generate D and B; D is the highest note in the chord-scale, but B is the last-born note, and has a higher vibration-number in the genesis.

Now we come to a remarkable arrangement of Nature. The minor does not grow in the same way out of this third chord's top. Two features come before us: first the minor chord grows out of the major, but it is *taken not from the top but from the middle*, from a rib out of his side. B, the middle of the major dominant chord; B, the last-born of the major genesis; B is the point of departure in the outgrowth of the minor mode. The feminine is a lateral growth from the masculine. Another feature: it *grows downward*, like a drooping ash or willow. Its first generated chord is its dominant, and its last is its subdominant. Its middle chord, like the middle one of the major, is its tonic. Still further, it is *generated by division*, not multiplication; B45 is divided by 3 and by 5 for the root and middle of this highest chord, E and G. E15 is divided by 3 and 5 for the root and middle of the tonic chord, A and C. A5 is divided by 3 and 5 for the root and middle of the lowest chord, D and F. Thus we have the whole generation of the elements of music, six generations of harmony, like the six days of creation. Up to this point the whole process and aspect is *inverse*; growing from a middle; growing downward; growing by division;- while the major is growing from the top; growing upward; growing by multiplication. But here the inverse aspect ends. The generating primes of the major are 3 and 5; 3 and 5 are also the generating primes of the minor. In this essential phase of their creation their comparison is *direct*, not inverse.

At the extremes of these two operations we find D the top of the major dominant, and D the root of the minor subdominant; and while all the other notes, whether produced by multiplication of the major roots or division of the minor tops, are the same in their ratio-numbers, the two D's, by no speciality of production, are nevertheless specifically diverse by one comma in their vibration-number, and make a corresponding diversity in the intervals of the two modes. These, the Ray and Rah of the Sol Fa expression, originate a very interesting and somewhat mysterious feature in this great twofold genetic scale.

This, then, is the mathematical origin and structure of the Genesis of [Scientific Basis and Build of Music, page 67]