Keys, Circle of 5ths


Recall, that in the western musical system we're discussing there are 12 distinct tones and their octaves (this is refered to as the 12-tone system). We call the collection of these notes the chromatic scale.

Recall also, that we only use 7 letters ( and accidentals) to represent these 12 notes, and their octaves. The letters being A,B,C,D,E,F,G.

Recall that the smallest interval (distance between notes) is a half-step 1/2 (the distance playing a note on a string and the next fret up or down). Recall also that a whole-step W, is equal to the distance of two adjacent half-steps. (May 3rds lesson)

Recall, that the distances between the letter-named notes has been defined the following way: A to B = whole step, B to C = half-step, C to D = whole step, D to E = whole step, E to F = half-step, F to G = whole step, G to A = whole step. (May 3rd)

This leaves 5 notes unnamed. We use letter names with accidentals attached to describe them.
There are 5 common accidentals. They are natural (play the letter-named note when written), sharp #, (play the note 1/2 step above lettered name); flat b, (play the note 1/2 step below lettered name); double sharp x, (play the note W step above lettered name); double flat bb, (play the note W step below lettered name).
By above, I mean of a higher pitch (twords the bridge), and by below I mean of a lower pitch (away from the bridge, twords the nut), if on the same string.

The 5 missing notes are called: A#/Bb, C#/Db, D#/Eb, F#/Gb, G#/Ab. So the note A#/Bb could be called either A# or Bb, and any time that you can use two names for the same note, they are said to be enharmonic equivalents of each other. So A# is enharmonically equivalent to Bb. B# is enharmonically equivalent to C. Gx is enharmonically equivalent to A,etc. Which way you call a note is generally based on what key you're in (more below), and possibly if you're ascending or descending.

Recall that a tonal center is a note that other notes (when played in a tonal context) gravitate twords. It's the note that it feels right (the best) to end on. This may sound rather subjective; but it's the note that when ended on, you feel like it's finished. We refer to the tonal center (also called the tonic or root note) as the "1" from which we define our other notes' distances.

Recall, that the major scale is the scale whose step pattern is: WW1/2WWW1/2. That is, it is a 7 - note scale which has a whole-step distance between the 1rst and 2nd notes (of the scale), a whole-step distance between the 2nd and 3rd notes, a half-step distance between the 3rd and 4th notes, etc.

It is common practice when writing major scales (and most other 7 note scales), to use each letter once and only once. So if we wanted to write a 7-note scale with a tonal center on C, the 7 notes would be named : C-D(something)-E(something)-F(something)-G(something)-A(something)-B(something). The somethings would be either nothing (such as B) or would be an accidental. Each letter is used once, and no letter is used more than once. What those somethings are is based on what scale you're playing.

Suppose you want to know what the names of the notes are in the C major scale. It's tonal center is C, and it's a 7 note scale, so every letter name is going to be used and the first note will be C. Now the step pattern for the major scale is WW1/2WWW1/2, so the D(something) 2nd note is a whole-step above the 1rst note. We find that D is a whole-step above C, so the 2nd note is D. Continuing this pattern of comparing the step pattern with the letter-named notes, we find that the C major scale consists of the following notes: C-D-E-F-G-A-B. There are no sharps or flats in the C major scale.

Now, we shall define a key as the collection of notes found in the major scale of the same name.

Therefore, since the C major scale has no sharps or flats, the key of C has no sharps or flats. What about the other 5 notes in the chromatic scale? they are not "in" the key. They are "out" of key. So which notes are in or out of key depends on whether or not they are in the major scale of the same name.

So here I will give the notes in the keys, and I leave it up to the reader to verify that these are correct by remembering that there are 7 notes, so each one gets a different letter and then accidentals are used to conform the notes to the step pattern (or intervallic pattern) of the major scale.

Key of C = C,D,E,F,G,A,B,C.
Key of G = G,A,B,C,D,E,F#,G
Key of D = D,E,F#,G,A,B,C#,D
Key of A = A,B,C#,D,E,F#,G#,A
Key of E = E,F#,G#,A,B,C#,D#,E
Key of B = B,C#,D#,E,F#,G#,A#,B
Key of F#= F#,G#,A#,B,C#,D#,E#,F#
Key of C#= C#,D#,E#,F#,G#,A#,B#,C#

For reasons explained below, I'll stop there and start again.

Key of C = C,D,E,F,G,A,B,C.
Key of F = F,G,A,Bb,C,D,E,F
Key of Bb= Bb,C,D,Eb,F,G,A,Bb
Key of Eb= Eb,F,G,Ab,Bb,C,D,Eb
Key of Ab= Ab,Bb,C,Db,Eb,F,G,Ab
Key of Db= Db,Eb,F,Gb,Ab,Bb,C,Db
Key of Gb= Gb,Ab,Bb,Cb,Db,Eb,F,Gb
Key of Cb= Cb,Db,Eb,Fb,Gb,Ab,Bb,Cb

Recall, from above, that a flatted note is 1/2 step lower in pitch than the note with the same letter name with no flat (e.g. Gb is a 1/2 step lower than G). If we raise the pitch of Gb by a 1/2 step we have G. Same applies in reverse for sharps. F# is a half-step higher in pitch than F, and if we lower the pitch of F# by a 1/2 step we have F.

Now, looking at the first set of keys (key of C, Key of G, etc.). Recall from above that the key contains 7 notes that correspond to the 7 notes of a major scale, with same letter name, also that each letter (with or without accidental) is used in each key above. Recall also that we worked out the C major scale from the step pattern: WW1/2WWW1/2 converting that into numbers we get 1-2-3-4-5-6-7-8(1).
Now notice that the next key listed has its root note the 5 of the previous key (G is the 1 of G major and the 5 of C major). So if we modulate the step pattern so that the 5 of the major scale is the first note at the start of the step pattern, we get a new step pattern of WW1/2WW1/2W (this is the mixolydian mode for those curious) which converted to numbers gives 1-2-3-4-5-6-b7-8(1). In order for us to have this coincide with the major scale (keys are based on major scales remember) we need to raise the 7th note 1/2 step. So the key of G has the same notes as the key of C except for the key of G's 7th note which is a 1/2 step higher than the same letter name in the key of C.
Looking to the next key, the key of D has the same notes as the key of G except its 7th note has been raised (for the same reasons stated earlier). Notice also the note previously raised in the earlier key of G (F#) is the 4th note of the new key (key of D), a 5th (perfect 5th) above the old key (key of G). This is interesting. In general, switching from a key to another key a perfect 5th above the original key, the new key needs to be corrected by raising the new 7th note a 1/2 step.
Consider going in the opposite direction. So instead of going up a perfect 5th from G to D, we are going down a perfect 5th from D to G. Looking at the key of D, G is the 4th note, so I could consider it going up a 4th (more on interval inversion next week). If we modulate the step pattern of the major scale so that the 4th note is in front of the step pattern, we get a new step pattern of WWW1/2WW1/2 (the Lydian mode) which when converted to numbers gives us 1-2-3-#4-5-6-7-8(1). Again this is close to our major scale but we will need to lower the pitch of the 4th note by a 1/2 step. So the key of G has the same notes as the key of D, except the key of G's 4th note (C) is a half-step lower than the same note name in the key of D (C#).
In general, switching from a key to another key a perfect 4th above the original key, the new 4th note needs to be lowered a 1/2 step.

All this brings us to the circle of 5ths (circle of 4ths).
Draw a pie graph with twelve equal slices (a circle split into 12 equal regions). Make it big. If you can do it, try to center one of the slices at the top of the circle. In the closest to the top, place the words "key of C (no sharps or flats)". Fill in the rest of the keys with sharps listed above, in a clockwise direction. Now go back to the piece with "key of C" in it and label the next piece counter-clockwise "key of F (1 flat)". Fill in the 2nd set of keys (the ones with flats in them) going counter-clockwise. You'll notice there's 3 pieces at the bottom of the circle that have 2 keys in them. It's ok. They're enharmonic keys.:
Key of Db (5 flats) = Key of C# (7 sharps)
Key of Gb (6 flats) = Key of F# (6 sharps)
Key of Cb (7 flats) = Key of B (5 sharps)

At the top of the circle draw an arrow going from key of C twords Key of G (clockwise), and above the arrow, put the words "circle of 5ths". Then place an arrow from above key of C twords Key of F (counter-clockwise) and place above that arrow the words "circle of 4ths". You've just created your own circle of 5ths (circle of 4ths).

Looking back at the lists of keys above going in 5ths, all new sharp keys contain the previous sharps plus 1 new sharp (e.g. key of D contains F# from key of G plus one new sharp C#). So going in a circle of fifths the sharps are added in a specific order:
F#, C#, G#, D#, A#, E#, B#.
The same applies for flats (going in a circle of 4ths from the key of C), except the order is reversed:
Bb, Eb, Ab, Db, Gb, Cb, Fb.

This becomes important when writing key signatures. A key signature is used in standard notation (after the clef, before the time signature) to tell the performer what key the music is in. This is extremely helpful when writing, because it means you don't have to write as much. A key signature tells you when you're reading the music to assume that unless otherwise told differently the following notes should be affected the following ways. So for example the key of A (3 sharps) would have its 3 sharps written down in the order F#,C#,G#, on the staff, after the clef, before the time signature. And the performer would know that everytime they read an F,C, or G, that these notes were to be played F#,C#, and G#. If the composer then wants to write down a normal G note (G natural), he would place a natural sign before that particular note (and all other G notes in the same measure would be G naturals unless another accidental was used which would then tell you how to play these notes for the rest of the measure). After that measure was over unless otherwise indicated you would follow the key signature again.
Of course, you can always switch keys in the middle of the music too. Usually when this happens you see a measure with no notes in it, but naturals on all previously affected notes, and then a new key signature.

How can I read a key signature quickly?
Recall that the key of C has no sharps or flats, so if you don't see a key signature, then you're in the key of C.
Recall also that going in the circle of 5ths, the last sharp added was the 7th note. So find the last sharp in the key signature and go up a 1/2 step (next adjacent line or space) and there is your key. (e.g. Key of G has one sharp F# which is a 1/2 step below G).
Recall also that going in a circle of 4ths, the last flat added was the 4. So the last flat written down is the 4 of the key. note: when a key has more than one flat in it, then the 2nd to the last flat written down is the name of the key. (e.g. Key of Eb has 3 flats: Bb,Eb,Ab written down in that order. The 2nd to the last flat written down is Eb, the key you're in). This works for all flat keys except the key of F which has only 1 flat.

Here is a listing of key signatures.
(The following is in standard notation, not TAB. This is best viewed from my website rather than through a text only browser. I appologize in advance, and the URL is above.)

Key of C
|---------|
|---------|
|---------|
|---------|
|---------|


Key of G
|-#-------|
|---------|
|---------|
|---------|
|---------|


Key of D
|-#-------|
|         |
|---------|
|  #      |
|---------|
|         |
|---------|
|         |
|---------|


Key of A
    #
|-#-------|
|         |
|---------|
|  #      |
|---------|
|         |
|---------|
|         |
|---------|


Key of E
    #
|-#-------|
|         |
|----#----|
|  #      |
|---------|
|         |
|---------|
|         |
|---------|


Key of B
    #
|-#-------|
|         |
|----#----|
|  #      |
|---------|
|     #   |
|---------|
|         |
|---------|


Key of F#
    #
|-#-------|
|      #  |
|----#----|
|  #      |
|---------|
|     #   |
|---------|
|         |
|---------|



Key of C#
    #
|-#-------|
|      #  |
|----#----|
|  #      |
|-------#-|
|     #   |
|---------|
|         |
|---------|


Key of F
|---------|
|---------|
|-b-------|
|---------|
|---------|


Key of Bb
|---------|
|  b      |
|---------|
|         |
|-b-------|
|         |
|---------|
|         |
|---------|


Key of Eb
|---------|
|  b      |
|---------|
|         |
|-b-------|
|   b     |
|---------|
|         |
|---------|


Key of Ab
|---------|
|  b      |
|----b----|
|         |
|-b-------|
|   b     |
|---------|
|         |
|---------|


Key of Db
|---------|
|  b      |
|----b----|
|         |
|-b-------|
|   b     |
|-----b---|
|         |
|---------|


Key of Gb
|---------|
|  b      |
|----b----|
|      b  |
|-b-------|
|   b     |
|-----b---|
|         |
|---------|


Key of Cb
|---------|
|  b      |
|----b----|
|      b  |
|-b-------|
|   b     |
|-----b---|
|       b |
|---------|

Recall from last weeks lesson that the major scale has 7 modes of which it itself is the 1rst mode (ionian mode). And that the 6th mode of the major scale is the aeolian mode also known as "the minor scale". Since all modes of the same major scale share the same notes, that means that corresponding (relative) major and minor scales (ionian and aeolian modes) share the same notes. Since the keys are based on the major scale. We can notate minor keys as well (key based on the minor scale). find the 6th note of the major scale, and that is the root note of the minor scale. (parallel major and minor share the same root note and have different key signatures).
Here is a listing of (relative) major and minor keys:
Key of C = Key of Am (no sharps or flats)
Key of G = Key of Em (1 sharp)
Key of D = Key of Bm (2 sharps)
Key of A = Key of F#m (3 sharps)
Key of E = Key of C#m (4 sharps)
Key of B = Key of G#m (5 sharps)
Key of F# = Key of D#m (6 sharps)
Key of F = Key of Dm (1 flat)
Key of Bb = Key of Gm (2 flats)
Key of Eb = Key of Cm (3 flats)
Key of Ab = Key of Fm (4 flats)
Key of Db = Key of Bbm (5 flats)
Key of Gb = Key of Ebm (6 flats)

If you've got room on your circle of 5ths, you could write in the relative minor keys. (Key of Am in the Key of C slice, etc.)

What if I have some exotic scale that I've written a song in. All of my melodic and harmonic structures are in say A gypsy minor = A,B,C,D#,E,F,G#. Do I write the notes D# and G# into the key sig.? NO. No-one who reads will understand (most likely), they'll just count the number of sharps or flats and play in the key with that number of sharps or flats in it. Being an ex-note-reader myself, I can tell you that most of those people are fairly hypnotized and don't know how to handle a situation that they haven't seen before.

Well, I had intended to discuss intervals, transposition, and what to do with the other 5 notes not in the key, but I guess that will wait till next week.

How do I change all those numbers to letters (for notes, chords, etc.)? Here's a transposition chart simianmoon.com/snglstringtheory/guitar/8theory3.html

Any questions? Feel free to ask.

Peace,
Christopher Roberts
snglstringtheory@aol.com


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Last updated July 12, 2001
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