Simple and compound INTERVALS

So far, we examined only intervals not bigger than an octave. Such intervals are called simple intervals. However, intervals bigger than an octave, like the ninth, tenth or eleventh occur quite often. Such intervals are called compound intervals. 

The good news is that knowledge of the simple intervals can be easily applied to compound intervals. The key is to break a compound interval to an interval spanning one or more perfect octaves plus a simple interval. This is another application of the octave equivalence principle. For instance, a ninth can be broken to the perfect octave plus a second. From this, it follows that the interval qualities of the ninth are the same as the interval qualities of the second: diminished, minor, major and augmented. The next figures illustrate this.

Figure: The major ninth as the perfect octave plus the major second

Figure: The minor ninth as the perfect octave plus the minor second 

Figure: The diminished ninth as the perfect octave plus the diminished second

Figure: The augmented ninth as the perfect octave plus the augmented second  

The number of pitches in a ninth can be calculated as the number of pitches in the perfect octave plus the number of pitches in a second minus 1. The next table illustrates this. All that was said in this chapter for the interval of ninth can be similarly applied to any compound interval.