For practical application, the musical connotations that lie concealed in Sanskrit sources are of the highest importance to psychology and to the sciences. As stated in The Secret Doctrine, I, p. 555: "Sound is a tremendous occult power," which western physics is commencing to discover through supersonic research. With respect to physiology, the body is described by H. P. Blavatsky in Studies in Occultism (Psychic and Noetic Action) as:
an Æolian Harp, chorded with two sets of strings, one made of pure silver, the other catgut. When the breath from the divine Fiat brushes softly over the former, man becomes like unto his God — but the other set feels it not. It needs the breeze of a strong terrestrial wind, impregnated with animal effluvia, to set its animal chords vibrating. It is the function of the physical, lower mind to act upon the physical organs and their cells; but, it is the higher mind alone which can influence the atoms interacting in those cells, which interaction is alone capable of exciting the brain, via the spinal "center" cord, to a mental representation of spiritual ideas far beyond any objects on this material plane.
As to the silver string, its metallic structure is not subject to alterations due to temperature, humidity and other terrestrial factors that affect organic matter most rapidly. Furthermore, experiment has indicated that the molecular vibratory rates of platinum, gold and silver are in the proportions of 3, 6 and 9. Also, the oscillatory equilibrium may be altered by vibratory impulses created by striking the same chord in three octaves, representing the third, sixth and ninth of the scale. The third, as dominant, may induce a rearrangement of the oscillatory vibrations. The harmonic sixth reduces the oscillatory range of vibrations, bringing the neutral, or laya centers (neutrons in physics) closer together in densification. The enharmonic ninth extends the vibratory range to effect a greater tenuity, or etherealization, in the mass. Hence, Blavatsky presents it as the psychologically spiritualizing "string" of the human harp that induces intuitive consciousness by the vibratory action of the pituitary body on the pineal gland.
The striking similarity that the basilar membrane in the ear bears to the keyboard of a piano has been commented upon by Sir James Jeans in his Science and Music. An amplification to include the entire physique has been discussed by J. W. Keely who stated:
The normal brain is like a harp of many strings strung to perfect harmony. The transmitting conditions being perfect, are ready, at any impulse, to induce pure sympathetic assimilation. The different strings represent the different ventricles and convolutions. The differentiations of any one from its true setting is fatal, to a certain degree, to the harmony of the whole combination.
All abnormal discordant aggregations in these resonating convolutions produce differentiation to concordant transmission; and, according as these differentiations exist in volume, so the transmissions are discordantly transferred, producing antagonism to pure physical action.
The question arises, what are these aggregations and what do they represent, as being linked with physical impulses? They are simply vibrometric resonators, thoroughly subservient to sympathetic acoustic impulses given to them by their atomic sympathetic surrounding media, all the sympathetic impulses that so entirely govern the physical in their many and perfect impulses (we are now discussing purity of conditions) are not emanations properly inherent in their own composition. They are only media — the acoustic media — for transferring from their vibratory surroundings the conditions necessary to the pure connective link for vitalizing and bringing into action the varied impulses of the physical.
In the technique of music, Daniel de Lange, draws additional parallelisms with the consciousness. He states in Thoughts on Music that we need three keynotes to form a scale and presents them thus:
Attention is drawn to the fact that everything in music has a threefold basis and De Lange summarizes this foundation as follows:
a. Three different elements: Melody-Rhythm-Harmony. b. Three notes, three times repeated for Melody. c. Three beats, three times repeated for Rhythm. d. A chord of three notes (in thirds) three times repeated for Harmony.
We may, then, relate Atman, or spirit, to Harmony, Buddhi, or soul, to Rhythm as the temporal relation between Duration and Time, and Manas, or mind, to Melody as a melodic living of life. With reference to the chords, De Lange's formula is:
a. Increasing of vital force I — V b. Diminishing of vital force I — IV c. Conclusion V — I
It should be noted that the primary classification of chords is:
Western music does not reach above the fifteenth harmonic, whereas Hindu music embraces the thirtieth. In the composition of the diatonic scale, the initiated Pythagoras accepted only the interval of the fifth.
Further, enlightening interrelations between man and the musical scale are set forth in The Musical Scale and Man: an Analogy, by George de Cairos Rego, Lucifer, 1893. The most pertinent points from this article were quoted in The Theosophical Forum for June, 1948.
Mathematically, we might say that the Bhagavad-Gita is a dissertation on how to construct a dodecahedron (first shape in Nature of Pythagoras) from the icosahedral form of the Astral Light and its reverse process, in order to perceive the divine pattern of the Cosmic Architect. In further explanation of the fact that "the Deity geometrizes," as stated by Judge, attention is invited to the brilliant exposition of the geometric processes involved by F. J. Dick. In his The Pythagorean Solids, he states:
In the first place, they may be all considered as generated by Twelve Points on the surface of the Sphere, at equal adjacent distances or by six diameters of the sphere mutually inclined at angles whose tangent is 2, the number of the octave in music. Joining each of the twelve with every other point, we have 66 lines, of which 36 are internal. Six of the latter being diameters, there remain 30, intersecting at 20 points, which give the 30 edges of the Internal dodecahedron. The 30 outer, or external lines of the 66, form the edges of the Icosahedron.
Joining one set of alternate corners of the Dodecahedron by 12 lines a Cube appears. So far, there are 33 points defined, including the center of the sphere. Joining opposite corners on each Cube-face by 12 lines, two interlaced Tetrahedrons appear. These define, by their intersection, 6 new points and 12 new lines forming the Octahedron, beautifully poised in the heart of the Sphere.
Thus only 39 points, including the central point, are needed to define the Pythagorean solids, only one solid form being repeated, the Tetrahedron, which in fact is seen to repeat itself ten times. For between the interlaced Tetrahedron corners and the eight faces of the included Octahedron, eight smaller Tetrahedrons are seen.
The interlaced Tetrahedrons suggest the origin of the plane symbol — the interlaced triangles; but the full beauty of the symbol does not appear until we notice that the axis of symmetry of the Tetrphedrons coincides with the diagonal of the Cube, and that the orthographic projection of all these on a plane perpendicular to the diagonal gives a perfect hexagon with the interlaced triangles in the center. The interlaced Tetrahedrons — one a reflection of the other — in fact, define the eight corners of the Cube. The Tetrahedron is "3" and the Cube is "4" (or 6). So we see one way in which the "three fall into the four," and why it is a septenary, and a decad, as well as a three, or a four, according to the various aspects and interrelations considered of the electric, rotary, magnetic, or vibratory forces symbolized by the various lines.
The number Five penetrates the whole system of the Five solids in a remarkable way. Thus there are 24 pentagons visible, and by joining other corners of the Dodecahedron, Five Cubes are seen, which of course produce Five Octahedrons, and twice that number of principal interlaced Tetrahedrons. Five has been said to be the Number of Life.
Confining ourselves to one rectangular system, we find Four axes of symmetry for the Tetrahedrons and Three for Cube and Octahedron. Thus there are really 73 principal lines in the complete system defined by the 39 points. A study of the three principal orthographic projections shows that the circle should be divided into 3, 4, 5, 6, parts, and the products of these, or 360 degrees. Certain angles are found in abundance, such as 36, 60, 72, 90, 108, 144; and their combinations and products by 10 and 12, and their multiples, give figures bearing a strong resemblance to the various cyclic periods of eastern chronology. Periodic orbits are vibrations on a large scale.
Twice the perimeter of an Icosahedron-face divided by the perimeter of a Dodecahedron-face is 3.1416, the value of pi used in all ordinary scientific and constructional work.
Cyclically, the 18 of the Bhagavad-Gita is the Chaldean period of 18 years in the Saros. The name is from Sar or circle and Saros was the Babylonian god whose circular horizon was the visible symbol of the invisible. The horizon, of course, is the plane, or diaphragm, that divides the upper hemisphere of 180 degrees from the lower. (See page 114, Vol. I, The Secret Doctrine.) Certain additional data may serve to supplement the foregoing outline. Sat, Chit, and Ananda have their lower hemispheric reflects in Atman, Buddhi and Manas. The Christians have the Holy Trinity, as have all other religions. It is epitomized in Aum, or A (Agni or fire), V (Varuna or water), and M (Maruts or air). In western theology it is AVM or Ave Maria. There are three generators of the key in music and three harmonic series. Also, there are three principal Lokas and five subsidiary ones; as well as three Upadhis. Six is the first perfect number that is equal to the sum of its aliquot parts. In the sixth race man will have six senses and these for the thrice-born who unites his Manas and Buddhi in his Atman make eighteen. Krishna in speaking to Arjuna, states that: "My Prakrit (Mulaprakriti) is divided into eight parts — earth, water, fire, wind, ether, mind, intuition, and egotism." Further, Krishna specifies: "Understand my Paraprakrit (Daiviprakriti), as something distinct from this. This Daiviprakriti is the one life by which the whole Universe is supported." In brief, it is the Holy Ghost of Christianity, or the active intelligence of self-consciousness. From it emanate all force or energic manifestations. As such, it is differentiated from its crystallized twin, Mulaprakriti, as substance or matter.
In elaboration, the 3 parts (mind, intuition and egotism) correspond to the 3 Gunas, Sattwa (light or truth), Rajas (desire or willed activity), Tamas (darkness or inertia). Kapila, author of the Sankhya philosophy, held that Mulaprakriti, or the essence of substance, had no existence in itself and was a combination of the 3 Gunas. Likewise, as a trinity, the three produce the 5 senses as instruments. They, in turn, produce the 5 subtile elements (sound, tangibleness, odor, visibleness and taste) together with the 5 Tattwas or ethers that are their transmissive agents. Lastly, the subtile elements produce the five gross elements, and their gaseous prototypes (Aether, hydrogen, oxygen, nitrogen and carbon). This gives 3 + 5 + 5 + 5 to equal 18. In the "Prakrit" of Krishna the 5 elements are 5/8 or .625, and this is the Golden Section or ratio. The total 8 of the "Prakrit" plus Daiviprakriti equals 9 and the ratio is a tone in music, and that of diameter to side of square of equal area in any circle as given in the Rhind Papyrus and as noted by Plato in Timaeus. These form the Octahedron of the solar forces as they lie within the dodecahedron of the Zodiac and, perchance, within the icosahedron of the Milky Way. To explicate, Krishna says:
Know that Prakriti or nature (substance) and Purusha, the spirit, are without beginning. And know that the passions and the three qualities are sprung from Nature. Nature or prakriti is said to be that which operates in producing cause and effect in actions.
Thus, whether it be in crystallography, botany and biology (Mendelian law), chemistry (Mendeleef's tabulation of elements), atomic physics or other science, the octave of the octahedron of solar forces and of harmony is the determining factor.
Placement of the Bhagavad-Gita chronologically gives it the dynamic character of its applicability to our own era. A paraphrase of the Bhagavad-Gita would read, "The Holy Song of God Himself, who, at the beginning of Kali-Yuga or the dark age, descended upon earth to aid and instruct Man." Kali-Yuga commenced with the death of Krishna in 3102 b.c. and it has 432,000 years to run. With respect to time, Krishna asserts: "There dwelleth in the heart of every creature, O Arjuna, the Master Iswara who by his magic power causeth all things and creatures to revolve mounted upon the universal wheel of time. Take sanctuary with him alone, O son of Bharata [India], with all thy soul; by his grace thou shalt obtain supreme happiness, the eternal place." We might glean from this that the time-space continuum spoken of so glibly by modern physicists is, still, terra incognita to the western mentality.
Specifically, the descents of Krishna are cyclical and the date of 3,102 b.c. does not mark the authorship of the Bhagavad-Gita. To Arjuna, Krishna states:
I am the Samvatsara among the years (which are five in number), and the spring among the seasons, and the Margasirsha among the months, and the Abhijit among the asterisms (which are twenty-eight in number).
According to the Commentary on the above:
This clearly points out that at one time in the first year called Samvatsara, of the quinquennial age, the Madhu, that is, the first month of spring was Margasirsha, and Abhijit was the first of the asterisms. It then coincided with the vernal equinoxial point, and hence from it the asterisms were counted. To find the date of this observation: There are three asterisms from the beginning of Mula to the beginning of Abhijit, and hence the date in question is at least 16301 — 3/7 X 90 X 72 = 19078 or about 20000 B.C. The Samvatsara at this time began in Bhadrapada, the winter solstitial month.
The three Gunas correlate force and matter in the six dimensions of space-time (length, breadth, thickness and past, present and future) . In conclusion, let us remember that the icosagon is the eighteenth rectilinear figure, and 18 squared = 324, which is the significant number of the entrance to Solomon's Temple. Through knowledge that evolves into wisdom and eventuates as worship, we may attain to "The Vision of the Universal Form." Then, we may say with Arjuna: "My delusion is destroyed; and by thy favor, Divine One, I have recovered my senses, I remain free from doubt, and will do thy bidding."
In order to discover the successive layers of scientific knowledge that lie concentrically concealed in the matrix, which is the Bhagavad-Gita, requires great erudition. It is as H. P. Blavatsky states written in Devanagari characters, with thirty-five consonants and sixteen vowels utilized to express the Sanskrit words. Each letter of that alphabet has a numerical equivalent as in the gematria of Hebrew, as well as other significations. Personal and place names may designate cosmological forces, astronomical functions, stellar bodies, or supramundane entities. Permutations, transpositions and the use of unknown Senzar terms may, also, serve to conceal the facts of physics that western science has commenced to investigate in such dangerous realms as atomic fission and supersonics. Finally, as asserted of the Vedas by Subba Row, there is "a distinct dual meaning — one expressed by the literal sense of the word, the other indicated by the meter and the svara-intonation."