Given the essential discontinuity between the domains in a pattern of alternation, the key question is whether there is any way of comprehending and communicating the nature of the transformations between the elements in the pattern, other than "superficially" in purely right-hemisphere (dramatic) terms. Furthermore, it would be useful to clarify the basis for the emergence of each domain within the pattern. A recent study by Ernest McClain, a musicologist, demonstrates that the "father" of political philosophy, Plato, has further unexplored insights to offer concerning these matters, especially in view of his aesthetic concerns (which correspond to Attali's requirement). McClain points out that great care must be taken in exploring Plato's political allegories because of his considerable use of puns metaphor and humour as a form of presentation appropriate for arguments comprehensible to a musically and mathematically informed audience. It is appropriate to follow Mcclain's lead because he draws attention to a language which can be used to clarify the nature of alternation.

McClain demonstrates with considerable musico-mathematical precision how Plato conceived four very different tuning systems whose characteristics he described through the four different communities (Callipolis, Ancient Athens, Atlantis, Magnesia) which are the subject of his later dialogues. As McClain says, they are:

"each vividly, presented but each necessarily "sacrificed" to let the alternatives come into view. This mode of thinking, or manner of talking, is appropriate for the realm of alternative aesthetic structures which are equally appealing - from one point of view or another - but mutually incompatible in time. Not only do Plato's musical cities come to be, but each must pass away - as each tone, each mode, each rhythm must pass - to allow the next to come into focus. There is no dialogue which "fixes" Plato's thought for us. The Republic and Laws are so opposed in spirit - the first proposing a communal brotherhood with few laws and common wives, children and property, the second satiated with law and central government - as to appear to be the work of two different men....Plato is in no sense what we have come to understand as a "Platonist". Neither is he a Pythagorean. His Pythagoreanism is but a prelude to philosophy, to "the song itself...which dialectic performes", a prelude to which Platonists have declined to listen, although it establishes the multiple perspectives from which Plato understood himself." (31, p. 132-3)

The constrants and possibilities of developing a tuning system within which harmonies and discords can play themselves out allows McClain to demonstrate, using Plato's material:

• limitation: "In political theory as in musical theory, both creation and the limitation of creation pose a central problem. Threatening infinity must be contained. Conflicting and irreconcilable systems...must be coordinated as an alternative to chaos. Limitation, preferably self-limitation, is one of Plato's foremost concerns" (31, p. 1 4) "The political lesson - a musical analogue - points to the impossibility of founding a lasting state on any model which lacks an internal principle of self-limitation..." (31, p. 19??)
• inevitability of degeneration: McClain demonstrates how the expansion of any system, musical or political, leads to its degeneration. Plato's well-known theory, concerning the transition between five kinds of ruler, through aristocracy to tyranny, whilst no longer of interest in those terms, acquires new relevance as a metaphor in the light of McClain's analysis
• just distribution in practice: Plato provides a unique response to the central problem of how a whole is to be divided up into parts which can be harmoniously related. The musical language he uses clarifies the impossibility of achieving the ideal solution to this problem, whether in music or in social systems. The many possible tuning systems model the variety of "intuitive" approximations to this solution (#14). The best approximation is achieved by "tempering", namely through a slight deformation of the ideal distribution amongst the parts, in order to achieve harmony within the whole. As McClain demonstrates, the Republic is from a musician's point of view a treatise on equal temperament, namely on the ways of approaching the fundamental musical problem arising from the incommensurability of certain musical intervals. In Plato's terms justice does not mean giving each man "exactly what he is owed" but rather moderating such demands in the interests of "what is best for the city" (31, pp. 5 and 55). His communities model tuning systems which achieve this with different advantages and disadvantages to the quality of the whole and to that of the parts. But what is important here is not the models but the language which interrelates these possibilities.
• dialectics of opposites: The language used requires, and embodies, a critical process of turning back to examine anything that has been assumed. "It is this turning back to criticize one's initial assumptions which separates Plato from all philosophy developed from "first principles"...No assumption we can make...makes any sense until we have "turned back" to study them also from the opposite point of view" (31, p. 8 and 33).

McClain's analysis provides a much richer understanding of how and why alternatives may be distinguished, and of how the sets of categories may be derived by which a "seductive" pattern of functions (or institutions) is defined. It shows the need for sufficient variety to "contain" or "carry" interesting harmony, but marks the emergence of various limits necessary for the integrity of the system. But although the pattern of alternatives clarifies the nature of the required container, the art of choosing and moving between them remains (delightfully) elusive, as pointed out in a study (30) of Vedic musically-encoded philosophy to which McClain refers in an earlier work:

"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."

In this sense much can be learnt from current interest in "techniques" of improvisation in music groups in which each instrument is free to respond to the others in a "dominant" or "subservient" manner:

"...each musician must search for missing material in the performance of the neighbour (pitches from the first, length from the second) and react to it in different ways: imitate, adapt himself to it (if need be further develop), do the opposite, become disinterested or something else (something "unheard of")" (102)