Research article
Issue: № 3 (7), 2016


This paper considers a special type of theoretical comment on language form and geometrical inherent in modern Chinese, and Korean linguistics. Relevant concepts such as functional geometry, a diagonal geometry, reflecting the theoretical description of the specifics of tone and language which is a development in linguistics of the ancient Chinese geometrical formal logic associated with generating capabilities of the operation the introduction of the "definite description".

Robert Kilwardby – Archbishop of Canterbury – who introduced the notion of universal grammar in Comments to Presciano noted that the subject of science should be the same for all people [13]. The subject of grammar – relevant language exists in the mind, in abstraction from the concrete forms. R. Kilwardby compares the grammar with geometry: just as geometry is distracted from the differences in form and grammar needs to be distracted from the superficial differences between the languages.

Modern Oriental linguistics quite successfully used the idea of geometrization of linguistic forms primarily phonetic. Chinese linguistics in considering phonological perspective draws on ideas of functional geometry, which allows scientists to formalize the phonological change specifications and to demonstrate differences in the rules of functioning of the units of the phonetic level in the tonal languages/ This rules differ from the generally accepted rules governing the use of the language and behavior of the linguistic sign.

S. Duanmu [7] creates functional geometry for the analysis of the standardized Chinese language which based on articulatory characteristics



Fig. 1. Functional geometry for the analysis of normalized Chinese [7]


The sound in the phonological geometry S. Duanmu correlated with the units of the parameters which define the fuzzy boundaries of the segment more precisely, the contours of the last, define the location of the sound phenomenon in space, in General, and tonal space, in particular. Such a concept allows to synthesize various approaches to the analysis of the phonetic level, primarily tonal language and to harmonize different levels of phonological analysis.
John Goldsmith [89] notes that a multi-level representation provides a solution to the conceptual problems raised by the feature asynchrony in connection with the matrix formalism. If we recognize a function is not a matrix entities, and independent groups or segments with their own rights, certain specific principles of grouping and rules correlation with acoustic effects, it is quite natural to assume, as suggested by John. Goldsmith that they can use to illustrate the behavior of the real sound associations and to engage in processes such as enlargement, reduction, erasure and insertion.

The phonetic content of the segment is the unit of consideration the phonetic language system in the  feature geometry is deployed at two levels: feature level and class level (including the root). The class level consists of the root tier,  the level of the laryngeal tier, the level of the supralaryngeal tier,  level "space", "manners and tone level.

 M. Halle and G. Clements [9]  consider  that much in the production of sound depends on the capabilities of the geometry of the oral and nasal cavities of a subject, generating a speech unity. M. Halle and G. Clements propose the classification of geometries and configurations of the oral and nasal cavities during the formation of the sound, including four categories of parameters:

a. laryngeal configuration;

b. degree of nasal cavity stricture (open/closed);

c. degree and type of oral cavity stricture;

d. a pairing of an active and a passive articulator.

The tonal geometry can be explored as the form of the feature geometry.  M.J.W. Yip [19]  summarizes four possible models of tonal geometry.  

The first model is connected with such cases  when  tone features are entirely independent of each other, and there is no tonal node      dominating them both [17], [10].  



Fig. 2 .  The geometry of tonal balance (tone of harmony)


The second model can be found when  two tone features are sisters under a Tonal Node, and each half of the contour   tone is entirely independent [4], [5], [6], [15].



Fig. 3 .  The geometry independence of tonal contours


The third model is releted to the register features.   The register feature is the Tonal Node, dominating the tone features [18], [10].  



Fig.4  The geometry of the identities of register-based characteristics and tone site (tone of Bush)


The forth model  is connected with tone features which are dominated by a node of their own, called Contour, which is a sister to the register feature, and where both are dominated by a Tonal Node [1], [16]. 



Fig.5. The geometry of synthesis of the tonal contour and tonal characteristics


Geometric ideas are also relevant characteristics of the syllabic structure of the Chinese language. Describing synchronous phonology and creating a scheme for one of the traditional Chinese language syllabic patterns, Ch.-Ch. Cheng  [3]  based on the functional geometry. As for Mandarin Chinese syllabic system with the prominent scientist finds it necessary to speak about existence of two basic types of models:

a) The Initial-Final model

声母—韵母样式                   shēngmǔ – yùnmǔ yàngshi

b) The Onset-Rime model

节首—韵基样式                        jiéshǒu – yùnjī yàngshi

Modern Korean linguistics addresses the problem of identifying the correct sound values of the vowels in the study Hunmin jeong’eum haerye [Explanations and Examples of the  Correct Sounds for the Instruction of the People, Haerye hereinafter]  document 1446, which is a guide for studying and mastering the alphabet Hunmin Jeong’eum [Correct Sounds for the Instruction of the People, Jeong’eum hereinafter], introduced in the reign of Sejong and significantly changed the spiritual and the language situation.

The interpretation of vowels in Haerye based on the philosophy of Yin and Yang and the law of harmony. At the time of creation of the Korean alphabet, the principle of vowel harmony, (G2-principle) (VH – vowel harmony), according to Y.-K. Kim-Renaud [Kim-Renaud], has provided a taxonomy of word boundaries in contrast to the modern Korean language in which G2 is the principle used with respect to sound symbolic words and some an initial vowel change.
Many linguists believe that the Great change in the system of vowels in the Korean language took place in the XV century and is still the vowel system has remained virtually unchanged medieval Korean vowels are not different from modern vowels of the Korean language.

A comparison of the two systems of vowels, or rather, two States of the Korean vowel space, based on the diagonal of the analyses Ch.-W. Kim have to create a "folded", "strapped" diagonal graphic image contact of these states, or a contact space in time with itself. Very similar to each other systems – the harmonic groups – separated by a diagonal. Ch.-W. Kim [11] describes the Korean vowel harmony as a diagonal harmony, or the harmony of the diagonal:


Fig. 6.  Korean diagonal vowel harmony, or the harmony of the diagonal (Ch.-W. Kim)


Feature Haerye is also a method of specificity of articulation of a vowel sound and explains the mechanism procedures for the preparation of the body – the oral cavity as a resonating environment and some architectural structures to the signification itself, in sound and through sound. The construction of such "organizational" comment draws Chinese.
Chinese characteristic pair 淺” and “深” represent the acoustic features of ‘sharp’ and ‘heavy’ respectively, which reflect the perception of the hearer. Features of sharp or heavy correlate directly with the position of the tongue − front or rear. Chinese characteristic pair “縮” and “不縮 Express the retraction of the tongue, creating a perceived sound. And finally, a rather unusual feature of the “蹙” can be translated for linguistic purposes as ‘closed but not completely’, or often ‘inverted’, ‘assembled’. In other words, the expression "口蹙" could mean "lips that are collected in such a way that his mouth opened so slightly as possible when pronouncing the sound". In turn, “口張” describes stretched lips.

The value of descriptions damn vowels given in Here, is seen in the fact that through verbal commit simultaneity of the movement of the lips and formed the state of the mouth and oral cavity – architecture of the oral cavity, is created and fixed motor-dynamic" image of the sound level of the conditioned reflex.

The feature  geometry and   diagonal geometry,  provide an absolutely elegant formalization of phonological rules developed in generative phonology, and adapts this system of rules in functional-theoretical perspective to current needs speech synthesis.

However, noting the linkage of the functional geometry of the ideas and formalisms of generative grammar N. Chomsky, you should not forget about the ancient Chinese geometrical formal logic, for the theoretical constructs which the obvious importance of drawing, figure, scheme.

According to A. A. Krushinsky [14], a drawing depicting the device of reasoning, not just illustrating it, declares itself in the following two facts of Chinese culture: 1) the nonlinear structure of ancient Chinese texts, leading to schemes of similar texts. 2) trigrams and hexagrams "I" directly consisting of the features.



Fig. 7.  Descriptive geometry trigrams [14]


Such reasoning is in the class of reasoning built according to the fundamental classification scheme of the "three materials" (sancai) : Sky-Earth-Man. A. A. Krushinsky arguments of this type determines how the TM-reasoning.

Originating power of elementary deductive TM-scheme due to the odd dynamic nonequilibrium nature of the number ‘three’. Identifying hexagrammos prototype of one or another of TM-reasoning allows us to recover the logic of it. TM-arguments represent the implementation of a logical structure, namely the operation of introducing the so-called "definite description".

Naturtalent, in this case, is understood as existential, quantificare necessary for the introduction of a definite description. While the model-theoretic aspect of the existential quantification, i.e. not syntactic,  by  the semantic level  of descriptions. 

Thus, the use of geometrization of modern Oriental linguistics in the description of the phonetic features of tonal language should be considered not only as another confirmation of the explanatory potential of generative grammar, but as a continuation and development of geometrical ideas of  ancient formal logic.


  • Krushinskij A.A. Logika «I czina»: dedukciya v drevnem Kitae [Logic "I czina": deduction in ancient China]. – M., 1999.