Atorène’s course starts with the presentation of the Philosophical Week, which is the musical interval of the Last Cooking, then continues with the musical notation and Law of Attraction. Before getting to the Egg’s Densities Variations, and Degrees of Fire, the Canseliet’s apprentice provides the reader unfamiliar with the mathematical laws of the proportions of the sound with the construction of notes, intervals, and scales, and Pythagoras, as well as Zarlino’s, range.
The pages I have translated from “Le Laboratoire Alchimique”, 1981, are a real and comprehensive music theory course to provide solid foundations to figure out the variations of sounds from Canseliet’s Philosophical Egg during the famous seven whistles and the philosophical and mathematical implications of the resulting musical scale, through the ponderal (weight) accretions.
Readers unaware of music theory are recommended not to skip the theoretical parts to jump to the chapter on the Rhythms of the Universe, as the egg behaves just like a music resonator. And only by knowing the music theory might we understand what Canseliet did not say.
My translation from “Le Laboratoire Alchimique”, 1981:
Music Theory Course for Alchemists: The Week
Where do the days of the week come from?
From ancient Egypt, answers Dio Cassius Cocceianus (Nicaea in. 155 – in Bithynia. 230). He’s right, Egypt is the melting pot of the Week, and the passage of the witness up to our civilization was carried out mostly by Jews.
Monday is the day of the Moon, Lunae dies; Tuesday day of Mars, etc. Saturni dies is very deformed and was adopted by the Jews on the Sabbath (latin: sabbatu, greek: sabbaton, the Jewish sabbath, the day of rest, Spanish: sabado) and Sunday is the Lord’s day (latin: dominica, implicit diem: day of the Lord, Dominus). The English here is clear: for Saturday: Saturday, the day of Saturn; and on Sunday, the day of the Sun: Sunday; or, in German, sonntag (day: dies in latin, day in English; tag in German. Sole: solis, in latin; sun in English; sonne in German).
So we have the sequence of the celestial bodies Moon, Mars, Mercury, Jupiter, Venus, Saturn, and the Sun. A priori seems to be before a common disorder, as the progression gives heliocentric Mercury, Venus, Earth, Mars, Jupiter, Saturn, etc., while the classification using the ancient wisdom is: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn.
A large number of investigators question this point. We will provide them with an explanation from the range of Pythagoras.
We have the planets in the order in which, according to the Tradition, they dispense their influences on the athanor and associate the sounds emitted by the philosophical Egg. To simplify, let’s call them according to the usual succession of notes in the solfeggio (without seeking a rigorous value).
Day of Moon 1 sound do C
Day of the Mercury 2 sound re D
Day of Venus 3 sounds mi E
Day of the Sun 4 sounds fa F
Day of Mars 5 sounds sol G
Day of Jupiter 6 sounds la A
Day 7 Saturn 7 sound si B
Let’s continue now, as the master of Samos, the great Pythagoras, by successive fifths, with a reduction of the octave. We get, starting from do:
do
do x 3/2 = sol
sol x 3/2 = re
re x 3/2 = la
la x 3/2 = mi
mi x 3/2 = si
si x 3/2 = fa ( being strict, fa sharp)
And ordering the planets that govern the area in relation to the succession of fifths, we immediately obtain the exact order of the days of the week. They are, in some way, the “chorded days” of the Hebdomas Hebdomadun, the week of the weeks:
do = Lunae dies = Monday
sol = Martis dies = Tuesday
re = Mercurii dies = Wednesday
la = Jovis dies = Thursday
mi = Friday dies = Veneris
si = Saturni dies = Saturday
fa = Solis dies = Sunday
We have seen that the seven notes indicated by Canseliet in his letters do not match what we have read above. So let’s go on to find out.
Sounds Features
The simple sounds, which don’t exist in nature, are caused by a sinusoidal vibration: they can appear dull and monotonous. The superposition of many sinusoidal vibrations forms complex sounds and suddenly takes life and develops depth.
As every sinusoidal vibration is multiple or submultiple of another, it comes with arbitrarily defined fundamental frequency or fundamental sound. The other frequencies will then its harmonics which Boetius (1), in Middle Ages, did compare to subsequent circles originated by a stone thrown into the water.
Without mentioning the lasting, one’s ear detects the musical sound through three qualities:
– Intensity. The sound is barely audible (the amplitude of vibration is weak) or, on the contrary, so strong that it is necessary to close the ears ( large amplitude vibrations ).
–Pitch. The sound is sharp (high frequency) or grave ( low frequency. By convention was fixed in 1959, the “la” at 440 hertz. So to understand, we add that the human voice has an extension, approximately to the set of different textures (2), ranging from 80 to 1200 hertz.
–Timbre. A violin’s la (A) cannot be confused with the piano la (3). Timbre is caused by the harmonic frequencies of a fundamental sound; multiples and their fundamental sound, each with their amplitude, are produced by the same instrument simultaneously.
We would need to add the transitory ( transitory phenomenon). Timbre characterizes the steady state of a sound, but between the start and steady state, the harmonics vary continuously. The transitory is equally produced at every modification of sound; in the same way, music and speech hardly present fixed sounds. Equally, they are mostly composed of transitory, which precisely determines the real timbre.
The musical effect of two simultaneous sounds depends on the ratio of their frequencies, not on the absolute value of the frequencies: is this ratio to be called interval?
Manlius Severinus Boetius ( 480 around 526 A.D ) philosopher and lettered in the musical field. His fundamental work is De institutione Musicae, which became the main source for medieval theorists. The musical elements are defined according to the Pythagorean theory;
Texture; register of the human voice in the most favorable field of singing;
The “la” is the central la of the piano keyboard;
Intervals
One can measure the sound pipes’ lengths ( and canes) and vibrating strings to determine intervals. The ancient didn’t talk of frequency but length. For a sound frequency to appear inversely proportional to the length of a canna or string, it is enough to pass from one to another to reverse the ratios.
Conversely, in one attaches various masses to the end of equal-length strings, the frequency is, this time, proportional to the square root of the mass.
And if the strings are of different materials, the frequency is inversely proportional to the density square. The same law applies to the gases insufflated in the musical pipes: if one increases the temperature, the gas becomes less dense, and the sound becomes sharper.
For instance,
1) if a sound pipe emits a do (C) with gas at 300 °, at 450 ° C – taking a thermal expansion coefficient of 1/273 – we will have
2) if a string of density 16.5 emits a do, increasing the density to 20.6 we will have:
do x √² 16.5/20.6 = do x 1/1.117 = si flat,
( Octave down. Applying this law to cooking, the third sound would be lowered, just in theory, of a minor key).
It is time to define the intervals, which were empirically selected by the ear. It was the ear to have headed and set the music rules. Why do our senses detect the laws of harmony? This is a good mystery.
The octave interval 2/1
The frequency of a sound is double of the other b.
a = 2b
The fifth interval 3/2 = 1.50
It forms the arithmetic average of the octave:
The fourth interval 4/3 = 1.333
It forms the harmonic average of the octave:
The major third interval 5/4 = 1.250
The minor third interval 6/5 = 1.200
We will not enumerate them all, but it’s already possible to understand why the musicians use only certain sounds – notes -, chosen to present harmonious intervals between them.
Anyway, we note the beautiful numeric association:
2/1, 3/2, 4/3, 5/4, 6/5.
Theorists have tried to make a simple musical range compatible with the Ear’s needs. Building a musical scale means ordering notes within an octave.
To be continued at Atorène, Music Theory Course for Alchemists. Part 2