The Rhythms of the Universe
Let’s return to our table of the Great, or Last, Cooking. To understand what we are talking about, get a glance at Brouaut’s Frontispiece, the Organ Pythagorean Proportions , as well as the article which has originated the whole, Canseliet, the Art of Music & Weight.
the figures that you will find turn out to be very close to the range of Zarlino, but we find the same figures in the theories of the world:
– for semitones (1.066) we have: 1.0670 and 1.0622;
– for minor tones (1.1111): 1.1144 and 1.1113;
– for major tones (1.125): 1.1217 and 1.1247; doubling the tonic weight to close the octave, we have also: 1.1292;
– for minor third (1.200): weight 5/weight 3 = 1.20097; w1 x 2/w6 = 1.19956;
– for major third (1.250): w6/w1 = 1.25015; w6/w4 = 1.24999;
– for fourth (1.333): w4/w1 = 1.33394; w6/w3 = 1.33657; w7/w4 = 1.32772; w1 x 2/w5 = 1.33306;
– for fifth (1.500: w5/w1 = 1.50030; w6/w2 = 1.48633; w1 x 2/w4 = 1. 49932;
– etc. By doubling the eighth of the seven weights you will also get new third and other intervals. Admitting up to five centigrams of absolute measurement error, you get a relative error of 4 per 100,000 of each tone, up to 3 per 10,000 eighth.
Undoubtedly, the differences between the ratios of the cooking and the Western music intervals can not be due to inaccuracies in weighing. And that even if the differences derive from contingent influences, as an atmospheric disturbance. In any event, the alteration remains extremely small.
If, out of curiosity, one tries to place the results in a harmonic series, it is necessary, even in this case, starting from a fifth below the tonic. Here is a very close series:
Weight 1 W2 W3 W4 W5 W6 W7 W8?
48/32 54/32 60/32 64/32 72/32 80/32 85/32 96/32;
series which is derived from the following roundings:
48.0 53.842 60.005 72.014 80.025 85.013 –
rounding the group of third averages, fourth and fifth, mentioned above, and forming again the eighth, a for the accuracy are found the following values:
Weight 1 W2 W3 W4 W5 W6 W7 W8
164.7 185.3 205.9 219.6 247.05 274.05 292.8 329.4
As of weight 1 as the basis – as already measured before cooking – one will thus come to the theoretical series, in grams:
Weight 1 W2 W3 W4 W5 W6 W7 W8
164.7 185.3 205.9 219.6 247.05 274.5 292.8 329.4
One will get the same results with the harmonic scale, except the weight n. 7: 164.7 x 85/48 = 291.65. The equivalence with musical notes will then be:
Weight 1 W2 W3 W4 W5 W6 W7 W8
do re mi fa sol la si flat do
This range can be found all around the world: it is one of the ten Indian Thâta; or, among the Persian sects dastgâh, what is called rast-pandjgah; amomg the Arabs, between twelve main maquâmat, it bears the name of ouchaq.
Density Variations
When we have established comparisons we were talking of weights: we have to be able to distinguish between “measurements of weights” and “measurements of masses “, we focus on this point because if the mass increases the volume does not vary.
In the chapter on the Transmutations ( Le Laboratoire Alchimique) we have seen that the transmutations are in general accompanied by a change in the mass of the order of ±20%.
Let’s call “V” the volume and “D” the density,” I “the index of the initial metal,” p “that of the precious metal; according to Newtonian mechanics one should expect the following relationship:
Vi Di = Vp Dp (mass conservation).
But, since the mass varies, we need to evaluate that VP – and this alone, at least as regards the gold – will be modified:
Vp = K V’ (where “K” is the coefficient of variation).
The variation thus will oscillate between the theoretical volume and the actual volume:
K = Vp / V’p
The association of the metal and the energy embodied in the Philosopher’s Stone seems to undergo a mysterious law of equilibrium. On the surface, everything happens as if the matter, in becoming royal, goes to achieve a certain “size”, like a vegetable.
In the cooking things go otherwise, and the phenomenon, always of relativistic order, appears, if one can say so, even more strange.
Remaining fixed the volume observed, we say:
V x Di = V X Dn / In
being “i” the index of the first detection of weight; “n” that of a detection of weight between 1 and 7; I is the interval of the degree “n”; “V” and “D” are respectively the volume and density.
It follows that:
In = Dn/ Di
In this case is the density that varies! It behaves like a wave.
The Degrees of Fire
The student will observe the time intervals in this area, even small variations, and for the first time that of 22 minutes on 24 hour, that’s to say in minutes: 1440/1418: he will rebuild without difficulty the process, even what concerns the last parameter which we will discuss, or rather talk about: the temperature. Most of the authors have shrouded it in mystery, but Philalethes is sometimes generous. It is necessary, he tells us in his Rules:
“…… the degree of heat which can be obtained from the lead (327 °) or by the tin in the merger (232 °) ….. So give start to your degree of heat, for the kingdom where nature left you …..”
The investigator who will not fail to read the works of Fulcanelli and Canseliet, finds that the fourth degree indicates 340 for the second and 500 for the seventh.
It is only a question of scale; so the degrees of the Master of Savignies can be integrated into our system degree-gram by the relation:
T° G = T° Cans. x 2/3 * PA – 42.
His board of fire wheel can be inferred, even if you have a simple equation. For those who do not know how to count, here’s development:
1° degree 310
2° degree 340
3° degree 370
4° degree 390
5° degree 435
6° degree 475
7 degree 500
8° degree 555
And now, child of the science, ora, lege, relege, labora et invenies ( pray, read, re-read, work and discover).
See also Brouaut’s Frontispiece, the Organ Pythagorean Proportions , Canseliet and the Art of Music and Weight , Hieronymus Bosch and the Concert in the Egg and Piero della Francesca and the Philosophical Pendent Egg , The Secret Night Chant of a Stradivarius Tree ;