Music as an Analogy
for Economic Order
in Classical Antiquity
by Dr. Michael Hudson, ISLET
©
in Jürgen Backhaus (ed.),
Karl Bücher. Theory, History, Anthropology, Non-Market Economies
(Marburg:Metropolis Verlag 2000): pp. 113-35(page 11-15 of the manuscript uploaded here)
Music and economics each are abstract in their own way, and few people see much of a connection today. There is of course the "economics of music," but as Prof. Senn observes, music is a profession whose members are among the least economically motivated. Performing a musical work is so creative an act that amateurs do it without remuneration, and aspiring musicians sometimes even pay for the privilege of performing in major concert halls.
Not many people deem the Dismal Science to be aesthetic. Few economists practice it for their own creative enjoyment. Whereas music may be performed simply for the joy of it, economics subjects everything to the measuring rod of money, and deals on a mundane level only with that part of life that can be quantified in terms of prices and costs.
The term "harmony of interests" is of course well known, and Henry Carey wrote a book by this title, which inspired Friedrich Bastiat's "economic harmonies." The metaphor extends back at least to classical Greece. This essay sketches how musical principles were used as early analogues for economic relations and good social order.
Harmony
The first musical dimension is the scale itself. Its twelve tones (the seven notes A through G, plus the five sharps or flats that make up an octave) must be tempered so that they resonate harmoniously. There are mathematical relationships to such tuning, as the tones are proportional to string and tube lengths. The Pythagoreans demonstrated such relationships with a monochord, an instrument whose single string could be divided a movable bridge (the kanon) into halves, thirds and smaller proportions to produce the basic musical intervals.
Any discussion of natural proportions provides an analogue for distributive justice and social order. The mathematical ratios underlying music's harmonic relations were related to worldly political relations as well as applied on the cosmological level to music's sister science, astronomy (the harmony of the spheres). As Edwin Minar observed in his Early Pythagorean Politics in Practice and Theory (1942:33), "the most important element of Pythagorean morality is 'armonia, which means in practice that subjects must be 'persuaded' to accept willingly the dominance of their natural superiors."
Alas, only a few well‑born individuals could enter the select company who determined policy under Pythagorean‑oligarchic regimes. These opponents of democratization found it natural that a small landowning class should hold onto what its ancestors had taken during the Dark Age that followed the collapse of Mycenaean civilization c. 1200 BC. Disharmony stemmed largely from people -- especially the demos -- not knowing their proper place in this social order. The forces of democratic change were countered by idealizing a harmony in society based on "co-operation" with (i.e., obedience to) hereditary leaders controlling religion, culture and the court system. It is in this political context that their musical philosophy must be understood.
To the casual scholar the name of Pythagoras of Samos (c. 570-497 BC) is associated with the earliest Greek writings on tuning, geometry and mathematics. But Walter Burkert (1972:9) warns that we can believe almost nothing of the ancient traditions regarding his scientific discoveries, Pointing out that "the musical experiments which are attributed to Pythagoras are physically impossible," Burkert suspects that the acoustical discoveries associated with his name stem from two later followers from Tarantum: Archytas c. 400, and Aristoxenos c. 325, creating a "Pythagoreanism without Pythagoras."
Elaborating on what the Pythagoreans had started, Plato (c. 429-347) placed music at the head of his quadrivium at the Academy he founded in 387 at Athens. In this earliest and most vaunted educational institution of antiquity, music emerged as antiquity's most highly politicized art -- not training for musical performance, but the mathematics of tuning as a body of intellectual symbolism for the epoch's anti-democratic political forces. Just as tuning the scale was a matter of proportions, so well-proportioned societies were held to reflect mathematical relationships which preserved the status of the wealthy oligarchic families.
The Pythagorean clubs, from Croton to Athens
Around 750 BC, Syrian and Phoenician merchants established trade relations throughout the Mediterranean. Populations recovered, creating pressure for access to the land that had been monopolized by warlords. In city after city, commercial revival set in motion pressures for the demos citizen-army to improve its economic status. Starting with Sparta and followed by Corinth c. 557, the wealthy landed families who sought most inflexibly to maintain their hereditary power were overthrown by populist "tyrants."
This was the century in which Pythagoras grew up on the island of Samos. Herodotus (3.39ff.) reports that c. 532 the island experienced a social revolution led by Polycrates, who exiled the rival aristocrats and broadened economic opportunities for the population by promoting handicrafts, a large public works program and the navy. Freed from oligarchic control of the land, Samos prospered.
We cannot understand what made Pythagoreanism and its music theory so influential without understanding the vehicle by which it was spread: the political clubs (hetaeries) which were the basic building blocks of Grecian society in the absence of strong state organs.
Calhoun (1933:13ff.) has traced these clubs back Homeric Greece, a region of small settlements ruled by chieftains surrounded by companions who provided supporters to their cause. Gradually, their power had to be shared with the families who established themselves as a landed aristocracy. Each leading family had its retainers, and each popular leader or contender sought to attract others into his political club.
So typical did these clubs become throughout Greece that most of the aristocracy were "clubmen," that is, members of hetaeries composed of about twenty friends who were roughly equal in age and came from similar social backgrounds. These clubs typically held banquets and drinking bouts, and became the natural vehicles for hatching plots and organizing political initiatives. Kylon became an early tyrant of Athens by means of such cliques. Later, as rivalries developed among the leading families, Peisistratos and Cleisthenes used their own clubs as instruments of political manoeuvering.
As the transition occurred from aristocratic to democratic rule throughout Greece, such clubs were mobilized to block further democratization. They helped fix law suits, planned legislative initiatives and attacks on rivals, and on occasion directed political coups. In this evolution into political organizations involved in covert dealing and influence peddling they have been likened to New York City's Tammany Hall.
Pythagoras became the patron saint of the most anti-democratic clubs. They used the principles of musical harmony as a patina of pseudo-science to give intellectual legitimacy to a movement whose worldly consequences were anything but harmonious. The Pythagorean clubs became a network of civic cults rising above the local sphere to which most clubs related. There seems to have been some connection with the Delphi temple (the name Pythagoras means "voice of Pythia," the snake-goddess of Delphi and its oracle). They have been likened to the Free Masons, in that they served as a kind of Council of Foreign Relations or New World Order.
Fleeing Samos, Pythagoras and some followers are reputed to have settled in Croton, in southern Italy. Known as Magna Graecia ("Greater Greece"), the region had been colonized by the Greeks in the seventh and sixth centuries BC. Its most prosperous city was Sybaris, whose living style was so luxurious that the adjective "sybaritic" has survived in modern languages. The city issued the region's earliest known coins, and Athenaeus (XII.518) relates that "the Sybarites were the first to forbid noise-producing crafts from being established within the city, such as blacksmiths, carpenters, and the like, their object being to have their sleep undisturbed in any way; it was not permitted even to keep a rooster inside the city."
With the flowering of commerce, Sybaris had experienced its own democratizing revolution. A populist leader, Telys, seized power and exiled the families who had monopolized the land and forced the population into debt.
Just as Samians such as Pythagoras had done, the exiles from Sybaris sought refuge in Croton, at the altars in the marketplace. Telys demanded their return, probably to punish them. Croton's leaders debated what to do, and are reputed to have been swayed by Pythagoras reminding them of the sacred obligation to protect suppliants. Croton accordingly went to war against Sybaris. (Burkert 1972:116 points out that this story sounds suspiciously as if it were based on contemporary plays, The Suppliants, by Aeschylus and Euripides.)
Sybaris was attacked by Croton in 510 BC. And just as harmonious relations had characterized Sybaris at peace, so music played a role in its war. According to an anecdote repeated by Athenaeus (XII.520), the Sybarites "carried their luxurious refinement to such a point that they even trained their horses to dance at their feasts to the accompaniment of pipes. The people of Croton knew this when they made war on the Sybarites." As the cavalries opposed each other on the field, Croton's musicians began to play the horse-marching music, whose tune reportedly was revealed by a Sybarite flute player seeking revenge for some insult. When the horses heard the pipers, they went into their ceremonial march and became useless for battle, dancing away with their riders to the side of Croton.
The majority of Sybarites and disenfranchised debtors are reported to have wanted the land to be divided by lot, but the victorious Crotonites gave control to their own aristocracy to divide among themselves, and Iamblichus reports that "the populace forsook them" (Guthrie 1987:118). In fact the city was destroyed, in a manner that Burkert calls "the worst atrocity wrought by Greeks against a Greek city in that era." It was an example of oligarchic misbehavior rivaled only by the Athenian dictatorships a century later, in which Pythagoreans also played a subversive role as would-be Guardians acting quite unlike the ideal of philosopher kings.
Croton's victory enabled it to support oligarchic parties in other cities. "A common method," writes Calhoun (1933:140ff., cited in Minar 1942:27), "was to organize a Pythagorean society in each city, which then aided them in seizing power." Most of these clubs had about twenty members, and they typically met in the gymnasia, a popular civic center for aristocratic gatherings. (Croton's "mother" lodge was uniquely large, numbering about three hundred.) They were centers of power among the leading families, working with other clubs to control public offices by covert manoeuvering and financial subsidies that did not stop short of outright bribery. Forming the brotherhoods from which autocratic leaders were chosen, their political program was to restore the so‑called "ancestral constitution (patrios politeia), basically the old authoritarianism that had survived from the Dark Age.
As for their scientific pretensions, Minar (1942:33) depicts them not as objective musical or mathematical groups. "There is very little even in the most abstruse philosophical doctrine that can be called scientific. The Pythagoreans made some genuine contributions in mathematics and perhaps in music, but it may fairly be said that one of their chief concerns was to discourage anything like experimentation."
Pausanius (6.131) describes Croton's Pythagoreans as being early supporters of Sicily's dictator Gelon, who came from a family of hereditary priests of the underworld. He seized power over Gela in 491, and was soon invited to help crush the region's popular uprisings. Much like a modern Latin American military caudillo, he turned power in Syracuse over to the local landed nobility. In 478 he was succeeded by his younger brother Hiero, who exemplified how oligarchies are prone to internecine warfare by intervening against Croton. His younger brother Thrasybulus succeeded him in 467, but was so unpopular that the Syracusans revolted and brought the tyranny to an end.
By this time aristocratic tyrants were being overthrown throughout the region and democratic regimes set up (Diodorus 11.67‑72). Croton's warlords in Sybaris were overthrown in 467, and around 450 the Pythagorean meeting place in Croton itself -- the house of Milo -- was burned down, with most of the club members in it. Throughout southern Italy the Pythagoreans were driven out, reflecting popular anger at the regimes they had propped up. Diogenes Laertius depicts this "as a blow for freedom from tyranny" (Burkert 1972:118f.), and Appian observed that the south Italian Pythagoreans, "and in other parts of the Grecian world some of those known as the Seven Wise Men, who undertook to manage public affairs, governed more cruelly, and made themselves greater tyrants than ordinary despots." (A second and final expulsion of the Pythagoreans from Italy occurred around 390, leaving only Tarantum as a major center.)
Most of the Pythagoreans who managed to escape emigrated to establish new bases on the Greek homeland, especially at Phleius and Thebes. In Samos, which had become an oligarchy, the Pythagoreans were welcomed into the local political clubs as fellow lodge members so to speak. In return, they were able to give these clubs a pseudo-cosmology to rationalize their economic ideology. No ruling class ever before had needed such a rationale. But as divisions between oligarchies and democracies emerged, the new brotherhoods developed into early examples of sectarianism.
The way in which the Pythagoreans built up their position as advisors to the oligarchies remains an object lesson in how two opposing systems of religion, culture and political idealism first came into being in the West. Pythagoras appears to have been a master cult-maker. Burkert (1972:178, 165) points out that if we look at that element of his legend not influenced by Plato's subsequent mathematizing, he appears as "the hierophant of Great Mother mysteries with an Anatolian stamp" and the doctrine of rebirth, probably taken from Indo-Iranian Zoroastrian sources. He adopted pre-existing Greek cults and, even more important, Grecianized Near Eastern prototypes replete with common meals, a secret body of knowledge and ritual taboos typical of cults of the sort that anthropologists have described as characterizing secret societies throughout the world.
4
Mysticism, especially esoteric number mysticism, seems inherently hierarchic, yet the doctrines of reincarnation and earth deities seem to have been adopted from the Near East first by the Orphics as a popular movement. What Pythagoras did was adopt them to the upper classes, turning these cults into a would-be religion along the way. The historically close links between authoritarianism and mysticism are well illustrated by the way in which the Pythagoreans elaborated the hetaeries into an allied type of association, the thiasos.
They clubs engaged in political activity and the self-promotion of their members, but with a mystical cultish overlay that provided a seemingly objective, even cosmological legitimization for their self-serving ideology. As Oldfather (1938) explained their ideas of rule and order, "Pythagoras was the founder of the very theory of aristocracy and the chief mover in the oligarchic reaction against democracy. . . . The spiritual affinity between these principles and those of certain modern totalitarian states would seem to be fairly obvious." Their elitism is reflected in a verse cited in Iamblichus's Life of Pythagoras (conveniently collected along with related Pythagorean documents in Guthrie 1987): "Like the blessed gods, he revered his friends, but reckoned others as of no account."
But the followers of Pythagoras were not able to develop their cults into a full-fledged religion. They served mainly as the intellectual predecessors of Platonic philosophy. What survived was just enough reference to natural law and cosmology to provide a mantle for authoritarian deductive system-building.
In Athens, the Pythagorean clubs joined to seize power during the rule of the Four Hundred (411-407 BC), and again under the yet more dictatorial Thirty backed by Sparta (404-403). Theopompus and Posidonius describe Athenion, the leader of the oligarchic Four Hundred, as a Pythagorean who, "at the first opportunity, cast aside the mask of philosophy and became a tyrant."
Being so dissonant in their own behavior, it seems ironic that the oligarchs could have made musical harmonics their rallying cry. What they really were doing was using an attack on the popular music of their day as a highbrow way of denouncing the mobocracy (ochlocracy), not unlike the efforts of Allan Bloom at the University of Chicago in modern times. Democracies were denounced as being radical innovations and, at the same time, decadent in falling away from the "ancien regime," most notoriously in their musical tastes.
The elaboration of Pythagorean musical-social theory by his Tarantum followers
If Pythagoras is reputed to have studied in Babylonia and Egypt, much of his wisdom may have been mediated by Delphi, the central planning coordinator for Greek colonization and political development. Delphi's symbol as the seat of 'secret wisdom' was the tetrad of numbers 1, 2, 3 and 4. "The important thing in Pythagorean musical theory was not the function of the proportion but the meaningful numbers," concludes Burkert (1972:400). "The 'Fourness' which is the 'harmony' in which the Sirens sing, suggest the numbers 1, 2, 3, 4," which happen to contain the harmonic ratios of the musical fourth (4/3), fifth (3/2) and octave (2:1), "and thus comprehend the orderliness not only of music but of the universe, and the sum of these four numbers is 10, the 'perfect' number."
This kind of numerology probably was all that Pythagoras himself drew upon. It became a kind of mathematical puzzle that gave a patina of higher wisdom to the clubs established by his followers. More refined acoustical and musical-political philosophy came more than a century after the death of Pythagoras in the first half of the fourth century BC, at the hands of Archytas of Tarantum (428-347). 5
Archytas developed the musical scale into a political metaphor for the scales of justice. What gave music this imagery of social balance and just proportion was the ability of its mathematics of harmonic ("geometric") proportions to serve as an analogy for how inequities of wealth and status rendered truly superior men equal in proportion to their virtue -- which tended to reflect their wealth. By this circular logic the wealthy were enabled to rationalize their hereditary dominance over the rest of the population.
Archytas emphasized that there were different kinds of proportion. Simple arithmetic proportion is characterized by the progressions 1, 2, 3, 4, or 2, 4, 6, 8. Each number in the series stands an equal distance from the next. On a graph this progression appears as a straight line.
But this is not how musical scales work. Whatever the key or clef, the relative proportions among the intervals and string lengths remain constant as they are transposed higher or lower. Each octave is double the frequency (or half the string length) of the tonic (i.e., from C to C' or from G to G'), while the interval of the fifth (C to G, or C' to G') sounds always in the ratio of 3:2. Musical intervals rise by a process of multiplication (and descend by division). Thus, the proportions between the intervals remain constant, being doubled or otherwise multiplied in the ratio 2, 4, 8, 16 and so forth. This is known as geometric proportion. On a chart, this exponential series looks like an ascending wave. Each higher tone or number in such a series stands increasingly far from its predecessor, just as the aristocracy should remain proportionally superior to the population at large.
Following Harvey (1966), Ste Croix (1981:414) explains why the discussion of musical proportions became central to the cosmology of classical Greek politics: "The equality exalted by democracy was said to be a kind of arithmetical proportion in which each number (representing a man) stands at an equal distance from its neighbor (2, 4, 6, 8 etc.). But this, it was claimed, fails to take account of the real value of each number (each man) and therefore introduces flagrant inequality, for the higher up the scale, the smaller the ratio at each step; hence, in political terms, the better the man, the less his worth is rewarded," i.e. in proportion to his status. "Geometric proportion, which is not employed by democracy, is much fairer, in that the ratio at each step up the scale (2, 4, 8, 16, etc.) always remains the same; hence, in political terms, what each man receives is always equal to his worth," usually determined by his inherited wealth and status. In other words, "Inequality is true equality," at least on a logarithmic scale.
The word logarithm means "ratio number." It derives from logos and arithmos, the logic of knowledge, for "mathematics" at first meant general knowledge, before Platonism focused it on the study of numbers, in the sense of his quasi-Pythagorean political philosophy as a hidden or secret knowledge. The musical scale happened to be the pre-eminent logarithmic scale known to antiquity. The other use of exponential calculations was to measure the doubling times of a financial principal at interest, but this link with the ungentlemanly calculation of usury hardly would have given the doctrine of proportions the character of a divine cosmology.
While students found an understanding of music's harmonic nature by making this type of calculation, they also learned a form of mathematical reasoning that prepared them for recognizing two opposing concepts of proportional justice. The egalitarian democratic ideal of distributive justice was arithmetic. If all men gained the same amount as their society prospered, the least wealthy gradually would catch up with the wealthiest individuals. But geometric proportions preserved different ratios intact as the octaves (or by analogy, wealth) rose. With the doubling of wealth, the richest individuals still would have twice as much as men of moderate means, rather than each party gaining an equal amount of wealth (virtue). The less affluent thus would not be able to close the economic gap. Aristocratic "geometric" justice would maintain the pre-existing proportions even as economies grew more prosperous.
Not until Bach's Well-Tempered Clavier would the "democratic" even temperament system be introduced to Western music. By this time, music had lost its political connotations. What the democrats of antiquity did to was maintain the tradition of Nemesis, the "fair divider" and the avenger of hubris, that is, of the arrogance of the wealthy in injuring the economically weak. This is why Plato asserted in his Laws (IV.757) that the legendary Lycurgus "banished the study of arithmetic from Sparta, as being democratic and popular in its effect, and to have introduced geometry, as being better suited to a sober oligarchy and constitutional monarchy. For arithmetic, by its employment of number, distributes things equally; geometry, by the employment of proportion, distributes things according to merit. Geometry . . . has in it a notable principle of distinction between good men and bad, who are awarded their portions not by weight or lot, but by the difference between vice and virtue. This, the geometrical, is the system of proportion which God applies to affairs."
Plato condemned the study of arithmetic (and even mechanics) "as having egalitarian tendencies" and thus being "a danger to the soul," notes Benjamin Farrington (19‑‑:28f.). The philosophy of "one man, one vote" ignored the extent to which their wealth makes richer men better than poorer ones.
These are the lines along which Cicero (De Republic ("On the Commonwealth" I.43 and 53; see also II.39‑40) also rationalized political power as being proportioned to men's economic status. Paraphrasing Plato's Republic (545ff.), he wrote that: "Once the insatiable gullet of the people is parched with a thirst for freedom, and once the thirsty populace has been led by its bad servants to drain draughts, not of decently blended, but of undiluted freedom, they are continually censuring and accusing and incriminating their magistrates and leaders." Many private citizens
would do away with all distinctions which mark off the magistrates, are extolled to the skies and rewarded with honors.
Thus, it inevitably comes about that under such a government everything is full of liberty. No authority is exercised in any private home, and the evil extends even to the dumb animals, until finally the father fears his son, the son slights his father, and every feeling of respect is gone. Thus men are indeed free. There is no distinction between citizen and foreigner; teachers fear their pupils and flatter them; pupils scorn their teachers; the young affect the gravity of age; and old men revert to youthful pranks in order not to be tiresome and displeasing to the young. Even slaves conduct themselves with undue freedom; and wives enjoy the same rights as their husbands. And even the dogs and the horses and the asses live in such an atmosphere of freedom that they run on us and make us give them the right of way.
The result is "boundless licence."
The deity, Plato concluded in his Laws, "protects and maintains the distribution of things according to merit, determining it geometrically, that is in accordance with proportion and law." In sum, if music was an analogue for social order, then antiquity's "first order" took on the connotation of "best" (Greek aristos; viz. also arete, "virtue"). This became the canon of oligarchic wisdom and the social cosmos it envisioned.
"Canon" is a word for rules to be followed. It originally signified a reed or hollow tube, and hence a rod or rule. This gave it the connotation of measurement, and as noted earlier, by the fifth century it came to mean the movable bridge on a monochord. The canon of oligarchic law and that of music theory thus came to share a common mathematical and ideological core.
Tuning and Temperament
On the individual plane, tuning became a metaphor for the subordination of personal egoism to the common weal. In music this involves tempering each note slightly from its natural overtones to make an "unnatural" equally tuned scale in which all the tones avoid sharp dissonances. Likewise, individuals must temper their natural self-indulgent inclinations, so as to avoid dissonant clashes. Like the tones in the scale, each individual in society must be somewhat tempered from his raw "natural" proclivities, so that all may live harmoniously with one another.
Musically, this tempering is a complex mathematical process, in which the numbers three and two play an important role. These are precisely the numbers that Pythagoreans used to denote male and female respectively (adopting ancient Near Eastern usage). An octave can be doubled by multiplying by twos, but this will only generate the same note on every higher frequencies. To generate the entire scale by means of the Circle of Fifths (3/2), the number three is needed. The musician proceeds from C to G, and then to D, by multiplying 3/2 by 3/2 = 9/4. The octave of "4" is 8; hence, 9/4 (D'/C) = 9/8 (D'/C'). The entire circle of fifths may be generated by keeping even powers of 2 (i.e., 2n) in the denominator, while the numerator is expanded by 3p.
All the notes of the musical scale can be derived in this way. Starting at C, the second overtone (after the octave C') is G', whose next different overtone (after C") is a fifth higher: D. From there, the circle of fifths runs to A, E, B, F#, C#, G#, F (actually, E#), and then back to C. Well, almost to C, for the note actually is B#, slightly off from a simple 2n multiplication by octaves. There is a slight divergence, called the Pythagorean comma (72/71). This micro-interval is what makes tuning by a circle of fifths clash with tuning by thirds.
The worst problem in tuning occurs in the interval of three whole tones, e.g., between C and F#/Gb in the "natural" untempered methods of tuning. If the ratio of the octave is 2:1, then the ratio of C to F# represents the square root of two -- an irrational number. (Burkert [1972:441] notes that the harmonic mean discovered in the context of Pythagorean music theory has a major use precisely in approximating the square root.)
McClain (1976:xi; see also 1978:38.) explains the obscure technical analogy drawn in the Republic (587c) where Plato states that the tyrant is 729 times as bad as the good man. Some translators (e.g. Francis Cornford) simplify the text by omitting the seemingly obscure number. But to the musician trained in acoustics, the number 729 has a particular meaning: It corresponds "to the tritone (36 = six fifths above the fundamental), the worst possible dissonance in the musical systems known to Plato." His number thus refers to tyrants creating dissonance in an otherwise harmonious society. 8
Another analogy with tuning the scale is alluded to in the myth of the three Fates: Clotho, Atropos and Lachesis. "The interval CE in Pythagorean tuning gives a C that is too low, an E that is too high: hence Clotho's and Atropos' adjustments. Lachesis's task is to make Ab and G# coincide, adjusting one with each hand. 'Plato saw the necessity of temperament for systems meant to function in harmony, be they musical scales, planetary orbits, or communities of just men,'" writes Joscelyn Godwin (1983:298f.).
Rhythm
Just as measurements are needed to temper the scale, so rhythm governs the beat of time as the musical piece is divided into measures. The rhythmic principle is that of a metronome. Its essential principle is regularity.
As Buecher emphasized, rhythmic music was used in antiquity to make labor tasks more "total," enhancing productivity by immersing the workers' spirit in their assigned job. Athenaeus (XIV.618) describes many professions as having their work songs. One of the major professions was of course the army. "The brave Lacadaemonians march to battle with the music of flutes, the Cretans with the lyre, the Lydians with Pan's-pipes and flutes, as Herodotus records (VI.114). Many of the barbarians also conduct diplomatic negotiations to the accompaniment of flutes and cithera to soften the hearts of their opponents."
Elsewhere,Athenaeus (XII.518) epitomized the licentious behavior of the Etruscans by remarking that rhythm played a role in their leisure as well as in their work: they "knead bread, practise boxing, and do their flogging to the accompaniment of the flute."
Rhythm became a source of authority in antiquity -- first the rhythm of calendrical time, and then by overseeing the tempo and rhythm of music. The calendar was the first economic organizing principle of time, as far back as the Ice Age. A major role of chiefs was to act as calendar-keepers, partly because the calendar governed the periodic gathering times for the group festivals (Marshack 1972 and 1997).
By Mesopotamian times the calendar dictated the weights and measures that were needed for account-keeping, that is, for measuring the grain, beer and other commodities that were disbursed by the temples and palaces on a monthly or other periodic basis. The public sector's administrative month had to be standardized to a 30-day "solar" basis rather than retaining lunar months, whose length varies between 28 and 30 days.
Musical leaders held a similar position of control in classical Greece. The choral dance leaders who beat time -- the aisymnetes -- provided the name for an official by analogy. Aristotle (Politics 1274b, 1285a) called Pittacus, the popular tyrant of Mitelene c. 600 BC, aisymnetes in the sense of "elective monarch," as he retired voluntarily after ten years in office. The root of this word was "equal" (aisa < iso), because each measure had to be of equal length in order to beat the rhythm correctly, so that the notes of the various instruments would sound concordantly in the harmony intended by the composer.
Public music and dance performances were paid for by imposing special taxes on the wealthiest Athenians. The aristocrat designated as choregos had to foot the bill. He typically used his obligation as a means of gaining prestige through the excellence of his performances. Athenaeus (XIV.633) cites this as one example of the decadence of his time in emphasizing the sponsorship rather than the technical performance of music. The term choregi formerly was used, "not, as today, of the men who hired the choruses, but of those who led the chorus, as the etymology of the word denotes."
9
Noise
If music connoted social harmony, then noise signified the ultimate social dissonance. And although Plato associated the tritone with tyranny, noise was a phenomenon of the crowd, the ochlos that made up what aristocrats scornfully called the ochlocracy.
Silver (1995:181) has traced this metaphor back to Sumerian mythology. Pettinato, he observes, "sees a connection between the 'noise' in the Mesopotamian myths and the se'aqah ('outcry') heard by the Lord in Genesis 18.21 and the story of Gomorrah in Genesis 19." He notes that Von Rad (1972:211) finds that outcry "is a technical legal term designating the scream for help of one who suffers a great injustice. The cry was (c)hamas 'Foul play!' (Jer. 20.8; Job 19.7), a term that has the same force as Akkadian (c)habalu ('to oppress, wrong, deprive a person of something to which he has a right') (Speiser 1964:117, n.5; CAD A.1)." An echo of this usage is found in Isaiah 5.7: "And He hoped for justice, but behold, violence. For righteousness but behold an outcry."
Musical decadence
In decrying decadence, few have exceeded the pessimism of Plato in his last days. His musical cosmology reflects the degree to which the wealthiest families controlled education and its elitist kosmos. As Karl Popper has described in The Open Society and its Enemies, the upshot was a censorial attitude that has characterized authoritarianism through the ages.
Plato's condemnation for mixing social ranks (admitting the demos into the ranks of policy-makers alongside his Guardians) found its counterpart in his disdain for mixing musical styles. His Laws would have banned certain kinds of music, but the real enemy was democracy's economic program of redistributing the land and cancelling personal debts. In archaic times, Plato points out (Laws 700‑701a), each musical form had its own proper place.
Knowledge and informed judgment penalized disobedience. There were no whistles, unmusical mob‑noises, or clapping for applause. . . . But later, an unmusical anarchy was led by poets who had natural talent, but were ignorant of the laws of music. Over-intoxicated with love of pleasure, they mixed their drinks ‑‑ dirges with hymns, paeans with dithyrambs ‑‑ and imitated aulos‑music in their kitharoedic [zither] song. Through foolishness they deceived themselves into thinking that there was no right or wrong way in music ‑‑ that it was to be judged good or bad by the pleasure it gave. By their works and their theories they infected the masses with the presumption to think themselves adequate judges. So our theaters, once silent, grew vocal, and aristocracy of music gave way to a pernicious theatocracy . . .
This wonderful word "theatocracy" anticipates the bread and circuses of Rome. In this passage Plato remains a model for subsequent conservatism in disparaging modernist tendencies.
By this time Aristoxenos decried the decadence of his times a few years later, denouncing musical decadence had become a political code for anti-democratic propagandists. Few people were able to recall the old musical arts, he accused: "Now that our theaters have become utterly barbarized and this prostituted music has moved on into a state of grave corruption," few people recall what the art of music used to be.
An observation of von Fritz (1940:31) should be borne in mind here. Although Aristoxenos claimed "that Pythagoras liberated Sybaris from tyrannical rule," it is known that "The downfall of Sybaris coincided with the downfall of Telys' rule. To call the destruction of a city her liberation from tyranny reveals certainly some political bias." It was the same bias that shaped his musical preferences.
To the above passage Athenaeus (XIV.632) adds his own view that
It happened that in ancient times the Greeks were music‑lovers; but later, with the breakdown of order, when practically all the ancient customs fell into decay, this devotion to principle ceased, and debased fashions in music came to light, wherein everyone who practiced them substituted effeminacy for gentleness, and licence and looseness for moderation. What is more, this fashion will doubtless be carried further if someone does not bring the music of our forebears once more to open practice.
A historian of archaic choreography (Miller 1986:17) explains his disappointment at discovering that choreia, the aristocratic sponsors of Greek dramatic choruses, evolved via Latin chorea to survive in modern English "as a medical term signifying 'a convulsive disorder . . . characterized by irregular involuntary contractions of the muscles, especially of the face and arms,'" much as arthrum ‑‑ the root of "joint," "harmony" and "art" ‑‑ survives as arthritis. "The tragic fate of my noble Greek word forced me to question my naive assumption that the mighty themes of order and harmony could be conveyed through the centuries on a verbal vehicle so frail and easily overturned."
The Siren's song of enchantment is now the police and ambulance siren. And Calliope, once the highest muse, has descended from her lofty status to give her name to the raucous merry‑go‑round organ. In such a way the muses have fallen.
Is there perhaps a parallel here with economics?
Musical and economic decadence
"It is a striking paradox," remarks Burkert (1972:369), "that music, which is the most spontaneous expression of psychic activity, at the same time admits, or rather even challenges, the most rigorous mathematical analysis." Cannot the same thing be said for economics and people's universal drive to improve their status? And by the same token, if Pythagorean musical mathematics was able to divorce itself from the real acoustical world and enter the realm of speculation as window dressing for the most avaricious classes in power, is not economics today just as prone to unworldly self-indulgence with a covert political agenda?
Decrying the cacophony of popular music in his day, Plato introduced a form of intellectual decadence of his own. Discussing the necessary subjects for the education of the Guardians (Rep. 530d), he made music the focus of its quadrivium, following its sister science astronomy, alongside mathematics and geometry. He was not referring to audibly performed music, however, but to pure number theory beyond the plane of experience.
If, as Burkert (1972:479) has remarked, "Music theory was at first more a number game than a science," the same can be said for modern economics. Calculus is now used as a kind of symbolic reasoning by economic model-builders to indoctrinate students in the idea that all economies tend to settle at a just and equitable balance, to which they return automatically if any disturbance happens to occur. Economics has become a "science of assumptions" whose purpose remains what it was two centuries ago: moral philosophy with a libertarian free-trade outlook opposing government regulation and advocating that planning be left to private enterprise.
A famous story about Pythagoras describes him as passing a blacksmith's shop one day and listening to the sounds made by hammers, recognizing the intervals of the octave, fifth and fourth. Upon investigation, he is said to have found that the hammer weights were related in the ratios 2:1, 3:2 and 4:3. Yet these proportions refer to string lengths, not weight. The octave would have been produced by a hammer 4 times the weight (i.e., the square of doubling). "It is all cosmo-history," concludes Burkert (ibid.:375), adding that "Later presentations of Pythagorean musical theory tried to derive as much as possible from a priori considerations, and to refer as seldom as possible to experience and experiment. Even the basic facts are -- apparently -- derived from speculation, and everything else is derived from calculation of ratios."
This sounds remarkably like modern economics. The study of music in classical Greece, especially under the influence of the Platonists, did not refer to practice. The monochord was not a performing instrument. It was a theoretical exercise that pandered to the self-importance of the upper classes to rationalize the existing inequity (status and prestige) from which they benefited. This logic was used in the fight against democratic movements.
Just as contemporary music has lost the classical tonal organizing principles, so today's economic theory has dropped its concerns with society's long-term dynamics, indulging in mathematical speculation without empirical relevance. What has been lost sight of is the economy's core, its asset structure and the exponential growth of debt charges against land, capital and labor. Most of every economy's assets consist of real estate and the financial debt claims on it. These dynamics determine an economy's political counterpoint and the evolving shape it takes, yet they are ignored by today's post-classical mathematical models.
If the badge of economics as a science deserving a Nobel Prize has become its ability to be mathematized, this is only because of the unrealistic assumption that there is an inherent tendency of economies to settle without any public oversight at a stable equilibrium. Without diminishing returns and the satiability of wealth, these models have no singular solution. At least the Bronze Age mathematics taught to scribal students calculating how debts multiplied exponentially made no such assumption. The Mesopotamian acknowledgement of the rapid doubling times of debt -- and how much more rapidly debts grew than the economy's means to pay -- thus appears more "modern" than today's non-financial theories of economic growth.
Likewise, classical "wisdom literature" decried the insatiable addictiveness of wealth and economic power. Music theory may have been drawn into the public relations campaign of the ancient class war, but economics (at least as expressed in philosophy, political writings and the popular theater) had not yet become a politically self-serving apologetics as has now become the case.
In addition to leaving practice behind, a striking parallel between modern economics and Pythagorean music theory is its tendency to promote its ends outside of the democratic process, often in covert ways. By no coincidence, the first application of Chicago School economics was imposed by military force in Chile, by the coup d'etat that saw the murder of the elected officials and the assassination and disappearance of political opponents. This event, now cited as inaugurating modern international privatization programs, is the closest counterpart to the Athenian dictatorships of the Four Hundred and, later, of the Thirty. Libertarian economics, elaborated by think tanks and endowed by public relations institutions for the wealthy, with their own roster of heroes from Ludwig von Mises to Friedrich von Hayek and Milton Friedman, represent a modern analogue to antiquity's Pythagorean clubs.
Yet these liberal economists have been unwilling to recognize the phenomenon of geometric progression. It occurs most notably in the case of debts generating interest and dividends that are relent so that the debt burden grows at a compound rate. This financial dimension precludes a meaningful "stable equilibrium" from being established, by creating a tendency for society's debt claims to grow exponentially, in excess of the means to pay.
Today's economic models assume that equilibrium is achieved by diminishing returns and diminishing marginal utility (or as systems analysts would say, negative feedback). But if increasing returns are the norm, if consumer addiction, debt and wealth addiction (classical hubris) grow exponentially, then economic models will not have a single determinate solution. But the singularity of mathematical solution has become the badge of "scientific" economics.
In this respect economic phenomena have lost the metaphor with musical proportions that existed in classical antiquity. Instead of "modulation" from one economic period or "key" to the next, economics continues in a steady monotonic state. Any change in institutions must be imposed from without rather than occurring from within, yet the ideology opposes such regulation. In this conflict between assumptions and reality, modern economics has run up against much the same problem that plagued Platonized Pythagorean music theory.
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Democrats who opposed the aristocratic program were told that they would have to go to school to "understand" the oligarchic mathematics of "harmonic proportions" that served as the code phrase for "unequal equality."
So we have (l) religion, (2) cults, (3) leisure, (4) sports (the gymnasia), hence "public figures" such as sports heroes (viz. Alcibiades), (5) the educational system (capped by Plato's Academy), and finally (6) the justice system and courts. In the end, the oligarchs won as they would do throughout the remainder of history: the old fashioned way, by tricks. For (7) the electoral process weighted in favor of the rich, and specifically by landlords.
The ULTIMATE cheating is legitimizing the theft! This is done by propaganda. Note not only Rome's second and "peaceful" king Numa (rumored by mythology to have been tutored by Pythagoras), but Servius for trickiness (in Tribes chapter.)
Third world students often come to the United States to study international economics in the hope of understanding why the international specialization of labor and domestic wealth relations are so unequal. They are distracted to the study of calculus. For what purpose? They can never use this arcane mathematizing. It can never have real numbers attached to it, for its categories are irrelevant. But the students are shunted aside. It is explained to them that all exchange IS equal, because it is all in equilibrium. Hence, both sides balance.
In the process of learning this, they are co‑opted or distracted. And just as not many third world students can travel to North America or Europe to study. (The root of our word school is scholia, originally meaning leisure. One use of leisure in classical antiquity was indeed to study (and hence to become a scholar). The other was to practice cavalry tactics, the military leadership whose rank in the army was defined by the amount of land they held. The leisure class (and until the present century, the cavalry officer corps) historically has been the wealthy rentier class, monopolizing the army as well as culture and religion -- and most of all, the land and the money it generated.
Examples: Loki, legal trickery. Insurance companies (pro rata), health care. All in the mathematical details of the contracts.
Another way of tuning the scale is by thirds. The interval of the (major) third is the second different overtone, following C, C', G' and C'', namely, E. C-E-G thus forms the basic triad of music. However, to make it resonate harmoniously with all the other notes of the scale, it too must be tempered.
Music, like labor, must work in a disciplined way, to the thousandth of a second. Yet to take this principle to its extreme leads to the alienation of performing repetitive tasks (numbing).
Even new CDs of musical performances from the 1930s are as speeded up as old 8 millimeter silent films, because the "original" European recordings were issued closer to 75 RPM than the nominal 78 RPM.
Music leads to disequilibrium, by means of dissonance. There is periodicity (as the broadest form of rhythm). That would be akin to the business cycle (repetition of the basic theme on a higher level).
A Stradivarius violin: not only does it not depreciate in value, but you have to play it to keep it in tune and keep its wood vibrant.
The distinction between productive and unproductive: reinforces the inner harmonic structure, vs. distracts or dissolves it. There is an alternative, of course: carrying it to a higher level (modulation in music; the generation of a new stage of development in economics).
In society, the new "stage" comes from a breakdown. One thinks of Beethoven's floating dissonances, RESOLVING themselves in the new higher modulation. (Which is implicit in the opening four to eight bars of the musical piece.)
Dear Mason, August 13, 1997
"They said it couldn't be done." You will notice that I have indeed been able to work land monopolization (and debt, of course) into my musical analogy for economic decadence at the end of this article, and along the way for the Pythagorean support of landlords in the Crotonite attack on Sybaris (from which our adjective sybartic comes). So what do you think of THIS? (Pity there is no Georgist literary journal to circulate this. If we had such an organ, I'd do the English version there and publish this essay in German for Juergen.)
Dear Wolfgang,
I have now filled out my musical essay (and have not even gotten around to revising my essay on Buecher and economic anthropology). I never dreamed that it would take an entire month. But it quickly became obvious to me that I could not decontextualize the association between music and social order from the institutional setting of this philosophy: the Pythagorean clubs. This led me to discuss the evolution and political role of these clubs, in order to put their musical philosophy in perspective.
I don't want this to displace my major essay on Buecher's anthropology itself. I gather that I will have two essays in this volume (as other authors have done in some of your earlier volumes). Please confirm this; if I had to choose, my anthropology essay comes first, because this essay will probably be placed in my book on the Collapse of Antiquity. (Sorry for the University of Chicago barbs -- but remember, I'm also a U of C graduate. Its Prof. Bloom's travesty that I'm attacking here, and the Chicago Schoool's links to the Pinochet dictatorship in Chile, which seems a remarkable reincarnation of the Pythagorean clubs.)
I hope I haven't lost the "poetry" of my thoughts in the process. It was because of your kind comment that I took so long to elaborate my essay by finding the appropriate scholarly passages. Tell me if you think they weigh things down too much. But I do want to keep the parallels between musical and economic decadence at the end -- that was the ultimate point that I was making.
(Somehow, Peter Senn always seems to bring out the best in me. He begins on my wavelength, but always comes from a different direction, and I want to approach the same subject from my own perspective. Tell him we make a good team.)
Yours,
Michael
From Wolfgang
Dear Michael,
Many thanks for cc'ing the musical comments to me. I read it with great
pleasure, and I sent Juergen a note (unsolicited) that it's eminently
publishable. I didn't know we shared that interest, too; the (social and
epistemological) theory implications of musicology form one of my favorite
side areas, and I've just been a referee for the new Chairs in musicology
both at Berkeley and Princeton. (Well, not that that means that I actually
*know* anything.)
A few very small comments from my side: of course, there's a difference
between music and rhythm, and Buecher addresses the latter. Greek music,
as far as I can see, is singularly rhythm‑free (of course, we don't quite
*know* that, but that's how I interpret the fragments we do have).
In any case, I agree with your use of music in Plato, but there's more to
that. After all, the constitution of the NOMOI is to be established by the
preamble being sung; there is the question of whether it's the
emotion‑stirring quality of music and drama/poetry in the POLITEIA that is
seen as the big problem, etc. Not that you need to be exhaustive on "Plato
and Music" in a paper like that, but I think some of these features have
direct bearing on your topic. One could also mention that Plato's "bad
music ruins the polis" argument has very emphatically been used by Allan
Bloom in _The Closing of the American Mind_ for today. This is a very,
very bad book, but that passage has been very much discussed, and thus it
might be interesting to refer to.
Since you so very nicely employ etymology, I am not sure whether Plato's
works should really be referred to by their common English names; as far as
I can see, usually they aren't anymore in the scholarly literature. NOMOI
are arguably not what we would call Laws, and a POLITEIA is certainly not a
Republic. But this might be an indiosyncrasy of mine. On the other hand,
regarding the much‑debated translation of arete', I think that in the end
it IS actually virtue, only that we have a strange attitude for the latter
word these days.
Is "Well‑Tempered Klavier" the usual expression? I would think it should
be "Well‑Tempered Piano" or "Wohltemperiertes Klavier".
For the tendency for simple crescendo in American orchestras, and then the
culmination in silence, it struck me that Bruckner's IXth, 3rd movement, is
the perfect example for that. And it is also in harmony the last time that
the harsh dissonance in the end is resolved in that friendly bird‑song like melody.
As regards star conductors replacing more anonymous music‑making, this is
indeed (it seems) a comparatively recent phenomenon on your scale, but
already 250 years ago, the Master of Music at the European courts (and I
would liken him to the conductors) would often earn the highest salary
within the civil service (although the primadonna Italian singers and
dancers might top him).
This is already it. My assistant Rainer Kattel, whom you've met in
Heilbronn, just published a very interesting essay (I think) on arete' and
polis in Xenophanes' thought; I've asked him to send you an offprint. Have
you received Erik Reinert's outline for the 1998 Oslo meeting? Your
influence is very noticeable! I was going to do something polis‑related,
but I think it should be about money theory, after all.
All best,
Wolfgang
Walter Burkert, Lore and Science in Ancient Pythagoreanism (Camb. Mass, 1972).
369 "It is a striking paradox that music, which is the most spontaneous expression of psychic activity, at the same time admits, or rathEr even challenges, the most rigorous mathematical analysis."
1 We know Pyth's ideas only through the later light of neo-Platonism. Much is retro-jected, above all his musical and mathematical theories. This was largely Plato's additions and
7 those of Archytas and Aristoxenus, both of who came from the neo-Pyth'n center of Tarantum after about 400 BC. The book on Ph. attributed to Philolaus was forged by Speusippus, and derived from the late Plato. Such forgeries were made possible by the fact that Pyth. wrote little down, and kept his knowledge limited to his cults.
10 This created a "Pythagoreanism without Pythagoras," increasingly Platonized.
Mysticism, especially highly educated number mysticism, seems inherently hierarchic today, but the doctrines of reincarnation and earth deities seem to have been adopted from the Near East first by the Orphics as a popular movement. What Pyth. did was adopt it to the upper classes.
115 After 510 Croton became the dominant city in southern Italy. This ended in 450, when "the house of Milo, which ws the meeting place of the Pythagoreans in Croton, was burnt down by their opponents, and only a few of those present escaped." Diaearchus (fr. 34) says that the uprisings took place 'everywhere.'
118 A long anti-Pyth'n tradition represented Pyth. and his pupils to be tyrants. Appian (Mith. 28) says that 'also in Italy, some of the Pythagoreans, and in other parts of the Grecian world some of those known as the Seven Wise Men, who undertook to manage public affairs, governed more cruelly, and made themselves greater tyrants than ordinary despots.'
Diogenes Laertius depicts the revolt against the Pyth'ns "as a blow for freedom from tyranny." This tradition goes back to the fourth century. It may be why Aristoxenus found it important to depict Pyth. as an opponent of Polycrates, as an emigre in search of freedom.
119 Far from being "a model of free government under aristocratic guidance," Croton was more in the character of "a detestable tyranny."
"In fact, cult society and political club are in origin virtually identical. Every organized group expresses itself in terms of a common worship, and every cult society is active politically as a hetairia." Plato's Academy was a cult organization.
Burkhert sees Pyth. as a shaman, and relates his ideas on metempsychosis to this. Hdt attri-butes the idea to Egypt (2.123), but the doctrine he describes actually is that of south Italy.
132 The orphics had mystery cults and mendicant priests. The Pyth'ns appear to have taken over these doctrines and practices on behalf of the upper classes.
Pyth. is reported to have traveled in B'ia and Egypt. Certainly, the "Pyth. triangles" and music theory seem to have been long known here, which were later attributed to Pyth. as "Grecianizing" them, at least via higher aristocratic education.
161 Heraclitus (fr. 81) calls Pyth. the chief of swindlers, and accuses him of having made from the books of others, his own sophia, polymathia, kakotechnei," that is "disingenuous rules by which anyone attains an end," apologetics, charlatanism, attaining fame through ignoble deception, a medicine man. His name means "voice of Pythia," ie of Delphi.
165 If we look at that element of the Pyth. legend NOT influenced by Plato and his mathematizing, Pyth. appears as "the hierophant of Great Mother mysteries with an Anatolian stamp," and the doctrine of rebirth, probably taken from Indo-Iranian Zoroastrian sources.
187 The tetrad of numbers 1, 2, 3 and 4 add up to 10, "the perfect triangle," for it contains the harmonic ratios of a 4th, 5th and 8ve (4/3, 3/2 and 2:1 respectively). And it is the symbol for Delphi as the seat of 'secret wisdom.' See p. 400, q'd below
This suggests that Pyth'ns was attached to pre-existing Greek cults.
BURKERT,187 The musical philosophy came later, as a theoretical-political overlay, to make the doctrine exclusively upper-class.
178 Pyth was a master cult-maker. Again, based on Near Eastern prototypes. He picked up special ritual taboos and applied them to all life, i.e., eat no meat except sanctified sacrifices.
"The more selective the society, the more careful ar the 'taboos.' Fasting, abstention from particular foods, and rules of sexual behavior play an important role. It is of first importance that the 'wise man' -- the priest, the hierophant, the shaman -- who claims a special position in the social organization, gain and maintain through a special ascetic regimen, the special powers that belong to him."
179 "All kinds of societies that are bound together by cult have their esoteric aspect -- even political clubs, trade guilds, and those of physicians."
182 It would have been too radical to reject animal sacrifice, which "was the focal point of the traditional religion, that is of the official cult of the polis. To renounce it would have been more than religious reform. It would have meant a complete overturn of traditional ways." this is the goal of Zarathustra's gospel (the fight against sacrifice of the cow, Yasna 44:20; 92).
190 "The 'sacred' animal is sacred just because one day it will be slaughtered and eaten."
"If Pythagoras himself was a kind of hierophant, he found no successor; the Pythagoreans were left with their acusmata applying no longer to festivals but to normal life, which, as a consequence, seemed to others abnormal."
191 Plato (Rep. 364b-e) complains that the Orphics "promised individuals and whole cities expiation for their sins, at the cost of a little sacrifice and a pleasant dinner."
"Everywhere are rules, regulations, and an ascetic zeal for discipline; life is penos, which must be endured."
197 Aristotle recognized a twofold practice of the Pyth'ns: a transmigration myth, the legend of Pyth., and on the other hand "a philosophy of number connected with mathematics, astronomy, and music," which he does NOT trace back to Pyth. and whose chronology he ledaves in abeyance. He thus broke from the Platonists.
207 "Whether the word mathematikos 'concerned with the subjects of learning,' came to have its narrower sense 'mathematician' precisely among the Pythagoreans or only in the Academy, the history of the word cannot decide whether the mathematici were descended from Pythagoras or Hippasus." "In the Clouds the mathetys is an established type."
208 Aristotle asks, "But what connexion has all this (number theory, geometry, music tgheory, and astronomy) [to do] with the doctrine of transmigration . . .?"
369 The octave contains 6 whole tones a fifth 3.5, a fourth 2.5.
The distinguishing feature of the musical scale is that it was the pre-eminent LOGARITHMIC scale known to antiquity -- except for the calculation of (compound) interest, mash-mash in B'n. Hence, logos-arithmos, the logic of knowledge/arithmetic. Log-arithm means "ratio number."
371 One of the few pre-Platonic points in the reconstruction of Pyth'ism is the mathematical theory of music.
One adds intervals by MULTIPLICATION (and subtracts by division). "To halve an interval means the extaction of a square root." This is like doubling the size of a cube.
You can double the scale by multiplying by twos. But you need 3's to generate the circle of fifths (3/2). You "add" a fifth by multiplying 3/2 by 3/2 = 9/4. We know that the octave of 4 is 8. Thus, 9/4 = 9/8. We hae a whole town. The scale is generated by having 2n in the denominator (even powers of 2) with powers of 3p in the numerator. (We get back to the basic octave by getting E# for F, and B# for C!)
371 When Plato (Rep. 530d) discusses the necessary subjects for the education of the 'Guardians,' he leads with music, following astronomy. They are 'sister sciences, as the Pyth'ns say, and we agree.'
372 But he is not referring to AUDIBLE music, but pure number theory above and beyond experience.
374 The monochord with a movable bridge, the kanon, the only 'instrument' on which Pyth'n musical theory can be demonstrated with any approach to exactitude.'
Ie, it gave the illusion of science -- much like economics today of the Chicago School type, denying practice. The study of music in classical Greece, and especially under the influence of the Platonists, was thus much like economics today. It did not refer to practice. Its "instrument" was the academic kanon, not a performing instrument. It was presented to the upper classes to rationalize existing inequity ("status"), prestige. And this logic was used to fight against democratic movements.
375 The story about Pyth. passing a smithy and listening to the sounds made by hammers -- the 45h, 5th and 8ve - are impossible. It is all cosmo-history." The story represents the hammer weights as being related in the ratios 4:3, 3:2 and 2:1. But these proportions refer to string lengths, not weight.
376 Ptolemy, Harmonics, p. 16.32ff, 1.8 p. 17.7ff shows why these experiments do not work. The 8ve would be produced by 4 times the weight (i.e., the square or suare root), but this law does not seem to have been discovered in ancient times.
378 Many musical theorists of the period were not Pyth'ns. "What distinguished the Pythagoreans was apparently not a special knowledge, inaccessible to others. Rather, something which may well have lost its interest for professional musicians came to be prized among them as a fundamental insight into the nature of reality."
383 Ossification: "Later presentations of Pythagorean musical theory tried to derive as much as possible from a priori considerations, and to refer as seldom as possible to experience and experiment. Even the basic facts are -- apparently -- derived from speculation, and everything else is derived from calculation of ratios."
399 "In fact the practical significance of Pythagorean musical theory is minimal." Indeed,
400 "The important thing in Pyth'n musical theory was not the function of the proportion but the meaningful numbers. . . . The 'Fourness' which is the 'harmony' in which the Sirens sing, suggest the numbers 1, 2, 3, 4, which group themselves into the fundamental concords 2:1, 3:2, and 4:3, and thus comprehend the orderliness not only of music but of the universe, and the sum of these four numbers is 10, the 'perfect' number."
466 One might call this numerology, or arithmology (Delatte's word, to be preferred on philological grounds.)
469 There is much number superstition.
me: The Dorian scale, for instance -- palindromic rather than actually sounding the best.
If the Pyth'ns said"all is number," their later oligarchic followers said "all is proportion." This is above all a musical concept, at least in terms of explaining its mathematics.
479 "Music theory was at first more a number game than a science."
414 Aristoxenus, fr. 23: "Pythagoras seems to have honored, most of all, the study of numbers, and to have advanced it in withdrawing it from the use of merchants and tradesmen, likening all things to numbers . . ."
422 The quadrvium was "not merely a Pythagorean import brought by Plato from Italy." "It was the cultural influence of the Academy that brought the system of the 'four fields' to their position of special prominence. The 4 mathemata (mathematics, astronomy, music and geometry).
429 Neubebauer's 1928 suggestion has been proved, "that the 'Pythagorean theorem' had been used routinely for centuries in Babylon, and was therefore obvfiously not a discovery of the Greeks."
438 "The term logos, in its mathematical sense of 'relation, ratio, proportion,' has been attributed by von Fritz to the Pythagoreans, and conjecturally, to Pythagoras himself." von F. believes that its origin lies in music theory. But to the Pyth's it became something "hidden."
439 "Now a distinctive feature of the Greeks' calculation of proportions, and in particular of Pythagorean musical theory, is the occurrence of certain terms like epitritos logos, epogdoos logos, and the more general epimorios logos, which from a German or an English point of view seem odd. Their sense is quickly evident; epipriton, for example, 'a third in addition,' means 1 + 1/3 or 4/3. But the question remains, what made these ratios so important that they alone, in the Greek language, have special names, whilc a fraction like 3/5, unlike 6/5 (epipempton), can only be expressed in a cumbersome circumlocution. The answer is simple: they were terms used in the calculation of interest. Whoever lends money expects to get his principal back and a specified fraction of it in addition. This could be epitriton (4/3, or 33 1/3% [Xen. Vect. 3.9, Isaeus fr. 79 Sauppe, Arist. Rhet. 1411a17]), epipempton (6/5, or 20%, Xen. Vect. 3.9), more usually ephekton (7/6, or 16 2/3%, Demosth. 34.23), sometimes epogdoon (9/8, or 12 1/2%, Demosth. 50.17), at the lowest epidekaton tokon (interest of 1/10; this was what the gods received). It is precisely the tenth or fifth that must be added, 'extra,' because the other party lays claim to it."
Thus, music and interest were the two most usual purposes of calculation (and ceremonially, building sites, which were frozen music, as McClain has shown).
"But the calculation of interest is in fact called logixesthai: logisoumai tous tokos, says Strepsiades (Clouds 20). Logixesthai refers to the elementary techniques of calculation learned at school, whose culmination and most difficult part was the calculation of interest (Hdt. 2.16.36).
441 The harmonic mean discovered in the context of Pyth'n music theory actually has another use: approximating the square root. Iamblichus says the 'most perfect proportion' is 12:9=8:6, and that Pythagoras introduced this from Babylon. The Babylonians used it to zero in on the square root. But "the Babylonians did not know the concept of proportion; but the 'mean' may very well have been employed in calculation."
448 "Logous ("proportions") may be geometric, financial or musical. "It is not the fact that mathematics is mathematical or geometrical that moved the Pyth'ns so deeply, but that an everyday concern like music, impinging on us directly through the senses, turns out to conform to mathematical rules."
But before Hippocrates, there is no indication of any Pythagorean geometry.
457 Aristotle says that Hippasus was the first to 'publish and construct' the 'sphere of the twelve pentagons,' that is, the dodecahedron."
Von Fritz (1940:92) has ascertained that the overthrow of the Pythagoreans occurred not only in Croton, but throughout all southern Italy, reflecting the popular anger at their conspiratorial activities. "The great anti-Pythagorean outbreak, including the burning of the house of Milon at Kroton, between 450 and 440 C . . . led to the first emigration of Pythagoreans from Italy and the estblishment of Pythagorean centres at Phleius and Thebes. . . . The final exodus of the Pythagoreans from Italy (except Archytas and his friends in Tarentum) c. 390," led to the transplantation of the pythagoriatai in the Greek motherland."
100 "After the revolution of c. 450, the Pythagoreans, we are told, again tried to create a center of their activities, this time at Rhegion."
31 Aristoxenos claimed "that Pythagoras liberated Sybaris from tyrannical rule." But it is known that "The downfall of Sybaris coincided with the downfall of Telys' rule. To call the destruction of a city her liberation from tyranny reveals certainly some political bias."
87 "The last Pythagoreans may have had every reason to make the rbellion of the middle of the fifth century appear as restricted as possible, but they can scarcely have committed the gravest errors concerning the one single event in which their revered teacher had been personally involved.
89 Pyth. may have died by the time his followers migrated to Metapontum, and simply his spiritual presence lived on to accompany them.
100 Von v. notes the/"There is a striking resemblance between the form of Pythagorean
101 'rule' and the way in which Plato and the Academy later tried to take part in active politics." But this was not a result of Pythagorean influence on Plato, despite his testimony in the seventh letter.
Calhoun, George Miller (1933), Athenian Clubs in Politics and Litigation [1913, repr. Rome 1964 as Studia Historica 7).
1 Thuc. (8.54.4) describes the extension to Athens of the oligarchic movement which had its inception in Samos in 411. Pisander visited "the sworn associations which already existed in the state for the management of lawsuits and elections," and persuaded them to unite for the purpose of overthrowing the democracy.
Aristides was "the great exception to the common practice of the age, as the one man who attained political eminence solely by personal worth and integrity, unsupported by club affiliations. For he, according to Plutarch (Arist. 2), kept aloof from clubs, believing that the power derived from such associations was an incentive to unjust action." Also Socrates. In Plato's Apology (36B) he said he avoided matters which engaged most Athenians: finance, the attainment of office, political parties, and clubs.
They indulged in bribery, fixing trials, conspiracy, false witness, assassination.
5 Club members were "partisans," political adherents, "clubman," "co-conspirator," "companion." They engaged in cabals (hence the cabalism of Pyth'n "wisdom").
7 "After the revolution of 411, which had been organized and directed by the cubs, etairos often bore the added implication of 'oligarch,' and was employed without any qualifying attribute to designate the member, not merely of a political club or hetaery, but of an oligarchic club, a 'clubbist.'" This is first found in Thuc. "He first tells us that the promotoers of the movement organized into a conspiracy those of the army at Samos who
8 were 'suitable.'"
11 "The oligarchic party did not organize clubs to resist the democracy which Cleisthenes founded, but merely adapted to the changed conditions an institution of great antiquity which had long before played an important part in the struggles between the rival aristocratic factions."
12 The conflict to which Aristotle alludes, between Cleisthenes and Isagoras for the archonship, "was not between these aristocratic clubs on the one side and the commons on the other, but between the clubs which were supporting Cleisthenes and those which took the part of Isagoras, and the expression used by Aristotle (Cons. Ath. 20; Hdt 5.66, 69-70) refers to an inter-club struggle in which the party of Cleisthenes proved to be the weaker."
These clubs operated WITHIN the larger factions that defined Athenian politics.
"Aristotle's account ... shows conclusively that the clubs were not first organized by the oligarchs after the expulsion of Isagoras as a means of secretly resisting the encroachments of the newly established democracy. They had already existed under the old aristocracy and had doubtless played their part in the struggles between the factions of the Hill, the Coast, and the Plain."
13 "These clubs were part of the system by which Pisistratus and his sons were enabled to maintain their authority against attacks from within." Hetairies of the tyrants are mentioned.
And Hdt says that Cylon's attempts to establish a tyranny constituted a hetaery.
14 From the earliest Athenian historical records, the clubs are found. They were comparatively small bodies of close friends and age-fellows, attaching themselves to a leader of wealth and social standing. They often helped leaders direct a coup, or "fix" law suits, or sponsor legislation. These were almost invariably done via clubs.
15 The original meaning was a close relationship between members of the Homeric nobility.
We cannot understand what made Pythagoreanism and its music theory so influential in antiquity without understanding the vehicle by which it was spread: political clubs (hetaery) and elite schooling.
CoO8 The club relationship usually involved an equality of age. And clubs usually held banquets. The entire etiquette of eating was basically designed for these clubs.
Homer depicts kings and chieftains scattered in little settlements, "whose respective power and prestige corresponded roughly to the number and rank of the hetairies who sat at their boards, followed their leadership in war, and acknowledged their authority in time of peace."
16 "By a gradual process, extending over a considerable period of time, this powerful class appropriated to itself the kingly functions, and the state became a formal instead of merely a virtual aristocracy. The new condition engendered rivalry of a more pronounced nature between the great families of the nobility, a rivalry which made doubly important the possession of hetairoi, and