14-12-2013, 02:40
The noteworthy thing about the order of the sharps and flats is that they are the reverse of one another. The sharps go in fifths and follow the circle clockwise starting at F and going to B while the flat go in fourths and follow the circle counterclockwise starting at B and going to F.
The sharps and flats ALWAYS follow this order. You would never see just C sharped by itself in a key signature. It must appear with F. Only F can appear in a key signature by itself. Likewise B cannot be sharped in the key signature without sharping from F to E clockwise along the circle. The same goes the flat side of the circle.
So we have a key signature with 5 flats in it? How could the circle of 5ths tell us what key that is? We would bisect the circle such that one of the half-circles has five of the flatted scales isolated in it--only five. Which five?
Well, you know that if there are five flats in the signature they must be in a certain order, in this case, BEADG. So draw a line from G-flat to C. Now you have the five major scale designations with flats in the title isolated in one of the half-circles. Now turn this line one notch clockwise. You end up on D-flat and that is the key with five flatted notes (and difficult to play bass in because there are no open notes).
But look at the other half-circle! It contains only one sharped scale designation--F-sharp. When you turned the line one notch clockwise, the other end of the line (which is in the sharp side of the circle) ends up on G. And what is the major scale who only sharp note is F? Yes, that would G major.
Let's try another one. Suppose we have a key signature with three sharps in it. Which is it? Well, it if it has three sharps then what is the sequence? F-C-G. So we bisect the circle of fifths so that one of the half-circles contains F, C and G all sharped. Look carefully. If you picked the FCG at the top of the circle, you would be wrong! They do not have sharps in their titles. Instead, look at the bottom of the circle. At 6 o'clock, there is an F-sharp. Going clockwise, there is a D-flat but D-flat is also C-sharp so there is our F- and C-sharp. We need G to be sharp too so we also include the A-flat since A-flat is also G-sharp. So we draw our bisecting line from A-flat straight across to D. Now we rotate the line one notch clockwise and the end of the line in the sharped side of the circle moves to D. So D major is the key with three sharps--FCG.
What about the other half circle? That side has three flats in it--BEA. That is the correct sequence for flats. Now when we rotated the line clockwise one notch, the end of the line in the flatted side of the circle comes to rest on E-flat. So E-flat major is the scale with three flats--BEA.
Okay, okay. So the circle can show you how to determine a key based on the number of sharps of flats. But can it tell us which notes are sharped or flatted in each key signature? Yes, it can.
![[Image: circle_of_fifths.gif]](http://playtheaxe.com/theory/lesson09/circle_of_fifths.gif)
Use the above figure for reference. To determine the flats, drop back two notes on the circle. G major gets one sharp so drop back two spaces on the circle to F major and that is the note that gets sharped in G major. Trigonometrically, draw a line from G to the center of the circle and go 60 degrees counterclockwise (remember that each note represents 30 degrees of arc). Moving to D major, which has two sharps, drop back 60 degrees to C and that is the next sharp so D major has two sharpsâF and C. And so on.
For flats, we look at the note on the opposite side of the circle. So the note opposite F is B so that is the note that gets flatted in F major. Trigonometrically, we drop back (or move forward) 180 degrees to find the flats. The next note of the circle is Bb and will get two flats. We already know that one will be B and the other is 180 from Bb which is E so Bb major is flatted at B and E. And so on.
The special case is C which has no key signature (no sharps or flats). If we drop back 60 degrees as in the manner of finding sharps, we find ourselves at Bb which, if sharped, simply becomes B. Or if we cross the circle 180 degrees to find the flats, we end up at Gb, which, if flatted, simply becomes F. So, as the circle shows, C has no naturally occurring sharps or flats.
Next we'll investigate how chords figure into the Circle.
The sharps and flats ALWAYS follow this order. You would never see just C sharped by itself in a key signature. It must appear with F. Only F can appear in a key signature by itself. Likewise B cannot be sharped in the key signature without sharping from F to E clockwise along the circle. The same goes the flat side of the circle.
So we have a key signature with 5 flats in it? How could the circle of 5ths tell us what key that is? We would bisect the circle such that one of the half-circles has five of the flatted scales isolated in it--only five. Which five?
Well, you know that if there are five flats in the signature they must be in a certain order, in this case, BEADG. So draw a line from G-flat to C. Now you have the five major scale designations with flats in the title isolated in one of the half-circles. Now turn this line one notch clockwise. You end up on D-flat and that is the key with five flatted notes (and difficult to play bass in because there are no open notes).
But look at the other half-circle! It contains only one sharped scale designation--F-sharp. When you turned the line one notch clockwise, the other end of the line (which is in the sharp side of the circle) ends up on G. And what is the major scale who only sharp note is F? Yes, that would G major.
Let's try another one. Suppose we have a key signature with three sharps in it. Which is it? Well, it if it has three sharps then what is the sequence? F-C-G. So we bisect the circle of fifths so that one of the half-circles contains F, C and G all sharped. Look carefully. If you picked the FCG at the top of the circle, you would be wrong! They do not have sharps in their titles. Instead, look at the bottom of the circle. At 6 o'clock, there is an F-sharp. Going clockwise, there is a D-flat but D-flat is also C-sharp so there is our F- and C-sharp. We need G to be sharp too so we also include the A-flat since A-flat is also G-sharp. So we draw our bisecting line from A-flat straight across to D. Now we rotate the line one notch clockwise and the end of the line in the sharped side of the circle moves to D. So D major is the key with three sharps--FCG.
What about the other half circle? That side has three flats in it--BEA. That is the correct sequence for flats. Now when we rotated the line clockwise one notch, the end of the line in the flatted side of the circle comes to rest on E-flat. So E-flat major is the scale with three flats--BEA.
Okay, okay. So the circle can show you how to determine a key based on the number of sharps of flats. But can it tell us which notes are sharped or flatted in each key signature? Yes, it can.
For flats, we look at the note on the opposite side of the circle. So the note opposite F is B so that is the note that gets flatted in F major. Trigonometrically, we drop back (or move forward) 180 degrees to find the flats. The next note of the circle is Bb and will get two flats. We already know that one will be B and the other is 180 from Bb which is E so Bb major is flatted at B and E. And so on.
The special case is C which has no key signature (no sharps or flats). If we drop back 60 degrees as in the manner of finding sharps, we find ourselves at Bb which, if sharped, simply becomes B. Or if we cross the circle 180 degrees to find the flats, we end up at Gb, which, if flatted, simply becomes F. So, as the circle shows, C has no naturally occurring sharps or flats.
Next we'll investigate how chords figure into the Circle.