Digital Sound & Music: Concepts, Applications, & Science, Chapter 3, last updated 6/25/2013
clockwise, you’re shown G as the next key up from the key of C. The key of G has one sharp.
The next key up, moving by fifths, is the key of D, which has two sharps. You can continue
counting up through the circle in this manner to find successive keys, each of which has one
more sharp than the previous one.
Starting with the key of C and moving counterclockwise by intervals of fifths (“counting
down”), you reach successive keys each of which has one more flat than the previous one the
keys of F, B♭, E♭, and so forth. Counting down a fifth from C takes you through C, B, A, G,
and F five lettered notes taking you through seven semitones, Counting down a fifth from F
takes you through F, E, D, C, and B. However, since we again want to move seven semitones,
the B is actually B♭. The seven semitones are F to E, E to E♭, E♭ to D, D to D♭, D♭ to C,
C to B, and B to B♭. Thus, the key with two flats is the key of B♭.
The keys shown in the circle of fifths are the same keys shown in Table 3.7 and Table
3.8. Theoretically, Table 3.7 could continue with keys that have seven sharps, eight
sharps, and on infinitely. Moving the other direction, you could have keys with
seven flats, eight flats, and on infinitely. These keys with an increasing number of
sharps would continue to have equivalent keys with flats. We’ve shown in Figure
3.22 that the key of F#, with six sharps, is equivalent to the key of G♭, with six
flats. We could have continued in this manner, showing that the key of C#, with
seven sharps, is equivalent to the key of D♭, with five flats. Because the equivalent
keys go on infinitely, the circle of fifths is sometimes represented as a spiral.
Practically speaking, however, there’s little point in going beyond a key with six
sharps or flats because such keys are enharmonically the same as keys that could be represented
with fewer accidentals. We leave it as an exercise for you to demonstrate to yourself the
continued key equivalences. Key Transposition
All major keys have a similar sound in that the distance between neighboring notes
on the scale follows the same pattern. One key is simply higher or lower than
another. The same can be said for the similarity of minor keys. Thus, a musical
piece can be transposed from one major (or minor) key to another without changing
its composition. A singer might prefer one key over another because it is in the
range of his or her voice.
Figure 3.23 shows the first seven notes of “Twinkle, Twinkle Little Star,”
right-hand part only, transposed from the key of C major to the keys of E major and
C minor. If you play these on a keyboard, you’ll hear that C major and E major
sound the same, except that the second is higher than the first. The one in C minor sounds
different because the fifth and sixth notes (A) are lowered by a semitone in the minor key, giving
a more somber sound to the sequence of notes. It doesn’t “twinkle” as much.
Circle of Fifths
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