circumstances. And if we may add D to the subdominant chord of d F A C, so we may also, in other circumstances, add the subdominant chord as harmony to D, thus - D f a c, and no discord occur. There is only the interval of a second between F and G in this dominant 9th, and only an interval of a second between C and D in this subdominant 6th; a second standing alone is a discordant interval, as a poison by itself may kill; but as a poison by the processes of nature in chemistry compounded with something else may be an excellent medicine, so may a second when mixed and compounded with something else in music become an excellent harmony. Music is a great apothecary, skillful in compounds.
Having found the framework of the major scale by multiplying F1 three times by 3, find the framework of the minor by dividing three times by 3. But what shall we divide? Well, F1 is the unbegotten of the 25 notes of the great genetic scale; B45 is the last-born of the same scale. We multiply upward from F1 for the major; divide downward from B45 for the minor. Again, B45 is the middle of the top chord of the major system, a minor third below D, the top of that chord, and the top of the whole major chord-scale, so B is the relative minor to it. Now since the minor is to be seen as the INVERSE of the major, the whole process must be inverse. Divide instead of multiply! Divide from the top chord instead of multiply from the bottom chord. Divide from the top of the minor dominant instead of multiply from the root of the major subdominant. This will give the framework of the minor system, B45/3 = E15/3 = A5/3 = D1 2/3. But as 1 2/3 is not easily compared with D27 of the major, take a higher octave of B and divide from it. Two times B45 is B90, and two times B90 is B180, and two times B180 is B360, the number of the degrees of a circle, and two times B360 is B720; all these are simply octaves of B, and do not in the least alter the character of that note; now B720/3 is = E240/3 = A80/3 = D26 2/3. And now comparing D27 found from F1, and D26 2/3 found from B720, we see that while E240 is the same both ways, and also A80, yet D26 2/3 is a comma lower than D27. This is the note which is the center of the dual system, and it is itself a dual note befittingly.