Liberation of Integration, Universality and Concord
through pattern, oscillation, harmony and embodiment
- / -
Originally prepared for the 5th Network Meeting (Montreal) of the United Nations
University's project on Goals, Processes and Indicators of Development (GPID) as a
contribution to the discussion on integration of the findings of the project. [searchable PDF version
, with annexes]]
Abstract: Demonstrates that many widely advocated approaches to integration are
relatively simple (if not simplistic) options in a context which is subtler and more
complex (at least in a mathematical or topological sense). It is however possible that
such elegance is also an indicator of vital properties of symmetry, harmony and balance.
These are desirable in any domain in which integration is sought and even necessary for
that integration to be both brought about and sustained (by its inherent
comprehensibility). The relevance of ordered patterns of time is explored, especially in
the light of the evolution of concepts of integration in music and harmony seen here as a
precursor of new approaches to psycho-social organization. Attention is also drawn to the
special significance this has for transforming understanding of possibilities of
individual identification with processes ordered over time.
This paper is an exploration of the range of ways in which 'things can be put
together' or conceived as being interrelated. In undertaking this it is hoped that
widely advocated approaches to integration may be shown as simple options in a context of
subtler, more complex possibilities, many of which are essentially more
'elegant', if only in the mathematical or topological sense. It is possible,
however, that this elegance is also an indicator of vital properties of symmetry, harmony
and balance, which are desirable in any domain in which integration is sought and
even necessary for that integration to be brought about.
The domains in which integration is of considerable concern may be indicated by
reference to the sub-projects of the UN University's project on Goals, Processes and
Indicators of Development of its Human and Social Development Programme. For example, how
are the different 'models' implicit within the following sub-projects to be
integrated in each case, especially when there is some degree of incompatibility
- visions of desirable societies
- alternative ways of life
- development processes or concepts of development
- alternative strategies and scenarios
- human needs (rights, and values)
- psycho-social human development (including images of man)
- world models (or cosmologies) (1)
In each case alternatives can be formulated in the light of different patterns of
priorities. The question is how such alternatives are to be reconciled in practice in a
Although integrative skills may be successfully applied to a situation, their elusive
nature can be partially defined by the ways in which such skills may fail or be used to
conceal abuse. The following approaches to integration or synthesis stress the manner in
which an impression of integration can be created even if little is achieved. It is partly
base on material assembled in a section on 'Integrative Concepts' in the
Encyclopedia of World Problems and Human Potential (2) which identifies some 620 such
concepts. The bibliography therein has recently been complemented by a bibliography of
1600 items on 'the relationship between and the structure of science, philosophy, and
social/political organization' (3).
(a) Reduction in variety: A simple way to ease the integrative problem
is to reduce the diversity of elements present in the situation using an
argument for standardization and against any 'hodge podge' mixture of elements. This of
course eliminates some minority interests. In the extreme case of destructive or
'meltdown' synthesis, all variety is eliminated.
(b) Reduction in quantity: By eliminating a significant number of
the elements, the problem may also be eased. The argument that can be used
is that they are well-represented by the variety of elements that remain
and that any
'proliferation' of elements is disorderly. In practice this results
in the absorption of some elements by others, such as in the case of minority
(c) Simplification: Subtleties and nuances, possibly defended by specific
minority groups, may be ignored. Interconnecting webs of relations can be ignored.
(d) Tokenism: Emphasis may be placed on the image or desirability of synthesis
in order to conceal inability to achieve any steps towards it.
(e) Temporary synthesis: In a dynamic situation it may be possible to achieve
some measure of integration in the short-term by ignoring factors temporarily absent or
only emerging over longer time cycles.
(f) Coloured synthesis: A significant degree of synthesis may be achieved, but
from a particular viewpoint or in terms of a particular mode, approach or strategy. The
narrowness of such a synthesis, coloured by the perspective of those who achieve it, may
be difficult to communicate within the framework established by that synthesis.
(g) Enforced synthesis: In some instances, as with a dynamic set of minority
interests, a form of integration may be imposed by constraining the dynamics (although
without reducing the number or variety of the elements).
(h) Dogmatic synthesis: An impression of synthesis may be achieved by
stating frequently and forcefully that it has been achieved and thus eroding expectation
that a greater degree of synthesis is possible.
(i) Laissez faire synthesis: By reinterpreting the nature of synthesis or
integration, it may be deemed to exist under any circumstances as the pattern of
interaction amongst the elements. No intervention is required, although if undertaken it
would merely add to the pattern of interaction.
(j) Agglomerative synthesis: Appropriate integration may be assumed
to have been achieved simply by ensuring the juxtaposition of the various
elements or viewpoints. This corresponds to the use of the prefix 'multi' (eg
in multidisciplinary). In books reflecting such a multidisciplinary synthesis,
it is the binding which provides the synthesis, given the absence of any
relationship between the constituent disciplinary chapters.
(k) Comparative or cross-referential synthesis: Integration may be
asumed to have been achieved by recording comparisons between the perspectives
or elements. This often corresponds to the use of the prefix 'cross' (eg
(i) Cross-impact synthesis: Integration may be assumed to have been
achieved by taking into account the constraints and feedback loops emerging
from other disciplinary perspectives. This may correspond to use of the prefix 'inter-' (eg in
interdisciplinary). Note however that it is only with the emergence of a new level of
order that a synthesis breakthrough may be said to have occurred (this may correspond to
the use of the prefix 'trans-' as in trans-disciplinary).
Approaches to integration
1. Integrative skills
Although during meetings there is much discussion of 'integration' and there
are many attempts at producing a 'synthesis', the skills called upon seem to be
poorly understood, hard to communicate, and very difficult to put into practice. It is
therefore useful to note very different domains where integrative skills are practice
successfully, even if it is not immediately clear what can be learnt from them for use in
a meeting environment.
(a) Design and composition: This is the process through which creative intuition
influences the selection of elements and the manner and proportion in which they are to be
balanced -- what is to be put together and how. In each of the following the configuration
of elements tends to relate to an emergent focal point:
- Composing music
- Painting a picture
- Flower arrangement (Ikebana)
- Building and community design
- Interior decoration
- Designing a meal (or menu)
- Putting together a group, a team, or an evening party
- Writing a novel
(b) Managing dynamic situations: This is the process whereby the relationships
between a complex set of given elements is kept in focus. Examples are:
- Leadership of a group (including use of charisma)
- Production of a show
- Conducting a military campaign
- Controlling a chemical plant
- Scheduling railways, deliveries, etc
- Making a party 'go' (hosting)
- Conducting an orchestra
(c) Analyzing complex situations: This is clearly oriented to understanding
whatever can be analyzed irrespective of whether this leads to broader synthesis. Examples
- Operations research
- Systems research
- Management research
- Political analysis
(d) Communicating synthesis: This is the process whereby a sense of wholeness or
unity among diverse parts imparted to others, even if only as a symbol or token of what
may later be achieved in practice.
- Environmental appreciation ('One Earth')
- Art education
- Art of speaking
- Political commentator
(e) Embodying synthesis: Whereas each of the above is in some way a manipulation
of synthesis, however necessary, there seem to be instances where a person acts as the
focal point for synthesis and is so perceived by those whose interests are reinterpreted
and focused in this way. Examples are perhaps:
- Spiritual leaders (including saints, gurus, and charismatic evangelists)
- Political heros (including statesmen, military and revolutionary leaders)
- Cultural heros (including pop-stars, film-stars)
2. Conventional integration
The most systematic approach to interdisciplinary integration is probably that of Erich
Jantsch (4), as outlined in Annex 1. There are two extremes in the conventional approach
- (a) 'agglomerative': In this case alternative models are conceived as
co-existing in such a way that their incompatible features do not result in undesirable
conflict between them (see above).
- (b) 'fusion': In this case deliberate efforts are made to reconcile the
apparently incompatible features of the models, such that a new transcendent model emerges
to replace them. This may be achieved by excluding some models which cannot be
incorporated in this way. Fusion may only be 'house tidying' with similar
The first approach tends to be unsatisfactory in an increasingly complex society in
which undesirable conflict does result from incompatibilities between the models.
The second tends to be unsatisfactory, either because of conflict arising from what is
excluded, or because such fusion is quickly perceived as a constraint on further
development if the model is successfully implemented. The more successful it is, the more
its proponents will resist any further reconceptualization. Such models do not acknowledge
their limitations, the need for their limitations, and the need for their eventual demise.
They are conceived as a 'final solution' detached from the processes which
brought them (temporarily) into being.
3. Ecological integration
As a first step in the search for subtler patterns of integration we may consider a
situation exemplified in ecological systems although typical of more complex organized
systems. Consider two species in an ecosystem as being analogues of two conceptual models
in a psycho-social system.
The processes that characterize species X may, in the interaction with Y, be
accelerated or in some way enhanced (+), or may be unaffected (0), or may be decreased
(-). The same is true for species Y.
When such possibilities are cross-tabulated, it becomes evident that there are nine
qualitatively different coactions. Ignoring the (0,0) coaction, the remaining eight are as
+ + symbiosis - - synnecrosis
+ o commensalism - o amensalism
+ - parasitism - + predation
o - allopathy o + allotrophy
This scheme was elaborated by E Haskell (5) who made it into the basis for a periodic
coaction coordinate system. It provides a rich method for exploring species interaction.
Under certain conditions it may be desirable to view the relationship between models in
this light. Note that in an ecosystem an interaction with a 'negative' component
(e.g. parasitism) is not necessarily 'bad'. It may be part of a complex
interspecies web or merely the corrective mechanism for a temporary imbalance between
species. For the relationship between species is of course not rigidly determined. Species
rise and fall numerically in relation to each other. Homeostasis is achieved by
compensating patterns of oscillation around a condition of dynamic equilibrium.
It is interesting that few 'meta-models' even attempt to handle the
relationship between models. Each of the latter tends of course to claim some form
of exclusive validity viewing any alternatives as heretical, sub-optimal, or distortions
of the most realistic. It could be said that, in comparison with the ecosystem case,
models are defined at the 'species level' and that few, if any, have been
successfully defined at the 'ecosystem level'.
The 'species level' provides a distinct reproducible pattern of organization,
whether in the case of species or of conceptual models. The presence of other
'species' necessarily gives rise to an inter-species dynamic which is associated
with a logical hiatus, since there is a distinct logical discontinuity between any
such species-level perspectives. As will be discussed further below, it would appear that
the ecosystem level logic cannot be adequately contained or expressed through a separate
logic, it must necessarily be modelled by the a-logical pattern of inter-species dynamics.
1. Use of incompatible modes in practice
Before going on to a more systematic exploration of integration patterns, it is useful
to note down some examples in which practical results are achieved by
'oscillation' between essentially incompatible or mutually unacceptable modes:
(a) Two or multi-party political systems: in which one of the parties
takes power with the other(s) 'in opposition' to its philosophy
(b) Rotating chairmanship/secretariat/meeting locations: wherever consensus
cannot be achieved on a single individual or location, perceived as emphasizing one
tendency in contrast to others (which must therefore be represented in their turn).
(c) Interrogation/brain-washing procedures: in which an individual is
progressively broken down by the alternating use of kindness (the traditional cigarette)
and torture, often by a 2-person team of interrogators exemplifying these characteristics.
(d) Management/leadership: which is frequently required to apply
appropriate doses of 'the carrot' or 'the stick' to ensure
appropriate team performance.
(e) Educational challenge and encouragement: whereby the teacher alternates
praise and reinforcement with exposure to new challenges through which the student
achieves confidence in the skills acquired.
(f) Healing care and therapeutic challenge: through which healing is achieved by
alternating periods of rest and care with periods in which the individual exercises the
(g) Formal and informal liaison: may be used as complementary alternatives
essential to balanced functioning, whether in intra- or inter-organizational contact or in
relations between individuals (as in the case of formal marital and informal extra-marital
(h) Strategic advance and retreat: are complementary alternatives necessary to
adaptation (by a general) to changing circumstances of conflict. Inability to switch into
the alternate mode is to court defeat.
Note that in each case the transition from one mode to the other is through a decision
governed by qualitative judgemental factors combining art and science beyond the realm of
simple models and logics.
Within some oriental cultures the ability to move smoothly between two such essentially
conflicting modes is modelled by the circular process of inhalation and expiration. For
this reason much emphasis is placed on eliminating defects in this process through
breathing exercises for the individual. (But, strangely, never for a group).
2. Model mixes in space/time
It is important to recognize that integration can be achieved in space and/or time. For
- a range of models co-existing on different parts of a spatial surface and interacting in
- transformation over historical time between a range of models, each successively
(periodically) occupying the space.
Note that it is unlikely that these two limiting cases are independent of one another.
It is more probable that they engender each other in space- time as do rotation and
revolution in any solar system model, for example. In fact such spin and orbital motions
are part of a set of six basic motions which also includes: expansion-contraction, torque,
involuting- evoluting, and precession (6, point II, 400.654 and II, 986.857); These may
suggest other forms of integration in space-time, as well as introducing the less-evident
(spiral) evolutionary movements. As a complete set, each of these 'motions' is
necessary to the existence of the others.
Further possibilities for integration are indicated by the following:
- at a particular time, a particular mix of models may be present in space, thus excluding
the manifestation of other possible mixes of models which may later emerge (at its
expense). The mix need not be a simple agglomeration but may itself be highly integrated
(e.g. as a tensegrity).
- any possible integration (or symmetry) in space can be matched by possible integration
over time. (The two possible symmetries may be considered as isomorphic, or as
mathematical equivalents). This will be discussed below.
Patterns and rhythms
The question now is whether we can identify the nature of the series of patterns or
rhythms in the light of the first few members of which we are more or less aware.
- 1-element :
- (a) Space: This is the case of the occupation of space by a single model - which can be
represented by a point.
- (b) Time: This is the case of the single source-event spherical wave pattern.
- (a) Space: This is the case of the simultaneous occupation of space by 2 models. These
can be represented by 2 points, and their relationship by a line connecting them.
- (b) Time: This is the case of one model (mix) periodically replaced by a second, which
in turn is replaced by the first. Again these can be represented by 2 points, and their
relationship by a (bidirectional) line between them.
- (a) Space: Other cases of the simultaneous occupation of space by N models (or model
mixes) can each be represented by an appropriate configuration of points connected by
lines according to the relationship between them.
- (b) Time: Other cases of one model (mix) periodically replaced by a succession of (N-1)
other models, before it recurs, can also be represented by an appropriate configuration of
N points with lines between them.
The simpler possibilities for N elements are clarified in Annex
2. Note that the
'relationship' indicated there by a line could, in binary terms, be considered
either as one of 'compatibility' (space) or 'consonance' (time),
indicated by '-', or as one of 'incompatibility' or
'dissonance', indicated by - Integration indicated by the degree
of symmetry which in the time case is related to recurrence.
Annex 2 only focuses on patterns which are significant in 2 dimensions. These patterns
are in fact those which have been the focus of attention in the classic communication net
experiments (7). A valuable approach to more complex patterns, particularly in relation to
time, are the Chladni figures visualized by vibrating powders on a metal sheet (8).
Another source is the range of progressively more complex patterns from graph theory (9).
Reference should also be made to Johan Galtung's suggestions regarding the use of graph
In previous papers (11, 12) the limitations of the 2-dimensional approach have been
criticized as a preliminary to considering the significance of the simple 3-dimensional
patterns, especially in relation to tensegrity. The latter achieve stability as
patterns of oscillation around a dynamic equilibrium condition. The concept of oscillation
will now be considered in more detail.
1. Conventional example
The simplest example of oscillation occurs with 2 states (models) between which the
system moves. A number of examples were given above, of which the most typical is perhaps
the classic 2-party political system.
Oscillation as a phenomenon has been extensively studied in physical and
electromagnetic systems where it is an aspect of vibration and wave motion. Such studies
should suggest interesting questions for oscillating in psycho-social systems. For
(a) An oscillation results when an elastic medium (for example a spring)
is displaced from its equilibrium or rest state. When the displacing force
is removed, the elastic medium tends to snap back, to regain its rest state,
and then to overshoot it because momentum cannot be lost instantaneously
- and thus the 'simple harmonic' cycle
recommences. In general, for a given mass, the greater the elasticity, the higher will be
the frequency of oscillation; whereas for a given elasticity, the larger the mass, the
lower will be the frequency. What is the 'elastic medium' in the
(b) An oscillating system contains energy. At the extreme of the displacement, the
energy is stored in the elastic material as potential energy. When passing through the
equilibrium condition the material is not strained; and the energy is entirely in the form
of kinetic energy of motion. Thus, oscillation involves a constant interchange between
potential and kinetic energy. Can the transformation between two types of energy be
recognized in the psycho-social case?
(c) Technologically, it is practically impossible to build a machine that transfers
energy from one place to another without having its operation accompanied by oscillatory
phenomena of some kind. Machines waste energy, and give rise to material fatigue and often
noise. Are these side-effects recognized in the psycho-social case?
(d) Most physical systems deviate at least slightly from pure harmonic motion.
Such deviations contribute, for example, to the quality of musical sound
from instruments. It can be shown that any oscillatory phenomenon encountered
can be constructed by adding together a number of component oscillations,
each of which is harmonic. What are the
'deviations' in the psycho-social case?
2. Psycho-social interpretation
A useful way of describing the periodic behaviour of simple harmonic oscillation is to
employ the sine curve whose complete cycle thus represents the complete oscillatory cycle.
This may also be viewed as a projection of motion in a circle.
a, c, and e = points of maximum kinetic energy
b and d = points of maximum potential enrgy (max. displacement)
In the psycho-social case, it is at point (a) that maximum momentum has been acquired
towards the realization of Model A. At point (b) the 'maximum distortion' of the
system in this direction has been achieved and a restoring force enters into play which
progressively phases out Model A, such that at point (c) the maximum momentum towards the
realization of Model B has been acquired. This in turn achieves maximum
'distortion' at point (d) when a reverse restoring force enters into play.
It is most important to note that within the Model A perspective, for example, there is
no way in which the reversal at point (b) can be logically acknowledged or accepted
(except possibly as a temporary set back). Model A necessarily strives to extrapolate
along the curve (a) - (b), presumably to some static 'plateau' curve of
'A-perfection'. The increasing momentum from points (b) through (c) must
necessarily be viewed by the proponents of Model A as the proliferation of unresolved
problems and 'irrational' tendencies, which are seen to achieve their maximum
deployment at point (d).
Obviously the proponents of Model B see this sequence in exactly the opposite light and
would strive to extrapolate along the curve (c) - (d), presumably to some static
'plateau' of 'B-perfection'.
The cycle therefore involves two 'inversions' of logic (comprehension
discontinuities) between the two models which are incompatible and as such mutually
incomprehensible (except that what is partially 'comprehended' is used to fuel
the antagonism between them). This 'irrationality', as related to the circular
projection above, recalls the manner in which mathematicians have succeeded in interrelating
positive and negative 'irrational' quantities by use of the Argand circular
It is this inability to handle curvature which traps the proponents of each model in
the linearity of whatever portion of the curve they are associated with. It appears
linear, just as the earth appears flat to a rational observer insensitive to longer range
Nevertheless, despite the mutual incompatibility, of the models, in the real-world
dynamic situation each is effectively defined in terms of change to or from the other.
3. 'Multiphase' oscillations
The argument above has focused on two extreme states (models) between which oscillation
occurs. As indicated in the discussion of Annex 2, combinations of states may be envisaged
between which oscillation can take place. Some of these are 'damped' as
discussed in a subsequent section.
In a three phase oscillation, for example, Model A would be replaced by Model B, to be
replaced by Model C, replaced in turn by Model A. Namely a triangular configuration.
Many such configurations are possible and can be represented by 2- dimensional
configurations. Note however that the longer the chain of models in a circular sequence,
the more difficult it is to comprehend the sequence as a whole. An interesting example of
a 64-phase sequence is that of the the sequences of changes associated with the Chinese I
Ching (or Book of the Changes). It is unusual in that a justification for switching from
one model to the next is given, thus implying a holistic perspective 'meta' to
that which is explicit.
4. Coupled and damped oscillators
Whereas the previous section focuses on a succession of models, it is also possible to
envisage, for example, the simultaneous presence of 3 oscillating systems A/B, C/D, and
E/F. If the oscillations of one affect another then the two are coupled. Such coupling may
have amplifying or dampening effects.
A system set into oscillation by some initial displacement will not continue to remain
so indefinitely unless energy is supplied from some external source. An oscillation cannot
create energy. The oscillation gradually dies away and is said to be damped. The decay
will be slow if the mass of the oscillator is large, and slow if the initial frequency is
high. An oscillator absorbs energy from a source at maximum average rate at the resonance
frequency, namely the frequency at which it prefers to oscillate. At this frequency it
loads the energy source to maximum extent.
Dampening effects may be counteracted by coupling with other oscillators as note above.
In Annex 2 the focus is on 2-dimensional configurations. But even in the simplest
2-phase case, the existence of that oscillating system is only possible by virtue of an
appropriate contextual system within which it is embedded. (e.g. attachment of spring and
gravitation governing movement of a mass). If the oscillation is described in the form of
motion in a circle, the question to ask is how that circle is 'balanced' when
considered as a rotating wheel. For either the wheel is unrelated to anything else (or
includes everything), or it must be joined to its environment in some way, especially if
energy is received to maintain the oscillation. But, just as the models associated with
each phase of the oscillation are insensitive to the cycle as a whole, any cyclic
perspective is equally insensitive to the forces required to maintain the cycle in stable
relationship to its environment -- namely to compensate for the instabilities associated
with and generated by its existence.
If the configuration of such contextual forces is rendered explicit, and integrated
with the 2-dimensional cyclic configuration, one probable result would take the form of a
tensegrity (12, 13). This may be considered as a spherical pattern of coupled
oscillations (usually three or more interwoven cycles).
In string-and-stick models of tensegrities, for example, when a stick is displaced by
application of stress, the whole system undergoes symmetrical modification to accommodate
the local movement. The system's symmetry is not deformed; the system expands as a whole
or contracts as a whole. Ability to respond as a system means that local stresses are
being uniformly transmitted throughout the structure, and uniformly absorbed by every part
of it. We have here a classic case of synergy; behaviour of whole systems, unpredicted by
knowledge of the parts or of any subset of parts.
A complex tensegrity is never quite still, however lightly the tendons are stretched.
There will always be minute oscillations, tiny stick displacements at the order of
magnitude where elasticity multiplication is truly enormous and compensating forces have
enormous advantage. The equilibrium point 'is that ideal condition of rest which
nothing real ever attains, and about which a tensegrity in particular dances an eternal
jig of pre-Socratic derision' (14, pp. 12-19).
Organization of time
The previous sections have considered progressively more complex ways in which
oscillations can be interrelated into some 'macro-pattern'. The progression has
been guided by what is known about the organization of space, given the argument of
Annex 2 that these indicate equivalents for organization over time. Note that this
progression has in effect moved from:
- 1 - dimension : spring-type oscillation
- 2 - dimensions: coupled oscillations in cycle to
- 3 - dimensions: tensegrity configurations of oscillations
The question is now whether more clarification can be obtained from the manner in which
time is organized. The above argument has not focused on the possible distinctions
between oscillations, and yet oscillations organize time in different ways depending on
their characteristics. Some of these ways may be more significant and may thus indicate
opportunities opportunities for more viable temporal configurations of models -- possibly
with corresponding simplifications for configurations in space. The point of departure is
the recognition that oscillation 'organizes' time by determining a
characteristic complete cycle. This is composed of both the
'incompatible' half cycles of the simple example discussed earlier. It
encompasses the incompatibilities typified by polarized perspectives only capable of
recognizing/accepting the swing of a pendulum in one direction (or the other). It is the
periodic complete cycle which characterizes the organization in time.
In developing the argument, oscillation in psycho-social contexts may be considered:
- (a) either in terms of macro-historical cycles, namely as the period of years in
which Model A and Model B might be successively employed, as in the 2-party political
- (b) or in terms of the micro-historical event cycles, namely as the period of
hours/days in which Model A and Model B each take and lose the initiative in the ongoing
interaction between them, again using the 2-party political example.
Since the micro-historical cycles are more easily perceptible and appear less abstract
than the macro-historical, the remaining argument will focus on them. In fact of course,
'macro' cycles with periods of decades or centuries could also be subject to the
same approach (cf the work of Pitirim Sorokim). Relationships between micro and macro
cycles will be explored in a later paper.
Since the human perceptual apparatus organizes ('integrates') oscillations
with considerable sophistication in the process of hearing, this argument will focus on
indications suggested by musical sound. Analogous arguments could be developed on the
basis of the organization of oscillations in the process of seeing colours, but since
sound can be discussed with less ambiguity, and with more precise exploration of
possibilities of integration, this is to be preferred. (On colour, see: Johannes Itten.
Art de la Couleur. Paris, Dessain et Toira, 1974)
2. Oscillation and musical sound
The perceptual apparatus distinguishes sounds as noise or tone. Noise is usually
identified not by its character but by its source. Tones are recognized as being more
independent of their source, are more organized, and as such are more amenable
to integration into musical compositions. The choice of sounds for music making has been
severely limited in all places and periods by a diversity of physical, aesthetic, and
cultural considerations. Tones are generated as oscillations.
Within this context it is now possible to consider how a series of events involving the
interactions of Model A and Model B -- a characteristic defence-attack,
challenge-response sequence in any diplomatic incident, for example -- might be usefully
perceived as a particular 'tone'. The suggestion is that there are
characteristics which enable events to be recognized as part of a familiar pattern. When
such characteristics cannot be recognized, a succession of events is considered as
incidental/accidental 'noise'. When the events do fall into a recognizable
pattern, this 'tone' can then be used as a higher unit of analysis
through which the development of the stream of events can be integrated for comprehension.
The individual events generated by incompatible models responding to each other are thus
encompassed by a pattern usefully characterized by a tone. The tone is independent of the
particular event sequence which functions as an 'instrument' to render it
Clearly the conventional approach in society is to recognize events generated by an
opposing model and to respond with a counter-event governed by one's own model. The
'tone' is not perceptible at this level.
The question is how to create 'instruments' (meta-models?) which could generate
tones, in order to move beyond the present subjection to the essentially uncontrollable reactive
dynamics of event-level interaction. If society could discover when particular tones are
an appropriate response to circumstances, it would no longer need to be torn by the
dualities of event-level interaction. Note however that event patterns are still required,
since it is through them that society functions. It is their status which is dramatically
changed. In this sense 'planning' becomes 'composition', which works
not by using a set of events to achieve something but by using tones (namely
'Music is time made audible' (Susanne K Langer). Perception of music depends
largely on the ability to associate what is happening in the present with what has
happened in the past and with what one expects to happen in the future -- whatever the
probability that the expectation will be fulfilled.
The previous section clarified the integration to the tonal level. It is useful to
consider three dimensions of time as structured by music for comprehension (noting that
recent thinking contests Einstein's one- dimension concept of time). Within this context
it is again possible to consider how models in a psycho-social system might be integrated.
- (a) Tempo is the pace of the fundamental beat of the music, namely the rate which
tones occur, whether singly or as grouped by some rhythm. A fast tempo corresponds to the
social condition associated with a 'fast pace' of life. Events and their
compensating counter-events succeed each other rapidly. Note that distinctions are not
made between the duration of event pair patterns.
- (b) Rhythm is an ordered alternation of contrasting elements (of whatever tones).
The mind apparently seeks some organizing principle in the perception of music. It
instinctively groups regular and identical sounds into twos and threes (possibly of
different duration), stressing every second or third beat, and thus creates from an
otherwise monotonous series a succession of strong and weak beats. There are six principal
rhythmic modes or metres (also found in poetry): trochee, iamb, dactyl, anapest, spondee,
and tribach. Rhythm not regulated by metre may be considered as a seventh mode. Thus one
event pair pattern may be followed by two event-pair patterns whose total duration equals
that of the first. This is the dactyl metre (-uu). Note that distinctions are not made
- (c) Melody is an organized succession of groups of musical tones (called
phrases), in which there may, occur repetition (the same phrase repeated), contrast (a
completely different phrase), or variation (the phrase altered, but in such a way that its
identity remains perceptible). Respecting the rhythm and tempo, melody is therefore a a
memorable sequence of event-pair patterns (tones) of different pitch integration more
subtle than the repetition of a single tone, however rhythmic.
Four basic types of musical form are distinguished in ethnomusicology: iterative,
the same phrase repeated over and over (as in some chants); reverting, with the
restatement of a phrase after a contrasting one (as in sonata-allegro, aria, and rondo
refrains); strophic, a larger melodic entity repeated over and to different
strophes of a poetry text (as in hymns, traditional ballads, and instrumental variations);
and progressive, in which new melodic material in continuously presented).
But what is the significance of tone?
4. Significance of tone
All sound is composed of a complex of oscillations of a certain frequency (which
determines the wavelength). Tones are characterized by four attributes revealed in their
oscillatory wave form:
- (a) Pitch, or high-low aspect, is a direct product of oscillatory frequency.
- (b) Timbre (tone colour) is a product of the total complement of simultaneous
motions enacted by any medium during its oscillation.
- (c) Loudness is a product of the intensity of that motion; an eight-level
continuum from pianissimo to fortissimo is used.
- (d) Duration is the length of time that a tone persists.
Most musical tones differ from an ideal single oscillatory wave form. Any material
undergoing oscillation imposes its own characteristic oscillations on the fundamental
oscillation. The material would probably oscillate in parts as well as a whole.
These partial wave forms bear harmonic relationships to the foundational motion
that are expressible as simple integer frequency ratios of 1:2, 3:4, etc. One way of
expressing this is to say that half the body (e.g. a stretched string) is oscillating at a
frequency twice as great as the whole; a third of it is oscillating at a frequency three
times greater, etc. Tones are in practice composites of such 'overtones' which
are ignored by the untrained car. It is however the presence or absence of overtones and
their relative intensities that determine the timbre of any tone.
Tone is primarily characterized by pitch, or frequency of oscillation. Man's aural
perception of pitch is confined within a span of roughly 15 to 18,000 cycles per second,
with 440 cycles per second having been adopted as the middle point on the keyboard. It is
now useful to ask the question what is the frequency range of psycho-social event-pair
patterns to which man is sensible? What are the 'tones' he can detect?
Clearly there are some event cycles whose frequency is so low that man cannot be
directly sensitive to their cyclic nature. Detecting the cyclicity of such phenomena is
anal;ogous to detecting the curvature of the earth's surface. The cycle of a human
'generation' is barely perceptible as such, and even a year or a month are long
cycles to many. At the other extreme, one indicator is the period of seconds associated
with fast conversational repartee. Even more rapid would be the mind
'experiments' of protagonists in any game or fight in which each runs through
the action options open to him and the probable responses of the adversary (e.g. chess,
fencing, business negotiation, etc). Cellular processes in man are however beyond the
range of his sensitivity.
In this light is it possible that psycho-social functions are each associated with a
characteristic event cycle frequency? And, when such functions are activated in a
particular case, is this frequency accompanied by the presence of harmonic frequencies,
namely associated functions? Before clarifying these possibilities, it is necessary to
consider the whole question of harmony as it has been elaborated for music.
Musical sound is usefully regarded as having horizontal and vertical dimensions. The horizontal
aspects are those considered so far, namely those that proceed in time. The vertical
aspect is the sum total of what is happening at any given moment. This includes the
result of notes that sound against each other in counterpoint. In the case of melody and
accompaniment, it includes the underpinning of chords that the composer gives to the
principal notes of the melody.
In music, harmony can be broadly defined as the sound of two or more notes heard
simultaneously. In practice this can include notes sounded one after the other in cases
when the ear creates its own simultaneity and perceives the harmony that would have
resulted had the notes been sounded together. It is also the succession of harmonies that
gives a piece of music its distinctive personality.
It should be understood that harmony is an optional additional form of organization or
integration. Rhythm and melody can exist without harmony and in fact most of the world's
music is nonharmonic, using unharmonized melodic lines often with a sophisticated rhythmic
The concept of harmony and harmonic relationships is not an arbitrary creation. It is
based on certain relationship among musical tones that the ear accepts almost reflexively,
and that are also expressible through elementary scientific investigation. A stretched
string divided by simple arithmetical ratios (1/2, 2/3..) and plucked can demonstrate that
the intervals (or distances between tones) sounded before and after the division are the
most fundamental that the ear perceives. Occurring in the music of nearly all cultures,
whether in melody or harmony, these intervals are the octave, the fifth, and the fourth.
Returning to the considerations of the previous section, the question now becomes one
of whether there are natural or fundamental harmonies between psycho-social functions? In
other words when considering the expression of a particular function, should advantage be
taken of the possibility of accompanying it by a function 'harmonic' to create a
'chord' which imbues the lifestyle with greater quality -- or, at least,
increases the quality of the moment? The quality of the moment rta has remained a
prime concern in the development of sanskrit- based culture.
6. Consonance and dissonance
The interplay of consonance and dissonance is the very foundation of harmonic music.
Consonance can be defined as the normal range of tone combinations accepted as implying
'repose' by theorists and composers of a musical culture during a given
period. Dissonance therefore refers to any sounds outside this range. Many attempts
have been made to link consonant with pleasant, smooth, stable, beautiful, and dissonant
with unpleasant, grating, unstable, and ugly. Whilst such attributions may be meaningful
in a giving musical context, difficulty arises in generalizing to all such contexts. Such
'objective' classifications are now held to be value judgements.
Dissonance has always been recognized as the prime element creating movement in
harmony. When the ear recognizes a certain harmony as unstable within the given musical
context, it 'demands' that this instability or tension be rectified by
resolution to a stable harmony. Without dissonance music would be hopelessly static. The
historical development of music can however be seen as one of exploring different
approaches to the treatment of dissonance so that the musical flow is an ordered
alternation of tension and relaxation.
This suggests a useful way of perceiving the relationship between psycho- social models
in society. How compatible or 'consonant' should they be? Is some degree of
incompatibility necessary for the dynamic of society? What methods are available for
managing the transition between compatibility and incompatibility?
In music, the understanding of which specific chords and intervals constitute
consonance has altered dramatically from the origin of (Western) harmony as indicated in
Musical composition is in a stage of intense experiment. Although concepts of classical
harmony have lost their importance it is not a question of the dissolution of harmony but
rather of the uses to which such harmonies are put, and the changing relationship of
harmony to musical structure. There are organizational systems emerging that point to a
clear control and regulation of musical elements that may in future be analyzed in terms
of a new, fundamentally different harmony. This may offer a means of relating the above,
essentially Western concepts of composer-oriented music, to the body of unharmonic,
non-Western music which is often performer-oriented. Significantly, however, music of
every epoch and harmonic organization is appreciated by growing audiences.
The above stages are not only helpful as an indication concerning the nature and
concept of integration, it has been suggested by many authors that the musical form or
code conditions social organization in many subtle ways. Furthermore, the new developments
in music are a response to the condition of society and the emerging codes indicate the
basis of the organization of society in the future. These points have been most recently
and forcefully argued by Jacques Attali (15). This perspective will be further discussed
7. Harmonic goal
In the previous section the descriptive emphasis is on the vertical harmonic
relationships, if any, between tones and the ordering which governed them. Here the focus
will be on the horizontal ordering 'where the music is going to'. This is of
course helpful in understanding how an integrative goal, or the goal of an integration
process, can be understood. It is also helpful in showing how the status of such goals has
been brought into question. The evolution of the harmonic goal is described in Annex 3.
Contemporary music may be said to be 'goal free', or to call upon the
listener to be responsible for any goal he chooses to derive from the music. The emphasis
is very much on: the response of the individual listener, the context to
which performers respond (including audience response), and increasingly the process of improvisation.
The separation between traditional musical roles is breaking down (e.g. between
listener/audience, performer, conductor, composer). The goal lies in the appreciation of
the moment whatever the range of sounds which define it.
8. Fugitive integration
The fugue is often considered to be the most complex and highly developed type of
composition in Western music. The argument above suggests that much could be learnt about
new approaches to socio-political integration from a study of integration in music.
Many aspects of have already been explored. Here the focus is on the significance of
the relationship between distinct 'voices' and themes, which is of course basic
to polyphonic and symphonic integration. In the socio-political sphere it is usual for
advocates of a proposal, a model, a cosmology or an ideology to propagate it as though it
alone should achieve dominance (ad aeternam), effectively excluding alternative
approaches. Within the musical framework this can lead to pieces which are either
immediately monotonous and boring, or whose interesting characteristics quickly become an
intolerable imposition unless balanced by other pieces in the musical diet (cf. the life
cycle of a 'hit' record). There is of course no musical continuity between the
succession of such separate pieces of music. This lack of integration is analogous to the
equivalent situation in society where the advocates of the alternatives, evoked by
overstress on a particular model, compete in parallel or in succession for constituencies
and resources for their own approaches. In the fugue however the relationship between
these competing voices is explored within a musical continuum. This represents a new level
of integration. In effect the concept (model, etc) is explored, inverted, countered,
distorted, etc within an overriding set of rules which permit a new level of freedom. The
rules ensure a more exciting balance of tension and harmony.
Could it be that one dimension of the challenge of socio-political integration is
illustrated by the problem of interrelating seemingly hostile or incompatible
'voices'. And that counterproposals and counterarguments need to be set in a
larger context to which we are as yet insensitive? And does the time dimension over which
arguments and counterarguments are developed need to be better understood in terms of an
integrated socio-political process? Such a process brings out both the essential
inadequacy of any particular proposal and the manner whereby it can be counterbalanced and
enriched by complementary proposals which together as a process bring about a new level of
integration. The implications of the fact that music has 'progressed beyond' the
fugue are discussed in the main paper. But it would appear that the lessons it offers for
socio-political integration have not yet been considered.
Liberation of integration
1. The remaining problem
Such an outcome may well be satisfactory to those who favour the appearance of anarchy,
however positively it is evaluated. The reality of the situation, as mentioned above, it
that music of every type continues to have its adherents. In effect the musical goal of
contemporary music has been 'detached' from the music and reappears in the
search for increasing degrees of liberty which composers/performer/listener can be brought
to share. This marks the achievement of the progressive liberation from the various forms
of domination built into the harmonic goals noted above.
But, by now emphasizing the experimental styles of contemporary music, such a goal
effectively aims at domination, by a particular 'liberating' style, of the other
musical styles, each preferred by significant 'constituencies'. Any such stance
of 'contemporary is best' inserts such music into a linear historical stream in
which that dominating statement has been made at every stage. It does not face up to the
atemporal reality of musical appreciation in society - and the corresponding range of
preferences for forms and degrees of order and integration.
This of course epitomizes the dramatic problem in society today. Different models are
preferred simultaneously (or as alternatives) whilst often being mutually incompatible.
This was the point of departure of this paper. Are there any indications of the nature of
the next level of integration which would respond to this paradox without introducing new
forms of dominance?
As a first indication of a direction for exploration, the notion of a harmonic analogue
to the crossword puzzle can be considered. In such a puzzle rows and columns would be all
based on different harmonic principles - covering the complete range. The art would
lie in making the points of intersection meaningful. But, as a flat bounded matrix, this
is not satisfactory. As argued elsewhere (11), a more interesting development would be to
wrap the flat surface around a sphere (or a polyhedral approximation to a sphere). In this
way the surface is unbounded and without any privileged central points. Symmetry
relationships then emerge as factors in a new level of integration. The tensegrity
approach is particularly relevant to relating incompatibles brought together in this way
In such a 'cross-harmony' model each row and column would need to correspond
to a different (non)harmonic organization. How can different styles of music be
interrelated, preserving their identity, but bringing out a transcendent harmonic order?
If it can be done with music, then may be it could be done with psycho-social models.
3. Comprehending the language of pattern shifting
The suggestion in the previous section can be viewed as a crude approximation to a
highly sophisticated approach based on the 4,000 year- old chanted hymns of the Rg Veda of
the Indian tradition. A very powerful exploration of this work by a philosopher, Antonio
de Nicolas (17), using the non-Boolean logic of quantum mechanics (18), opens up valuable
approaches to integration. The following themes are explored in the de Nicolas study:
- Interrelating formal languages based on tone
- Toward reintegrating the individual in action
- Integration embodied: the re-imaging of man
- Pluralism: integration through community dialogue
- Integrative renewal through sacrifice
- Integrative vision encountered in movement
The unique feature of the approach is that it is grounded in tone and the shifting
relationships between tone; It is through the pattern of musical tones that the
significance of the Rg Veda is to be found.
'Therefore, from a linguistic and cultural perspective, we have to be aware
that we are dealing with a language where tonal and arithmetical relations establish the
epistemological invariances... Language grounded in music is grounded thereby on context
dependency; any tone can have any possible relation to other tones, and the shift from
one tone to another, which alone makes melody possible, is a shift in perspective which
the singer himself embodies. Any perspective (tone) must be 'sacrificed' for a
new one to come into being; the song is a radical activity which requires innovation
while maintaining continuity, and the 'world' is the creation of the
singer, who shares its dimensions with the song.' (17, p. 57)
4. Limitation of vision-based metaphors
De Nicolas contrasts this perspective with that of languages governed by vision:
'Thus, in a language ruled by the criteria of sight, vision may mean the sum of
perspectives from which a fixed object can be seen, plus the theoretical perspective of
the relationships holding amongst different perspectives of the object, plus the mental
acts by which those perspectives, relationships and visions are performed. In any event,
the invariant object is the condition for the variations in the meaning of vision. The
object is the condition for the variations in the meaning of vision. The invariant object
is, therefore, not a reality, but a theoretical precondition (phenomenal or noumenal) for
a whole system or method for establishing facts. Therefore, it is no wonder that when
people speak of transcendence, within this framework, they are mostly forced to speak in
mystical terms of things unseen or unseeable, either in terms of religious experiences, or
in terms of modern physics. In a literal sense, in the latter two cases, speech is aboutno things by the same criteria of the speech used to designate things.
Whereas in a language governed by sound:
'In a language ruled by the criteria of sound, perspectives, the change of
perspectives and vision, stand for what musicologists call 'modulation'.
Modulation in music is the ability to change keys within a composition. To focus within
this language, and by its criteria, is primarily the activity of being able to run the
scale backwards and forwards, up and down, with these sudden shifts in perspectives.
Through this ability, the singer, the body, the song and the perspective become an
inseparable whole. In this language, transcendence is precisely the ability to perform the
song without any theoretical construct impeding its movement a priori, or determining the
result of following such movement a priori. Nor can any theoretical compromise substitute
for the discovery of the movement of 'modulation' itself in history. The human
body would then be asked to lose the memory of its origins; a task the human body refuses
to do by its constant return to crisis.
It is up to the philosophers to discover the language ruled by the criteria of
sound, rather than presuppose a priori that the only language universally human is the one
ruled by the criteria of sight.' (17, p. 192)
5. Integration through four complementary languages of music
Given the importance of sound and music as a major integrative factor across cultural
boundaries, and given the size of the audience which music now has through radio and
cassettes, the possibilities of this route merit further exploration. Integration
modelled on sound may be inherently more comprehensible to more people than integration
modelled on sight.
It is interesting to note a tantalizing relationships between this study and that of
Jacques Attali who structures his study of the political economy of music in terms of
'quatre formes possibles de diffusion de la musique, retrouvant les quatre structures
fondamentales que peut avoir un graphe' (15, p. 63). These are 'networks'
associated with: ritual murder or sacrifice, presentation, composition, and reproduction.
De Nicolas on the other hand structures his study in terms of four
'languages' distinguished by their intentionality: images and sacrifice,
existence, embodied vision, and non-existence. The first three seem to be related to those
of Attali, and it is the non-relationship of the last which is significant in both
perspectives. Attali's concept of the sacrificial aspect (15, pp. 43-91) as an attribute
essential for the renewal of social structures is intimately related to the Rg Vedic
concept (17, pp. 139-154). Such efforts to show the functional significance of sacrifice in
relation to social integration need attention in a period when 'nobody is willing to
sacrifice' advantages acquired under the present systems in crisis. The implications
of the relation between the two studies could also be further explored in the light of
number-governed sets (19).
De Nicolas study has already inspired an exploration of the tonal underpinnings of the
Rg Veda by a musicologist, Ernest McClain (21), which is interesting in its own right.
This helps to understand the interrelatedness of perspectives and the mnemonic value of
their expression through vivid symbols (gods, dragons, etc). McClain clarifies the musical
significance of the four languages and, in this context, their relevance to integration:
'The four Rgvedic 'languages' de Nicolas defines have their
counterparts in the foundation of all theories of music. His 'language of
Non-Existence' (Asat) is exemplified by the pitch continuum within each musical
interval as well as by the whole undifferentiated gamut -- chaos - - from low to high. His
'language of Existence' (Sat) is exemplified by every tone, by every distinction
of pitch, thus ultimately by every number which defines an interval, a scale, a tuning
system, or the associated metric schemes of the poets, which are quite elaborate in the Rg
The 'language of Images and Sacrifice' (Yajna) is exemplified by the
multitude of alternate tone-sets and the conflict of alternate values which always results
in some accuracy being 'sacrificed' to keep the system within manageable limits.
The 'language of Embodied Vision' is required to protect the validity of
alternate tuning systems and alternate metric schemes by refusing to grant dominion to any
one of them'. (21, p. 3). 'The embodiment of Rg Vedic man was understood... as
an effort at integrating the languages of Asat, Sat and Yajna to reach the dhih,
the effective viewpoint, which would make these worlds continue in their efficient
embodiment' (17, p. 136).
The whole notion of dialogue between perspectives which is the basis of the Rg Vedic
approach needs, however, to be related to current investigations of conversation theory
as summarized by Gordon Pask (20).
But, despite the richness of the Rg Vedic model, the de Nicolas study raises questions
which he does not address:
- (a) If the model is so powerful, why has it not been more widely accepted?
- (b) Since the Rg Veda is basic to the Indian tradition, why has it not been more
significant for the social problems of that country?
- (c) Since it purportedly draws people into action, why has it not clarified the problem
of acting collectively in pluralistic settings? What does a 'Rg Vedic
organization' look like?
- (d) In its own terms it is a language and can only be a partial expression of the
Language whose existence it points to. How is this paradox to be handled?
- (e) Why is the importance of modulation stressed when this paper shows it as being only
one phase and possibility in the range of approaches to harmony?
- (f) Is it a paradoxical necessity that the very openness and fluidity of its philosophy
should be based on a set of hymns which has remained unchanged (although each
interpretation is conceived as a renewal)?
These are however points to be fed into any further exploration of the possibilities so
successfully opened up by de Nicolas. It is interesting, in the light of this paper's
opening comments on the UN University's GPID project, that many of the governing
preoccupations of that project are interrelated in the Rg Vedic approach.
Conclusions and implications
1. Range of approaches: This exercise has brought into focus an intriguing range
of approaches to integration. As intended this exploration reached as far as seemed
feasible. Clearly in doing so it moved beyond familiar ground and the approaches to
integration which have been attempted by the social sciences. So whilst in the early
stages the approaches appear as 'models' of integration, the subsequent stages
take on the aspect of 'analogies', and the final stages could simply be
considered as 'metaphors'. This is not to deny the value of the final
possibilities, rather it highlights the fact that it may be our attitude or problems of
comprehension which reduce possible models to 'superficial' metaphors.
Conversely, the sterile inadequacy associated with models may result from their function
as metaphors -- 'taken too far'.
2. Locus of incompatibility: A key factor in considering the value of these
various possibilities appears to be where one chooses to 'locate' the
'incompatibility' or hiatus between alternative modes (or models). Locating
it at the level of the single oscillatory cycle must necessarily 'push' any more
sophisticated approaches to integration into the realm of analogy or metaphor. For
conceptually we have not yet digested such a cycle involving incompatibility. If however
the incompatibility is modelled by dissonance between tones (based on oscillations), the
apparent drift is only encountered further towards the end of what could usefully be
perceived as a continuum. This raises the interesting question of how incompatibility or
discontinuity is 'contained' (or nested) at a lower level. (For example the
oscillatory left-right motion of walking is a complex problem of balance which a child
must learn -- once learnt the jerky discontinuity of the broken cycle disappears and
'walking' may be comprehended at the 'tonal' level, later still
walking merely becomes an aspect of dancing or other patterns governed by
'harmony' of some kind).
3. Beyond the broken cycle: It is certainly appropriate to consider that in our
attempts to reconcile societal alternatives we are at the 'broken cycle' level
(just 'limping' along). The attempts to move beyond this in envisaged policy
proposals seem 'monotonous' (lacking any sense of 'rhythm' and 'melody').
Perhaps the non-Western cultures endowed with a greater sense of rhythm and rhythmic
organization will provide the understanding to move us all into a new mode in which the
Western understanding of harmony can be used. On the other hand, it is important to
recognize that it is often those rhythmically-oriented segments of Western culture, for
which current social science thinking is sterile and meaningless, but which need to be
integrated into the process whereby social alternatives are envisioned. (This aspect of
integration also needs to be considered in relation to the social scientist, who in other
roles expresses a well-developed sense of rhythm and harmony, but whose professional
thinking may in this context resemble that of a learner on a musical instrument).
4. Resonance: The possible significance of the concept of resonance between an
oscillatory cycle and its bounding environment merits further reflection. It is
significant in relation to the use of available energy, to affecting the environment, to
enhancing environment cycles, to destroying 'crystallized' structures, etc.
Entrainment of one oscillatory cycle by another should also be considered. In a world seen
in terms of movement these two phenomena are significant in terms of the prenuptial dance
and the process of conception.
5. Harmonic goals: The concept of harmony and a harmonic goal may also be used
in evaluating such phenomena as a conference or an academic paper as
exercises in integration. In the case of a conference there is some merit in seeing it at
the broken cycle level trying to get together a coherent tone. But it may also be seen in
terms of polyphony and the challenge of harmonizing different voices. But in the light of
the historical evolution of harmony, the value of moving the conference through a series
of consonant and dissonant 'chords' to a tonic goal may be viewed as somewhat
simplistic (The closing phases of most conferences these days reveal the superficiality of
that goal). In a separate paper suggestions have been made concerning non-linear agendas,
weaving consonance and dissonance at a 'tensegrity conference', which could
correspond to another level of harmonic integration (22). It is tempting to see the use of
non-sequiturs, inconsistency and anecdotes in a conference or a paper as corresponding to
chromaticism in music. Edward de Bono's call for the use of 'po' to break
sequence is also relevant (23). For a more extreme example consistent with the historical
evolution of harmony, Christopher Jones random number generated conference paper should be
noted (23). It aimed to break down the whole approach to 'conference think'.
6. Concepts of progress: The Rg Vedic approach however casts a valuable light on
many aspects of integration. Firstly the whole motion of a historical sequence progressing
towards 'greater' or 'better' integration is seem to be only partially
associated with linear thinking - partially because it would be a Boolean-logic approach
to stress only the non-linear aspect. This relates to the whole question of whether
progress is an illusion (25). In one sense there is no convergence to better integration,
only a more integrated understanding of the present moment - which is however - where we
7. Choice and integration: It is however this ahistorical context which frees
the individual's power of choice. The individual can choose to be moved by a 'less
sophisticated' form of harmony - rejecting the greater freedom of contemporary music,
for example. The ultimate freedom is the freedom to be unfree, bound by particular
8. Dialogue and integration: Given, the UN University/GPID stress on dialogues
and integration, the Rg Vedic focus on dialogue between contrasting perspectives and its
relationship to integration is valuable.
9. Harmony of harmonies: Perhaps the subtlest aspect of the Rg Vedic model is
that which confronts the problem of the integration of alternative approaches to
integration. This is the distinction between languages which can each only partially
express the insights of a Language which can only be expressed through them. This is the
problem of the harmony of harmonies, in which the alternatives appear and disappear
as patterns of ripples on the surface of a sphere.
10. Theory vs. Praxis: Extremely valuable is the Rg Vedic oscillation between
theory and praxis as inherently incompatible but necessary to each other. It is refreshing
to see those related as yin- yang complementaries - with the hope that some androgynous
perspective may emerge (26).
11. Integration of what?: The whole notion of a range of tones suggests a
fundamental question: what are the different things that need to be integrated to bring
about a quantum change? And what is the necessary harmony of that integration in order for
the change to occur? Why cannot we focus more clearly on the relationship between the
factors which generate and control the various 'waves' (27) to which our
societies are subject? (*) What are the forms of organization that are required?
12. Individual self-image: But aside from its relevance to the various aspects
of human and social development mentioned at the beginning of this paper, the whole notion
of harmony is of special relevance to the concept of the individual and to the
individual's concept of herself or himself. Given the variety of roles/persona through
which the individual expresses himself, the concept of 'harmonizing' such voices
in one way or another is very intriguing (e.g. the notion of polyphony). Also the notion
of organizing one's time and awareness in terms of a 'melody' of such voices,
perhaps with some overall harmonic goal. At this level a certain convergence can be seen
with the affective and dramatic content which composers have conventionally associated
with certain forms of melody and harmonic organization - most crudely in the musical
accompaniment to films. A challenge for the individual is then to experiment with subtler
harmonies whilst maintaining the option to move between them. This is an organic approach
to maintaining continuity of awareness, rather than being subjected to a 'broken
cycle' style of life. As such, concepts of harmony are relevant to the question of
13. Individual as keystone for integration: This paper started by suggesting
that more elegant forms of integration might not only be desirable but also necessary
for effective integration to be achieved. But whilst our values now stress the importance
of centering social development on the human being, the Rg Vedic model would appear to go
beyond an indication that this is desirable. It would appear that, to bring about the kind
of integration which is required by the conditions of our society, it is essential that
integration be embodied, transmuted and expressed through the individual in movement. The
individual is in this sense the dynamic 'keystone' to an integration relevant to
human social development.
'With the Classical Physics viewpoint of the world, we were primarily concerned
with discovering notes, classifying them and aiming, through their different
classifications, to compose a symphony that would eventually sing the world so conceived.
Suddenly, with the discoveries of Modern Physics we have realized that the symphony was
already there; that the songs were already being sung, and that the true sound of any note
was embedded. One could say that one single note is the whole song; that in order to play
one single note, one has to know the whole song; or that while playing one single note one
is playing the whole symphony. Silence underlies both as a condition of possibility.
Perhaps this musical metaphor helps clarify what has preceded it.' (De Nicolas,
'We can't put it together; it is together' (The Updated Last Whole
Earth Catalog, 1974)
Annex 3: EVOLUTION OF HARMONY
For Western music, harmony has evolved over the centuries
A. Vertical harmonic organization (the moment)
(a) Ancient Greece: Harmony based on the succession of tones within an octave. Scales
were used as a basis for singing in unison. Melody was synonymous with harmony.
(b) 6th to 9th century: Use of any 12 such modes (scale patterns of tones and
semi-tones) in which the notes also had characteristic functions.
(c) 9th century: Only the simplest 'perfect' harmonic ratios were accepted:
fourth, fifth, octave. This allowed the addition of one or two voices which exactly
paralleled the original melody. Later these voices acquired melodic independence, possibly
moving contrary to the original melody.
(d) 12th to 15th century: Inclusion of other intervals, thirds and sixths, and in some
cases, seconds and sevenths. This was associated with the development beyond 3-part
scoring to 4-, 5-, and 6-part scores, thus further enriching the harmony of voices.
(e) 15th century: Introduction of additional notes outside the mode, thus breaking down
the distinction between the 12 classical modes and foreshadowing the major/minor mode
(f) 16th century: The tonic, or keynote, triad then became the point of departure and
of arrival in a composition and in its component phrases.
(g) 17th century: Greater emphasis was then placed on expressive melodic line
harmonically underpinned by a base line as the generating force upon which harmonics were
built (often by improvisation) -- contrasting markedly with the interweaving of parts of
(h) 19th century: Deliberate use was then made of unresolved harmonies (unstable chords
used as self-sufficient entities) and of ambiguous chords. Although rooted in tonality,
every possible device is used to complicate or obscure the tonal sense.
(i) 20th century: Use of chords seemingly conforming to classical practice but which
are resolved in unexpected directions. Tonality exists in the sense that there are
extended stable areas that give the impression of being in some definable key, but the
intense use of notes outside the scale of the basic key (chromatism) makes it nearly
impossible to group the unity of a work in terms of its adherence to a clear tonal plan.
(j) 20th century: Use of atonality, abandoning the traditional duality of consonance
and dissonance (eliminating the concept of a single predominant key as tonic). Break away
from traditional scales in recognition of the power of context and the sense of a
continuum between consonance and dissonance.
(k) 20th century: Emphasis on performer improvisation/interpretation catalyzed by
indeterminacy procedures making any concept of overall harmonic direction irrelevant.
Musical composition is currently in a phase of intense experiment. Although concepts of
classical harmony have lost their importance, it is not a question of the dissolution of
harmony but rather of the uses to which such harmonies are put, and the changing
relationship of harmony to musical structure -- and the emergence of a new, fundamentally
B. Horizontal harmonic organization (over time)
(a) Up to 15th century: In the use of 7 to 12 harmonic modes, the harmonic goal was
governed by the given scale pattern. Although chants were sung unharmonized and in a
rhythmically free manner, there were constraints and there was a proper final note for a
(b) With the development of melodic independence between voices (polyphony) and the use
of dissonances within the composition, emerged an emphasis on the resolution of such
tensions through consonances at the end of compositions as the point of arrival. This
reinforces the idea of the cadence, or the finality of the keynote of a mode on which
pieces normally ended.
(c) From the 16th century: Devices such as the suspension were used as a way of
enhancing, through dissonance, the resolution to consonance and the sense of completion of
the final chord. In a suspension one note of a chord is sustained while the other voices
change to a new chord. In the new chord the suspended note is dissonant. One or two beats
later the suspended note changes pitch so that it resolves into, or becomes consonant
with, the chord of the remaining voices. This reinforced awareness that harmony moves
through individual chords towards a goal.
(d) 17th century: The concept of a key was developed as a group of related notes
(belonging to either a major or minor scale), plus the chords formed from those notes, and
the hierarchy of relationships among those chords. The keynote, and the chord built on it
is a focal chord towards which all chords and notes in the key gravitate. Given chords
assumed specific functions in moving toward or away from harmonic goals, the main goal
being the tonic key or keynote - of which there were a total of 24 possibilities. These
derive from the 12 major key scales and 12 minor key scales (each of 7 tones). The most
common movement from chord to chord is through 'strong' intervals (fourths,
fifths, seconds) which have the' fewest notes in common.
(e) 18th century: Modulation, or change of key, became an important factor because it
allowed the composer to exploit the listener's ability to sense the relation between the
keys. Modulation was usually to a 'dominant' key which was a 'strong'
interval' apart. After the modulation there is a process of return to the initial
key. During this process the harmonic movement tends to pass rapidly through many chords
and often with momentary diversions into many new keys thus dramatized as unstable -- and
in this way lending greater impact to the eventual return to the stability of the original
key. This modulatory scheme from tonic to dominant key and back to tonic key formed the
basis of large-scale musical forms, although often with additional refinements (such as
secondary dominants) to strengthen the sense of completion of the tonal journey.
(f) 19th century: There was increasing disavowal of modulation, in terms of any tonal
goal. By deliberately failing to resolve dissonances, or by creating ambiguity so that it
was unclear whether resolution had been achieved, the status of the harmonic goal was
redefined. The listener was called into an active role to respond to the
'questions' raised by the unresolved elements and to define the unity to be
supplied. This blurring was also counter-balanced by an emphasis on continuous, goal-less
melody. Two simultaneous tonalities (polytonality), neither dominating the other as a
tonal goal, were also used.
(g) 20th century: With the advent of serialism, no single note could any longer serve
as a harmonic goal. Whereas melody, from being synonymous with harmony (Ancient Greece),
became the surface of underlying harmonies (16th century), and then bore its own harmonies
(into the 19th century), serialism provided a melodic sequence out of which harmonies were
generated. Such harmony effectively became the surface, or final result, of melody.
Contemporary music may be said to be 'goal-free', or to call upon the
listener to be responsible for any goal he chooses to derive from the music. The emphasis
is very much on: the response of the individual listener, the context to which performers
respond (including audience response), and increasingly the process of improvisation. The
goal lies in appreciation of the moment whatever the range of sounds which define it.
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7. See summary in ref. 12
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