As a consequence of all these things, these intervals are called “Perfect”.
On the other hand, notes F and G are very affine to note C, due to the particular relationships among their frequencies, from the physical point of view. If we compare Table 3 with Table 1 in Chapter 2, we will see that, apart from the 1 st and 8 th intervals, only the 4 th and 5 th have the same number of whole and half steps in both the ascending and the descending scale. Intervals in the descending C Major scale. Table 3 shows these intervals and also indicates the number of whole steps contained in each of them. It is very illustrative to verify that, in the descending C Major scale, every interval between the highest C and any other note in the scale is minor or Perfect. Therefore, the inversion of the interval can be understood in these two different ways. But, in descending order, there are 4 natural notes (D – C – B – A) and a distance of 2.5 W, that is, a P 4 th. Thus, between D and A there are 5 natural notes in ascending order (D – E – F – G – A) and a distance of 3.5 W, so it is a P 5 th. But the same result is reached by changing the ascending character of the interval to descending. In practice, the inversion of an interval is achieved by raising the lower note one octave or by lowering the higher note one octave. So, in the first one, the P 5 th becomes a P 4 th (5 + 4 = 9 and both of them are P) and, in the second one, the M 3 rd becomes a m 6 th (3 + 6 = 9 and M becomes m). We can check these two rules in the two previous examples. The Perfect interval, however, remains Perfect. When inverting intervals, the Major is transformed into minor, the minor into Major, the Augmented into diminished, the diminished into Augmented, the double Augmented into double diminished and the double diminished into double Augmented. The sum of the interval numbers of a given interval and its inversion is always 9.In the inversion of intervals, the following two rules apply: And, if we invert the interval E – G, which is a M 3 rd, we obtain the interval G – E, which is a m 6 th. Thus, if we invert the interval D – A, which is a P 5 th, we obtain the interval A – D, which is a P 4 th. The inversion of an interval consists, simply, in interchanging the order of its notes. Hexatonic scales and their associated chords Diminished scales and their associated chordsġ6. Chord finder and the major-minor systemġ5.