Interval Structure

Each major tetrachord must be present in two different major scales.

-Diagrammed in Circle of fifths/Circle of fourths:

-If we go clockwise around the circle, moving up in pitch is a fourth interval, moving down in pitch is a fifth interval.

-If we go counterclockwise, moving up in pitch is a fifth interval, moving down in pitch is a fourth.



A major scale is (WH,WH, HS), WH, (WH, WH, HS).

We can derive the major scale from the circle as follows:

-Moving in a clockwise direction (starting from C), for each scale in the circle add another flat. The note that gets the flat is the fourth note in that scale. This can be done until C flat major is reached (Then we’d have to start deleting flats and end up with identical key signatures for different major scales? No, we just wouldn’t be able to construct the scales without introducing sharps.)

-Moving in a counterclockwise direction, we add a sharp to each new scale. The note that gets the sharp is the seventh note in that scale. This can be done until the C sharp major is reached.



A diatonic interval is created when the upper note of an interval is contained within the major scale built from the lower note.

-A diatonic interval is classified as major (2nds, 3rds, 6ths, 7ths) or perfect (4ths, 5ths, and 8ths)

-perfects are distinguished from majors as perfect intervals occur in nature (as part of the overtone series of the lower note?)

A chromatic interval is created when the upper note of an interval is not contained within the major scale built from the lower note.

-chromatic intervals include minor, augmented, and diminished



A major interval reduced by a half step becomes a minor interval

-A major 2nd interval is a whole step
-A minor 2nd interval is a half step

A minor interval reduced by a further half step becomes a diminished interval

A major interval increased by a half step becomes an augmented interval

A perfect interval reduced by a half step becomes a diminished interval

A perfect interval increased by a half step becomes an augmented interval


– minor 7th has the same span as augmented 6th

– diminished 7th has the same span as major 6th

- diminished 5th has the same span as augmented 4th

Four basic types of triad:

-major: root, major 3rd, perfect 5th

(since major and perfect intervals are contained within the scale on which they’re built, this triad is always within the scale of the root)

-a major triad occurs from the 1st note (1st-3rd-5th), the 5th note (5th-7th-9th), 9th and so on of a major scale

-minor: root, minor 3rd, perfect 5th

-if we build a triad from the second (2nd-4th-6th), 6th note (6th-8th-10th), 10th and so on of a major scale, a minor triad naturally occurs

-augmented: root, major 3rd, augmented 5th

-this triad is not found within any major scale. This accounts for the somewhat restless quality associated with the augmented triad.

-diminished: root, minor 3rd, diminished 5th
-a diminished triad naturally occurs starting at the seventh degree of a major scale