Piano Power: Diatonic Scales
In the previous article Diatonic Scales (Part 1) you were left to construct the remaining major scales which use sharps. They are A, E, B, F#, C#. Here's what they look like upon completion:
In the example above the seventh step E#, if played on the piano, is actually the note F. The relationship, E# = F, (where the same note can be represented by different symbols) is known in music as an enharmonic relationship. So if E# = F then why not write the above scale as:
Well, changing step 7 from and E# to an F certainly makes it easier for a pianist to read. And, to any listener, the scale would sound the same. However, it doesn't quite look like a major scale anymore. If you recall, our original definition of a major scale is a series of eight consecutive notes. Perhaps I should have stated it more clearly in the definition--the phrase, "consecutive notes" implies consecutive letter names. Therefore, the sixth step (D#) must be followed by some kind of an E (in this case an E#).
Now that we've cleared up that matter, look at ex.5 below. It contains not only an E#, but also a B# which is the enharmonic equivalent of C.
In C# Major, all of the letters of the musical scale have been sharped and we have reached the end of the line for major scales that use sharps. What would happen if we went on to G# Major? Does it even exist? Well, theoretically it does. However, it would be impractical for a composer to employ because the seventh step would have to be raised to Fx (the 'x' being the symbol for a double sharp) and Fx is the enharmonic equivalent of G. So, it can get really confusing.
Here is what G# Major would look like with Fx on the seventh step:
G# MAJOR (Theoretical)
With G# Major, we have begun a new theoretical cycle of scales whose roots (first note of the scale), comprised of ascending fifths (G#, D#, A#, E#, B#...), are similar in their development to the original cycle (G, D, A, E, B...) though far more complicated from a visual perspective.
Can you see the similarities between G# Major (ex.5a) and G Major (ex.5b)? G Major was derived from C Major whose notes were all naturals (meaning no sharps or flats were present) and a sharp was added to the seventh degree. Similarly, G# Major was derived from C# Major whose notes were all sharps and a double-sharp was added to the seventh degree.
In the same manner, D# (containing an Fx and Cx) would be similar to D (containing an F# and C#). A# would be similar to A. E# would be similar to E...and on and on.
Major Scales That Use Flats
In the above major scales, the sharp sign (#) was used to raise notes a half step. In the following scales we will be using the flat sign (b) to lower notes a half step. Initially, when we constructed our first few scales, we began on C and went up five steps (ascending fifth) from C to G to construct a new scale. Let's try going down five steps (descending fifth) from C to F and construct a new scale from that point.
When constructing the sharp scales, corrections were always made that involved steps 6-8. With the construction of flat scales, our focus shifts to steps 3-5. Looking at the above example, we notice that most of the conditions (whole and half steps intervals) have been met. However, interval 3-4 (A-B) is a whole step and should be a half step. Additionally, interval 4-5 (B-C) is a half step and should be a whole step.
Remedy: Lowering the B to a Bb serves the dual role of changing interval 3-4 to a half step (A-Bb) and interval 4-5 to a whole step (Bb-C).
Looking at F Major we notice following:
* The root of the scale (F), is the 4th note of the C scale (and is also five steps below C).
* A newly flatted note (Bb) was added at the 4th step of the scale.
* It is the exact same set of notes as the C scale, except for the new note, Bb. Therefore, we could say that F Major inherited all of the notes of C Major, except for the Bb.
To construct our next scale, we would count backwards in the F Major scale (ex.7) from step 8 to step 4 (F-E-D-C-Bb). We arrive at Bb and construct a new scale from that note:
Once again, everything looks fine except for steps 3-5. D-E is a whole step and should be half step, while E-F is a half step and should be a whole step. We remedy the problem by lowering E to and Eb.
Looking at Bb Major we notice following:
* The root of the scale (Bb), is the 4th note of the F scale (and is also five steps below F).
* The root of the scale (Bb), was newly flatted in the prior scale (F Major).
* A newly flatted note (Eb) was added at the 4th step of the scale.
* It is the exact same set of notes as the F scale, except for the new note, Eb. Therefore, we could say that Bb Major inherited all of the notes of F Major, except for the Eb.
Let's construct one more of the flat scales in the cycle of descending fifths. Counting down five steps in Bb Major, we arrive at Eb and begin our construction on the Eb an octave below:
Once again there is a problem with steps 3-5. G-A is a whole step and should be a half step. A-Bb is a half step and should be a whole step. We remedy the situation by lowering the A to an Ab.
Looking at Eb Major we notice following:
* The root of the scale (Eb), is the 4th note of the Bb scale (and is also five steps below Bb).
* The root of the scale (Eb), was newly flatted in the prior scale (Bb Major).
* A newly flatted note (Ab) was added at the 4th step of the scale.
* It is the exact same set of notes as the Bb scale, except for the new note, Ab. Therefore, we could say that Eb Major inherited all of the notes of Bb Major, except for the Ab.
You should now have enough information to construct the remaining major scales that use flats. They are: Ab, Db, Gb and Cb.
In the next article you will learn about key signatures and intervals. Intervals--the distance between and including two notes--are easy to understand if you have a firm grasp of the major scales. In the meantime, practice saying the letter names to all of the major scales out loud until you have memorized them. Be able to easily recite them going both up and down. Don't panic, there's only a finite amount of information to learn.
Example: D Major
Going Up: D-E-F#-G-A-B-C#-D
Going Down: D-C#-B-A-G-F#-E-D