¹ Stauffer, Donald, Shakespeare's World of Images (New York, 1949), pp. 89–90Google Scholar. On “imperfection”, Tillyard, E.M. writes in Shakespeare's History Plays (London, 1956), pp. 244–5Google Scholar: “Richard II is imperfectly executed, and yet, that imperfection granted, perfectly planned as part of a great structure.” And: “Richard II lacks the sustained vitality of Richard III, being less interesting and less exacting in structure and containing a good deal of verse which by the best Shakespearean standards can only be called indifferent.” Cf, Wilson, J. Dover, ed., King Richard II (Cambridge, 1939), pp. lxxiii–ivGoogle Scholar: “what he had to do in Act V he did either in a great hurry or in a mood of lassitude or indifference. Even the undoubtedly Shakespearean soliloquy at the opening of scene v, falls considerably below Act IV as dramatic verse.”

² See Altick, Richard D., “Symphonic Imagery in Richard II,” PMLA 62 (1947): 339–52, 361–5CrossRefGoogle Scholar; Felsen, Karl, “Richard II: Three-Part Harmony,” Shakespeare Quarterly 23 (1972): 107–11CrossRefGoogle Scholar; Leonard Barkan, “The Theatrical Consistency of Richard II,” ibid., 29 (1978): 5-19.

³ The edition used, unless otherwise specified, is Ure, Peter, ed., King Richard II (London, 1956)Google Scholar. Classical thought on order and harmony, based on mathematics, can be traced back to the mysterious philosopher of the 6th century B.C., Pythagoras, whose precepts are known solely through the “Pythagoreanism” of his students and in later classical restatements. On Pythagoreanism generally, see Burkert, Walter, Lore and Science in Ancient Pythagoreanism, trans. Minar, Edwin L. Jr. (Cambridge, Mass., 1972)Google Scholar; Philip, J.A., Pythagoras and Early Pythagoreanism (Toronto, 1966)Google Scholar; Kahn, Charles H., “Pythagorean Philosophy before Plato,” in Mourelatos, A.P.D., ed., The Pre-Socratics (New York, 1974), pp. 161–85Google Scholar. Aristotle informs us that the Pythagoreans held mathematics as the basic principle of all things, including nature, justice, soul, reason, music, and the heavens: Metaphys., A 4 985b-986a; edition used, Ross, W.D., ed., Works of Aristotle (Oxford, 1966)Google Scholar. The Pythagorean Archytas, a contemporary of Plato, describes three mathematical proportions: the arithmetic, ab = b-c, the geometric, a/b=b/c, and the subcontrary, a-b/a=b-c/c: Archytas, frag. 2, Diels, H., Die Fragmente der Vorsokratiker, Griechisch u. Deutsch. fifth ed. by Kranz, W. (Berlin, 1934–1938), ch. 47Google Scholar [hereafter D/K]. Fragments of the Pythagoreans are most accessible to English-speaking readers in Freeman, Kathleen, Ancilla to the Pre-Socratic Philosphers (Cambridge, Mass., 1966)Google Scholar. In the Gorgias Plato says that the Pythagoreans believed the geometric proportion to represent the justice which bound the universe together: Gorg., 507E-508A; edition used, Jowett, B., ed., The Dialogues of Plato (New York, 1937), I, IIGoogle Scholar. Similarly, see Aristotle, , Eth. Nich., V 3 1131bGoogle Scholar. Of geometric proportions, the most satisfactory is the “golden section” where in a/b = b/c, b and c add up to a. When a line a is cut so that its two parts, b and c, are to each other as are a and b, then you have the proportion in which each of the lesser quantities, is .618, or ((√5-1)/2, of the greater. Mathematically, this most aesthetically pleasing proportion is demonstrated by Euclid: see Heath, T.L., ed., The Thirteen Books of Euclid's Elements (New York, 1956), VI: 30, with comment, pp. 96–100Google Scholar, where, as in Heath, , A History of Greek Mathematics (Oxford, 1921), I: 304Google Scholar, lore about the section is attributed to Pythagorean sources. Also on the “golden” or “divine” section see Dantzig, Tobias, The Bequest of the Greeks (New York, 1955), pp. 55–63Google Scholar, and Huntley, H.E., The Divine Proportion: A Study in Mathematical Beauty (New York, 1970), pp. 23–6Google Scholar. On medieval and early modern thinkers' fascination with the concept (Fibonacci, Kepler, Luca Pacioli), see Joseph, and Gies, Frances, Leonard of Pisa and the New Mathematics of the Middle Ages (New York, 1969), pp. 77–84Google Scholar. Philosophically, the proportion is stated most clearly in Plato's Pythagorean dialogue Timaeus, 31C-32A; this passage is treated as a proportion of the golden section in Dantzig, p. 55, as a geometric proportion in Cornford, F.M., Plato's Cosmology (London, 1966), pp. 43–52Google Scholar, and Taylor, A. E., A Commentary on Plato's Timaeus (Oxford, 1962), pp. 96–9Google Scholar.

⁴ Heninger, S. K. Jr., Touches of Sweet Harmony: Pythagorean Cosmology and Renaissance Poetics (San Marino, Cal., 1974)Google Scholar. On Sidney, see p. 3. Of the general interest in Pythagoreanism: “the Renaissance accepted this rich tradition with syncretistic zeal, and even elaborated on it.” (p. xv) On the ready availability and popularity of Pythagorean numerology on proportion, Heninger seems to coroborate the plausibility of my thesis: see especially, pp. 94, 103, 109. He points out the deliberate interweaving of “cosmic correspondences” with terrestrial processes like politics, but his discussion of Shakespeare does not treat R.II in much detail, except that “both Richard and Bolingbroke, when measured against the sun-king ideal, are shown to be lamentably deficient in one way or the other.” (pp. 345-6). On the availability of classical cosmological lore to Shakespeare and his age see note 6.

⁵ Timaeus, 47 D.

⁶ Generally, on “music of the spheres” and its relation to harmony in the soul: Spitzer, Leo, “Classical and Christian Ideas of World Harmony,” Traditio 2(1944): 409–64Google Scholar, and 3(1945): 307-64. Also Guthrie, W.K.C., A History of Greek Philosophy (Cambridge, 1967), I: 295–301, 306–19Google Scholar, and Heath, T.L., Aristarchus of Samos: the Ancient Copernicus; a History of Greek Astronomy (Oxford, 1913), pp. 105–15Google Scholar, as well as Burkert, pp. 350-68, and Philip, pp. 123-33. Plato's, Republic, 617BGoogle Scholar, is the earliest explicit description of what is clearly a doctrine of Pythagorean origins. Aristotle, , De Caelo, II, 9 290 bGoogle Scholar, offers another. Most lore about “music of the spheres” comes from later sources in antiquity, who offer a bewildering array of opinions, contradicting one another as to how many notes were included in the harmony, or what Aristotle might have meant when he said, in De Caelo, that the notes varied according to the “distances” of the bodies involved. For a collection of all the sources, see van der Waerden, B.L., Die Astronomie der Pythagoreer (Amsterdam, 1951), pp. 29–37Google Scholar. Neither the standard musical intervals played together, nor the notes of an octavé (corresponding to the spheres of the fixed stars and the seven planets?) produces harmony: Heath, , Aristarchus, p. 115Google Scholar, Philip, p. 127, Guthrie, p. 301. Shakespeare's great contemporary Johann Kepler attempted to deal systematically with the concept, and eventually based the universal harmonic ratios on angular velocities (Casper, Max, Kepler [London, 1959], pp. 264–90Google Scholar).

Cicero and Vergil both contain substantial traditions about celestial harmony, of which, it is thought, Shakespeare may have availed himself. There is extensive debate on Shakespeare's familiarity with the classics. For contrasting views, Baldwin, T.W., William Shakspere's small Latine & lesse Greek (Urbana, Ill., 1944)Google Scholar, maintains his Latin was substantial, but his Greek negligible (II: 617-61);, while Thomson, James A.K., Shakespeare and the Classics (New York, 1966)Google Scholar feels that even his Latin was rough, and that his Aristotle could have come from simple Latin secondary sources like Erasmus' Colloquies. Of interest is Thomson's contention that the slightly inaccurate paraphrase of Aristotle, , Eth. Nich. I. 3 1095aGoogle Scholar in T. and C. II. ii. 166-7, was probably taken from Erasmus' identical error. But Thomson fails to notice that Bacon (Adv. of Learning II. xxii. 13Google Scholar) makes the same error. He would probably be unwilling to argue that Bacon got his knowledge of Aristotle from Erasmus. Also, note that Donnelly, Ignatius, The Great Cryptogram (New York, 1972), pp. 13–20Google Scholar, firmly believes the author of Shakespeare's plays to be a classics scholar, maintaining that many classical works with parallels in Shakespeare were not in translation in the sixteenth century. On the use of Cicero and Vergil, see Baldwin, II: 493-4, 599-600. Plutarch resolved on the geometric proportion in trying to calculate the basis for music of the spheres, despite what would then be distances between bodies incongruent with observable phenomena: De Anim. Procreatione, 31. That Shakespeare seems to have been thinking about the Moralia when composing Act V. v. 1-66, see Sigismund, R., “Uebereinstimmendes zw. Shakespeare u. Plutarch,” Shakespeare Journal, 18(1883): 180Google Scholar.

Classical tradition is confusing on the audibility of “music of the spheres.” Aristotle scoffed at the theory because no one seemed able to hear the music. Sources from later antiquity concluded it a sound all were used to. (See Guthrie, p. 297). Naylor, E.W., Shakespeare and Music (London, 1896), pp. 154–6Google Scholar, presumes that Shakespeare, like Lorenzo in M. V., thought that human mortality prevented its being heard. In the prison scene Richard has transcended his own mortality and become universalized, so there is no problem for him to become attuned to the music.

⁷ On Fibonacci, see sources in nt. 3, especially Gies, , and Struik, D.J., ed., A Source Book in Mathematics, 1200-1800 (Cambridge, Mass., 1969), pp. 2–4Google Scholar.

⁸ The early evolution of decimalized mathematics in Europe is somewhat obscure, but it seems clear that it was in some currency before the popularization of Simon Stevin's work on the subject in the late 16th and early 17th century. Struik, pp. 7-11.

⁹ Ribner, Irving, “The Political Problem in Shakespeare's Lancastrian Tetralogy,” Studies in Philology, 49 (1952): 171–84Google Scholar; Sanders, Wilbur, The Dramatist and the Received Idea (Cambridge, 1968), pp. 158–93Google Scholar.

¹⁰ Philolaus, frag. 21, D/K, 44, and Freeman, pp. 73-7. On Daniel's attempt to synthesize change and permanence in the universe, see Ferguson, Arthur B., “The Historical Though of Samuel Daniel: A Study in Renaissance Ambivalence,” Journal of the History of Ideas, 32 (April–June, 1971): 185–202CrossRefGoogle Scholar.

¹¹ T. and C. I. in. 75-137; Tillyard, , The Elizabethan World Picture (London, 1956)Google Scholar, and History Plays, pp. 10-20.

¹² Philolaus, frag. 14, D/K, 44; Freeman, p. 76. Mowbray's body/prison equations balance Richard's in the prison scene.

¹³ See particularly Spitzer, above, note 6.

¹⁴ On the repetition and meaning of “music” in R. II. see Williams, Pieter D., “Music, Time, and Tears in Richard II,” American Benedictine Review 22 (Dec. 1971): 472–85Google Scholar. Williams points out that most of the references to music are connected directly either with Richard or his followers, which “might remind one of the king's unio mystica with the Great Harmony of the Universe,” and suggest something like the divine right of kings (p. 474); yet he is rather unadventurous in supposing that the incidence of music in Act V. v. serves only to relieve a long soliloquy, to stimulate Richard into speaking in images, and to reflect his inner collapse (p. 478).

¹⁵ On the significance of “time” in this play generally, see Montgomery, Robert L. Jr., “The Dimensions of Time in Richard II,” Shakespeare Studies, 4 (1968): 73–85Google Scholar, and Grivelet, Michael, “Shakespeare's ‘War with Time’: the Sonnets and Richard II,” Shakespeare Survey, 23 (1970): 69–78Google Scholar. It is also interesting to note that some form of “time” appears in the first and last lines of the play.

¹⁶ Greg, W. W., The Shakespeare First Folio (Oxford, 1969), pp. 2–3Google Scholar, for example, is convinced that S. intended at least some of his plays to be published. (Others might line up with Harbage, Alfred, Shakespeare's Audience (New York, 1941), p. 11Google Scholar: “Shakespeare obviously had elected to write not for all time, but for the moment.”

¹⁷ While the First Quarto is probably very close to the original or autograph manuscript, there is no way of knowing how close. (See Pollard, A.W., ed., King Richard II: A New Quarto (London, 1916)Google Scholar, introd., p. 100, and Ure, R. II, p. xv.) In modern editions, Act IV. i. 154-318, which had been left out of the early Quartos because the subjects of deposition or abdication were too delicate for discussion in Elizabeth's lifetime, were added from later editions. (That in itself suggests that Shakespeare had some idea of posterity for the original.) Some lines, furthermore, are restored. John Dover Wilson restored one at Act I. i. 280. (No other editors are inclined to suppose with him that a whole scene is missing between Act V. iii and iv.) All editors agree that the several lines of apparent prose at Act V. v. 100-1 should be, or were, originally two lines of blank verse. Also, fragmentary lines are a problem; the occasional “Sirrah,” “Tut-tut,” or “Amen,” scrupulously excised from long lines by Wilson, and rendered individually in his edition, may have been thrown in by actors. A more economical and perspicacious restoration of short lines is Ure's Arden edition, which has a total lineation of 2751 compared to Wilson's 2757. A proportional divison of the 2751 lines according to the “golden section” leads one to Act III. iii. 143-4: “What must the king do now? Must he submit?/ The king shall do it … .” Richard as king simply gives up; the surrender of a king marks the inception of cosmic disorder, yet there is order in his restoration to his true nature. The language in Act III is noteworthy. Can it be an accident that the phrase “King Richard” disappears after Act I. iii, then appears no fewer than seven times in Act III. iii, directly before Richard gives in utterly, and finally is employed only by the Queen and the Gardener in the fourth scene in a context in which Richard is no longer king, but deposed? Is it coincidence that Richard comments sarcastically after giving up: “What says King Bolingbroke? Will his majesty/ Give Richard leave to live till Richard die? (173-4) Compare the frequency of the “time” image in Act IV (especially underscored by the brevity of the whole scene) with the inception of “time” in the latter part of the prison scene.