symbol is pronounced sharp and it means higher than.

Theory Thursday: Welcome!

Starting next week, I'm going to post a weekly lesson on music theory, geared specifically at guitarists. If you play a different instrument, you should be able to follow along, too (it's just that as a guitarist, I'll be using my instrument for the examples).

We're going to start from the very beginning, assuming very little knowledge of anything related to music theory. These lessons aren't going to teach you the skills you need to play the guitar, but rather the goal is to get you the knowledge you'll need to make your own music or have a deeper understanding of other people's music.

What you need to know:

• A very basic understanding of the guitar (or whatever instrument you play):
• How to tune a 6-string guitar to standard tuning
• How to hold the instrument and properly fret and pick

What IS Music Theory?

There are a lot of confusing and contradicting notions about music theory. Some folks will tell you it’s a set of restrictive and oppressive rules, others will say, “You don’t need to know that stuff! it’ll only make you play with less FEEL! Famous guitar player X didn't know theory, so you don't need to know it either... Blah, blah, blah...”

My goal is to set the record straight and shed some light on some of this confusion.

Music theory is basically two things:

1. It is the spoken language of music. In other words, it’s a common set of terms and concepts that enable us as musicians to express musical ideas without necessarily having an instrument in-hand.
2. It is the mechanics of music. In other words, it is the examination of the relationships between musical tones, rhythm, and intermingled moments of silence, and how these work with and against each other.

Music theory is less about rules, more about observations.

Music theory is a broad and deep topic; it's so deep that you can focus on music theory as an entire college degree focus -- all the way up to the Ph.D. level! We're not going to go nearly that deep. The goal here is to get you to a conversational level of music theory so that you can be effective at communicating with your musician peers and collaborators. Hopefully this will also help you unlock a vault of knowledge that will also help you become a better musician or songwriter.

I'll see you next week with the first lesson!