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A Visual Introduction to the Musical Structure of Plato’s Symposium (For Reference Only, Not Publication) * May 15, 2008 Abstract The musical structure of Plato’s Symposium is illustrated with a series of pic- tures, diagrams, and graphs. Various, easily measurable kinds of evidence for the existence of a musical scale embedded in the dialogue are presented visually, so that patterns that stretch over the course of the dialogue can be surveyed at a glance. Since a picture is worth a thousand words, the following series of pictures and diagrams illustrates the arguments of a companion essay, 1 and is an expanded version of some slides prepared for a talk on its central findings. The diagrams aim to convey the sometimes subtle evidence of the essay in a concise and readily accessible way. The essay laid out the textual and historical evidence for the surprising claim that Plato’s dialogues were organised around a musical scale, and that certain symbols and keywords were introduced into his narratives to mark out the regular intervals of that scale. Plato’s Symposium is particularly suitable for introducing and displaying these musical structures. The series of speeches, from Phaedrus to Alcibiades, breaks the text into discrete and objectively distinguished parts whose lengths reveal further evidence for the underlying musical scale. To say that Plato organised his dialogue around a twelve-part scale is, in the first place, to say no more than that he made a twelve-part outline of this text and allocated the same number of lines to each part. The essay reviewed evidence that the lines in clas- sical texts were counted in ways perhaps similar to the way we count words or pages. As before, this essay concentrates on exhibiting the evidence and avoids references to later theories of allegory and literary symbolism. It is important to make a clean case for the existence of the musical organisation before entering into debates about its ideology. It is clear, however, that the notion of forms beneath appearances is a thor- oughly Platonic idea, and that the notion of an imperceptible musical and mathematical structure comports well with the kind of Pythagoreanism on display in the Timaeus. * Draft. Comments and criticism but not quotes are welcome. Prepared for blind review. I would like to thank .... I would like to acknowledge the support of ... This is an expanded version of illustrations prepared for a seminar at the University of .... 1

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Page 1: Introduction to Kennedy's Plato Theory

A Visual Introductionto the Musical Structure of Plato’s Symposium

(For Reference Only, Not Publication)∗

May 15, 2008

Abstract

The musical structure of Plato’s Symposium is illustrated with a series of pic-tures, diagrams, and graphs. Various, easily measurable kinds of evidence for theexistence of a musical scale embedded in the dialogue are presented visually, sothat patterns that stretch over the course of the dialogue can be surveyed at a glance.

Since a picture is worth a thousand words, the following series of pictures and diagramsillustrates the arguments of a companion essay,1 and is an expanded version of someslides prepared for a talk on its central findings. The diagrams aim to convey thesometimes subtle evidence of the essay in a concise and readily accessible way.

The essay laid out the textual and historical evidence for the surprising claim thatPlato’s dialogues were organised around a musical scale, and that certain symbols andkeywords were introduced into his narratives to mark out the regular intervals of thatscale. Plato’s Symposium is particularly suitable for introducing and displaying thesemusical structures. The series of speeches, from Phaedrus to Alcibiades, breaks the textinto discrete and objectively distinguished parts whose lengths reveal further evidencefor the underlying musical scale.

To say that Plato organised his dialogue around a twelve-part scale is, in the first place,to say no more than that he made a twelve-part outline of this text and allocated thesame number of lines to each part. The essay reviewed evidence that the lines in clas-sical texts were counted in ways perhaps similar to the way we count words or pages.

As before, this essay concentrates on exhibiting the evidence and avoids referencesto later theories of allegory and literary symbolism. It is important to make a cleancase for the existence of the musical organisation before entering into debates about itsideology. It is clear, however, that the notion of forms beneath appearances is a thor-oughly Platonic idea, and that the notion of an imperceptible musical and mathematicalstructure comports well with the kind of Pythagoreanism on display in the Timaeus.

∗Draft. Comments and criticism but not quotes are welcome. Prepared for blind review. I would like tothank .... I would like to acknowledge the support of ... This is an expanded version of illustrations preparedfor a seminar at the University of ....

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Figure 1: Pythagoras’s Slate in the Foreground of Raphael’s School of Athens (left,detail) Bears a Diagram of the Pythagorean, Six-to-Twelve Musical Scale (right)

1 The Twelve-Note Scale

The historical background of a scale with twelve, regularly spaced notes was surveyedin the companion essay.

The diagram above illustrates the Pythagorean association between the principle notesin a musical scale and the integers up to twelve. This was known to the Renaissancethrough works like Ficino’s translation of Theon’s On the Mathematics Useful for Un-derstanding Plato.

[In this draft, some large gaps have been left at the bottom of pages.]

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Octave,a 6:12or 1:2 ratio

Beginning of the dialogue.

At the centre of the Symposium, the climax ofAgathon’s speech: lyrical praise of Eros, a procession,loud approval; Socrates begins to speak.

End of the dialogue.

Figure 2: The Symposium is Divided into Twelve Parts, Corresponding to a Twelve-Note Musical Scale

As the above figure shows, the scale divides the text of the dialogues into twelve equalparts, with Note 1 near the beginning of the text.

The centre of the Symposium is emphatically marked. In a dialogue devoted to love, theconclusion of Agathon’s speech with its rousing rhetorical fireworks in praise of Erosflanks one side of the centre. Socrates, the philosophical hero of the dialogue, beginsto speak at the centre.

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Pausanias’ speech fills the second twelfth.

Eryximachus’ speech fills the third twelfth.

Aristophanes’ speech fills the fourth twelfth.

Agathon’s speech fills the fifth twelfth.

Figure 3: Lengths of Speeches, Measured End to End

The lengths of the speeches in the first half of the Symposium strikingly show how theunderlying musical scale has been used to organise the dialogue.

The figure shows simple and objective measurements of the interval from the end of onespeech to the end of the following speech. The speeches are surrounded by comments,repartee, or short cross-examinations, and this figure treats all such banter as part of thefollowing speech. A later section explores the fine structure of this banter, and showsthat it too has lengths determined by the underlying musical scale.

The location of each note is marked by a passage with certain key, symbolic terms (seebelow). A speech, therefore, tends to stop just before or just after a note, dependingupon whether it contains the marking passage or not.

The speeches after the centre of the dialogue have lengths longer than one-twelfth (seebelow).

The lengths of speeches can be easily and objectively measured, and therefore arethe focus here. A careful reading of the dialogues will show that many of their fea-tures, from narrative and argument to key symbols and definitions, have been organisedaround the musical scale.

2 Harmonic and Disharmonic Notes

Measurements of length provide some evidence that Plato was counting lines whencomposing his dialogues, but do not in themselves show that the twelve-part structureis a musical scale. Another form of evidence shows a consistent connection betweenthe stichometric organisation and a musical scale.

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Figure 4: Two Strings Struck to Test Harmony

Some pairs of notes sound better together than other pairs. Two notes an octave apart,for example, ‘harmonise’ with each other.

The Pythagoreans noticed that pairs of notes which sound well together are producedby pairs of strings whose lengths stand in simple, whole-number ratios like one-to-twoor three-to-four. A pair of notes an octave apart, for example, are produced by stringswhose lengths have a one-to-two ratio.

The Pythagoreans went further and found ways to rank notes according to whether theywere more or less harmonious when paired with some fixed note. The series of noteson a twelve-note scale can all be separated into two classes as follows:

Harmonious Notes: 2, 3, 4, 6, 8, 9

Disharmonious Notes: 1, 5, 7, 10, 11

Here, the twelfth note is used as a fixed standard of comparison, and each note is playedtogether with this standard. The successive pairs – 1 and 12, 2 and 12, and so on – areranked according to whether they are more or less harmonious.

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Harmonic Notes

Pausanias: all gods must be praised,heavenly vs. common Eros

Pausanias’s concluding praise of heavenlyEros: leads to virtue

Aristophanes begins with praise ofEros: philanthropic, healing powers

Agathon’s peroration: praise of Eros,procession, loud approval, Socrates

Diotima describes the Formof Beauty in itself at the note

The top of Diotima’s ladder at note:her vision of the Form of the One

Figure 5: Harmonious Passages at Harmonious Notes

The twelve-note musical scale and the theory of relative harmony provide a key to thestructure of Plato’s dialogues.

Plato’s dialogues are full of value-judgements: philosophy is valued over other pur-suits, the soul over the body, truth over falsity, dialectics over mere disputatiousness,and so on. As a general tendency, the locations of harmonious notes contain passageswith positively valued concepts.

This figure shows that important concepts or passages within the dialogue are carefullylodged at the locations of notes (at 1/12, 2/12, etc.), and that more ‘harmonious’ con-cepts are located at more harmonious notes. The coloured bars show the locations ofthe harmonious notes: the longer the bar, the more harmonious the note.

The top of Diotima’s Ladder where the Form of the One is described is a philosoph-ically key passage in the Symposium. It is located at a note: the harmonious ninthnote.

The harmonious notes are marked either by descriptions of the forms, perhaps the mosthighly valued concepts in Platonism, or by praise of the god of love.

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Hangovers from the previous night;Eryximachus condemns drunkenness.

Aristophanes asks not to be mocked:Socrates’ fear and aporia before speaking.

Diotima’s elenchus of the young Socrates:Eros is not a god.

Alcibiades calls Socrates an hubristees;compares him to an ugly, pipe-playing Satyr

Alcibiades’ shame and anguish afterbeing rejected and dishonoured by Socrates

Disharmonic Notes

Figure 6: Disharmonious Passages at Disharmonic Notes

There is a dramatic contrast between the passages at the locations of the harmonic anddisharmonic notes. Instead of the forms or praise of Eros, the disharmonic notes aremarked by shame, insults, contradictions, mockery, and hangovers.

As will be discussed below, the positive concepts at harmonic notes are part of pas-sages in which language is used to promote social harmony: agreements, praise, etc.The negative concepts at disharmonic notes are, in contrast, associated with languagewhich produces social disharmony. These instances of verbal or social harmony anddisharmony mark the notes.

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Phaedrus: myths, shame ethics

Puasanias: love and pederasty

Eryximachus: erotic harmony

Aristophanes: myth of true love

Agathon: arty rhetoric

Socrates: the nature of erosAgathon’s peroration

Diotima: elenchus, myth ofsex and seduction among gods

Diotima: Form of Beauty

Diotima: Ladder, Form of One

Alcibiades: Satyr, seduction

Alcibiades: rejected, war

Disharmonic Intervals Harmonic Intervals

Figure 7: Regions near Harmonic Notes have Positive Themes, and Regions nearDisharmonic Notes have Negative Themes

The over-arching structures of Plato’s dialogues have been much debated. They some-times seem meandering or disjointed. They do not follow common shapes like ‘de-velopment, crisis, resolution,’ nor build slowly to a concluding climax. Remarkably,however, the sequence of topics in his dialogues does conform to this Pythagoreantheory of relative harmony.

Careful study of the dialogues shows that a region in the musical scale near a harmonicnote is dominated by more positive concepts and, similarly, a region near a disharmonicnote is more negative. More specifically, the region stretching from a little before anote in the scale almost to the next note generally shares the earlier note’s degree ofharmony. (For example, Socrates’ elenchus of Agathon occurs as the disharmonic,seventh note is approached.)

This is strikingly illustrated by the Symposium. The speech of the notorious Alcibi-ades lies in the most disharmonic region of the dialogue. Similarly, Agathon’s suspectspeech, which Socrates criticised for lacking truth, lies in the next most disharmonicregion. On the other hand, the philosophical peaks of Diotima’s speech and the mar-velous mirth of Aristophanes’ speech occupy harmonic regions.

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Suicide, body

Death as liberation, virtues

Recollection, forms

Proof of immortality, forms

Vices, evil, doubt

Socrates’ equanimity

Disharmony,soul is not a harmony

Form of Beauty, hypotheses

Forms, soul is immortal

Geography of the Underworld

Tartarus, River Styx

Disharmonic Intervals Harmonic Intervals

Figure 8: In the Phaedo, Regions near Harmonic Notes have Positive Themes, andRegions near Disharmonic Notes have Negative Themes

Study of the other dialogues confirms this correlation between positive or negativeconcepts and the series of regions between the notes.

In the Phaedo, the regions after the eighth and ninth notes, as in the Symposium, de-scribe the forms. On the other hand, the region around the last two disharmonic notesdescribes Hell and the filthy River Styx.

The argument that the soul is not a harmony, which explicitly mentions ‘disharmony,’follows the disharmonic seventh note. Similarly, in the Symposium, Eryximachus’ dis-cussion of erotic ‘harmony’ followed a harmonic note.

This pattern is remarkably consistent across the dialogues. Although there may besome uncertainty about the precise locations of the notes, studying the ‘harmonic’ char-acter of these longer passages in the regions between notes does not depend upon anyprecise measurement of locations within the text.

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Figure 9: Passages Alluding to the Golden Mean

One way of confirming the relevance of the Pythagorean theory of harmony is to showthat other Pythagorean concepts appear in the Symposium. The Golden Mean, a math-ematically significant number approximately equal to 0.618, has been a theme in laterPythagoreanism as well as among cranks and numerologists up to the present day. Sev-eral scholars have interpreted the Divided Line passage in the Republic as an allusionto the Golden Mean. Remarkably, this passages begins 61.7% of the way through thatdialogue.

Even more remarkably, the other dialogues also seem to allude to the Golden Mean atthe same point. In the Symposium, Socrates asserts that neither the ignorant nor thewise are philosophers, since both are perhaps content with their condition. In contrast,he says at 61.6% of the way through the text that the philosopher is at the mean or in themiddle between ignorance and wisdom. This associates the notion of a philosophical orethical mean with the mathematical notion of a mean, just as explicitly occurs in Aris-totle. At the parallel location in the Parmenides, a passage echoes Euclid’s geometricdefinition of the Golden Mean.

This is quite strong evidence for the underlying musical scale. On the one hand, a num-ber of scholars have argued for the possible or probable link between the Divided Lineand the Golden Mean. It is surprising to find the passage in the Republic near 61.7%.On the other hand, the passages at similar locations in other dialogues consistently referto mathematical or ethical means.

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Figure 10: A Classical Symposium (from the Tomb of the Diver, Paestum, c. 470B.C.E.)

3 The Quarternote Structure

This section introduces a further, musical concept and shows how it gives the speechesa more fine-grained structure.

One theme in the debates over musical theory in Plato’s time and long afterwards wasthe question of whether there were ‘quarternotes’ or smaller intervals between the usualnotes of a musical scale.2 The concept of a quarternote was discussed by Plato, Aristo-tle, Aristoxenus, and others, and was sometimes understood to be the smallest unit bywhich musical scales should be measured.

The intervals between the twelve ‘whole’ notes in the Symposium are further organisedaround a structure of quarternotes. That is, shifts between speakers, major turns inarguments, and central concepts are often lodged one, two, or three fourths of the waybetween the whole notes. The internal organisation of the speeches, both shorter andlonger, in this dialogue reveals this further, fine-grained structure.

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Agathon’s Speech,Length: 3/4

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Figure 11: Some Speeches Stop and Start at Quarter-Intervals

This figure shows two sorts of simple evidence for the role of quarternotes. The lengthsof Agathon’s speech is a multiple of the quarter-interval, and the lengths of the banterbefore the two speeches extend through one-quarter interval. This suggests that thedistance of one-quarter of the length between successive whole notes plays a role inthe organisation of the Symposium. Moreover, these speeches as well as the banterand repartee before them stop and start at quarternotes. Thus both the lengths and thelocations are evidence for the role of quarternotes.

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posium Aristophanes makes Zeus say: ‘And if they still appear

licentious and will not behave quietly, then I will cutthem in two all over again [i.e., into quarters], so that theywill go about hopping on one leg [instead of four]. (190d4-6)

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... the Pythagoreans ... [measure] audible concords and sounds oneagainst each other ... [Others] talk of ‘groups of quarter-tones’ ...[each is] a note in between, giving the smallest possible interval,which ought to be taken as the unit of measurement.(Cornford’s translation: 530d8 – 531a7)

Figure 12: Passages Alluding to Quarters at the Locations of Quarternotes

The figure above gives two examples of a kind of punning reference in Plato’s dia-logues to the musical structure. The Republic refers to quarternotes at the location ofa quarternote on its embedded scale.3 The Symposium refers to cutting into quartersat the location a quarternote. This limited evidence cannot in itself be convincing, butsuch puns are common in the dialogues. For example, the dialogues sometimes referto three near the third note, or four near the fourth note, and so on. The passages in thefigure show at least that Plato discussed smaller intervals between the main notes in amusical scale and add another kind of evidence, however limited here, for the role ofquarternotes.

Their brevity makes puns hard to interpret in rigourous ways. The scholarship on

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puns in classical or later literatures generally depends upon an argument from coher-ence. That is, by examining many examples and drawing on explicit discussions ofpunning, etymology, and allegory in related writings, secure interpretation of puns inindividual cases can be reached. During the last generation, a substantial literature onpuns in Homer, Aristophanes, Ovid, and Virgil has clarified the various motivations forpunning in classical literature.4 Sedley, in particular has argued that Plato’s Cratylusshould be read as evidence for a serious interest on Plato’s part in etymological puns.

The following figure introduces yet another kind of evidence for quarternotes and re-quires some introduction. Plato uses a subtle scheme for marking the locations ofmusical notes at regular whole and quarter intervals in the Symposium. The theory ofhis marking scheme is given in the Symposium itself. Examining first the theory andthen the passages marking the opening quarternotes in the dialogue will reveal muchabout Plato’s symbolic techniques.

The Symposium contains, in Eryximachus’ speech, an explicit theory of the nature ofmusic (187a1 ff.). It involves two combinations of opposites: of fast and slow, andof high and low. We might call these ‘tempo’ and ‘pitch,’ but for Plato the first is‘rhythm’ and the second is ‘harmony’ or ‘consonance’ (symphonia). Plato succinctlysummarised this view of music in the Laws:

... rhythm is the name for the order of the motion and harmony is thename for the order of the sound. (664e8-a2)

An uptempo or fast rhythm, for example, is one in which the mixture of ‘fast’ and‘slow’ is dominated by ‘fast.’ Both rhythm and harmony are thus types of blending or‘agreement’ between opposites.

Music establishes such agreements, according to Eryximachus, by implanting eros andhomonoia, or love and like-mindedness. Eros is therefore a mediating force whichreconciles disagreeing elements, and music is a science: the ‘erotics’ of rhythm andharmony, or of motion and sound.5

This theory of music is the key to the symbolism that Plato uses to mark the notes inthe Symposium.6 Careful examination shows that there is a definite similarity betweenpassages lodged at the locations of the notes through the musical scale. The figuresummarises the first four such passages in the dialogue, where the pattern is ratherheavy-handedly established.

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Motion: Socrates’ starts again, arrives at Agathon’s (175c4).Wise/Unwise: Socrates’ ‘wisdom’ requested by dramatist Agathon (c8).Invite/Agree/Harmony: Agathon asks, Socrates agrees to sit together (d3).Motion Stops: Socrates sits, motion ceases again (d3).

Motion: Apollodorus was going to the city (172a2).Wise/Unwise: young philosopher, ignorant inquirer. (173c2-5, b8-c2)Invite/Agree/Harmony: he is asked to stop and does (a4).Motion Stops: Apollodorus stops (a5).

Motion: walking along the road to the city (173b9).Wise/Unwise: ‘philosophy’ vs. worldly pursuits (c3-5 ff.).Invite/Agree/Harmony: agrees to recount the speeches (c2).Motion Stops: interlocutor is really ‘doing nothing’ (d1).

Motion: jokes about going to Agathon’s, departure (174c7, d4).Wise/Unwise: ‘wise’/phaulos, Socrates and Aristodemus (c7,d2).Invite/Agree/Harmony: invitation, agree to attend the dinner (d3).Motion Stops: Socrates stops on the road (d5-6).

Figure 13: Similar Passages Mark the First Four Quarternotes: Each Contains theElements of Music, Motion and Harmony

These four passages share a consistent set of features. At each note, there are wordsindicating some sort of physical motion like walking. Each passage also concludes withthe cessation of motion. Moreover, there is at each note some sort of agreement – eitherassent to a request or acceptance of an invitation – between a student of philosophyand someone else. Like a musician who rather emphatically begins with ‘ONE, two,three, four,’ the Symposium marks the interval between its initial quarternotes with arhythmically repeated pattern of passages.7

In short, there is a kind of rhythm (motion) and a kind of harmony (agreement) at thelocation of each note. The concepts, or perhaps the forms, of music mark the locationsof the notes. A Platonist might conclude that, since the forms are the reality beneathappearances, there is real music at each note.

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Figure 14: A Tabulation of the Occurrence of Music-Related Words in the Republic,Showing the Second and Third Musical Notes and Intervening Quarternotes

This figure shows the results a novel investigation which, once understood, providespowerful evidence for the existence of quarternote structure in the Republic.

In that dialogue, the locations of the whole notes are marked by clusters of musicaland music-related words (like lyre, chord, string, tone, harmony, noise, etc.). Carefulstudy of the passages at the whole notes produced a list of these words. In an effort toshow that these clusters occurred only at the locations of the whole notes, I proceededmechanically through the entire dialogue recording and tabulating the locations of thesekey, musical terms on my list. This led to a table giving the number of occurrences ofthese words in each Stephanus page. I was surprised to see smaller clusters of the keyterms at three regular intervals between each pair of successive whole notes. This wasthe first evidence for the existence of the quarternotes.

This chart shows the structure between the second and third whole notes. There is alarger number of musical terms spread over a larger number of Stephanus pages at thewhole notes, and smaller peaks at the quarternotes, but the histogram beautifully showsthe quarternote structure.

Tabulating the occurrences of a random list of words in the Republic would not haveproduced a regular structure. Thus my list of key terms and the graph reinforce eachother, and constitute a strong, visual form of evidence for the presence of quarternotes.

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4 Summary of the Evidence

The preceding illustrations aimed to assemble a range of independent, yet mutuallyreinforcing lines of evidence for the musical scale in the Symposium.

Simple evidence for the twelve-note scale:

• four speeches early in the Symposium are each about one-twelfth long

• these four speeches each begin and end near a whole note

• Socrates’ speech is three-twelfths of the entire text

• highlights of Diotima’s speech, the form of Beauty and the form of the One,occur at successive notes, and thus are separated by one-twelfth

• the rhetorical climax of the Symposium is located at its centre

Evidence from the Pythagorean theory of relative harmony:

• harmonious concepts are lodged at harmonious notes, e.g., the top of Diotima’sladder is reached at the ninth note

• disharmonious concepts are lodged at disharmonious notes, e.g., the River Styxat the eleventh note of the Phaedo

• regions after harmonious notes are filled by speeches about the forms or withpraise of Eros

• regions after disharmonious notes are filled by speeches about shame, insults, orarty rhetoric

• a similar pattern of regions occurs in the Phaedo (and other dialogues), showingthat this gives the general structure of Plato’s dialogues

• the musical structure was tied to another Pythagorean concept, the Golden Mean

Evidence for quarternotes between the twelve whole notes:

• the lengths of Agathon’s speech and of some banter are multiples of the quarter-interval

• the speeches of Agathon and Socrates each begin at a quarternote

• an explicit discussion in the Republic of quarternotes is lodged at the location ofa quarternote

• a reference to quartering at the location of a quarternote in the Symposium

• the four passages marking the Symposium’s first four quarternotes are similarand contain references to motion and agreement, i.e., to the elements of music

• a tabulation of the music-related terms in the Republic clearly shows a regularseries of peaks at the locations of whole and quarternotes.

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5 Appendix: Locations of the Musical Notes

As discussed in the companion essay, the measured locations of the musical notes onthe Symposium’s musical scale are surprisingly accurate, despite the changes the textmay have undergone during its transmission. The Stephanus pages have significantlyvariable lengths but, in the Symposium and not generally in other dialogues, the intervalbetween quarternotes is coincidentally about one Stephanus page.

Note 0: 172a1, 1q: 173c3, 2q: 174c6, 3q: 175c5,Note 1: 176c5, 1q: 177c6, 2q: 178d2, 3q: 179d6,Note 2: 180e3, 1q: 182a3, 2q: 183a7, 3q: 184b1,Note 3: 185b6, 1q: 186c2, 2q: 187c8, 3q: 188d1,Note 4: 189d5, 1q: 190d6, 2q: 191d7, 3q: 192e1,Note 5: 193d8, 1q: 194e5, 2q: 195e8, 3q: 197a3,Note 6: 198a8, 1q: 199b4, 2q: 200b11, 3q: 201c4,Note 7: 202c7, 1q: 203c7, 2q: 204d4, 3q: 205d9,Note 8: 206e1, 1q: 207e5, 2q: 209a5, 3q: 210b1,Note 9: 211b4, 1q: 212b8, 2q: 213c3, 3q: 214c1,Note 10: 215c2, 1q: 216c5, 2q: 217c7, 3q: 218d1,Note 11: 219d6, 1q: 220d6, 2q: 221d8, 3q: 222e7,Note 12: 223d12

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Notes

1. Plato’s Forms, Pythagorean Mathematics, and Stichometry is under review.

2. The difference between a musical fifth and a third gave the basic interval of a tone(between note 8 and 9). A quarternote would be one-fourth of this distance. Theconcept and terminology for these smaller notes varied significantly during antiquity.See West, Barker, Huffman, etc.

3. This passage has been much debated. I have used Cornford’s translation here.Adam’s commentary discusses this passage.

4. See the companion essay for references.

5. This passage (187c4-8) lies at the second quarternote after note 3.

6. Each of Plato’s dialogues uses a different general scheme to mark its notes, but thescheme is usually explicitly (and obliquely) discussed in the dialogue. That is, eachdialogue gives the theory needed for the interpretation of its symbolic scheme.

7. From the first whole note until the advent of Alcibiades, the musical notes aremarked with various species of homologia but not with explicit motion (Alcibiadesappropriately reintroduces motion and disturbance). The narrator, however, is walkingto town while reciting the speeches. Thus, once the motion or tempo is established inthe opening quarternotes, it perhaps recedes into the background.

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