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5.1.1
WHAT
SCALES
HAVE
IN COMMON:
TONES
IN SIMPLE
FREQUENCY
RATIOS
Thousands of years ago in Africa, Europe, Asia and elsewhere,
people made discoveries, independently, about the connections
between tunes (songs) and scales (ordered collections of pitches
used in the tunes). Some scales eventually fell out of use. Others
became fixtures of the prevailing culture.
All musical-sounding scales consist of a small selection of
notes—typically five to seven intervals (six to eight notes) to the
octave. The notes that comprise scales everywhere tend to have
simple frequency ratio relationships with the first note of the scale.
You can play most widely-used musical scales on a piano or guitar,
regardless of the scale's culture of origin.
The Meaning of “Octave”
The term “octave” originally described the span of
the eight-note (seven-interval) diatonic order of tones and semitones. Now the
term simply applies to the interval associated with the frequency ratio 2:1.
So, whether a scale has five, six, seven, eight,
thirteen, or twenty-two notes, the span from the lowermost to the uppermost
note—the note with a frequency of double the lowermost note—is still referred to
as an “octave.”
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Figure 22 below shows the
(non-musical) chromatic scale. It's just a rack of 12 equally-spaced semitone
intervals—13 notes, including the tonic notes at each end, called the prime
or interval of unison and the octave.
To play the chromatic scale, you start with any note and simply
play adjacent semitones until you get to the next octave note.
Postmodern feline composers the world over use this scale.
FIGURE 22 Chromatic Scale
The scales in the following discussion use a variety of samplings
of tones from the chromatic scale.
5.1.2
MAJOR
PENTATONIC
SCALE
You will find this Pythagorean scale in every major musical culture
worldwide. The name pentatonic derives from the fact that it has five
intervals, although the scale has six notes, including the prime and
the octave.
You can play this scale on your guitar or keyboard starting from
any note, as long as you preserve the interval order, like this (the
dots indicate the notes; the labels between indicate the type of
interval between notes):
● tone ● tone ● aug 2nd ● tone ● aug 2nd ●
Figure 23 clarifies which tones you would select from the
chromatic scale to get the major pentatonic scale, and the size of
the intervals from tone to tone.
FIGURE 23
Major Pentatonic Scale (5 Intervals, 6
Notes)
This scale is widely used in Africa and Asia (it's the Chinese
Mongolian scale), in Celtic music, and in North American folk, gospel
and blues music. Some familiar songs that use the major pentatonic scale
are:
• “Auld Lang Syne”
• “Swing Low, Sweet Chariot”
• “Amazing Grace”
Here's an easy way to remember the interval order for this
important scale: play the black keys only on the piano, starting with
F♯ (that's the first (leftmost) key in the group of three black keys).
5.1.3
MINOR
PENTATONIC
SCALE
The minor pentatonic scale (Figure 24 below) uses the same notes
as the major pentatonic scale, but in a different order. The interval
order is as follows (5 intervals, 6 notes):
● aug 2nd ● tone ● tone ● aug 2nd ● tone ●
To remember the interval order for this scale, play the black keys
only on the piano, starting with D♯ (that's the
second—rightmost—key in the group of two black keys).
FIGURE 24
Minor Pentatonic Scale (5 Intervals, 6
Notes)
Both the major pentatonic and the minor pentatonic scales use
the same five black keys on the piano. Each scale has the same
number of “tone” intervals (three), and the same number of
“augmented 2nd” intervals (two). Yet these two pentatonic scales
sound markedly different from each other. How come?
Because, with any scale, each of the constituent tones forms an
interval with the tonic note. So, if you change the order of the
intervals, you change the character of the entire scale. Even if you
use the same number and same sizes of intervals.
It goes back to ratios of frequencies.
Each tone of a scale has a unique frequency ratio with respect
to the tonic note. If you move even one tone to a different position
within a scale, you change its frequency ratio with respect to the
tonic note—and with all the other notes in the scale. This changes
the sound of the entire scale. Consequently, it changes the
character of melodies crafted using the scale.
In other words, if you move even one tone in a scale, it becomes
a different scale with different melodic potential.
5.1.4
WHY
“SIMILAR”
SCALES
SOUND
SO DIFFERENT:
THE
STAIRCASE
ANALOGY
Think of staircases with differing heights of the individual steps. The
floor at the bottom of the staircase represents the tonic note. The
upper floor is the octave note. The intervals are the vertical
distances you go as you climb the steps. Each staircase is the same
overall height, connecting the lower floor to the same upper floor.
Figure 25 visually represents the difference between the major
pentatonic and minor pentatonic scales.
FIGURE 25 Scales As “Staircases”
Even though both pentatonic staircases have three regular-sized
steps and two large steps, the difference in the order of the two step
sizes means you have a different experience climbing each
staircase.
Just as re-ordering step-sizes makes for unique staircases and
climbing adventures, so re-ordering intervals makes for unique
scales and musical experiences.
A Horse-friendly Hotel with Chromatic Staircases
WARNING: DO NOT try to ride your horse up a pentatonic
staircase. As you can see in Figure 25 above, a pentatonic
staircase is too steep, and the steps are too uneven. Ex-Marshal
McDillon had to ban horses from all the hotels in Dodge City
because so many horses got hurt on the pentatonic staircases.
Marshal Puma has decided to keep the ban in place, despite her
falling out with Ex-Marshal McDillon and her affinity for cheap plot twists in
Classic Westerns.
If you're looking for a horse-friendly hotel, try the Fairmont Royal
York, a luxury hotel in Toronto, Ontario, Canada. Since the late
1940s, the Fairmont Royal York has welcomed strangers from the
West, especially strangers from Calgary, Alberta, Canada, to ride
on up to the registration desk on their horses. According to some
reports, this policy also applies to chuckwagon drivers with teams
of horses. The hotel even has specially-constructed smooth
chromatic staircases to make it easy for guests on horseback to
get around inside the hotel.
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5.1.5
BLUES
SCALE
The blues scale (Figure 26 below) is almost the same as the minor
pentatonic scale, except that it has an extra note in the middle. The
addition of that extra note, sometimes called a blue note, gives this
scale a considerably different sound from the minor pentatonic.
FIGURE 26
Blues Scale (6 Intervals, 7 Notes)
5.1.6
AN
ARABIC
SCALE
Figure 27 below shows a scale used in the Middle East. Try playing
it on your guitar or piano.
Compare this Arabic scale with the familiar major diatonic scale
(all the white keys on the piano, beginning with C). The Arabic scale
has four semitone intervals, including two consecutive semitones as
you pass through the tonic note. These dissonances give the scale
an exotic, other-worldly sound to Western ears.
You can play this scale starting with any note on your guitar or
piano. As usual, just make sure you preserve the order of the
intervals, like this:
● semitone ● aug 2nd ● semitone ● tone ● semitone ● aug 2nd ● semitone ●
FIGURE 27 An Arabic Scale (7 Intervals, 8 Notes)
5.1.7
INDIAN
OR WHOLE
TONE
SCALE:
AN
EQUAL-INTERVAL
SCALE
THAT
WORKS
Normally, an equal-interval scale sounds like rubbish. But here's an
Indian equal-interval scale that sounds musical (Figure 28). It has a
dream-like, fanciful quality. Almost surreal.
This scale contains consonant intervals with simple frequency
ratios (major thirds, minor sixths) and dissonant intervals (major
seconds, tritones, minor sevenths).
This whole tone scale below is one of many scales used in
Indian music. Another divides the octave into 22
“microtones”—intervals smaller than a semitone.
Impressionist composers such as Claude Debussy used the
whole tone scale in many compositions.
FIGURE 28 An Equal-interval Indian or Whole Tone
Scale (6 Intervals, 7 Notes)
5.1.8
A
CHINESE
PENTATONIC
SCALE
The major pentatonic scale (Figure 23 above) is the same as the
Chinese Mongolian scale.
The following pentatonic scale is also widely used in China
(Figure 29):
FIGURE 29
A Chinese Scale
5.1.9
HUNGARIAN
GYPSY
(ROMA)
SCALE
And, finally, to get your blood a-boilin', here's the Hungarian minor
scale, better known as the Hungarian Gypsy scale or the Hungarian
Roma scale (Figure 30).
Get somebody to play a fast tune with this scale. Dance until
dizzy.
FIGURE 30
Hungarian Gypsy (Roma) Scale
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