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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