Digital Sound & Music: Concepts, Applications, & Science, Chapter 3, last updated 6/25/2013
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Thus, the factor 1.05946 defines a semitone. If two notes are divided by a semitone, then
the frequency of the second is 1.05946 times the frequency of the first. The other frequencies
between semitones are not used in Western music (except in pitch bending).
Two semitones constitute a whole tone, as illustrated in Figure 3.3. Semitones and
whole tones can also be called half steps and whole steps (or just steps), respectively. They are
illustrated in Figure 3.3.
Figure 3.3 Semitones and whole tones
The symbol #, called a sharp, denotes that a note is to be raised by a semitone. When
you look at the keyboard in Figure 3.3, you can see that E# denotes the same note as F because
raising E by a semitone takes you to the note F. Thus, this key on the keyboard has two names
(although calling it F is more common). When two notes have different names but are the same
pitch, they said to be enharmonically equivalent.
The symbol♭, called a flat, denotes that a note is to be lowered by a semitone. C♭is
enharmonically equivalent to B. A natural symbol removes a sharp or flat from a note. Sharps,
flats, and naturals are examples of accidentals, symbols that raise or lower a note by a semitone.
3.1.3 Music vs. Noise
It’s fascinating to consider the way humans perceive sound, experiencing some sounds as
musical and some as noise. Understanding frequency components and harmonics gives us some
insight into why music is pleasing to our senses.
Consider the waveforms in Figure 3.4 and Figure 3.5. The first shows the notes C, E, and
G played simultaneously. The second is a recording of scratching sounds. The first waveform
has a regular pattern because the frequency components are pure sine waves with a harmonic
relationship. The second sound has no pattern; the relationship of the frequency components is
random at any moment in time and varies randomly over time. Sounds that are combinations of
harmonic frequencies make patterns that are pleasing to hear. They’re musical. Random
patterns produce noise.
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