The Diatonic System

The Diatonic System is basically the Major Scales used in "western music". It consists of 7 different intervals and one octave.These are numbered 1 thru 8. These SCALES are constructed of 2 tetrachords separated by a whole step. A tetrachord is composed of 2 whole steps and a half step. One way to visualize this is on the piano keyboard. Notice the E to F and B to C have no black key. These are the only two natural half steps. So in the key of C the 1st tetrachord or lower tetrachord is CDEF. The 2nd tetrachord or upper tetrachord is GABC. Putting them together follows the rule. Notice F to G is a whole step.

To Derive All the Sharp Keys

By taking the UPPER TETRACHORD in our example it is GABC, and making it the LOWER TETRACHORD then building the UPPER TETRACHORD one whole step above the 4th note in the LOWER TETRACHORD we get the key of G. By continuing this proceedure,starting with the key of C,we can derive all the Sharp Keys.

LOWER TETRACHORD

G to A = 1 whole step

A to B = 1 whole step

B to C = 1 half step

Whole Tone Separator between the TETRACHORDS

C to D = 1 whole step

UPPER TETRACHORD

D to E = 1 whole step

E to F# = 1 whole step

F# to G = 1 half step

To Derive All the Flat Keys

By taking the LOWER TETRACHORD and making it the UPPER TETRACHORD then building the LOWER TETRACHORD one whole tone below the 1st note of the UPPER TETRACHORD we arrive at the key of F. By continuing this proceedure,starting from the key of C, we can derive all the Flat Keys.

LOWER TETRACHORD

F to G= 1 whole step

G to A= 1 whole step

A to Bb= 1 half step

Whole Tone Separator between the TETRACHORDS

Bb to C= 1 whole step

UPPER TETRACHORD

C to D= 1 whole step

D to E= 1 whole step

E to F=1 half step

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