Interactive Circle of Fifths User's Guide

The concept of the circle of fifths is not a new one (see this Wikipedia article for more information), but there is more to this simple, yet profound structure than the traditional diagram can easily convey. The Interactive Circle of Fifths goes beyond the limitations of a static diagram without sacrificing clarity and simplicity. This User's Guide will help you get the most out of the Circle, while introducing some basic music theory concepts. However, this is not intended to take the place of an introductory music theory course. If you're new to music theory, you may find some of the terminology unfamiliar. In this case, you are encouraged to use the excellent resources available on the Internet (including Wikipedia) to learn more.

Using the Circle Offline: You can easily download a copy of the Circle to use when you don't have an Internet connection:

If you use Internet Explorer or Opera: Use the Save As... command in the browser's File menu, and save as type "Web Archive, single file (*.mht)". Once the web archive file is saved on your local machine, you can open it anytime.

If you use Safari: Use the Save As... command in the browser's File menu, and save as format "Web Archive". Once the web archive file is saved on your local machine, you can open it anytime.

If you use Firefox: As of this writing, Firefox doesn't yet support a "Web Archive" option like the other browsers, and its "Web Page, complete" option doesn't work with the Circle. However, you can use IE or Safari to create the web archive, as described above.

Basic Use

The Circle starts out with the key of C Major selected. To choose a different tonic, click an item in the Tonic table with your mouse. Likewise, to choose a different mode, click in the Mode table. To save a lot of clicking, you can also rotate the Circle clockwise by dragging upwards in either table, and counter-clockwise by dragging downwards.

The white rows in the Tonic table correspond to the fifteen classic Major key signatures that we learn about in music class, from C

(seven sharps) through C

(seven flats). The gray rows are more rarely used, and are included here for completeness. (When's the last time you heard a tune in E

Phrygian?)

Note on Minor Keys: The Mode table contains the entry "N. Minor / Aeolian". This refers to the natural minor scale, which consists of the same notes as the Aeolian mode. Unfortunately, in actual practice, music in the minor mode is rarely pure Aeolian. Instead, it typically uses a major V chord rather than the minor one called for by the Aeolian mode. It will also often include the ascending melodic minor scale. The details are beyond the scope of this Guide, but you should at least be aware of these complications so you're not surprised when you come across them in music.

To make matters worse, you may encounter the term "minor" in a number of different contexts: Harmonic minor, ascending and descending melodic minor, relative minor, and parallel minor. In this Guide, the term "minor mode" always refers to the natural minor in its pure Aeolian form, since this is the only one that fits entirely into the structure of the circle of fifths.

As you can see, the Circle is made up of three concentric rings. The large middle ring, the Note Ring, shows the names of all of the notes in the 12-tone chromatic scale. The seven notes in the key you have selected (that is, diatonic to the key) have a white background, and the other five notes have a gray background.

The innermost ring, the Degree Ring, gives, in Roman numerals, the scale degrees of the seven notes highlighted in the Note Ring. (The degree of a note is just its position in the scale, but this becomes very important when we work with chord progressions.) You'll also see a black arrow pointing out the tonic of the selected key.

The outermost ring, the Chord Ring, shows you what type of three-note chord, or triad, is rooted at each of the seven notes in the selected key. For example, in C Major, the triad rooted at D (that is, D-F-A) is a minor chord, but in G Major, the triad rooted at D (D-F

-A) is instead a major chord.

Example 1: Start with the Circle in its starting position, with C Major selected. The Note Ring shows that the notes F, C, G, D, A, E, B are diatonic to C Major. (That is, C Major has no sharps or flats in its key signature.) Put them in alphabetical order, and you have the scale C, D, E, F, G, A, B. The Degree Ring indicates the tonic (C) with a black arrow, and also shows, for instance, that G is the fifth, or dominant of this key (more on degrees later). The Chord Ring shows that in C Major, F, C, and G are major chords, D, A, and E are minor chords, and B is a diminished chord.

Example 2:

Now click G in the Tonic table, immediately above C. The circle rotates clockwise one position, and the Degree Ring now points to G as the tonic. Notice that F has dropped off one end of the Note Ring, and F

has been highlighted at the other end. This is an important lesson about the Circle: When you rotate it (whether by Tonic or Mode), you are simply taking a note at one end of the Note Ring and sharpening it (clockwise rotation) or flattening it (counterclockwise rotation). The other six notes remain the same. This means that the closer two keys are on the circle, the more notes they have in common. It also tells you, if you're searching for a key with more sharps, go clockwise; if you're looking for more flats, go counterclockwise. (Using the Tonic and Mode tables, remember that flat is down and sharp is up...just as in music.)

Example 3:

Now use the Tonic and Mode tables to select C Lydian. Notice that we've gone down one spot on the Tonic table and up one spot on the Mode table, and the Circle looks almost the same as it did in Example 2: The Note and Chord Rings are the same, but the Degree Ring has changed. C is now the tonic, and the other degrees have changed accordingly. From this, we can gather that changing modes is very much like changing from one tonic to another, and in fact, if we offset a change in tonic with an opposite change in mode, the new key will have the same notes as the old key (the keys are enharmonic).

Analyzing a Chord Progression

Analyzing a chord progression has two basic steps: Figuring out what key to use, and then figuring out the degrees of the chords.

Example 1: The chords for the Eagles tune "Take It Easy" are as follows:

G	D	C	G	D	C	G	Em	C	G
Am	C	Em	C	G	C	G	Am	C	G

(For simplicity, these examples show the chords for an entire song at once, omitting the relationship of the chord progression to the rhythmic and dynamic structure of the song: bar, verse, chorus, etc. This does not mean that you should ignore that relationship when you do your own analysis.)

The first step is figuring out the key. Select the Major mode and rotate the circle until you find a position where all of these notes are highlighted in white in the Note Ring and have the right type of chord (major or minor) in the Chord Ring. In particular, make sure that both A and E are within the blue Minor section of the Chord Ring. You'll find that there's only one choice that fits: G Major.

Note: It may seem as if we cheated a bit at the outset. How did we know to choose the Major mode, when we haven't figured out the key yet? Well, we actually could have started with any mode; the point of the first step is just to get the Note and Chord Rings in the right position. As we saw earlier, the selected mode only affects the Degree Ring, not the Note and Chord Rings. It's in the second step, where we figure out the chord degrees, that mode becomes important. (That said, most popular music is in the Major mode, so it makes a good first choice.)

The second step is to figure out the degrees of the chords. Translate these chords into their degrees by looking at the Degree Ring. The result should be:

I	V	IV	I	V	IV	I	vi	IV	I
ii	IV	vi	IV	I	IV	I	ii	IV	I

This is a classic chord progression. It begins and ends with the tonic (I, or G), and the three most common chords are the tonic, the dominant (V, in this case D) and the subdominant (IV, which is C). This strongly indicates that G Major is indeed the key of this song.

Example 2: Now let's look at the chords from the R.E.M. song "Losing My Religion":

This tune uses many of the same chords as "Take It Easy", but there are two new ones: F and Dm. If you still have the Circle positioned for Example 1 (G Major), then everything looks good

except for these two new chords. Instead of F, you currently have F

, and the D you have is Major, not Minor. Examine the Circle and you'll see that rotating it one step counter-clockwise will solve both of these problems. F

will be replaced by F and D Major will become D Minor. Am and Em will be unaffected by this rotation. Go ahead and use the Tonic table to rotate counter-clockwise from G Major to C Major.

Now it's time for the second step, figuring out the degrees. When we're done, we see a problem:

iii

This doesn't make much sense; secondary "color" chords (ii, iii, vi) are the most frequent, and—most important—the tonic (I) is not used at all. This strongly implies that, even though all of the chords fit the key we've chosen, we have the wrong mode, because the tonic is the chord you will hear as the harmonic "center" of the progression. In other words, even though we've found that all of the chords are in C Major, you simply won't hear the tune as C Major.

Now, if we eliminate the Major mode, there are six other modes this tune could be using. As we try each mode, we can offset the change to the Mode table with the opposite change to the Tonic table so as to leave the circle position unchanged. (That is, we will get a key that is enharmonic with C Major.) For example, we could go down a step to the Mixolydian mode, and up a step to G. This is all very well, but rather than spending the time to try out each of the modes in turn, we can use our knowledge of popular music and guess that if this tune isn't in the Major mode, then it's most likely Minor.

From C Major, move the Mode table down three spaces to get to the Minor mode. To maintain the Circle's position, you then need to move the Tonic table up three spaces, from C to A. This tells us that A Minor is the relative minor of C Major. After this change, all our chords still fit, but now the degrees of the progression look much better:

VII

Now we see several places where the dominant (v) or subdominant (iv) resolves to (is followed by) the tonic (i). We can also see that the most common chord is i, followed by v and iv. In addition, the tune begins with the tonic. These are all very strong indications that "Losing My Religion" is in the key of A Minor. (In fact, it's a bit unusual in that it is not only minor but pure Aeolian; it does not use any accidental chords, particularly the major V chord which is characteristic of songs that use the natural minor scale. See the Note on Minor Keys, above, for more on this.)

Note: So far, we have looked at two very simple examples, but most music is considerably more complex. Progressions will often contain accidental chords that are outside the key, and tunes may modulate from one key to another: It's common for an intro, chorus, or bridge to be in a different key from the rest of the song, because this generates the tension that makes for exciting music. If all but one or two chords in a progression seem to fit a key, you are probably dealing with accidentals, and you should go with the key indicated by the majority of the chords. If, on the other hand, the first part of a progression fits in one key, but you're having trouble with the rest, assume it's modulating, and try analyzing each section separately. (Keep in mind that modulation often moves between keys that are adjacent on the Circle, because of their close harmonic relationship.)

Example 3: This example is a bit more complex than the first two. The verse of The Beatles' "She Loves You" consists of these chords:

Em7

Gmaj7

Em7

The first thing to notice is that we now need to deal with chords that are not simple triads: Em7, Gmaj7, and G6. This won't be a problem in finding the key, because each of these chords is based on a triad we've already encountered. For our purposes, we can deal with Em7 as if it were Em, and we can treat both Gmaj7 and G6 the same as G. (This is a slight oversimplification, as will be explained in the Note at the end of this example.)

Note: If the discussion of chords in the preceding paragraph baffled you, this would be an excellent time to read up a bit on chord construction. There are many excellent resources on the Web, including several "chord finders" that will break down any chord—no matter how obscure—into its component notes.

To find the key of this piece, set the Circle back to the Major mode (always a good starting point) and find a tonic that has all of the chords (or in this case, their basic triads). You'll find that G Major has all of these chords except for Cm. This is our first example of an accidental (or non-diatonic) chord, and as mentioned above, this one accidental won't stop us from choosing G Major. Let's look at the degrees, to verify that we have the right mode:

vi7

iii

vi7

iii

Imaj7

vi7

Take note of how we've written the "special" chords, for example vi7 for Em7 and Imaj7 for Gmaj7. This is just a matter of adding the special suffix to the basic names we've already been using. On the other hand, the Cm chord is simply shown as iv, because it is the minor chord of the 4th degree of G Major. But aside from questions of notation, this progression looks good: The tonic is prevalent (including the extensions Imaj7 and I6) and there are several occurrences of the classic V-I cadence. This confirms that the verse of "She Loves You" is in G Major.

Note: As mentioned above, it's an oversimplification to say that we can just treat Gmaj7 as if it were a G Major chord. There are actually two different types of seventh chords built on the major triad: The major seventh chord (e.g. Gmaj7) and the dominant seventh chord (e.g. G7). This is important because these two chords each contain a different seventh note, and so they can't both appear in the same key.

To understand this, start with major triads. Take a look at the Chord Ring, and you'll see that any major triad appears in three major keys; for example, the G Major triad appears in the keys C Major, G Major, and D Major. Now look at the seventh chords based on that triad. Gmaj7 consists of the notes G, B, D, and F. Using the Circle, you can see that these notes occur in only two out of the three keys: G Major and D Major. G7 (the dominant seventh) consists of G, B, D, and F, and only the remaining key, C Major, has all of these notes.

Generalizing from this example, you now have a handy rule you can apply any time you encounter a dominant seventh chord in a piece of music: The root of the dominant seventh (in this case, G) will be the dominant (V) of the major key to which it belongs (in this case, C Major). In fact, this is why the chord is called the "dominant" seventh.

(What about music in modes other than Major? It's easy: You'll find that no matter what mode you use, when you look at the three notes in the red Major segment of the Chord Ring, the dominant seventh is always the most clockwise of the three, closest to the blue Minor segment.)

By the way, this kind of complication doesn't apply to minor seventh chords: They are built on the minor triad, and they appear in all three keys where that minor triad occurs. So for our purposes, you can treat minor sevenths the same as minor triads.

Transposing Music

There are many times when you'll find it necessary to transpose a piece of music from one key to another. For example, your vocalist might not be comfortable in the register of a certain song, or you might have a tune composed on the piano that is too difficult to play on the guitar. The Circle makes transposition simple by building on the analysis techniques you've already learned.

Example: Refer back to Example 3 in the previous section, where we analyzed the verse of The Beatles' "She Loves You". We determined that it's in G Major, and that the progression is:

vi7

iii

vi7

iii

Imaj7

vi7

Let's say you need to transpose this song up a whole step, from G Major to A Major. Simply set the Circle to A Major, and use the Degree Ring to translate these degrees into notes. (This is the opposite of the way you used the Degree Ring during the analysis process.)

Here is the result:

Amaj7

That was pretty easy, and if the new key doesn't work for you, you can simply repeat the process: Change the Circle position again and re-translate the degrees into chords. As you practice with the Circle, you'll start to memorize its layout, and you'll find that you can easily transpose without needing to write anything down. However, the most important part is to accurately analyze the key of the music in the first place, or your transposition won't come out right.

Note: In this example, we transposed a piece with an accidental chord (Cm) by simply treating it as a iv rather than a IV. But what if you have an accidental where the root is itself non-diatonic? For instance, imagine for a moment that "She Loves You" contained a Bmaj7 chord. You would look for its degree on the Circle and find that B isn't in G Major. The closest match is B, which is the third degree of G Major. In this situation, we would describe B as the flatted third of G Major, and write the chord as IIImaj7.

Transposing to A Major, we find that the third of A Major is C, and a flatted C is of course C. Therefore, our IIImaj7 chord becomes Cmaj7. We can confirm that this is correct by noting that C is one full step up from B, matching the rest of our tranposition.

Composing Music

The idea for a new song often begins with a few chords that sound good together. Maybe the line of a melody starts to take shape. Now you want to take this promising beginning and turn it into a complete tune. Is this where you run into trouble? Do you find yourself trying other chords at random, hoping to build a good chorus, bridge, or intro? When you find a chord that works, do you wonder why that chord was the "right" one? You can overcome these difficulties—and more—by figuring out the key of your new song and understanding its structure. The Interactive Circle of Fifths will help you through this process.

Example: You've got the beginnings of a song using the chords D, G, and Em, and you're looking for ways to expand on this start. What you need to do is figure out is what key your tune will use, because this will determine the chords that will sound right together. Given only three chords, there will be a number of possibilities, and you'll have to experiment a bit to find the one that matches what you're hearing.

Let's assume for the sake of this example that you're writing popular music, and you'd like to focus on the Major and Minor modes. (This is not to discourage you from trying other modes, as they can add a great distinctive feel to your music, but be aware that the harmonic "rules" of the other modes are trickier, and well worth further study.) Using the Circle, you'll find that D, G, and Em occur in D Major, G Major, B Minor, and E Minor. These are all candidates for your song, but we need to narrow down the choices. As in analyzing a chord progression, the next step is to use the Circle to find the degrees of the chords:

	D	G	Em
D Major	I	IV	ii
G Major	V	I	vi
B Minor	III	VI	iv
E Minor	VII	III	i

B Minor and E Minor don't look promising, since two out of our three chords would be secondary or "color" chords, and only the Em chord would be prominent. D Major and G Major are both strong candidates though, since you'll be using the tonic and either the dominant (V) or subdominant (IV). We need to choose one, so let's use the Circle to find all of the chords in D Major and G Major:

	I	ii	iii	IV	V	vi	vii°
D Major	D	Em	Fm	G	A	Bm	C°
G Major	G	Am	Bm	C	D	Em	F°

Note: Take a moment to notice the similarities and differences between these two keys. They are only one step apart on the Circle, so they have six out of seven notes in common. (Remember that when we move one step counter-clockwise, we flatten the note at the far end. In this case, C becomes C.) And of course they are both major keys, so they share the same harmonic structure. However, when you look at them from the point of view of individual chords, even the chords they have in common (Bm, D, Em, G) play very different roles in each key. The other common notes (A and F) produce completely different chords. This shows the importance of choosing the right key when creating your chord progression.

Now that we have all of the chords for each key, try some of these additional chords and see if they fit the song that is taking shape. In particular, try to work A or C into your progression. A is the V of D Major, so if it sounds good, work with D Major. If C sounds good, then continue with G Major, where it's the IV.

Remember the earlier Note on major seventh and dominant seventh chords? These unique chords can be very useful for finding the key. Referring to the Circle, you'll see that the major chords in a major key are the I, IV, and V chords. The seventh of the V chord is a dominant seventh, and the other two are major sevenths. For our example, here are the chords:

	IVmaj7	Imaj7	V7
D Major	Gmaj7	Dmaj7	A7
G Major	Cmaj7	Gmaj7	D7

Notice that we have two D seventh chords to choose from. This is handy, because you can try both flavors to see how they feel with your tune. If one works, that will tell you the key. Failing that, Cmaj7 and A7 will serve the same purpose.

Of course, there's much more to writing a song than just knowing what key you're using. But knowing the key—and understanding its structure—will provide a framework for the process of composition. Knowing the key means you know the notes and chords that are diatonic, and how they relate to each other. And when you go beyond the diatonic with accidentals and modulation, understanding the structure of the key will help you do it effectively. There's much more to learn about this topic, and you're encouraged to delve further into composition in general, and chord progressions in particular, with the Circle as a handy tool on your journey.

Reading Key Signatures

Recognizing key signatures is crucial to reading music, and the Circle makes it easy. A key signature is simply the pattern of sharps or flats shown on the musical staff to indicate the key of the music.

As described under Basic Use, rotating the Circle counter-clockwise adds flats, and rotating it clockwise adds sharps. To interpret this key signature, set the Circle to C Major (no sharps or flats) and then move down the Tonic table, rotating the circle counter-clockwise until three flats are highlighted. The result is the key of E

Major, where A, B, and E are flat.

Note that a key signature alone doesn't tell you what mode the music is in; in this example, the song could just as easily be in C Minor, the relative minor of E

Major. Since they are enharmonic, they have the same flat notes. For modes other than Major, either your sheet music may tell you the mode explicitly, or you can use the chord progression analysis techniques described above to determine the key.

Understanding Scales

We've covered keys, notes, and chords fairly extensively, but what about scales? A scale is made up of the seven notes in a particular key, in alphabetical order. It is usually played with the tonic at the beginning and end, making a total of eight notes, or one octave.

Example 1: Set the Circle to F Major, and simply play the highlighted notes in alphabetical order. You should hear the familiar "do-re-mi" pattern of a major scale:

Example 2: Now try the same thing with F Minor (natural minor), and you'll hear the difference: