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The Circle of Fifths; An Explanation, and More

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This really cool explanation of the Circle of Fifths was written by Matt J. Nall (RokedBeGeshem) and posted on The Ocarina Network.  He was kind enough to allow me to also host the article here in the Player Resources section.

Circle of Fifths

Click on the image for a larger view. 


Basic Anatomy of my Circle

In the very middle, you will find a web of red lines. These show intervals between notes, and are useful for finding intervals, forming chords, and looking nifty.
In a circle, connected by the lines, you will find black circles with red letters. These, going clockwise, are the notes of the chromatic scale.
Outside this you will find a dark grey band with numbers of accidentals notated on it. On the outside are black and red circles. Inside are bright red ones. The black circles represent Major keys, and the red ones, minor keys. The keys which share a position are called "relative."
Going out further, you will find key signatures written on the bass, then treble clefs. These show the number of accidentals, but more importantly, they show WHICH notes are sharpened or flattened.
On the very rim, you will find small red letters. Jesus said these. Treat them as sacred. These show which notes are sharpened or flattened for the less musically literate.

What is that Web Thing in the Middle?
Look at the innermost ring (red notes connected by a web of red lines). This, starting at C, and progressing clockwise up the chromatic scale, is not technically part of the "circle of fifths." It is actually a variant of something called the Mersenne Star, which is somewhat of a precursor to the modern circle of fifths. This web, like the Mersenne Star, is used to visualize the interval between two notes by counting the number of half steps. If you start at C, don't travel, and end at C, you have, obviously, traveled 0 half steps, and have a unison. If you start at C, and travel along the lines clockwise until you reach the first cross, then follow it back out, you will reach C# - this interval (of one half step, represented by one intersection along the web) is called a minor second. Another example - If you start at D, and proceed in for four intersections (4 half steps), and travel back out, you will reach G#, forming a Major third. And of course, if you follow a line all the way in, and then back out (7 half steps), you will have formed the interval called a perfect fifth.

What's so Special about Perfect Fifths, Anyway?
When arranged in order of perfect fifths, the keys of Major and minor scales have special relationships. This is what the circle of fifths does - visually illustrates these concepts. The circle (jumping out a little on my graphic) starts with C at the top, and progresses clockwise to the perfect fifth above C, which is G, and then on to the perfect fifth above G, which is D. Going in the other direction (counterclockwise), the circle ascends by perfect fourths (the inverse of a perfect fifth) - to F, then B?, and so on. Inside this circle, there is another, smaller circle (which starts with A at the top). Lets focus on the band between these two. 

Taking a Look at the Circle.
Where C and A are, at the top, the band displays the symbol for natural (?). This means that in a Major scale starting on C (and, on the inner circle, a minor scale on A) there are no accidentals (sharps or flats). As you move clockwise to G (and its relative minor, E) you will notice that there is now a symbol for one sharp (?). This means that in a G Major scale (and an E minor scale) there will one sharp - F?. Moving around, we then find 3 sharpss, 4 sharps, 5 sharps, and so on.
Going the other direction, we can see that instead of adding one sharp, we now add one flat (?) each time we progress. When moving on to the key of F, there is one flat. In B?, there are two flats, and so on. 
A song usually revolves around a particular note, and on a scale constructed around that note. This note is what we call the song's key. When we say a song is in the key of C Major, all it means is that it uses the C Major scale to get all (usually all) it's notes from - and, using what we've just learned, that means it will have no accidentals! A song in the key of A? Major, for example, will have four flats.

But How Will I Know WHICH Notes are Accidentals?
Over time, you will memorize ALL of this (scary I know). The circle is just a visual and conceptual aid. However, looking beyond the rings of Major and minor keys, we see helpful little bubbles called key signatures - which I have written for the bass and treble clefs. These are found in sheet music at the beginning of every staff, and they tell you the key of the song. Looking, by way of example, at the key of D, we see that both F and C are marked on the staff as sharp. This means that every F and C in the song (unless marked with a natural sign) will be sharp. (By way of cheating, for those who don't read music well, the sharps are notated on the outermost rim going clockwise, and the flats going counterclockwise.)

When I Get to the Bottom, Everything is Terrifying. What is that MESS?
You may be unfamiliar with the term "en-harmonic." It's the musical equivalent of "synonym." Just as "hot-dog" and "frank" both refer to the same thing, the names "C?" and "D?" are the same note (as you can see on the inside web which shows the chromatic scale and interval relationships). This is true of keys as well. "C?" and "D?" are the same key expressed differently, as are "F?" and "G?," and also "B" and "C?." 
The key of F? is written with the sharps F, C, G, D, A, E. The key of G? is written with flattened B, E, A, D, G, C. Notice on the outside rim that on the en-harmonic keys, some of the sharps and flats are in brackets. The way I intend for this to be read is as follows, in an example. 
Look at D?. Because we are considering the name D?, we are moving around from counter clockwise. Therefore, read the flats as "B, E, A, D, G" and ignore the ones on the end - these are sharps if you are coming the other way. Now, still talking in terms of flats, consider C?. The flats are "B, E, A, D, G, C, F." Because the bracketed notes are on the side we started from, they apply to this key. So, in the same way, F? has the sharps of "F, C, G, D, A, E."
The easiest thing to do is just learn the key signatures though...

Using This Knowledge
Let us look at the dark red circle for the key of A Major. Using what we know from the circle of fifths, we now know a lot about A. We know that A Major is relative to F# minor, because they both have three sharps. We know that our sharps in the key of A Major will be F, C, and G. We know how to write the key of A on a staff, and how to read it. We know that A is a perfect fifth above D, and a perfect fourth below E (and this is helpful for other instruments like guitar and piano, as it shows that a song in A Major will probably feature D chords, A chords, and E chords heavily). We also know that because it has only three sharps, it's a moderately easy key to play in. G?, however, has 6 flats, and is therefore to be avoided when possible. :-)

Revisiting Major and minor keys
Look at how the minor keys and the Major keys are arranged. Did you notice that the minor keys are moved around three steps counterclockwise? This is because the natural minor scale with no accidentals (A) is three half steps below the Major scale with no accidentals (C). They are written on the same position, even though they have different tonics, because their number of accidentals is the same, and because of this, they sound good together (because they use the same notes). In a similar way (which the circle doesn't show too well) A minor and A Major are considered familial as well, because they share the same tonic and also sound good together.

And Now for Something Completely Different
There is a handy little trick involving two circles of fifths. When you place one inside the other, pin them in the middle, and then rotate them, they can be used to transpose very easily. This can be VERY useful for an ocarina player, many of whom are forced to transpose constantly to fit songs into the limited range of our wonderful instrument. (Not everyone can afford triples :-( ) Because I like everything to be digital (read: I'm too lazy to go find a brad to make a paper one), I've made it easy for you to make such a tool by overlaying the two images called "transposition circle 1" and "transposition circle 2" in Microsoft PowerPoint - just center them on each other, and then rotate the inner ring. 

Transposition Circle 2


This is how it's used.

Let's say you have a song in the key of F# (an annoying key - lots of sharps, and doesn't fit on a 12 hole in C) and you want to put it in C to make it easier. Rotate the inner circle so that F# Major lines up with C Major. NOW, all the original notes from the F# Major key (the blue circles) will become the same as the gold note they now correlate to - F# is now C, so E is now B?, D? is now G, etc. etc.

In the same way, if you have song like this one (sheets here), which is in different keys, the same movement of the transposition circles will tell you what all your new keys are. Let's say we had a double (or better yet a keyed Aria...), and could play high G (the highest note in this sheet is high F). We might, then, want to raise these sheets up by a whole step so we could play in the next higher key, possibly to match a backtrack or another musician. Rotate until F (the starting key) lines up with G (this is a whole step higher), and now, the key of F becomes G, and when the song changes to A?, the new key will be B?. The final portion of the song, originally in B?, will now be in C. 

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