can briefly dwell on the law of the golden section which is based on the natural phenomena and is also marked in the Buryat epic. Man gradually came to the notion of the golden section as an expression of a certain harmony after having been observing for thousands of years the presence of some adequacy and order in the objects, processes and the interactions observed in the material world.
The golden section or the golden proportion divides something into the two parts so that the relation of the bigger or longer part towards the smaller or shorter one equals the relation of the whole towards the bigger part. This principle well coordinates the parts of the whole unit, it’s kind of the dynamic symmetry. This is found in the human organism, in the gene system, in the build-up of the ear, in the interlocation of the rod of retina of the eye apple, in the pulsation of the heart muscle, in the symmetrical biorhythms and the neuro-physiological structure of the brain, the proportion of the body and organs.
The key to its understanding might be found in the specificity of the mental activity of the human brain as an invariant of the betta-wave emerging during mental activity. Let’s recollect in this respect the ancient pyramids where one can observe the same phenomenon. This principle became an academic canon in architecture when it was understood that it was good to erect the building, the compositional properties of which should be invariant to the biorhythmic properties of man.
This principle is presented in painting too as it has been mentioned above. Its simplified variant is division of the canvas in proportion of 6 to 4 or 3 to 2 where the main figure should be located not strictly in the center. One can divide the picture into 5 parts then the golden section will be found in 3 to 2 relation. The main object is located in the point of the intersection. The visual and notional or semantic center may be located either in the right, left or the lower, upper part of the picture. This is prompted by the lay-out or the structure of the eye, the specificity of the activity of the brain and the regularities of the visual perception. Where there is the motion, growth and development, there is the principle discussed. In botany, biology this might be observed in the location of the scales in the cones of pine-trees.
It can be found in poetry as it has been mentioned above. Take, for instance, Pushkin’s novel “Eugene Onegin”. Its structure is based on the closeness to Fibonacci’s numbers: 8, 13, 55. Eugene’s letter to Tatyana breaks the last chapter into 2 parts: 32 and 19 verses. Let’s divide 32 by 19, we’ll get 1, 68 which is the criterion of the harmonic build-up in which the growth of the emotional strain is longer than the culmination and the fall.
In the compositional build-up of many musical works there is the highest point of culmination which is seldom situated in the central part of the work. In many eight-bar melodies of many composers like Skryabin, for one, the culmination is in the point of the golden section.
It helps to comfortably visualize something because it observes the laws of nature and psychology, physiology of the human perception. Everything in nature obeys that law: the eye-sight, the pulse of the heart, the brain biorhythm, etc. It is also observed in structuring of poems, music and painting, as we have already noted.
Roughly speaking, the relation 2 to 3, 4 to 6, 6 to 10 is best. For instance, the sculpture looks best if the pedestal is 3 parts and the figure is 2 parts. Fibonacci made up a series of the natural numbers which proved to be of great use. This is as follows: 1, 1, 2, 3, 5, 8, 13, 21, etc. The law of the formation of the terms of this series is quite simple: the first two members are 1, then each subsequent member is formed by adding up of the two preceding terms. For example: 2 = 1 +1; 3 = 1 +2; 5 = 2 +3; 8 = 3 +5, etc. The Fibonacci series is known not only to mathematicians but to naturalists and other specialists too.
It was not until the 90-s of the XX century that the principle of the golden section was first mentioned in the academic works of the Buryat Geser experts. The Buryat tales are noted for the specific structural build-up, the image-bearing units, but the Buryat scholars did not associate that symmetry with the principle of the golden section. It was discovered by a Buryat scholar S. Sh. Chagdurov. He devoted one of his books to the phenomenon of the Altan Kheblic which is a Buryat analogue of the golden section.
A comprehensive study of the role of this phenomenon in the Buryat uliger (epic) was carried out by D. B. Badmatsyrenova [2001]. The thesis is called “The principle of the golden section in the Buryat epic “Geser”. The “Altan kheblig” means the golden model. The “Geser” epic observes the laws of the poetical structuring, one of which is the principle discussed.
The “Altan kheblig” was first mentioned in the Buryat epic by Pyokhon Petrov, one of the best Buryat epic-tellers of the XX century. The principle appears when the uliger episodes are in dynamics, when there is the gradual growth, then the highest point, the culmination and, last of all, the fall or the end. This dynamic symmetry was studied in the various epics – uligers written down from well-known Buryat epic-tellers.
The academic collection of the musical folklore started in the 60-s of the XXth century by D. S. Dugarov. The uliger tunes are very old, they present kind of a melodious recitative. The uligers did not have a certain fixed melody. Each rhapsode possessed one or more tunes and used it when performing all the uligers (stories, epics) that he knew. The peculiarity of the Buryat folk music is pentatonism. The melody or tune is depended on the structure of the verse. The verse and the tune closely interacted. S. Sh. Chagdurov and D. B. Badmatsyrenova noted that the golden section point is usually in the third quarter of a musical phrase.
The golden section is marked in the compositional lay-out of the uliger (epic) and gives prominence to the culminating points which are found not in the center of the epical text but in its third quarter. The most important function of the golden section in the text is semantical, notional, dynamical, structuring and euphonic. It is the symmetry of the laws of motion and growth in nature.
Due to the principle of the Altan kheblig presented in the main constructive units of the epic of Geser the listeners could not but feel them. The rhapsodes and the listeners could not but get adjusted to the betta-wave which dominated and caused the feeling of joy and success. In the rhythmical build-up of the verse in “Geser” an asymmetric division into the syllables is observed, when in the first hemistich there are 5 syllables, in the second 3 syllables. The interrelationship of 5 to 3 is 1.66 which almost ideally corresponds to the proportion of the golden section.
In the scene of the struggle between Abai Geser and Orgoli tiger the beginning and the intensification of the action (384 lines) is one and a half times as longer as the culmination and the concluding lines (строка) (223 lines). The interrelation of the numbers 384 to 223 makes approximately 1.7 which is close to the mathematical expression of the golden section equaling 1.618. On the whole there are 607 lines in this scene which is one and a half times as longer as the number of the lines in the intensified action (384 lines). The relation of the two numbers, i.e. 607 and 384 is close to 1.6.
One can state that the principle of the golden section is traced in architecture, painting, poetry, music, as well as mathematics and the other areas of the natural and human activity. The principle of the Altan keblig, an original analogue of the golden section, is well presented in the text of the Geser epic which was called “the greatest epic of the humanity” by a well-known Russian poet and translator Vladimir Soloukhin. The shamans and narrators or story-tellers have good memory, artistry and expressiveness of speech. Owing to the gifted story-tellers and shamans, the skill for the masterly performance of the ancient pieces of poetry and prose remains well preserved up to now.
The religious cults and rituals
The ideas of the heavenly origin of the totemic forefathers of the Buryats as well as the ideas of the spirit-hosts of the localities, the shamans, the epical heroes are related to the archaic cult of the Eternal Blue Sky which is taken to be the highest divinity and the creator of all that is found in the Universe. The highest divinity, the Sky or the Heaven (tengri