The Evolution of the Major Scale
If we begin at D, then due to laws of physics,
the two most harmonically consonant notes with D (as with any note)
are either a perfect fourth above or a perfect fourth below
D
4th 4th
A D G
(figure 1)
D harmonizes perfectly with either A or G,
so why shouldn't the fourths surrounding THOSE two notes be consonant?
Using the knowledge that 4ths harmonize either up or
down, it is a simple matter to expand that formula to the interval of
a perfect fourth on either side of figure 1:
4th 4th 4th 4th
E A
D G C
(figure 2)
Rearranging the order of the notes in figure 2,
one will notice that it is the Ur-Scale:
"A minor pentatonic"!
A C
D E
G
(figure 3)
Scales built with this same formula continue to have
a lasting place in musics from all over the globe.
Taking this "logic of 4ths" (as in figure 2 above) one step
further,
the following 7-note tone row was discovered:
4th 4th 4th 4th 4th 4th
B E A
D G C
F
(figure 4)
which rearranged similarly to figure 3 above,
yields the radially symmetrical structure which is commonly known as
the "Natural Minor" or "Aeolian Mode".
A B
C D
E F
G
(figure 5)
This formula of scale degrees, continues to be in the
top three favorite tonal centers
for most musicians and composers.
The addition of the notes B and F into the A minor pentatonic mode,
creates an interval of great tension into the tone row, this special
interval is known as a tri-tone (the interval of 3 whole-tones).
The tension created by the tritone calls for
the B to resolve up a half step to the C,
and for the F to resolve chromatically down to the E.
B -> C E
<- F
(figure 6)
Once this cadence has taken place,
the natural resolution falls squarely on
the two defining notes of the C major triad (C and E).
These tension-resolution tendencies cement the major
scale's dominance over all other scales.
C D E
F G
A B
(figure 7)
What happens if you take this concept further?
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