to separate people or things into smaller groups or parts
to have separate parts, or to form into separate groups
to separate something into smaller parts and share the parts between people
to keep two or more areas or parts separate
to do a mathematical calculation to find out how many times a number contains a smaller number. This is usually shown by the symbols - or /; the inverse of multiplication or times
in a mathematical calculation, to contain a smaller number a particular number of times with no amount left over
to split

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]

When higher or lower octaves of any note or scale are wanted for convenience of comparison, multiply or divide by two, the octave-producer. [Scientific Basis and Build of Music, page 83]

The primitive laws of any science should be capable of succinct statement, but in combination with others they become more complex and delicate, and error is proved if in the developments they do not echo each other. If, therefore, musical harmonies are correctly gained, the same laws will develope harmonies of colour, and will agree with the colours of the rainbow, the circle of which is divided by the horizon. All who are interested in the laws which regulate these two sciences will doubtless know the interesting lectures delivered by W. F. Barrett (Professor of Experimental Physics in the Royal College of Science, Dublin), and the article written by him and published in the Quarterly Journal of Science, January, 1870, entitled "Light and Sound; an examination of their reputed analogy, showing the oneness of colour and music as a physical basis." I will quote shortly from the latter for the benefit of those who may not have met with it. "The question arises, Has all this ├Žsthetic oneness of colour and music any physical foundation, over and above the general analogy we have so far traced between light and sound? We believe the following considerations will show, not only that it has some foundation, but that the analogy is far more wonderful than has hitherto been [Harmonies of Tones and Colours, On Colours as Developed by the same Laws as Musical Harmonies1, page 18]

See Also

Electric Division
Figure 17.02 - Gravity divides multiplies and balances Light and Sound
Figure 2.4 - Undivided Light divides into all that is
6.5 - Cubes divide into six tetrahedrons

Created by Dale Pond. Last Modification: Sunday February 14, 2021 04:43:45 MST by Dale Pond.