genetic scale

There was, then, something of truth and beauty in the Greek modes as seen in the light now thrown upon them by the Law of Duality, at last discerned, and as now set forth in the genesis and wedlock of the major and minor scales. The probably symmetrical arrangement of the modes, all unwitting to them, is an interesting exhibition of the true duality of the notes, which may be thus set in view by duality lines of indication. We now know that B is the dual of F, G the dual of A, C the dual of E, and D minor the dual of D major. Now look at the Greek modes symmetrically arranged:


Thus seen they are perfectly illustrative of the duality of music as it springs up in the genetic scales. The lines reach from note to note of the duals. [Scientific Basis and Build of Music, page 46]

A third cause of difference of contrast in notes is the individual character which belongs to them according to their place in the genetic scale - that is, their birthplace character - the amount, namely, of centrifugal force which they have inherited. [Scientific Basis and Build of Music, page 61]

The great Genetic Scale, major and minor, the seed-bed and nursery of all, is that from which first of all the natural scale of the fifth arises into existence; and three fifths are generated in the major ascending side and three also in the descending minor side of the twofold genesis, giving us six fifths in all. At the top of the ascending genesis we find the major octave scale standing solid and in its perfect order and proportion; and at the bottom of the descending genesis we have the minor octave. [Scientific Basis and Build of Music, page 66]

This great genetic scale, the all-producer, the all-container, extends over six octaves on each side; for it is not till high in the sixth octave we get B in the major, and it is not till low in the sixth octave that we get F in the minor. It is in the fifth octave, however, that the note which is the distinctive mark of the masculine and feminine modes is generated. D27 in the major, and D26 2/3 in the minor, distinguishes the sex of the modes, and shows which is the head and which the helpmeet in this happy family.2 On the major side F, the root of the subdominant chord, that is the chord which is a fifth below the key-note C, is the root of all. This is the beginning of this creation. If we call the vibration-number of F one, for simplicity's sake, then F1 is multiplied by 3 and by 5, which natural process begets its fifth, C, and its third, A; this is the root, top, and middle of the first chord. From this top, C3, grows the next chord by the same natural process, multiplying by 3 and by 5; thus are produced the fifth and third of the second chord, G and E. From the top of this second chord grows the third and last chord, by the repetition of the same natural process; multiplying G9 by 3 and by 5 we [Scientific Basis and Build of Music, page 66]

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. [Scientific Basis and Build of Music, page 67]

The simple natural scale is the fifth; the compound natural scale is the octave; the harmony scale, or chord-scale, is the three fifths; the great genetic scale is six octaves; for, like the six creation days, it takes the six octaves to give birth to the elements of which the wondrous structure of our music is built up; the birthplace of B, the seventh of the octave scale, is the sixth octave of the great genetic scale. The area of the twelve major and twelve minor scales is twelve fifths or seven octaves, the twelfth fifth being a comma and the apotome minor in advance of the seventh octave. This is a quantity so small that it can be ignored in real music; and the two notes, say E# and F, joined to close the circle of this horizon of our music world. E# is the top of the twelfth fifth, and F is the top of the seventh octave; and they are practically, though not exactly mathematically, the same note. Illustrations of this will be found among the plates of this work. [Scientific Basis and Build of Music, page 79]

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. [Scientific Basis and Build of Music, page 81]

The Octave being divided into 53 commas, the intervals are measured, as usual, by these, the large second having 9-commas, the medium second having 8, and the small second 5. These measures are then made each the radius by which to draw hemispheres showing the various and comparative areas of the seconds. The comparative areas of the thirds are shown by the hemispheres of the seconds which compose them facing each other in pairs. The comma-measures of the various thirds thus determined are then made the radii by which to draw the two hemispheres of the fifths. The areas of the three fifths are identical, as also the attitudes of their unequal hemispheres. The attitude of the six thirds, on the other hand, in their two kinds, being reversed in the upper and under halves of the scale, their attitude gives them the appearance of being attracted towards the center of the tonic; while the attitude of the three fifths is all upward in the major, and all downward in the minor; their attraction being towards the common center of the twelve scales which Nature has placed between the second of the major and the fourth of the minor, as seen in the two D's of the dual genetic scale, - the two modes being thus seen, as it were, revolving [Scientific Basis and Build of Music, page 113]

See Also

dual genetic scale
Genetic Root
genetic number
genetic origin
genetic scale
genetic relation

Created by Dale Pond. Last Modification: Wednesday December 30, 2020 05:12:12 MST by Dale Pond.