The number of Diatonic Chords. In the major there are three simple chords, two compound chords, and two double compound, seven in all - subdominant, tonic, dominant, subdominant sixth, subdominant fourth, dominant seventh, and dominant ninth. In the minor there are the same number and order, making fourteen. It is not normal to the tonic chord to compound, but it may, in exceptional instances; the major tonic may, in a certain cadence, assume the top of the minor subdominant; and the minor tonic may assume, in a cognate case, the root of the major dominant.1
All compound and double compound chords are made up of notes already developed for the simple chords; there is no genetic developing of compound chords. Simple chords are all begotten in the genesis; they are true species; compound chords are only varieties of them.
Why do we compound? Because it produces variety, and variety is one of the aspects of the beautiful; Nature loves and abounds in variety, without violation of her unity. And further, all creation throbs with sympathy, one thing feeling and tending toward another, nothing content in isolation; and compound chords are chords reaching out after assimilation to an affiliation with other adjacent chords, that they may be able, through something in [Scientific Basis and Build of Music, page 70]