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Music Theory for Computer Musicians by Michael Hewitt

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12. Augmented and Diminished Intervals and Interval Inversions

So far, we have studied two distinct families of intervals—the perfect intervals, which include the first, fourth, fifth, and octave, and the imperfect intervals, which include the second, third, sixth, and seventh. There is yet a third family of intervals that we have not yet considered—the family of augmented and diminished intervals. Knowledge of these represents an essential foundation for the understanding and use of the augmented and diminished triads you will study in Chapter 18, “Chord Progressions and Root Movement.” It is also important knowledge for the understanding and use of artificial and exotic scales, which you’ll study in Chapter 22, “Exotic Scales,” and the use ...

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