Last time I gave you some homework (if the dog ate it I don't want to know!). You were going to work out the notes in all twelve of the major keys (if you've forgotten how to do this then take a look at part 2). To refresh your memory, here is the pattern of tones and semitones that make up a major scale:

Using this pattern, and making sure we don't mix flats ("b") and sharps ("#") we get these scales (remember, a scale is the pitches of a key lined up in order from lowest to highest):

A B C# D E F# G# A
Bb C D Eb F G A Bb
B C# D# E F# G# A# B
C D E F G A B C
Db Eb F Gb Ab Bb C Db
D E F# G A B C# D
Eb F G Ab Bb C D Eb
E F# G# A B C# D# E
F G A Bb C D E F
Gb Ab Bb Cb Db Eb F Gb
G A B C D E F# G
Ab Bb C Db Eb F G Ab

HINT 1: make sure you use each letter only once in each scale, that includes flats and sharps.
HINT 2: it is possible to create scales using alternative note names to the ones I've picked. For example you could build the scale of C# instead of Db. Both of these would have the same notes but they would use the alternative names. Do me a favour and stick with the ones I've used for the moment and we'll get to the alternatives later. The alternatives will involve weird concepts like "double sharps" and "double flats", I'll bet you can hardly wait!)

The scales we've produced don't seem to have any pattern of sharps or flats. Let's put them in order starting with no sharps or flats, followed by one flat then two flats, and so on until we've used all the flats. Then we'll go to five sharps followed by four sharps and so on. Confused? look, here's what I mean:

C D E F G A B C
F G A Bb C D E F
Bb C D Eb F G A Bb
Eb F G Ab Bb C D Eb
Ab Bb C Db Eb F G Ab
Db Eb F Gb Ab Bb C Db
Gb Ab Bb Cb Db Eb F Gb
B C# D# E F# G# A# B
E F# G# A B C# D# E
A B C# D E F# G# A
D E F# G A B C# D
G A B C D E F# G

You can view this as going up the hill of flats and coming down a slide of sharps:

(Mentally use whichever ride from a Gold Coast "World" will make this stick in your memory!)

Did you notice that you end up where you started? ...so, let's turn it into a circle!

Notice that because there are twelve keys here, what we have looks like a clock. Remember which way is clockwise. Now let's put in the names of the keys at each "hour point" on the clock, that way we will have the names of the keys and how many sharps or flats are in each of them:

Remember I said it's like a clock? Remember the "clockwise" way around the keys? When you memorise this cycle, do it clockwise. There are some really good harmonic reasons for this.

You'll find this cycle in all sorts of harmony and theory books, sometimes going the opposite way to ours, sometimes called the "cycle of fifths", sometimes called the "cycle of fourths", sometimes going the same way as ours.... rather than argue the toss about all the possibilities I'll just assume you listened to me and are going to treat it in the direction I've suggested. You can go the other way if you must but its going to make the rest of this section confusing!! By the way, let's also avoid all this "cycle of fifths" and "cycle of fourths" stuff and come up with a neutral name. I hereby dub this cycle:

"THE CYCLE"

That's what I'm going to call it from now on, you can call it "Harry" if you like but I'm sticking with The Cycle.

Here's The Cycle again with great big arrows showing the direction we're going to run around it:

THIS CYCLE IS GOING TO BE VERY USEFUL TO YOU IN YOUR STUDY OF HARMONY, NOT JUST FOR WORKING OUT KEY SIGNATURES BUT FOR LOTS OF OTHER GOOD STUFF. MAKE SURE YOU MEMORISE AND UNDERSTAND IT!!!!
(you should be able to work out from the capitals that I'm trying to emphasise something very important here. Remember, a key signature is just the number of sharps or flats in a key and what they are.)

Now that we've settled the name and the direction, here's my suggested way of memorising it:

If you start at the 12 O'Clock position with the key of "C" and pedal round the cycle until you're back home you'll get this pattern of keys:

C F Bb Eb Ab Db Gb B E A D G

This can be memorised by just saying the names of the letters and ignoring the flats, here's a crude phonetic version of what I'm suggesting;

see eff bead guh bead guh

All you have to remember other than this is that the first "bead guh" is all flats and the second one isn't!

WHAT ABOUT ALL THOSE SHARPS AND FLATS?

One of the great things about ordering keys like this is that the flats and sharps appear cumulatively. Once you've used a flat or a sharp, you keep using it and just add others. Confused? let me illustrate-

One flat is Bb
Two flats is Bb and Eb
Three flats is Bb, Eb and Ab
Four flats is Bb, Eb, Ab and Db
Five flats is Bb, Eb, Ab, Db and Gb
Six flats is Bb, Eb, Ab, Db, Gb and Cb

So... the order that these flats appear is:

Bb Eb Ab Db Gb Cb

If this sounds a bit familiar then you're getting the idea, these flats appear, in order, in the cycle starting at Bb (2 O'Clock) and moving clockwise.

Is that Cb confusing you? can't see it in the cycle? It's there, it's just in disguise! Remember "Every Fat Bus Conductor" ? Since there is no note between B and C (ignoring those pesky microtones) then B is one semitone below C, therefore "B" is "Cb".

The first flat key starts at 1 O'Clock (F). Counting from here (remember to move clockwise) you can work out how may flats are in each key. The order that the flats appear starts at 2 O'Clock (Bb), starting from here (moving clockwise remember) you can work out what those flats are.

Here's an example:

Q: What is the key signature of Ab major?

A: Ab is at 4 O'Clock, the first flat key is F (1 O'Clock) so count:

F=1, Bb=2, Eb=3, Ab=4.

So...
there are 4 flats in the key of Ab major. The first flat is Bb start from there and move clockwise round the cycle until you've got 4 flats... Bb, Eb, Ab, Db.
So...
these are the flats in the Ab key signature
so...
the scale of Ab major is:

Ab Bb C Db Eb F G Ab

This probably sound a bit complicated but once you get the hang of it you'll be rattling off key signatures and scales faster than a politician can make up lies.

HOMEWORK

Have fun working out scales with flats in them!

Next time I'll reveal the secret pattern of sharp key signatures, see if you can beat me to that!

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