A Player's Guide to Chords and Harmony by Jim Aikin Read Free Book Online Page A

would obscure the structure of the chord, for reasons that will be explained in Chapter Five. By learning the correct interval names, you'll build a solid foundation for more advanced concepts.
     

STACKING INTERVALS
    Already in this book you've seen a number of references to stacking intervals - placing one on top of another. The concept is simple, but a clear explanation won't hurt. When two intervals are stacked, the top note of the lower interval is the same as the bottom note of the upper interval. A few examples of stacked intervals are shown in Figure 2-8.

    Figure 2-8. Two intervals can be stacked by using the upper note of the first interval as the lower note of the second interval.

    As an exercise, you might want to choose a relatively large interval, such as a 5th or 6th, and work out which combinations of smaller intervals can be stacked to produce the larger interval. I've done this with the minor 6th in Figure 2-9. It's easy to do: Simply play the large interval on the keyboard, play any note between the two notes of the interval, and observe the intervals that this inner note forms with the outer two notes. In this case you're splitting an interval rather than stacking two intervals, but the results are the same.

    Figure 2-9. Any interval larger than a minor 2nd can be analyzed as two stacked intervals. Here are the primary ways of producing a minor 6th by stacking intervals. (Options such as C-D#-A6, which contain doubly diminished or doubly augmented intervals, have been omitted.)

     

INVERTED INTERVALS
    Generally, it's convenient to talk about intervals by stating the lower note first. When I refer to the interval C-G, for instance, you can safely assume that the C is below the G. But what about the interval G-C? Although the C is an octave higher than before, G-C contains the same two notes as C-G. But as Figure 2-10 makes clear, C-G is a perfect 5th, while G-C is a perfect 4th.

    Figure 2-10. The interval C-G is not the same as the interval G-C.
    These two intervals have a special relationship: The perfect 4th is called an inversion of the perfect 5th, and vice-versa. Another way to say this is that if we invert a perfect 5th by moving the lower note up an octave, we get a perfect 4th. We'll return to the subject of inversions in Chapter Three. In general, moving the bottom note of a chord or interval up by an octave (or, if necessary, two octaves) so that it's at the top produces an inversion. Likewise, moving the top note down by one or more octaves so that it's at the bottom inverts the chord or interval.
    Any pair of intervals that, when stacked, produce a perfect octave are inversions of one another. When two intervals have this relationship, we can also say they're complementary or reciprocal with respect to one another. The most important pairs of reciprocal intervals are shown in Figure 2-11. As you study this figure, you'll notice that inverting a minor interval always produces a major interval, and vice-versa. Inverting an augmented interval produces a diminished interval, and vice-versa. Inverting a perfect interval produces another perfect interval.
    The pairing of reciprocal intervals is important because inverting an interval leaves its harmonic identity and harmonic function intact. In other words, it sounds pretty much the same as it did before. You can verify this at the keyboard. Play the interval C-E, preferably by striking both notes at the same time. Then raise the C by an octave and play E-C in the same manner. Notice how similar the two intervals sound. In many situations, you can invert an interval in this way without changing the harmonic meaning of the passage. The sound will be slightly different, but the harmonic function of the chord that contains the interval will most often be exactly the same. (Figure 6-11 in Chapter Six provides a couple of examples of chords to which this rule doesn't apply.)

    Figure 2-11. When two intervals can be stacked to form a perfect octave, we