Zone scales as a universal language of design
Pavel B. Ivanov
Troitsk Institute for Innovation and Fusion Research (TRINITI)
E-mail: unism@ya.ru
Written: 18 December 1995
Revised: 11 March 1997
Abstract
A hierarchical approach to the description of structure formation processes in arts is presented,
which describes the development of various zone structures in music, literature and the visual
arts in a uniform way. A new look at the phonemic organization of language is suggested,
and the role of vowel successions in speech is related to that of melody in music.
This analogy is specifically applied to poetical intonation. Experimental tests
of the theory are proposed, and the possible practical applications are discussed.
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1. Introduction
Philosophizing about culture often refers to art as a specific channel
of communication between people, a kind of language different from
both the formal language of science and the "vulgar"
everyday speech. Art criticism may be quite meticulous about the
"message" of a work of art, and the problem of relating
the formal aspects of art production to the author's ideas and
intentions has been the pivot of theoretical aesthetics during the last
two centuries. The problem has acquired another aspect since
computers became widely employed in the analysis of arts, and then
as an instrument of the artist. The rapid development of multimedia
techniques gives a new impulse to the synthetic tendency in arts,
which requires a deeper understanding of the links between different
arts, and the new criteria of the artistic in general. Would it be right
to call the output of some computer program music, painting or verse?
Is there any algorithm for translating music into painting and back?
How artistic performance can be documented, to enable its adequate
reproduction in another environment and by other people? What in
the arts is culture-dependent, and what is its universal content?
These questions require constructive answers, which are only possible
within a general approach regarding the arts of all the times and
nations as different manifestations of the same thing, in different
circumstances.
Recently, I suggested a general hierarchical approach that could
provide the necessary framework for comparative analysis in arts
[1,2]. In that theory, human perception (including
aesthetic perception as a special case) was treated as a multilevel
phenomenon, with possible shifts of consciousness from one level to
another. At each level, the continuum of sensory images can be
decomposed into elementary conceptions selected from a
pre-defined set. Such conception sets are essentially discrete,
though their elements are continuous zones, so that any sensation
within a zone would be perceived as a variant of the same conception.
These discrete structures define the quality of a work of art,
that is, the combination of characteristic features which makes it
recognizable in the various performance forms. Combining hierarchical
approach with some informational and quantum-mechanical concepts leads
to a mathematical theory of musical scales describing the properties
of the already existing scales and predicting a number of new ones,
indicating their principal aesthetic properties and applications
[3]. The same structures were found in visual form
perception, so that a number of parallels in the developments of music
and the visual arts became evident [2]. It was natural
to admit that analogous hierarchies could also be found in the third
fundamental branch of art, in literature. Since synthetic arts of
today mainly combine, in different ways, the word with the sound and
the visual form, the discovery of scaling phenomena in the belles-lettres
resembling musical scales would mean the universal aesthetic
significance of scale hierarchies, making hierarchical approach
a kind of universal language to speak of the arts.
This work suggests a few considerations in support of the idea of
hierarchical scaling in speech, and especially artistic speech,
literature. Naturally, I cannot pretend to cover the problem in all
its complexity, and my article should rather be considered as a
proposal for further research, part of which being actually in progress.
The next two sections are dedicated to the description of hierarchical
scaling in music and the visual arts (painting, architecture, dance,
and so on). A discussion of the general conceptual background of the
application of hierarchical approach to aesthetic phenomena follows.
The succeeding sections formulate the principles of the hierarchical
description of language and outline the hypothesis of phonemic scales
in speech, together with some of its consequences for poetry. The
concluding remarks are concerned with possible applications of
the theory in the arts and related activities.
2. Musical scales
Any art is many-dimensional, that is, there are several parameters
that may vary smoothly within some interval. Thus, music could be
characterized by the distribution of sound frequencies, volume
dynamics, tempo variations, spatial distribution of sound sources,
and so forth. Painting could be described in terms of shapes and
their arrangement, colors, special effects etc. Apparently,
artists may use arbitrary combinations of these parameters, and
nothing prevents them from any choice. Still, the practice shows
that artistic work is never completely stochastic, and there are
strong limitations on the artist's creativity. For example, in
music, there is a 12-tone scale which governs the pitch organization
of most modern compositions. Many musical instruments are
"well-tempered" and cannot produce sounds other then the
twelve degrees of this scale; even the continuous tone shifts widely
used in modern music are generally recognized as modifications of
the same 12-tone scale rather then something self-defined, and
smooth pitch variations are just a way of transition from one degree
of the scale to another. Still, the 12-tone system is not unique
in music. Everyone knows the seven notes forming the diatonic scale,
which historically preceded the "well-tempered" scale.
The difference in pitch between any two neighboring notes of the
12-tone scale is the same, which is not so in the diatonic scale.
To reproduce the diatonic scale within the 12-tone system, one has
to associate the diatonic notes with some degrees of the 12-tone
scale. This embedding is not unique, and the different
embeddings result in different diatonic modes, thus forming
a two-level hierarchical structure. One more level appears when
one comes to consider harmony. The basis of the classical harmony,
the triad, can be treated in the analogous way as an embedding of
a three-tone scale into the same 12-tone system. Again, this
embedding is not unique, and the well known major and minor triads
arise as the possible variants. Thus, one obtains an alternative
language to speak of musical pitch, namely that of scale hierarchies
and scale embeddings.
This reformulation of the classical theory of music in terms of
interacting scales would be useless if it described the already
known facts only. However, it brings forth some new ideas. First
of all, one could ask which scales can be embedded into the 12-tone
system, and is there any scale that cannot be embedded. Why should
we confine ourselves with the three-level structure, not trying to
build more complex constructions? And, in general, is the 12-tone
scale the only universal scale permitting multiple embeddings?
These questions have been asked by many musicians and theorists
during the last centuries, and there are numerous misunderstandings
up to now. The most typical mistake is that the notes in a scale
are the exact points on the pitch axis, and a degree of a scale is
characterized with a definite sound frequency. This approach
manifests itself in the attempts to associate the musical intervals
with some simple frequency ratios, so that smaller numerator
and denominator would correspond to more consonant intervals, while
the ratios of greater numbers would mean dissonance. The actual
musical performance hence would be evaluated by the accuracy of
reproducing the pre-defined intervals, and the 12-tone system of
modern music is considered as a mere compromise in approximating
the greatest possible number of common intervals with a tolerable
accuracy.
This "numerological" approach has a long history, ascending
up to Pythagoras, or even to the magic consciousness of the primitive
peoples. It played an important role in discovering the non-linear
character of pitch perception, resulting in the internal overtone
(and sometimes undertone) expansions of any sound. Indeed, one can
never hear a pure tone with only one frequency present; non-linear
mental processes will make it enriched with many other frequencies,
and it is this harmonic structure of a musical sound that allows us
to prescribe it a definite pitch. Another valuable result of pitch
numerology was the construction of many scales other then the 12-tone
one, the systems of 19 and 31 tones being the most popular
[4-7]. Still, these new scales were generally
considered from the viewpoint of approximating the sets of
pre-selected intervals, and their own aesthetic potential was utterly
lost in this way.
One might say that the principal drawback of this approach is the
absolutization of discreteness in the human perception. The picture
changes drastically when one accounts for the intrinsic uncertainty
of pitch evaluation arising from the complex organization of human
activity and brain processes [1,2]. Actually, nobody
can determine pitch exactly, and nobody has any need to. Implicitly,
this idea was already present in the numerological approach when the
approximate intervals were introduced, which was a strong violation
of logic, since approximating the "consonant" ratio 3/2 with
something like 30001/20001 would result in a harshest dissonance
because of the very large numerator and denominator in the latter
fraction; however, such replacement produces no effect on human
perception, and the two intervals subjectively sound the same.
So, it would be natural to admit that a note is not subjectively
represented with a point on the frequency axis, but rather with
a frequency zone, so that all tones within the zone are conceived
as the same. This does not necessarily mean that the respective
frequencies cannot be resolved in hearing; all I say is that the
tones within a zone are functionally equivalent, that is,
they correspond to the same musical conception. Moreover,
the existence of perceptibly different tones within a zone is very
important in music, since it makes the minute adjustment of
intonation possible. In fact, the skill of a performer is mainly
the matter of proper intonation, and the mechanical reproduction
of the exact pitch sequences can hardly be considered as artistic
performance.
The zone nature of pitch perception has been experimentally
established by outstanding Russian scientist N. Garbuzov
[8]. He spent more than thirty years of his
life in thorough experimenting trying to prove that any side
of musical perception implies the appropriate zone structure,
including the perception of loudness, tempo, note duration,
and musical timbre [9-11]. The related results
were also obtained in many psychophysical experiments
[12], and it was H. Helmholz who suggested,
despite of his theoretical favoring of the "pure"
intervals, the Gaussian distribution as a model of an isolated
harmonic [13].
The idea of zone scales being adopted, the problem of determining
the pitch zones would arise. On the basis of hierarchical
approach, a mathematical model can be developed, predicting all
the possible zone structures and describing the hierarchies of
scale embeddings possible within each scale [1,3].
Though the model does not assume that a scale must contain an
integer number of zones per octave, all the computer-found
scales happen to be approximately periodic, with almost integer
number of zones per octave. Thus, there is a scale with 12.006
zones per octave (which obviously corresponds to the traditional
12-tone scale), as well as the scale with 6.943 zones per octave
corresponding to the diatonic scales. It has been found that
the scales with few zones per octave lack "temperament",
that is, their zones are not equally spaced within the octave.
This effect becomes negligible for the more "dense"
scales, since their zones always include the points of the uniform
division of the octave. In particular, the zones of the 7-tone
scale are spaced in accordance with the interval structure of the
classical diatonic sequences, while the zones of the 5-tone scale
reproduce the pentatonic interval structure.
Many properties of the existing scales can be described in this
mathematical model, including the typical usage of intervals in
each scale. Thus, some scales are modally labile, and their
intervals generally reveal themselves in melody, while in
harmonically labile scales intervals tend to appear in the
harmonic vertical. The 12-tone scale is stable both modally and
harmonically, and this explains its unique position in the
modern musical culture. Still, the theory predicts new stable
scales, including the already mentioned 19-tone and 31-tone
systems. The internal organization of these scales is quite
different from that of the 12-tone scale, and they cannot be
considered mere extensions of the latter.
This is a key point of the hierarchical theory. Thus, the
numerological approach defines the "consonant" intervals
once and for ever, so that all the musical scales were treated as
more or less crude approximations to the "ideal"
proportions; that is, music should be the same in all the scales,
with minor technical differences. This viewpoint has been widely
criticized ever since the beginning of the twentieth century, as
the interest to oriental and African music grew among the European
musicians. The traditional music of Asia has been acknowledged as
an independent branch in musical history, and the numerous oriental
musical modes were recognized as qualitatively different from the
European scales. Hierarchical approach permits to distinguish
different lines of scale development, one of which leads to the
chromatic system of the European music, and another results in
various generalizations of pentatonic. It is only in the 31-tone
scale, that the two lines merge together.
According to hierarchical approach, music in any scale should sound
differently, depending on the internal organization of this scale.
For example, the 12-tone music is not like the diatonic or pentatonic
music, though the intonations of the latter two can be somehow
modeled within the 12-tone scale. The analogous relations exist
between the 12-tone system and the 19-tone scale. One cannot
associate intonations of different scales in a straightforward way,
and transfer the ways of performance from one scale to another
without reservations.
Hierarchical description of scale formation introduces development
into the theory of music, so that the historical scales become the
necessary stages of this development, rather than the imperfect
copies of the same "ideal" scale existing without any
relation to human history. This change of view is analogous to the
L. Vygotsky's revision of traditional psychology, when the historical
development of concepts was established, in close connection with
the development of human thought [14].
3. Scales in the visual arts
The visual arts are different from music in much the same way
the spatial coordinates in physics differ from the time coordinate.
While, in music, the composition unfolds itself sequentially,
moment by moment, one can grasp the whole visual image at once,
and its parts are simultaneously present before the observer.
In principle, the points of a picture can be arbitrarily ordered
in viewing, while musical performance assumes an irreversible sequence.
However, the analogy with physics can be traced somewhat farther, and
one can recall that physical space is closely linked to physical time,
since they both manifest themselves only in a specific physical motion.
Modern physics derives the topology and geometry of space-time from
the interactions of material bodies (or fields), and the distinction
between spatial and temporal coordinates becomes relative. It would
be natural to expect the artistic space and time to be intertwined too,
and the remarkable fact is that the idea of combining music with light
became very popular in the beginning of this century, in parallel with
the relativistic revolution in physics.
In the history of culture, there were many attempts to correlate music
and painting [15]. The seven colors of rainbow seemed
to be a natural analog of the seven notes of the diatonic scale.
However, there has been little progress in this way until now. This
failure could be explained from the viewpoint of the modern theory of
color and the practice of computer color synthesis. The one-dimensional
ordering of colors in the rainbow has proved to be merely incidental,
since the actual color space is at least three-dimensional, with a
non-trivial topology.
Why the spatial organization of painting had not attracted that
much attention, though, logically, it should be the first in the
search of analogies between music and painting? I suppose, this
was mostly because there are several space coordinates, in
contrast with the single time dimension. Now, when the color
space has lost its apparent simplicity, the moment came to
revise the relations between the artistic space and time. This
revision could be performed on the basis of the hierarchical
theory of activity in general psychology [16].
Combined with the theory of scale hierarchies, it leads to the
conclusion that there is a direct analog of a musical interval
in the visual perception, namely the angle in the viewing plane
[2]. Musical pitch can be associated with a
direction in the plane, and the traces of this resemblance have
been found in the history of painting, sculpture, and architecture.
Since the mathematical theory of musical scales has revealed the
characteristic features of different scales, one can easily
observe that the level of scale development in the music of any
culture corresponds to the level of the development of spatial
forms in that culture's painting. Thus, pentatonic music would
be usually accompanied with pentatonic painting, arranging forms
around the distinct five directions in the plane and avoiding
definite geometrical shapes. The painting of Europe provides
the examples for the whole range of visual scales, from
pentatonic and diatonic to the 12-direction system, the analog
of the 12-tone musical scale.
The origin of this similarity between music and the visual arts
lies in the similar organization of activity. From the
psychophysical point of view, the evaluation of a plane angle,
involves the same internal operations as the evaluation of a
musical interval, all the complexity of scale hierarchies
growing from this elementary activity [2].
The situation is quite analogous to physics, where time intervals
are often measured by the distance one could cover in that time
moving with a constant velocity, while distances can be measured
by the time it takes to walk them at a definite speed.
Now we can return to color. In 1911, Russian painter W. Kandinsky noticed
that, in painting, color plays the same role as
instrumental timbre in music: the boarder of two colors produces
a line [17]. Kandinsky associated the principal
colors of his paintings with the timbres of different musical
instruments (or with the registers of one instrument). These
observations hold for the major part of modern painting, from
realistic to psychedelic. However, this does not mean that color
cannot be used like musical pitch (and that musical pitch cannot
be used for coloring). The evident example is the usage of
color and pitch in the impressionist art. More evidence comes
from psychosemantics. One can notice that any language has its
own collection of words and word combinations designating color.
This collection is not closed, since there exist standard ways
of generating new color terms. Nevertheless, all these terms
form a discrete set, tending to cluster in a kind of zones.
R. M. Frumkina experimentally investigated the relations of
subjective proximity in the field of color designations
[18]. She has shown that all the color terms
in Russian can be semantically grouped into seven distinct
clusters (and possibly several groups representing mixed colors).
This means that color is psychologically defined as an element
of a zone structure, just like a musical note is perceived as
a zone in some pitch scale. However, the collection of principal
colors obtained in these experiments did not coincide with the
rainbow sequence and cannot be arranged in a line.
It would be interesting to compare the perception of the visible
part of solar spectrum by people belonging to different cultures,
with different musical traditions. One could expect that the
dominance of pentatonic music would correlate with a five-color
sequence in the rainbow, contrary to the seven colors
distinguished by Europeans. I could also predict that, even for
Europe, there may be differences in the number of colors
distinguished in the spectral continuum, depending on the cultural
level of the sampling group and the conditions of observation.
This could be proved in a simple psychophysical experiment
measuring the differential thresholds of color perception with
varying width of the spectral band in view.
4. Fundamental duality
The description of scales in music and the visual arts can be
substantially generalized. It is well known that people are not
aware of everything they do, and the focus of awareness moves in
the course of activity from one conscious goal to another
[19]. This movement to a
pre-selected goal is called action, and any activity
unfolds itself in a sequence of actions, which can similarly be
implemented as the sequences of operations. On the level
of activity, the world is represented with a continuum of
possibilities, while any operation is essentially discrete, since
it cannot have subjective duration in both space and time
[2]. The level of action is intermediate between
activity and operation, and therefore awareness assumes a synthesis
of continuity and discreteness. This synthesis is naturally
reflected in the theory of zone scales.
I suggest that the way of unfolding activity into a sequence
of actions is a fundamental characteristic of a specific
culture, and it should reveal itself in any aspect of it.
This implies that every particular situation would be evaluated
by the people through a most general process called
categorization: at any level, the situation is
related to one of the discrete set of categories, each category
assuming a continuous zone representing the possible variations
of the same situation. Scale hierarchies in music and the visual
arts are examples of categorization, and I expect that the model
developed for the description of these hierarchies would be
applicable to any other cases, provided the appropriate variables
have been found.
The principal duality of continuity and discreteness can be a
useful source of theoretical ideas, and a criterion of
trustworthiness for any conceptual system. Thus, one should
always remember that any opposition is only valid within a
definite set of categories and may disappear on another level
of hierarchy, in another scale, where the "opposite"
things may belong to the same zone. In logic, it means that a
result of formal deduction should be considered as a hypothesis,
rather than a proof; because of the zone nature of the logical
truth, the formal conclusion may be found off the zone, or in
some other zone (like the round-off errors in real arithmetic).
Virtually, the very category of truth is a conceptual frame at a
definite level of consideration; in a restricted way, this fact
has already been acknowledged by modern mathematics
[20]. This relativity of appraisal is apparent
in the arts, where it is a common phenomenon that an act
inadmissible in one aesthetic environment becomes quite normal
in another. The musical example is the hierarchical understanding
of dissonance, which is defined as a violation of the zone
structure at some level of the hierarchy of scale embedding;
typically, there may be dissonances in harmony, modal dissonances
(altered notes), and scale dissonances (widely used in modern
music to produce a stratified texture).
Another type of theoretical fault is exaggerating the continuous
side of phenomena. In aesthetics, this tendency is represented
by intuitionism of any sort, overstatement of the spontaneous
creativity and the neglect of composition. The duality principle
says that no human activity can be completely spontaneous, and
some processes of categorization would be always present. The
artist may be unaware of the system of categories involved, and
it is the matter of aesthetic education to enrich the syncretic
creativity with a variety of conscious attitudes, which could
enormously enhance the expressiveness of art.
5. Scales in language
As everything in the world, art is hierarchically organized, and
literature constitutes a specific level of this hierarchy. This
level could be considered as intermediate between aesthetic and
scientific creativity. Language is designed to reflect any kind
of activity, including artistic work and speech production itself.
Still, the ways language is used in the arts is different from
that of everyday life, as well as from scientific reasoning or
philosophical discourse. The characteristic feature of the artistic
usage of language is that its conceptual aspect is of an accessory
significance here, and it is its ability to produce forms
that is important. This feature may be not obvious in literature,
since people are rarely distracted from the semantic side of their
reading. Still, such distraction does occur from time to time,
and most people know this unusual feeling of hearing the modulations
of speech with no regard to its meaning. This is the case when one
can enjoy the verse, or a song, in a foreign language; however,
people may have the same experience merely talking with somebody
of the commonest things. Great poets and writers feel it much
stronger than the ordinary people, and they follow that feeling
as they write.
Numerous ways of using the words to produce forms are known in
modern art. In the written speech, the word becomes visualized,
and its visual image may undergo most complex transformations,
according to the laws of the visual arts. In simple cases, it is
only the graphic form that changes, like in the compositions by
Richard Costelanetz [21]. More complex
compositions may involve computers, holography and fractal
theory [22]. Analogous transformations of the
sound of speech may be encountered in some varieties of modern
abstract music.
Of course, the way of hearing or reading a word cannot leave the
way of its aesthetic perception intact. Still, aesthetic experiments
with the visual image of the word, or its musical intonation, should
be rather referred to the sphere of synthetic art, being closer to
music or painting than to the belles-lettres. However, hierarchical
approach indicates that language must have its own means of form
production, which should receive more attention than they were given
before.
For further analysis, I will distinguish two levels of the artistic
usage of language. One of them is concerned with the wording itself,
with little relation to the content of the speech. The opposite
direction is to categorize the meaning of the words making them
symbols rather than designations of real things. These two
opportunities correspond to the distinction of outer and inner
speech described by L. Vygotsky [14]. Since,
according to Vygotsky, thought occurs in language, the both
directions of its development, from the internal scheme to speech
behavior and from the outer speech to its folded reflections, can be
aesthetically represented in human culture. Actually, the both
levels of the aesthetic categorization of language will co-exist
in any artistic work, with varying relative significance.
I should stress here, that my distinction of the two categorization
levels applies to both spoken and written language. Naturally, these
manifestations of the linguistic ability are quite different in their
modes of expression, they differ in structure and obey different
functional laws. Still, the both kinds of speech realize the same
process of thought becoming a linguistic form, and back, from a
particular arrangement to its subjective sense. Apparent difference
of spoken and written language is irrelevant to the essence of speech
production, which might be related to their common origin, the gesture
[23].
Hierarchical approach predicts that on the both levels of
categorization one might discover zone hierarchies analogous to
musical scales. Theoretical aesthetics and literary criticism
have done much to describe the variety of forms related to the
contents of an artistic text, which I will, for simplicity, call
the semantic level. Numerous laws of composition have been
suggested for both poetry and prose, though the lack of system
can still be felt in these studies up to now.
Semantic scales most clearly manifest themselves in the classical
narration. A story usually unfolds around a few main characters,
who are interconnected by typical situation links. This structure
admits some flexibility, and the characters of the story may
look differently depending on the situations they enter. This
behavioral variability defines a kind of behavioral zone for each
character, and the effect of dissonance is achieved when a
character acts in a way incompatible with its zone; however,
such acts are never arbitrary, they always belong to some
lower-level scale. Such dissonances are quite common in modern
literature, which is like the "emancipation of dissonance"
observed in contemporary music. The structures in the literature
of the former epochs were simpler, with less dissonances, and the
farther to the past we descend, the narrower collection of the
standard characters we find. The theory says that the primitive
forms of narration should be based on the diatonic (seven zones),
or even pentatonic (five zones) scale. Since these scales are
modally labile [3], the basic type of structure
they imply is a chain-like sequence of events, with no evident
final point; however, such "tonicality" may occur
locally (in a small fragment of the story), especially in the
diatonic scale. This conclusion is supported by the results of
the computer simulation of fairy tale production
[24], though more experiments and analytical
study are still waiting to be performed. For instance, it
would be interesting to relate the gods of the Ancient Greece
to the tones of the Perfect and Immutable System that
governed the ancient Greek music [25].
There is yet another area of semantic-level categorization, which
concerns the meaning of the words and phrases. The existence of
psychosemantic zones has been demonstrated in the above-mentioned
experiments by Frumkina [18]. Hierarchical approach
predicts that analogous zones could be found for the word meanings
in any particular field of human activity, which might be detected
in similar experiments. Thus, one could discover psychosemantic
classifications of emotions, motives, attitudes, or personal traits,
which are implicitly used in literature or artistic speech.
6. Articulation scales
Compared to the semantic level of categorization, available data
on speech production provides less evidence for hierarchical
scaling. Two scientific traditions exist in this area, representing
two polar abstractions described above: one is to study speech as
a psychologically continuous process, and the other is to consider
speech as a result of formal structure transformations, assuming
the existence of a priori defined sets of unchangeable elements.
The former line inevitably comes to attributing the laws of speech
production to something beyond the language, like social influence
or the construction of the brain. The latter trend closely adjoins
to the traditional linguistics, with its enumeration of grammatical
structures, the parts of speech, morphological categories and so on.
However, the understanding of the principal duality of the
continuous and the discrete sides of speech production is gradually
finding the way in linguistics as well, especially in the theories
based on the notion of functional semantic fields [26].
The idea of categorization in phoneme recognition becomes rather
popular in psychological research too [27].
Hierarchical approach is immediately applicable to the development of
language, that is, in comparative linguistics
[28]. It implies that the principal direction
of any development is from the primitive syncretism to ever more
complex zone structures (scales). Consequently, primitive
languages could not be highly structured, and their categories
had to be much more diffuse than those of modern speech. This
assertion does not agree with the traditional views.
For instance, let us consider comparative phonemics, studying
elementary portions of speech, the phonemes. Schematically, the
traditional approach is to compare many languages, and to
establish some formal rules transforming the phonemic system
of one language into another. The existence of such rules for
a number of languages is attributed to their common origin, and
the phonemic system of their "common predecessor"
is being reconstructed to describe the widest range of actually
observed transformations. Finally, one obtains a highly developed
system of phonemes, containing 11 or 12 vowels, 8 nasals and
liquids, and up to 28 consonants, with several substructure levels
[28, p.166]. Is it likely that primitive people,
living several thousand years before the first civilization on
the Earth, could develop that complex phonemics? One would rather
expect that the primitive languages distinguished only a few phonemes,
with very wide zones admitting a significant scatter in their
pronunciation. Originally, the phonemes were not separated enough
from syllables, and even from the whole words. This naturally
explains why ideograms always went first in the history of written
language, and why the syllabic stage preceded the true phonetic
writing in the history of hieroglyphs becoming letters. From this
viewpoint, the development of phonemics should be understood as a
gradual improvement of phonemic hearing, increasing the number of
distinguishable phonemes and tightening the range of their
pronunciation variations. This process followed different routes
in different places, and that is why there are many phonemic systems.
Further, since the development of phonemic scales is governed by
the same objective laws in any language, independently formed
phonemic systems would reveal the same structural features, and
there is no need to seek for a common predecessor to explain
this similarity. Hence, there is much more allowance for the
independent genesis of speech in many far-apart geographical
locations, and one does not have to imagine mass migrations at
the early stages of the human history.
These conclusions may be illustrated by the examples from the
history of music. Thus, the different versions of the pentatonic
scale can be found in the traditional music of any nation; however,
no one would deduce from this fact, that, say, the Chinese and the
Greeks would descend from the same people in the process of
divergent evolution. There are many particular variants of the
diatonic scale, and even the elements of the 12-tone system
independently appeared in several regions of the Earth.
Of course, I do not assert that there was no divergent evolution
at all in the development of phonemic systems. One can observe
such processes up to now, regarding the pronunciation in the
ethnic groups living in a foreign-language environment.
Thus, Russian speakers in the USA pronounce the words differently
from those living in Russia; this difference could be explained by
the interference with the American articulation habits, and a
faster rate of speech typical for English USA. However, the
possibility of the independent formation of analogous structures
in different languages makes comparative studies more difficult,
since there is a necessity to discriminate the different modes
of language development.
Phonemic zones exist in modern languages as well. For instance,
in Portuguese the same vowel can be pronounced differently depending
on its position in the word, or within a phrase [29].
However, in most cases, the zone nature of the phonemes is obscured
by the traditional rules of spelling, which rarely reflect the
actual pronunciation. The classification of phonemes in a particular
language is a non-trivial task, and the description of the
phonemic system may be influenced by theoretical attitudes.
Hierarchical theory predicts that modern pronunciation (at least
in Europe and North America) should be related to the pitch structure
of contemporary music, as well as the ways of constructing the visual
forms. It seems likely, that a direct correspondence can be found
between musical scales and the vowels in a language.
This point requires a deeper consideration. Both speech and music
are made of sound, so to say. Still, sound is used differently in
either case. While music is essentially the art of intonation,
speech grows from another side of sound, articulation.
Therefore, structures in speech should be derived from timbre rather
than pitch. The consonants do not seem to possess the timbre
definiteness necessary to produce a relatively stable patterns; their
articulation is transitory, compared to the vocalization of the vowels.
Three-dimensional spectra of phrases (which are now available on
screen using programs like Wave for Windows and Voice Toolkit) clearly
show that the major part of the sound energy is concentrated in the
peeks constituting the formants of the vowels, while the consonants
mainly define the form of the peeks. This is quite analogous to the
role of instrumental noise and performance accents in music, where
they modify the appearance of spectra, but do not affect pitch.
I conclude that the vowels of a language should form a kind of scale,
and the development of language is accompanied with the increase of
the number of distinguishable vowels, with more restrictions on their
actual pronunciation. Originally, there could be a single center of
vocalization, which would later split into a few distinct zones. This
hypothesis is supported by the development of phonemes in children's
vocalization on the early stages, before they begin to speak; the
insufficient separation of the vowels may also be a source of many
word deformations observed in the babies' speech. Still, more work
in this direction would be desirable.
The appearance of written language played an important role in the
history of phonemic scales. It codified the inventory of vowels
(scale zones) that already existed, thus making their usage much more
conscious, so that the features of the corresponding phone system could
be unfolded in full. On the other side, fixed alphabets constrained
further phonemic development, and the actual pronunciation of words
gradually became less resembling their spelling. The force of tradition
is rather strong in the language, and the outdated spelling rules
may even lead to the apparently retrograde evolution, when the number
of vowels would decrease. However, this process does not mean the
revival of some primitive phonological system; the zones of the scale
remain rather narrow, unlike the wide zones of the older scale with
the same number of zones. The typical example is modern Spanish, with
its five very distinct vowels. This phenomenon can be related to the
scale embedding in music.
Since it is rather difficult to determine phonemic zones in modern
languages, one could try to investigate the cases of speech behavior
that could reveal phonemic scales in a more clear way. I suppose that
the aesthetic potential of speech is based on the articulation scales,
and literature as a kind of art implies deliberate choice of sound
sequences. Poetry seems to be the most dependent on articulation part
of literature.
7. The art of speech
There is nothing new in the assertion that poets are rather careful
selecting the words and arranging them in the verse. The draft
manuscripts of many eminent poets show the traces of the poignant
search for exact wording, the feeling of the sound often dominating
over semantic considerations in this search. The verse should sound
right, this is the first formal requirement in poetry.
However, the existing theories of verse primarily concern the
rhythmic side of versification, while the rules of poetical
articulation merge in the background. Some attention paid to
rimes is not enough to explain the structure of the verse
(especially if it contains no rimes at all), and the descriptions
of the various kinds of sound repetitions (assonances, alliterations,
anaphors and epiphors, etc.), as well as phone confluence or avoidance,
usually treat them as arbitrary technical tricks. The hypothesis
of articulation scales provides a different view on the phonemic
structure of the verse. I conjecture that the alteration of vowels
in a verse is analogous to melodic movement in music, and the role
of the consonants is similar to that of instrumental timbres:
they modify the articulation of vowels and partially control speech
dynamics. Thus, the languages where many consonants may occur
together (like Russian and German) would be characterized by a
relatively slow rate of speech; deliberate confluence of consonants
is often used in poetry to slow down the recitation.
The similarity of a sequence of vowels to musical melody looks quite
natural from the practical point. Thus, in cartoon making, the
actual speech is often replaced with an imitation preserving the
general articulation and changing the "noise" component
of speech to make it incomprehensible. In many cases, this melodic
side is evident in poetry. For example, let us read the beautiful
poem by Robert Graves [30, p.103], discarding all the
consonants, with only vowels left:
She tells her love while half asleep,
In the dark hours,
With half-words whispered low:
As Earth stirs in her winter sleep
And puts out grass and flowers
Despite the snow,
Despite the falling snow.
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The effect becomes even more impressive if one allows for partial
vocalization of such half-consonants as [j], [w], [l] and [r],
which are known to be syllable-producing in some languages.
Of course, articulation melodies in modern poetry may be rather
complicated, and I must admit that there should exist some analog
of musical harmony. In the case of painting, I suggested the
process of intonation folding as the main source of harmonies
(chords), which were associated with the plane figures in graphics
[2]. The same holds in speech, and one might
regard a confluence of vowels pronounced as single vowels (vowel
fusion) an analog of a musical chord. Evidently, diphthongs
and triphthongs will be the first candidates for articulation
chords. Also, there are speech dynamics effects producing
vowel fusion in speech, and this is the most typical way of
introducing harmony into verse, similar to arpeggio or
hidden polyphony in music. Speech is rather difficult
to achieve true polyphony, though, I suppose, some examples might
be found in poetry.
Languages differ in their ways of arranging the succession of
vowels in time. Thus, diphthongs are relatively rare in Russian,
and the "chord" effect can only be achieved by the
dynamic means. There are also differences in the quality of
phonemes which would influence the aesthetic perception. For
example the above poem by R. Graves was written in English UK,
and it would loose much of its expressiveness when recited in
English USA — though possibly acquiring expressiveness of
a different kind. Translation from one language into another
may completely alter the articulation design of the verse,
especially when the interpreter tries to preserve the semantic
aspect. For instance, there are numerous interpretations of
the songs by The Beatles in Russia, which are characterized
by a rude discordance between the lyrics and music; the exact
reproduction of instrumental arrangement enhances this impression.
A perfect translation, preserving both the contents of the poem
and its articulation structure, is hardly ever possible. A
talented interpreter would usually prefer to change the message
of the verse to reproduce the general tonality. To continue the
previous example, many hits of Euro-American pop-music have been
translated into Russian and became true hits in Russia, though
the text of the One-Way Ticket never resembles that of the
Blue Hoarfrost, and the Yellow River has nothing to
do with the Carlsson. Similar examples can be found for
other languages: thus, the same Yellow River sounds as
Amerique in French (with a close reproduction of articulation),
and, inversely, Comme d'habitude has become My Way
in the English translation (with a quite different articulation scheme).
In this connection, one could recall that translating a musical
piece from one instrumental cast to another may require a
significant change in the notes too.
If poetical intonation is closely related to the succession of vowels,
the study of poetical texts from this angle would reveal many
interesting facts. The development of poetry might be traced in
connection with the development of musical scales and graphic
intonations, though the reconstruction of the true pronunciation
in the past is most difficult; the conception of zone hierarchies
might give some clues to such reconstruction.
8. Concluding Remarks
One might say, "Well, you may invent any theory. And what's the
use of it? Artists will create from their feelings rather than
from a cold reasoning, and most judges of their art will trust
the general impression rather than the detailed examining of the
composition."
I agree that syncretic impression plays an important part in arts;
in hierarchical aesthetics, art itself is described as the syncretic
level of creative reflection, as compared to the analytical level
of science, and the synthetic philosophical reflection. However,
formal methods are much more significant in design than it has been
commonly thought. The activity of an artist is always directed by
the nature of the material used, and the more developed are the
techniques applied the more creative freedom the artist attains.
A talented self-taught person can use the tricks discovered or
re-invented in one's personal experience, while an educated artist
has access to the treasury of expression means collected by all the
humanity in the course of many centuries. Education cannot replace
talent, but an educated talent is thousand times more powerful.
So, the search for the new modes of action is bound to lead to new
discoveries in art.
The theory of hierarchical scaling can be used in constructing new
instruments. For example, the keyboard of the 19-tone piano could
be organized in a special way [1]. Combining
different scales in computer music requires special software allowing
for convenient scale selection. Thus, the existing software for
MIDI programming is generally oriented to the 12-tone scale, and one
has to manually adjust the pitch shifts to write 19-tone music.
The analogy between musical scales and graphic intonations would
enable the development of new tools in the existing graphic packages,
and the zone nature of color perception assumes the possibility of
a new type of palettes and color transformations. One more aspect
of it is optimal tuning the ordinary instruments . Thus, the
traditional violin tuning by the pure fifths (with the 3/2 ratio of
frequencies for the neighboring strings) is optimal for performance
in the Pythagorean mode, while chords and temperation require more
effort [31]. For 19-tone performance, it would be
natural to tune the violin by the 19-tone ("harmonized")
fifths, which are somewhat smaller than the pure fifth.
Yet another possible application for the theory of scale hierarchies
is the notation problem. Usually, notation is thought to serve for
mere recording something with the best possible accuracy. Thus, the
traditional musical notation is rather incomplete, and there are
numerous coding formats in computer music that permit much more
performance control. Graphic programming languages (like ColorTalk
in the Fractal Design Painter) show the same tendency. I would argue
that the role of notation is more than passive recording, since it
logically orders the parts of the aesthetic whole. Notation reveals
the idea in the art, so that this idea could then be expressed in
different ways by many performers, or in the other arts. And the
concept of hierarchical categorization might help in designing new
notation systems, thus becoming a universal language of design.
I have already mentioned some psychological, linguistic and
culturological experiments suggested by hierarchical approach.
Of course, there may be more experimenting along the hierarchical line,
which might lead to a better understanding of scaling phenomena in
the arts.
Scale hierarchies can be employed in art criticism and theoretical
aesthetics. There may be educational applications, either stimulating
creativity or enhancing aesthetic perception. These and other
possibilities makes me hope that the ideas of hierarchical approach
will be of some use for the artists and the people they work for.
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