~ • ~ • ~ • ~
Chapter 4 discussed how the major diatonic scale with which
Westerners are so familiar developed from the application of simple
ratios of frequencies.
Historically, this scale did not emerge quickly or easily. The
“do-re-mi” major scale pattern of five tones and two semitones took
centuries of tinkering. Recall from Chapter 4 the order of tones and
semitones for the major scale—the white keys on the piano
beginning and ending with C:
● tone ● tone ● semitone ● tone ● tone ● tone ● semitone ●
Two whole tones, then a semitone, then three whole tones, then
another semitone: this pattern of tones and semitones is called the
FLAVOURS OF THE
Now, suppose that, instead of playing
C – D – E – F – G – A – B – C,
you were to start on a different white key of the piano, such as D,
D – E – F – G – A – B – C – D.
The pattern of tones and semitones shifts to:
● tone ● semitone ● tone ● tone ● tone ● semitone ● tone ●
Is this still the so-called “diatonic order”?
Yes it is. You still have five tones and two semitones. They're still
spaced the same way.
But when you play this scale, it no longer sounds like the familiar
“do-re mi” scale. It sounds a little weird, a little strange. By starting
on a different note—D—you change the order of the frequency
ratios of several of the notes of the scale with respect to the tonal
It's a different staircase.
Recall the pattern of curved arrows near the end of Chapter 4,
representing the dynamic relationships among the tones that make
up the “do-re-mi” major scale. That pattern of curved arrows does
not apply to this new scale.
Suppose you were to play all the white keys starting with E, like
E – F – G – A – B – C – D – E.
Now the pattern has shifts to:
● semitone ● tone ● tone ● tone ● semitone ● tone ● tone ●
Again, it's the diatonic order: five tones and two semitones, all
spaced the same way. But again, with a different tonal centre, this
scale sounds different from both the C-based scale and the D-based
scale. The E-based scale sounds Spanish. Or maybe Middle
You can keep doing this, playing a different scale on the white
keys only, starting on a different key each time—a different tonal
centre each time.
Next comes this one:
F – G – A – B – C – D – E – F
G – A – B – C – D – E – F – G
A – B – C – D – E – F – G – A
B – C – D – E – F – G – A – B
At this point, you've run out of scale possibilities—the next one
would be a repetition of the C-based scale, the one you started with.
So ... seven variants of the diatonic order, each starting on a
different white key of the piano. What's the musical significance?
A LA MODE
When the diatonic order was being sorted out several centuries ago,
composers and musicians were working with many scales. But it
took quite a while to settle on one or two favourites, for reasons
ultimately having to do with simple frequency ratios, harmony, and
something called tonality (coming up later in this chapter).
In medieval times, there were eight modes called the Church
modes or Gregorian modes. As the diatonic order gradually became
more entrenched, seven “modern” modes were recognized—the
seven variants of the diatonic order you just played on the keyboard,
each beginning on a different white key.
The seven modes have names. The scale you get when you play
the white keys on the piano starting and ending with C is called the
Ionian mode. The modern name for the Ionian mode is simply the
major scale—your basic familiar “do-re-mi” scale.
The scale you get when you play the white keys on the piano
starting and ending with D is called the Dorian mode. And so on.
You can play any of these modal scales anywhere on your guitar
or piano (i. e., starting on any note), as long as you preserve the
interval order for the mode.
Figure 31 below shows all seven modes and the interval orders
for each. These modes will be referred to henceforth as the “Church
modes” (which will no doubt irritate some history-of-music-theory
purists). Note that in Figure 31
T = Tone
S = Semitone
The Seven Church Modes (7 Intervals, 8
Notes), Each a Different “Cut” of the Diatonic Order
Ionian Mode (now known as the major scale)
Aeolian Mode (now known as the natural minor scale)
Of the seven Church modes, two are no longer thought of as
such—the Ionian and Aeolian modes—because the great majority
of the music of the West uses these two scales, now called the
major and minor, respectively.
As for the other Church modes, they faded into disuse roughly
around the Shakespearean era, some 400 years ago. Today, you
can hear some of the Church modes in some genres, such as heavy
metal, some British and Celtic folk music, and some so-called “art”
Chapter 6 discusses the inherent properties of the Church modes
that make it difficult for musicians to use them to create palatable
chord progressions. Chapter 9 discusses how you can use Church
mode scales to create compelling melodies, while using chord
progressions derived from the two modes now referred to as the major and
The Church modes have occasionally found their way into
popular songwriting. Here are a few examples of tunes that use
Church modes as scales (some recordings of these songs may be
in keys other than the original modal key):
Dorian mode (D to D, white piano keys only)
• “The End” (The Doors)
• “What Shall We Do With A Drunken Sailor”
• “Scarborough Fair” (folk song popularized by Simon and
On The Water” (Deep Purple)
• “The Way I Feel” (Gordon Lightfoot)
• “Green Onions” (Booker T & the MG's)
Como Va", "Evil Ways", and numerous others as performed by Carlos Santana ("King
of the Dorian Mode")
Phrygian mode (E to E, white piano keys only)
• “White Rabbit” (Jefferson Airplane)
Lydian mode (F to F, white piano keys only)
• “The Simpsons” theme
Mixolydian mode (G to G, white piano keys only)
• “Norwegian Wood” (The Beatles)
Wreck of the Edmund Fitzgerald" (Gordon Lightfoot)
• “Sweet Home Alabama” (Lynyrd Skynyrd)
you're unfamiliar with some of these songs, go to the Gold Standard Song List.
The website www.GoldStandardSongList.com has details on how to get the lyrics
and how to listen to excerpts.
Locrian mode (B to B, white piano keys only)
• The Locrian is a theoretical mode, too unsettled-sounding for
practical melodic use. It differs from all of the other modes in
that its fifth degree is not a perfect fifth interval (which usually
imparts some cohesion to a scale). It's a diminished fifth—the
(2,047 TO BE
In theory, how many different scales could there be?
More than you'll find on the skin of your average catfish.
Why so many?
Because scales are combinatorial. You start with a finite number
of items (all the notes of a chromatic scale), plus some rules about
picking and combining the items (the notes you choose from the
chromatic scale to make up your own scale). The more notes in your
original chromatic scale, the more “sub-scales” you can create.
Here are some scale construction “rules”:
• Start with an equal-interval chromatic scale. It can have any
number of notes, up to a maximum of, say, 30 in the octave.
(The more notes to the octave, the harder it is for your brain
to distinguish adjacent notes.) In the diatonic system, there
are only 13 notes in the chromatic octave, including the first
and last notes. But other musical systems divide the octave
into more than 13 notes. In theory, you could start with a
chromatic scale of, say, 30 notes to the octave, instead of 13.
• Pick any number of notes from the chromatic scale to create
a scale of your own. However, your scale must have a
minimum of three notes—the first and last notes of the
octave, plus one other note in between. The maximum
number of notes would be all the notes in the full chromatic
• The scale must be confined to one octave, with no notes
repeated except the prime and octave notes at each end.
Suppose you start with a chromatic scale of only three notes. Call
the notes A, B, and A, where the two “A” notes are the notes at
each end of the scale. According to the above rules, you could only
have one scale, comprised of three notes.
A B A
Now suppose you start with a chromatic scale of four equally-spaced notes, A, B, C, and A (three equal intervals). According to
the rules, you could create two scales comprised of three notes and
one scale with four notes:
A B A
A C A
A B C A
Next, start with a chromatic scale of 5 equally-spaced notes, A,
B, C, D, and A. The number of possible scales you could create
more than doubles to seven:
A B A A B C A A B C D A
A C A A C D A
A D A A B D A
Next, try a chromatic scale of 6 notes, A, B, C, D, E, and A. The
number of possible scales more than doubles again, to 15:
A B A A E A A B E A A D E A A B C E A
A C A A B C A A C D A A B C D A A B D E A
A D A A B D A A C E A A C D E A A B C D E A
And so it goes:
Chromatic scale of 7 notes
= 31 possible scales
Chromatic scale of 8 notes = 63 possible scales
. . .
Chromatic scale of 13 notes = 2,047 possible scales
As you know, the chromatic scale of 13 notes is the one from
which all Western musical scales are drawn. Here's a breakdown of
the 2,047 possible scales you can create using the 13-note (12
semitone) Western chromatic scale (Table 22):
TABLE 22 Number of Possible Scales Using a 13-Note, 12-Interval Chromatic Scale
So ... the familiar 8-note “do-re-mi” major scale is only one of 462
possible 8-note scales you could construct by selecting 8 notes from
the 13-note chromatic scale.
There are 330 possible pentatonic scales. (Recall that the
number of notes in a pentatonic scale is not five; it is six, because
the octave note occurs twice.)
Of all the 2,047 possible scales, only a small number lend
themselves easily to modulation (key changes) and harmony. Those
are the ones you'll find most useful.
Roedy Black's Guitar and Keyboard Scales Poster, available at
www.CompleteChords.com, displays guitar and keyboard fingering
diagrams in all keys for five of the most useful, commonly used
• Major scale
• Minor scale
• Major pentatonic scale
• Minor pentatonic scale
• Blues scale
Now, just for fun . . .
Q: How many scales could you theoretically create if you started
with a chromatic scale of 30 notes to the octave?
A: Precisely 268,435,455 possible scales. When you die, if there
is a hell, and you end up there because you've been bad,
they will have a 30-note chromatic scale. You will have to
memorize all the possible scales you could create from it. On
the other hand, if you've been good and you go to heaven,
you will meet Maurice Ravel, who will try to get you interested
in learning how to compose heavenly music with the whole
tone scale, which you may or may not find appealing,
depending on how long eternity lasts.
For purposes of creating harmony, the five Church modes that fell
into disuse lacked the vigour and dynamism of the scales that stuck
A “successful” scale (as far as your brain is concerned) needs a
mixture of two kinds of intervals:
1. Easily-processed simple-frequency-ratio intervals. These
intervals provide your ear with a sense of tonal recognition,
a “home,” a centre of gravity.
A note associated with the next-simplest frequency ratio after
the octave, namely, ratio 3:2 (scale degree 5) must be
positioned in the middle of the scale. It functions as a stable
counterweight to the tonic note.
At scale degree 5, a tune has travelled as far away from
“home” as it can get. Now it can only proceed either
downwards towards scale degree 1, or upwards towards
scale degree 1 (8).
Table 23 shows the first few overtones in the harmonic
series—the strongest overtones. You can see that the
overtones with frequency ratios associated with the
consonant scale degrees, 1 and 5 especially, and also 3,
appear most prominently.
Only at the sixth overtone does a dissonance finally make an
appearance. More on these phenomena in Chapter 6.
Fundamental and First 9 Overtones of the
“Middle C” Overtone Series
f x 2
f x 3
f x 4
f x 5
f x 6
f x 7
f x 8
f x 9
f x 10
1 : 1
2 : 1
3 : 2
2 : 1
5 : 4
3 : 2
9 : 5
2 : 1
9 : 8
5 : 4
2. Highly unstable, unbalanced intervals, especially a
“leading tone.” They function as pointers, directly or
indirectly, to “home.” In particular, a highly unbalanced
interval between scale degrees 7 and 1 (8) is required to
propel the tune upwards to that “home on high,” scale degree
Unstable, dissonant intervals give a tune (melody)
note-to-note impetus. As previously mentioned, unstable
intervals make it possible to create a tune that sounds like it
has a "sense of purpose" or "story." A road trip.
As a musical scale, the chromatic scale fails miserably. It has 12
semitones—all highly unbalanced intervals. Way, way too many to
function as a musical scale. To be sure, the chromatic scale also
contains all the simple-frequency-ratio intervals. But your brain can't
resolve them amid the din and cacophony of 12 dissonant
The Church modes don't succeed because:
• All of them except the Lydian wimp out at scale degree 7, the
all-important leading tone. Instead of a semitone pointing
strongly at 1 (8), they have a much-less-dissonant whole
tone. Not enough tension and propulsion to establish 1 (8) as
the note-of-notes, the alpha dog, the head honcho, the top
banana, the big cheese, the great enchilada, the prime kahuna: Elvis, King of Scale Degrees.
If you're a musical mode on the make, and you can't even
recognize that the cab driver showing you around Muscle
Shoals is Elvis, how can you expect anybody to take you
seriously enough to buy your music?
• Two of them, the Lydian and Locrian, form a tritone interval
with the tonic at scale degree 4. There's no counter-balancing
middle tone in these scales.
More on Church modes and harmony towards the end of Chapter
~ • ~ • ~ • ~
~ • ~ •
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