Digital Sound & Music: Concepts, Applications, & Science, Chapter 3, last updated 6/25/2013
Dotted Note Equivalence Dotted Rest Equivalence
. = + . = +
. = + . = +
.= + . = +
Table 3.6 Dotted notes and rests
Figure 3.18 Example of music with rests Key Signature
Many words in the field of music and sound are overloaded that is, they have different
meanings in different contexts. The word “key” is one of these overloaded terms. Thus far, we
have been using the word “key” to denote a physical key on the piano keyboard. (For the
discussion that follows, we’ll call this kind of key a “piano key.”) There’s another denotation for
key that relates to diatonic scales, both major and minor. In this usage of the word, a key is a
group of notes that constitute a diatonic scale, whether major or minor.
Each key is named by the note on which it begins. The beginning note is called the key
note or tonic note. If we start a major diatonic scale on the piano key of C, then following the
pattern 2 2 1 2 2 2 1, only white keys are played. This group of notes defines the key of C major.
Now consider what happens if we start on the note D. If you look at the keyboard and consider
playing only white keys starting with D, you can see that the pattern would be 2 1 2 2 2 1 2, not
the 2 2 1 2 2 2 1 pattern we want for a major scale. Raising F and C each by a semitone that is,
making them F# and C# changes the pattern to 2 2 1 2 2 2 1. Thus the notes D, E, F#, G, A, B,
C# and D define the key of D. By this analysis, we see that the key of D requires two sharps F
and C. Similarly, if we start on D and follow the pattern for a minor diatonic scale 2 1 2 2 1 2
2 we play the notes D, E, F, G, A, B♭, and D. This is the key of D minor.
Each beginning note determines the number of sharps or flats that are played in the 2 2 1
2 2 2 1 scale for a major key or in the 2 1 2 2 1 2 2 sequence for a minor key. Beginning an
octave on the piano key C implies you’re playing in the key of C and play no sharps or flats for
C major. Beginning a scale on the piano key D implies that you’re playing in the key of D and
play two sharps for D major.
Let’s try a similar analysis on the key of F. If you play a major scale starting on F using
all white keys, you don’t get the pattern 2 2 1 2 2 2 1. The only way to get that pattern is to
lower the fourth note, B, to B♭. Thus, the key of F major has one flat. The key of F minor has
four flats A♭, B♭, D♭, and E♭, as you can verify by following the sequence 2 1 2 2 1 2 2
starting on F.
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