Digital Sound & Music: Concepts, Applications, & Science, Chapter 3, last updated 6/25/2013
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that sounds respectable. From there you could improvise bass lines, solos, and arrangements by
playing notes that fit with the key signature and chord currently in use. In addition to fake books,
you can train your ears to recognize chord progressions and then fake the songs by ear. See the
learning supplements for this section to start training your ears and try experimenting with
improvising along with a chord progression.
3.2.4 Guitar Chord Grid
A guitar chord grid representation is of a chord sequence shown in Figure 3.44. The chord grid
corresponds to the guitar fret board. The vertical lines represent the six strings and the horizontal
lines represent the frets. A black dot represents a place on the fret board where you should put
one of your fingers. When all your fingers are in the indicated locations, you can strum the
strings to play the chord. Keep in mind that the chord grid shows you one way to play the chord,
but there are always other fingering combinations that result in the same chord. If the grid you’re
looking at looks too hard to play, you might be able to find a grid showing an alternate fingering
that is easier.
Figure 3.44 - Guitar chord grids for “Twinkle, Twinkle Little Star”
3.3 Science, Mathematics, and Algorithms
3.3.1 The Mathematics of Music
3.3.2 Equal Tempered vs. Just Tempered Intervals
In Section 3.1.4 we described the diatonic scales that are commonly used in Western music.
These scales are built by making the frequency of each successive note times the frequency
of the previous one. This is just one example of a temperament, a system for selecting the
intervals between tones used in musical composition. In particular, it is called equal
temperament or equal tempered intonation, and it produces equal tempered scales and
intervals. While this is the intonation our ears have gotten accustomed to in Western music, it
isn’t the only one, nor even the earliest. In this section we’ll look at an alternative method for
constructing scales that dates back to Pythagoras in the sixth century B. C. just tempered
intonation a tuning in which frequency intervals are chosen based upon their harmonic
relationships.
First let’s look more closely and the equal tempered scales as a point of comparison. The
diatonic scales described in Section 3.1.4 are called equal tempered because the factor by which
the frequencies get larger remains equal across the scale. Table 3.13 shows the frequencies of
the notes from C4 to C5, assuming that A4 is 440 Hz. Each successive frequency is

times
the frequency of the previous one.
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