Scale Theory: Major Scales
A scale is divided into two halves, called tetrachords. The scale degrees are determined by a formula outlining the intervals or steps. This formula (for every Major and Relative or Natural Minor) is as follows: tone, tone, semitone, {tone}, tone, tone, semitone – or whole (step), whole, half, {whole}, whole, whole, half. Since these scales are divided into two halves or tetrachords, each scale contains two distinct scales.
For instance, in both a C Major scale and the key of C Major (C, D, E, F, G, A, B), the interval formula yields not only a C Major scale, but a G Major scale as well. The G Major (or perfect fifth of the C Major scale) is found beginning on the second half or upper tetrachord – also known as the 5th degree. (Fig 15).
In order to form the G Major scale in its entirety, the interval formula of tone, tone, semitone, {tone}, tone, tone, semitone must be applied. From this point, one can see that the G Major incurs a raising or sharpening of the seventh note or degree – from F to F. Therefore, a G Major scale is in accord with the G Major key signature (G, A, B, C, D, E, F#).
As one can easily deduce, the procedure of following the tone, tone, semitone, {tone}, tone, tone, semitone pattern from the upper tetrachord or 5th degree will yield all of the twelve major keys and scales around the Circle of Fifths.
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