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Piano Power: Key Signatures and the Circle of Fifths
In the previous article Diatonic Scales (Part 2) you were left to construct the remaining major scales that use flats. They are Ab, Db, Gb, Cb. Here's what they look like upon completion:
Ab MAJOR
Db MAJOR
Gb MAJOR
In the example above the fourth step Cb, if played on the piano, is actually the note B. The relationship, Cb = B, is another example of an enharmonic relationship.
Cb MAJOR
In Cb Major, all of the letters of the musical scale have been flatted and we have reached the end of the line for major scales that use flats.
In keeping with the last article, let's see what would happen if we went on to Fb Major. It would be impractical for a composer to use this scale because the fourth step would have to be lowered to Bbb (the 'bb' being the symbol for a double flat) and Bbb is the enharmonic equivalent of A.
Here is what Fb Major would look like with Bbb on the fourth step:
Fb MAJOR (Theoretical)
With Fb Major, we have begun a new theoretical cycle of scales whose roots (first note of the scale), comprised of descending fifths (Fb, Bbb, Ebb, Abb...), are similar in their development to the original cycle (F, Bb, Eb, Ab...) though far more complicated from a visual perspective.
Can you see the similarities between Fb Major (above) and F Major (below)? F Major was derived from C Major whose notes were all naturals (meaning no sharps or flats were present) and a flat was added to the fourth degree. Similarly, Fb Major was derived from Cb Major whose notes were all flats and a double-flat was added to the fourth degree.
F MAJOR
Key Signatures
Definition: The Key Signature is an orderly arrangement of sharps or flats placed at the beginning of a piece.
The Key Signature has two functions:
1. It allows the composer to indicate at the beginning of a piece the particular scale he/she has chosen to write within.
2. Since it global indicator, it spares the composer the hassle of having to flat or sharp every note in the piece that corresponds with the scale he/she has chosen.
If we were to compose a piece in the key of A Major, an opening phrase might look like this:
Remember, A Major contains the sharps F#, C#, G#.
Using the key signature for A Major, we indicate the use of F#, C#, G#, at the beginning of the piece. The phrase now looks like this:
Upon seeing the key signature at the beginning of the piece, a musician automatically assumes that all written F's, C's and G's are to be played as F#'s, C#'s and G#'s respectively.
The Sharp Key Signatures
The key signatures for C Major and the sharp scales are listed below. Notice the specific order that the sharps assume as we progress from C Major to C# Major. The order of sharps is F#, C#, G#, D#, A#, E#, and B#, that forms a pattern of ascending fifths.
But why should the sharps form a pattern of ascending fifths? Because each new sharp in a key signature (the sharp furthest to the right) represents the 7th step of the new key. And since the roots of the scales (C, G, D, A, E…) form a pattern of ascending fifths, it follows that each of the 2nd, 3rd, 4th…7th steps of the scales would also form a pattern of ascending fifths if they were listed separately.
The pattern of sharps is easy to memorize. Just say the following about fifty times:
F#, C#, G#, D#, A#, E#, B#
Identifying Sharp Key Signatures
Given a particular key signature, how would you know right off the bat the key that those sharps represent? Is there a short cut or easy way to determine this? Have a look at the following key signature:
Remember, when we constructed the B Major Scale, all of the sharps of the previous E Major scale (F#, C#, G#, D#) were inherited by the new B Major scale. Additionally, a new sharp (A#) was added on the 7th step of the new B Major scale. Well, the 7th step (A#) is one half-step below the 8th step of the scale (B) which is also the root of the scale.
Review: To identify a sharp key signature, go one-half step above the sharp that is furthest to the right in the key signature. That will bring you to the root of the scale.
The Flat Key Signatures
The key signatures for C Major and the flat scales are listed below. Notice the specific order that the flats assume as we progress from C Major to Cb Major. The order of flats is Bb, Eb, Ab, Db, Gb, Cb, and Fb, that forms a pattern of descending fifths.
Why should the flats form a pattern of descending fifths? Because each new flat in a key signature (the flat furthest to the right) represents the 4th step of the new key. And since the roots of the scales (C, F, Bb, Eb, Ab…) form a pattern of descending fifths, it follows that each of the 2nd, 3rd, 4th…7th steps of the scales would also form a pattern of descending fifths if they were listed separately.
The pattern of flats is easy to memorize. Just say the following about fifty times:
Bb, Eb, Ab, Db, Gb, Cb, Fb
Identifying Flat Key Signatures
As with the sharp key signatures, there is an easy way to determine the key of a particular flat key signature. Let’s look at the following key signature:
When we constructed the Gb Major scale, all of the flats of the previous Db Major scale (Bb, Eb, Ab, Db, Gb) were inherited by the new Gb Major scale. Additionally, a new flat (Cb) was added on the 4th step. Counting backwards four steps (Cb, Bb, Ab, Gb) we arrive at Gb which is the root of the scale. Note that Gb is also the 2nd to the last flat in the key signature.
Review: To identify a flat key signature, simply identify the 2nd to the last flat in the key signature. That is the root of the scale. In the case of F major which only has one flat (Bb), count backwards four notes (Bb, A, G , F) to F. (It’s easier just to memorize that one flat signifies F Major.)
The Circle of Fifths
Around the circle, the ascending (sharp) scales are listed clockwise while the descending (flat) scales are listed counter-clockwise. Notice at the bottom of the circle that an overlapping of the sharp and flat scales occurs formed by the enharmonic relationships - B = Cb, F# = Gb, C# = Db.
Related MusicDish e-Journal Articles:
» Piano Power: Diatonic Scales - Part 2
(2000-08-20)
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