I. Intervals

II. Scale Degrees

III. Scales and Keys

IV. Modes

V. Intro to Modulations

VI. Modulations of Aeolian and Ionian

VII. Other Modulations and Ethnic Scales

VIII. 5, 6, 7, 8, 9, 10, and 12 Tone Scales

Part III: Scales and Keys

When you figure out exactly how much can be discussed when just talking about scales, you will be quite overwhelmed. However scales are of primary importance in music. Without melody compositions tend to be quite insipid.

This is probably a good time to briefly introduce a concept. An enharmonic note is the two representations for a single note. Ever note can be expressed in two ways. The chart at the end of this paragraph will summarize it all for you, but at the moment, two other definitions are needed to help understand the graph. A double flat (bb) is added to a note to make it, as expected, flatted twice. So Ebb is the same thing as D (and therefore enharmonic notes. A double sharp (x) simply sharps the note twice. So Dx is the same thing as E (and therefore enharmonic notes). This chart shows each notes and its equivalent. Note that some tones do not have two equivalents. This is just because of the way the note system is set up.

Let’s start be defining something. You have hopefully played a major (also called and Ionian scale, remember this! You will learn more about this in the next section) scale before (probably C Major). Well what qualities about this scale make it major? How is a major scale defined? All scales are defined by the difference in whole and half step between each note (or a larger interval in some cases). When I use interval notation (step difference) as I do below, I always represents whole steps by a “2” and a half step by a “1”.   Let’s dissect C Major.

                                                                   2    2    1    2    2    2    1

C ^ D ^ E ^ F ^ G ^ A ^ B ^ C

So we can conclude that a major scale is only a major scale if the differences between the tones follow the pattern: 2212221. When Pythagoras begin studying sound and tone way back 2400 years ago, he established a basic system of notes in what is called equal temperament. For now don’t worry about that terminology, but if you are interested, then go ahead and read up on the section of music systems. In the end, what you must understand is, when the music theory system was developed over time, a systematic method for organizing major scales was created. This system, called key signatures, is the basis for all Western scale music theory. Key signatures organize the musical scales by the sharps and flats.

The first step in understand key signatures is to understand the circle of fifths, the progression of the roots of the scales ascending and the circle of fourths the progression of the roots of the scales descending. This may not make any sense now, but just keep reading and it will become clear.

From previous music theory knowledge, you know that raising a note “sharps” it and lowering a note “flats” it. We will start with the circle of fifths. You will soon find what is so circular about it. Since it’s the circle of fifths, that means we have to go up a perfect fifth from the previous root to get to the next key.

We started in C Major. What is a fifth up from C? If you don’t know your fifths well yet, then starting on the desired note (in this case C), count up 7 half steps (see chart from section one to see that a perfect fifth is 7 half steps apart): C# D D# E F F# G.

G is a perfect fifth away from C. Therefore our new key is G Major. Let’s apply our whole/half step dissection to this key and see what happens; remember to start on G this time since it is G Major.

                                                                  2    2    1    2    2    2      1

G ^ A ^ B ^ C ^ D ^ E ^ F# ^ G

This looks pretty good doesn’t it? The pattern looks like it should. But wait? Is that an F#? Yes. G Major has a sharped note. This is to be expected. Since the circle of fifths ascends, goes up, all notes that are altered, raised to the black keys (or in some cases as we will see later, the white keys as well) will be sharped as well. We now have one sharp.

The next note, following the circle of fifths is what a D (since it’s a fifth up from G). So D Major is constructed like so:

D E F# G A B C# D

I didn’t include the step pattern this time since you already know it’s a major scale, and has to include those steps. Notice that when you start from D, you now have 2 sharps. Not only that, the sharp you had from the last key is also there.

Let’s up yet another fifth to A Major (a fifth away from D). This scale is now:

A B C# D E F# G# A

Once again, as expected, the previous tones are sharped, plus ones more tone. We can continue up in this fashion and eventually we’ll end back up at C and therefore covered all the sharped major (Ionian) scales.

Here is a reference chart with all the sharped scales (remember that since it’s major, the step pattern is always 2212221, never forget this!):

*Note that the root defines what “major” it is. So if the root is E, its E major (assuming you follow the major scale step pattern). If the root is B it’s B major and so forth.

For each key, you notice that a new sharp is added and the sharp from the previous key is retained. The final series of sharps you get when reach C# major is called the order of sharps. The order of sharps is: F#, C#, G#, D#, A#, E#, B#. A way to remember this order of sharps (which will be useful to know) is by using a mnemonic. The one I learned and still use is “Fat Cats Go Dancing At Every Ball”.

So what are sharped key signatures for? Well say we are composing a piece of music and C# Major. Every single note will be sharped! The page will be a mess and it will be near impossible to read. Key signatures are the solution to this problem. At the beginning of a piece of music, the notes that correspond to the key will be labeled. On the staff:

So now the song player knows that every time he sees one of those notes, F C G D A E B, he must remember to sharp it. It reduces the clutter on the page and makes it easier to read.

Quite often, though those notes are sharped, the composer may wish to pick a note not in the key. Using C# major again, let’s say a composer wanted a D natural instead of a D# (which would be indicated by the key signature). A natural sign (which you should remember from the basics section) is placed by the note to indicate that the pitch is lowered or raised to its original value:

Since D natural isn’t in the C# major scale, it is called an accidental.

Here are all the sharp key signatures (which were attained from ascending the circle of fifths as we did earlier).

[Pictures of all 7 key signatures]

Though you should probably memorize what key corresponds to what key signature, there is a method for determining what key is indicated by the sharps. Take D major for example:

[Picture of D Major key signature]

If you didn’t know that D major has 2 sharps, you could have figured this out simply by looking at the last sharp: in this case it’s a C#. Raise the C# a half step and what do you get? D. So the key is D major. Try it yourself with this key signature:

[Picture of B Major]

If you got B major you are correct. The last sharp is an A#. Raising this up a half step, we get B. So the key is B major.

Now it is time to move on to the circle of fourths, which is very similar to the circle of fifths.

Instead of going a fifth up, we now go a fifth DOWN, which is why all of these key signatures, unlike the ascending circle of fifths, will all be flatted notes. So why is it called the circle of (perfect) fourths? Because when you go down a fifth, that’s the same as going up a fourth. The first flat key signature is F major. F is a fifth down from C. However, going up, F is fourth UP from C. If you go down as fifth from F, you get the second flat key signature, Bb major. If you up a fourth from F you also get Bb. This explains why it’s called the circle of fourths.

Let’s start by looking at the first flat key, F major. You must go down a fifth from C to get to F.

                                                                  2    2    1      2    2    2    1

F ^ G ^ A ^ Bb ^ C ^ D ^ E ^ F

That pattern should look familiar by now…

As you can see, descending it has one flat. Now let’s go down another fifth to Bb. Apply the pattern.

Bb C D Eb F G A Bb

As with the sharps, the flats from the previous key stays and the new one is added. We can now compile the flat key chart. Since C is right in the middle with 0 sharps and 0 flats, I included it in both charts for the sake of clarity.

There is a mnemonic I use for the flats as well, but it’s not terrible amazing. It’s simply “Bead GCF”. You pronounce “GCF” as “Jicuff” or something like that. Whatever works…

There is of course, also a way to tell the key something is from looking at the flat key signatures. Let’s take a look at F major first. Well with F major, you have no choice. You just have to memorize it.

However with Ab major for example, you simply look at the second to last flat on the key signature. That will tell you what key it’s in. In this case, we have Bb Eb Ab and Db. The second to last flat is Ab, so the key is Ab major.

So now that we have the circle of sharps and flats, we can now connect the charts.

There is one last diagram left that you should see. The Circle of Fifths and Fourths and the explanation of enharmonic keys:

[Picture of Circle of Fourths/Fifths]

Note the bracketed key names. If you look you will notice that they are in fact the same keys, just one represented in flats, the other in sharps. These keys are called enharmonic keys. It is simply the place where the circle of fifths and the circle of fourths overlap. It doesn’t really matter which one of the two you use since they are both the same.