First, it is important to note that when using chromatics, a good rule of thumb to follow is when ascending, use sharps/naturals; when descending, use flats/naturals.
If you look at
Line A, you will notice two ascending chromatic scales starting on E. The first example is in a mode without any inherent sharps/flats, so sharps are added in the appropriate places. In the second example of
Line A, you see it is in a mode with 4 sharps (we'll just call it E Major). Notice the existence of F-doublesharps and C-doublesharps. They were used because G# and D# already existed in the key signature. It would have been bad musical grammar (and just silly IMHO) to write G-natural (nullifying the key signature) followed by a G#.
Line B is the same kind of deal but with a descending chromatic scale. This time, I started both examples on Eb. Again, the first example does not have accidentals listed in it's key signature, so I just added flats as necessary. The second example has 3 flats in it's key signature, so we wind up with a B-doubleflat, as not write A-natural (nullifying the key signature) followed by A-flat. Also notice the use of F-flats. Yeah, they're obnoxious, but as E-flats are already being used, it would have been silly to write E-natural followed by another E-flat.
Line C is a little bit more complicated. The first example shows an Ascending Chromatic scale, but it is being used in a mode with flats. We want to avoid
adding flats, so we cancel existing flats with natural signs, and add sharps as necessary. The same holds true for the Descending Chromatic scale in a mode with sharps - we want to avoid the use of
additional sharps, so we use naturals/flats as necessary.
Line D shows the proper use of accidentals when changing directions. The accidental used is dependent on the resulting direction of the turn around. So, in the first example, we go down from A to an accidental and
back up to A. Since, the resulting direction is
up, I will use a sharp. You could see how silly it would be to write A, A-flat, A-natural. The second example shows the opposite: approaching from an upward direction, resulting in a downward direction. Since the result is going
down, I used an Eb instead of a D#.
These are rules I adhere to because I prefer to be consistent across the board. However, as I mentioned in an earlier post, sometimes composers will write in a manner that is just easier to read as opposed to what is grammatically correct. A good example of this is in
Beethoven's Piano Sonata No. 8, Op. 13 "Pathetique." (
Note, clicking on that link will open a PDF file.) If you look at the first page, last measure, he uses a descending chromatic scale in the key of C minor. It is amusing to me that the rules used in this scale are inconsistent within this one measure! The scale begins on a high Eb, and descends D-Db-C. An octave lower in the scale, he writes D-C#-Cnatural. HUH? (It is important to note that I have not seen Beethoven's original manuscript, so this
could be the work of an editor and not his choice of notation.)
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), but here's my list