Empirical Aesthetics: Informational Approach|
Proceedings of International Symposium (Taganrog, Russia, 1997) pp.80-85
Scale Hierarchies and Culture-Historical Universality
Pavel B. Ivanov
Troitsk Institute for Innovation and Fusion Research (TRINITI)
The application of information theory and statistical methods to
the study of art phenomena may be quite successful if its purpose
is to study information processes accompanying aesthetic perception,
rather than reduce art to an abstract communication system.
Quantitative models are to extend the range of expression means
available to artists and indicate essentially new possibilities —
but never replace artistic creativity by computer simulation.
One of such models is presented in this paper. Being based on the
idea of informational comparison of elementary conceptions
(subjective representations) proposed by G. A. Golitsyn ,
this model is more than just a quantitative extension of the
scheme, since it pays particular attention to the qualitative
differences between the distinct levels of human activity.
Artistic creativity and aesthetic perception are hierarchically
organized. However, in different situations and aspects, this
hierarchy may unfold itself differently, manifesting various
hierarchical structures . A quantitative model built in the
framework of hierarchical approach has uniformly described all
the variety of scale phenomena in music, including the historical
development of scales along a number of cultural lines [3,4].
The model shows the ways of the formation of coherent collections
of pitch zones (scales) containing a number of subscales, some of
which may, in a definite context, play the role of modes, while
some other may be related to harmony. The theoretically calculated
parameters of the structures can be used to predict the principal
features of music based on a particular scale, allowing to
particularize and extend the set of expressive techniques
established in the musical practice. The important corollary
of the theory is the relativity of consonance and dissonance,
since the quality of a sound depends on the perceptive adaptation
to a specific collection of pitch scales.
The development of the psychological side of the theory along
the line of the well-known A. N. Leontiev's theory of activity has
discovered analogous mechanisms in visual form perception, thus
leading to the visual analogs of pitch scales [5,6]. Thus,
the curves in the plane have are akin to the melodic movement,
while plane figures resemble the chords. Both the discreteness
of the set of distinguishable objects and the possibility of
expressive variations within the respective zones have been
preserved in this way. Of course, the difference in the
"material" makes the perception of intrinsically
similar aesthetic phenomena apparently different; moreover,
the activities underlying the formation of graphic and pitch
scales are analogous in a limited region only, albeit rather
The parallels in the development of pitch scales and graphic
scales indicate that the processes of the same level usually
coexist in every particular culture, so that the mode of pitch
perception correlates with the mode of visual form perception
in any historical period. One might expect such correlation
for all the other forms of aesthetic perception, which would
support the hypothesis that cultural development must generally
proceed though an objective sequence of stages, which are called
culture-historical (or simply cultural) formations
. Within a definite cultural formation, the ways of people's
interaction with their material and social products are
relatively uniform, while the change of cultural formation
is associated with a significant shift in people's spirituality.
The process of the development and alteration of cultural
formations is relatively independent of economic and social
development, being intrinsically related to it.
The preferable usage of particular scales may be an indicator
of the stage of cultural development. If a zone structure has
formed in a certain area of perception, it may be transferred
to any other areas, thus becoming a universal categorization
base. In this sense, one could speak of "pentatonic"
or "diatonic" culture, and the quantitative analysis
of a single aspect of the spirituality of some historical
period (e.g. its art) may provide information on the culture
as a whole.
Graphic analogs of pitch scales originate from the similarity
of the schemes of a certain activity, namely, one-dimensional
categorization. The perception of such parameters as color,
or timbre, is known to be essentially many-dimensional, so that
a direct correspondence with pitch perception seems problematic.
However, according to the principle of the universality of
hierarchical scaling, one may suppose that color perception
should pass the stages similar to the levels of pitch perception,
with the formation of analogously organized scales (zone
structures). Psychophysical and psycholinguistic experiments
reveal relatively few basic categories in color perception,
which do not directly correlate with the spectral characteristics
of light and cannot, in general, be linearly ordered. The
experience of conform transformations of abstract paintings
acquired by the author together with French artist Guy Levrier 
supports the discreteness of the set of qualitatively different
variations and its zone nature.
One might conjecture that the informational mechanism of
one-dimensional categorization is the key to the development
of any other categorization schemes, the formation of relatively
omplex forms being mediated by the cultural crystallization of
one-dimensional scales, establishing them as a kind of standard.
This may be the cause of a delay in the development of zone
structures in color perception as compared to the development
of pitch or graphic scales.
Literature is one more branch of art where scale-like zone
structures can be discovered. The artistic usage of language
is different from that of everyday life, science or philosophy.
The conceptual basis of speech would not dominate here, and
the main function of language in the arts is to produce forms.
Thus, for instance, poetry intensely exploits the phonemic
side of speech, so that it is often more important how it
sounds than what it means in a verse. The transition to
the internal speech makes semantics rather than voicing the
material of art, and the zone structures arising here are
similar to those discussed above. This level often dominates
Semantic discreteness is apparent in epic genres: as a rule,
the narration centers on a few main characters interacting
through the typical positions in a number of standard situations.
A literature type is a zone of possible variants of behavior,
and the violation of zone boundaries (non-typical behavior)
is much like the chromatic function of dissonance in music.
Of course, the semantic scales of modern literature are much
more diverse than those of the past, and what might look a
strong dissonance then may be accepted as quite common today.
Many-thread organization and sharp conflicts of the modern
prose perfectly match the complex textures and chromatic
tenseness of modern music. On the contrary, a folk tale
is marked by strict "diatonicity" (or even
"pentatonicity"), and non-typical behavior of
the characters is practically impossible in it. Modal
lability of the pentatonic and diatonic scales correlates
with the typical construction of the traditional epic, with
its arbitrary concatenation of events assuming no beginning
or end and lacking global tensions.
Naturally, there may exist more abstract zone structures in
speech, with the transition from the semantic to symbolic
level. The examples of various symbol schemes are well known
in the literature.
External (uttered) speech is also the unity of discreteness
and continuity. Phonemics typically describes a kind of
"articulation zones", when distinct states of
articulation organs form a basic set of phonemes, of which
more complex speech units are constructed. As in music,
where the intonation may vary through an alteration of pitch
within a zone, each phoneme is represented by a large variety
of allophones in speech. However, linguistic tradition is
to consider the set of phonemes as pre-defined and constant.
The development of phonemic systems is usually treated as
mere transition from one subset of the complete phonemic
system to another, with a simplification and roughening of
some "primary" set, which could be
"reconstructed" using the well-developed methods.
Phonemic evolution looks quite differently within hierarchical
approach. Thus, pitch perception developed from mere
distinction of a few zones to pentatonic and diatonic, and
then to more complex structures. In the same way, primitive
languages could not have any regular phonemic systems, and all
they had was very few phonemes with extremely wide zones;
it is much later, with the formation of more refined perceptive
scales, that the number of distinguishable phonemes has
increased. The zones of vocals were formed first in this
process, since vocals are closer to the musical sounds,
though based on a different (timbre, format) mechanism of
hearing. One might state with much certainty that the
appearance of written language in Europe should be referred
to the "pentatonic" stage of phonemic development,
since five basic vocals have been fixed in the ancient
alphabets, and further phonemic differentiation resulted
in that new phonemes either were not reflected in writing
al all, or were denoted by the combinations of the already
existing characters, just like the traditional musical
notation bears the diatonic stamp and cannot always meet
the demands of modern music.
An important implication of the finite number of allowed
structures is that they may historically appear in
non-communicating phonemic systems. Traditionally,
phonemic parallels in different languages has been considered
as a sign of kinship, while hierarchical approach allows
phonemic correspondences due to the common laws of structure
formation, just like various kinds of pentatonic and diatonic
scales were independently discovered by quite different peoples.
The comparison of a phonemic system with a musical scale
brings a new insight into the organization of poetical speech.
It is commonly known that poets pay special attention to the
selection of words and their placement within the verse.
Still, it is rhythmic regularity that is generally recognized,
while the sounds are treated as accessory, enhancing or masking
the rhythm. Such techniques as assonance, alliteration, anaphor
and epiphor, phone contraction or avoidance are often described
as formal tricks irrelevant to the versification proper.
The theory of hierarchical scaling helps to appreciate the
role of poetic phone-writing, occupying the central place in
poetry. Purposeful phone arrangement makes the speech a verse
even in the absence of any elements of "poetical"
rhythm, like strophes, rimes, metrics, regular caesurae,
intonation repetitions etc.
I suppose that the alteration of vocals in the verse is analogous
to the melodic movement in music, while the consonants
articulate this alteration, like instrumental timbres
demarcate musical sounds, or determine the way of performance
of the poetic "melody" (dynamics, hues, strikes etc.).
This hypothesis is supported by the practice of poetry, as well
as by the observation of such phenomena as purely expressive
"cartoons" language, projection of speech onto a
different language, or transcriptions of poetic texts in various
phonemic environments. Despite the essential one-dimensionality,
the examples of harmonic thought can be found in poetry as well.
Thus, the hierarchical model of zone structure formation in
aesthetic perception gives a novel look to a number of art
phenomena already established and predicts new experiences
in the arts. The simplest informational mechanism lying in
its foundation is not sufficient for that on itself, and the
consideration of various reflection levels is required.
Still, informational methods and quantitative models are
quite possible in this area too, if historical development
of different cultures is accounted for.
- G. A. Golitsyn, Number and Thought, issue 3 (Moscow: Znaniye, 1980)
- P. B. Ivanov, Computability in Developing Systems (1996)
- L. V. Avdeev and P.B.Ivanov, Journal of Moscow Phys. Soc., 3, 331-53 (1993)
- P. B. Ivanov, Leonardo, 27, no. 5, 417-421 (1994)
- P. B. Ivanov, Leonardo Music Journal, 5, 49-55 (1995)
- P. B. Ivanov, Electronics, music, light. The abstracts of the conference (B. M. Galeyev, ed.) (Kazan: Fen, 1996), pp.93-96
- P. B. Ivanov, The Incarnations: Variations on a theme by Guy Levrier