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1 Tolkien’s Pythagorean ‘Dissonance’ in the Ainulindalë 2 of the Silmarillion 3 4 5 This article examines a notable yet perhaps overlooked feature of J.R.R. 6 Tolkien’s cosmogony in the Ainulindalë, the song of the Ainur, at the 7 beginning of the Silmarillion, with particular regard to the Pythagorean 8 elements that the author has elected to include. It will consider some relevant 9 passages of the text itself and then move onto some of the known or suspected 10 influences, their links with Christian thinking, Neo-Platonism and 11 Pythagoreanism, principally considering the impact of several ancient and 12 medieval sources. The question is scarcely one of whether or not Tolkien was 13 influenced by, and deliberately incorporated, Pythagorean elements into his 14 Silmarillion but by what epistemological routes these elements found their way 15 into his thinking, why he chose to utilised them and whether or not one crucial 16 aspect of Pythagorean musical theory, the role of dissonance, was self- 17 consciously adopted by the author or not. Was Tolkien intentionally borrowing 18 a fundamental feature of ancient musical theory or is his extensive 19 incorporation of it a by-product of the early Christian adaptation of 20 Pythagorean ideas? Or was it perhaps even an intuitive ‘discovery’, derived in 21 part from his education and background? Let us consider the evidence. 22 In the creation story at the beginning of the Silmarillion, the divine beings, 23 the Ainur, are summoned before their creator, Ehru Illúvatar (referred to also as 24 ‘the One’), to sing a song composed by that deity and from which, in a likeness 25 of it, the world, Arda, would be created. Immediately, one can detect a 26 parallelism with ’s Theory of Forms in Tolkien’s cosmogenic narrative. 27 This is a double creation myth that is both like and unlike others with which 28 Tolkien would have already been familiar. In fact it appears to have much in 29 common with the Hesiodic cosmogony in contrast to the creation in Genesis. 30 This can be observed in the process of order being formed out of chaos (the 31 Void), with the agency of the divine will of Illúvatar infusing every creation, 32 which is strikingly similar with the Stoic and Neo-Platonic concept of logos.1 It 33 is also very like Plato’s Theory Forms, where the song of the Ainur is the 34 pattern/Form/Idea of the world, which comes first, and then the actual, physical 35 creation comes next and ‘partakes’ of that pattern. I should add too that time is 36 a relative concept here as all events transpiring amongst the Ainur prior to the 37 creation of Arda occur in ‘eternity’ and therefore normal temporal referentials 38 do not strictly apply. Within the song being performed, one of the most 39 powerful of the Ainur, Melkor, introduces a sour note, so to speak: “it came

1K. R. Hensler, “God and Ilúvatar: Tolkien’s Use of Biblical Parallels and Tropes in His Cosmogony” in Mythmoot II: Back Again, Proceedings of the 2nd Mythgard Institute Mythmoot Conference Center at the Maritime Institute, Linthicum, Maryland, December 13- 15, 2013, 2-5.

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1 into the heart of Melkor to interweave matters of his own imagining that were 2 not in accord with the theme of Illúvatar”.2 3 There are multiple references to the “discord” of Melkor, with Tolkien 4 adding that “the melodies that had been heard before foundered in a sea of 5 turbulent sound”.3 Three times Illúvatar rose from his throne, with stern visage, 6 to intervene when Melkor’s discord seems to overwhelm the harmony. 7 Melkor’s dissonant additions are described as “loud and vain, and endlessly 8 repeated”. But even though Melkor appears to be rebelling against the divine 9 will, Illúvatar declares: 10 11 Mighty are the Ainur, and mightiest among them is Melkor; but that he may 12 know, and all the Ainur, that I am Illúvatar, those things that ye have sung, I will 13 show them forth, that ye may see what ye have done. And thou, Melkor, shalt see 14 that no theme may be played that hath not its uttermost source in me, nor can any 15 alter the music in my despite. For he that attempteth this shall prove but mine 16 instrument in the devising of things more wonderful, which he himself hath not 17 imagined.4 18 19 Ehru Illúvatar, whose will is paramount, mingles the dissonance of Melkor 20 into the triple harmony, folding that discordant melody into the “theme” of the 21 song which is the pattern of the world. And this will result in considerable 22 strife playing out in world itself, which will be the subject of Tolien’s other, 23 more well-known books. Whether ‘evil’ therefore was there all along in 24 Illúvatar’s plan or came about as a consequence of the free will with which 25 Melkor had been imbued, is a subject of much debate amongst scholars.5 It 26 opens up a range of possible discussions about free-will and whether or not it 27 resides with the creator alone or in the created subjects or, in some sense, both. 28 That is not the principal subject of this inquiry; although, it figures prominently 29 into it, given Tolkien’s religious and philosophical influences. 30 Melkor differs markedly from the other gods (the Ainur or Valar, as those 31 that would go into Arda would be called) in the Silmarillion. And he aptly 32 illustrates Pythagorean elements, with conspicuously Christian overtones, 33 incorporated into the narrative. Melkor is the greatest in power amongst the 34 other created divinities and, like Milton’s fictionalised archangel Lucifer he has 35 his own plans which he seems to think are at variance with those of the 36 Supreme Being. Akin to Milton’s Lucifer, Tolkien writes, “To Melkor among 37 the Ainur had been given the greatest gifts of power and knowledge”.6 He is 38 described in comparison to the other divine beings as follows:

2J. R. R. Tolkien, ed. by C. Tolkien The Silmarillion. London: George Allen and Unwin, 1977, 16-17. 3Ibid. 4Tolkien, The Silmarillion, 17. 5See for example C. Agan, “Hearkening to the Other: A Certeauvian Reading of the Ainulindale”, in Mythlore: A Journal of J.R.R. Tolkien, C.S. Lewis, Charles Williams, and Mythopoeic Literature, 34.1 (10), 2015, Available at: https://dc.swosu.edu/mythlore/vol34/ iss1/10 (accessed 17/04/20) and below. 6Tolkien, The Silmarillion, 16.

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1 …of these Melkor was the chief…and he meddled in all that was done, turning it 2 if he might to his own desires and purposes; and he kindled great fires. When 3 therefore Earth was yet young and full of flame Melkor coveted it, and he said to 4 the other Valar: “This shall be my own kingdom; and I name it unto myself!”7 5 6 Clearly, in the first instance, Melkor is meant to recollect the Christian 7 Devil, in both biblical traditions and in fiction. And we can pin down Tolkien’s 8 narratological links with the Bible virtually to chapter and verse. 9 When, for example, Illúvatar summons the Ainur before him to sing his 10 song, it reflects Job 1:6 (KJV): “Now there was a day when the sons of God 11 came to present themselves before the Lord, and Satan came also among 12 them.” The descent of Melkor into Arda to work his mischief following the 13 creation too recalls Isaiah 14:12 (KJV): “How art thou fallen from heaven, O 14 Lucifer, son of the morning! How art thou cut down to the ground, which didst 15 weaken the nations!” Melkor will stir up serious strife amongst the elves firstly 16 and then amongst men and other creations, stealing the Silmarills (gems of 17 power made from the magic of creation from the Two Trees, Telperion and 18 Lorien) and destroying the Two Trees themselves which were the only source 19 of light in the world before the sun and moon were made, causing wars and 20 other violent upheavals. He will eventually be cast into the Nameless Void (not 21 unlike the pit of Hell), though his evil would live on through his protégé, the 22 lesser deity known as Sauron. What is more, like Milton’s Lucifer, Melkor 23 adopts an uglier, darker aspect when he goes into Arda to work his evil: 24 “Lucifer [i.e. Satan] was so illuminated that he far surpassed the brightness of 25 the sun, and all the stars…this brightness was dimmed after Satan’s fall.”8 And 26 Melkor too dwells in darkness, obsessed with the Void even before being cast 27 into it, and concealing his deeds through a cloak of shadows cast by one of his 28 monstrous servants, the giant spider Ungoliant. 29 The parallels are too many to be coincidence; more could certainly be 30 enumerated but will be omitted for want of space here. Indeed, we have 31 Tolkien’s own words on the matter which attest his own position with relative 32 clarity: 33 34 In the cosmogony there is a fall: a fall of Angels we should say. Though quite 35 different in form, of course, to that of Christian myth. These tales are ‘new’, they 36 are not directly derived from other myths and legends, but they must inevitably 37 contain a large measure of ancient wide-spread motives or elements. After all, I 38 believe that legends and myths are largely made of ‘truth’, and indeed present 39 aspects of it that can only be received in this mode; and long ago certain truths 40 and modes of this kind were discovered and must always reappear. There cannot

7Tolkien, The Silmarillion, 20-21. 8J. Milton, ed. by A. W. Verity. . Vol. II. Cambridge: Cambridge University Press, 1929, 535, n. 132-3.

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1 be any ‘story’ without a fall –all stories are ultimately about the fall – at least not 2 for human minds as we know them and have them.9 3 4 But that is not a subject of dispute here. And there are many other mythic 5 features present in the work. Collins rightly calls Tolkien’s approach 6 “syncretic”, combining Indo-European (Sanskrit) and Latin linguistic and 7 religious elements and, in terms of literary/philosophical influences, he alludes 8 to such as Sydney, Milton, Spenser and Plato. The character of Melkor, in 9 particular, reflects aspects of the Judeo-Christian Satan, as indicated, as well as 10 Norse and other mythological figures such as the Scandinavian Loki and the 11 Celtic Bilé. Notably, though, Collins identifies a Pythagorean feature in the 12 song of the Ainur, adding that many “of the Valar inhabit the orbs of the 13 heavenly spheres, like the celestial intelligences of the pseudo-Dionysius, and 14 their heavenly music recalls that of Pythagoras, while the essential 15 dichotomies, particularly the emphasis of Concord versus Discord, reflect 16 exactly the personified polarities of the neo-Platonic Prudentius.”10 The role of 17 discord is fundamental to this analysis and it is this Pythagorean connection in 18 particular that this article is exploring in some further detail here as well as 19 presently adding an observation about it that has largely gone unnoticed by 20 other scholars. 21 The musical aspects of the Ainulindalë are numerous and sophisticated. 22 Collins points out that the song of the Ainur, with Melkor’s discordant blasts, 23 has been identified as a 3-part piece consistent with traditional sonatas and 24 cantatas, themselves having Classical roots.11 He identifies Melkor’s dissonant 25 tones as an “aesthetic challenge” for the supreme deity Illúvatar, alongside a 26 discussion of free will in the Christian context as well as recollecting some 27 points made by Geoffrey Chaucer (reflecting Boethius)12 and others on some of 28 the central problems inherent in Western, Christian . These points are 29 observable in the quotes above. And Collins associates the 30 harmony/disharmony of the song with Hegelian Dialectics: thesis, antithesis, 31 synthesis, as well as being in some ways analogous to the Christian paradox of 32 the “fortunate fall”. Indeed, as indicated, Illúvatar adapts Melkor’s dissonance 33 into the music, suggesting that the Hegelian observation carries some weight. 34 What is more, the narrative structure of the Lord of the Rings itself follows the 35 pattern prefigured in the song of the Ainur in the Silmarilion, keeping true to 36 the theme of Plato’s Forms as already noted. But apart from the brief mention

9Letter no. 131 To Milton Waldman (not dated, but probably written late in 1951), in H. Carpenter, ed., with the assistance of Christopher Tolkien. The Letters of J. R. R. Tolkien: A Selection. Boston & Sidney: George Allen & Unwin, 1981. 10Robert A. Collins, “‘Ainulindale’: Tolkien’s Commitment to an Aesthetic Ontology”, in Journal of the Fantastic in the Arts, 11.3 (43) 2000, 257-265. 11Collins, “’Ainulindale”, 259. See Webster, James, “Sonata Form”, The New Groves Dictionary of Music and Musicians, 20 vols., ed. Stanley Sadie. London: Macmillan, 1980. Vol. 17, 497-508. 12Chaucer writes, in the Nun’s Priest’s tale (477 ff.): “Wheither that Goddes worthy forwityng/ [Whether God’s divine foreknowledge]/ Streyneth me nedely for to doon a thyng, / [compels me of necessity to do a thing,]/ Or elles if free choys be graunted me / [or if free choice be granted me] / To do that same thyng or do it noght…[to do that thing or not …”

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1 of Pythagorean influences, Collins mainly focuses on literary, religious, 2 (modern and other) philosophical and structural elements playing out through 3 the song of the Ainur.13 But do Melkor’s tumultuous additions represent an 4 actual “challenge” to the will of Illúvatar? Halsall, for example, has pointed out 5 that Melkor’s dissonance not only merges with the song of the Ainur, arguing 6 that it is clearly part of Illúvatar’s divine plan from the onset.14 7 McIntosh has identified the relevant philosophical background behind the 8 Ainur’s Music as ultimately being derived from the mathematician and 9 philosopher Pythagoras (6th c. B.C.) and indicates that this has naturally 10 received frequent mention in discussions of the subject.15 We shall see that it 11 does indeed appear to be derived from Pythagorean musical theory, likely 12 transmitted through Christian re-interpretations and particularly that of 13 Aquinas. Scholars have mainly focused on the obvious homage to the 14 ‘harmony of the spheres’, which has been traditionally ascribed to the 15 Pythagoreans. On this, Aristotle has written that “they took the elements of 16 number to be the elements of all things, and the whole cosmos to be harmony 17 and number” and that, according to them, “the movement of the stars produces 18 a harmony, that is to say, the sounds they make are concordant”.16 Yet, within 19 both the song of the Ainur as well as in Pythagorean tuning, any continuous 20 concord is broken by one or more dissonant notes. The very musical scale 21 itself, along with any harmonious concord it may produce, is mathematically 22 impossible without also generating some dissonant notes. 23 Consonance and dissonance are features of harmony, as observed by the 24 Pythagoreans, who also extended this mathematical understanding to broader, 25 ‘cosmic’ phenomena, as Aristotle has observed. Any division of the musical 26 canon will produce some notes that are more harmonious and some that are 27 less so. The dissonant notes might be omitted from the range chosen by a 28 composer, or used in differently effective ways.17 The 20th century composer, 29 Benjamin Britten, for example, a contemporary of Tolkien, utilised dissonance 30 very effectively to convey in his music the disruptive upheavals of the First 31 World War.18 In relation to Tolkien and the song of the Ainur, it is the 32 ‘dissonance’ of Melkor that stands out and which principally connects to

13Collins, “Ainulindale’”, 259-60. 14M. J. Halsall, Creation and Beauty in Tolkien’s Catholic Vision: A Study in the Influence of Neoplatonism in J.R.R. Tolkien’s Philosophy of Life as “Being and Gift”. Eugene, OR: Pickwick Publications, 2020, 57. He also notes that Benjamin Britten combined dissonance in his musical works from April 1930, following the First World War perhaps to reflect the discord that conflict introduced into human life. And Tolkien was well acquainted with that discord. 15J. McIntosh, “Tolkien’s Pythagorean ‘inversion’: reality isn’t ‘like’ music, it ‘is’ music”, in The Flame Imperishable, https://jonathansmcintosh.wordpress.com/2012/07/30/tolkiens-pytha gorean-inversion-reality-isnt-like-music-it-is-music/1/1 (accessed 12/03/20). For other references to Pythagoreanism in Tolkien, see also Collins, “‘Ainulindale’”, 257-265. 16Aristotle, Metaphysics, I.5.986a; On the Heavens, II.9.290b12. 17See J. B. Kennedy, The Musical Structure of Plato’s Dialogues (London: Acumen, 2011), 37- 38. 18A. Whittall, “The Study of Britten: Triadic Harmony and Tonal Structure”, in Proceedings of the Royal Musical Association, 106 (1979 - 1980), 27-41.

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1 Pythagorean musical theory and its subsequent reception by the Neo-Platonists 2 and Neo-Platonist Christians in particular. I have discussed these ‘wolf 3 intervals’ or ‘wolf tones’ (the more dissonant notes) in detail in another 4 article.19 However, I will summarise Pythagorean tuning briefly here. Their 5 musical scale is operationally defined through intervals composed of 3, 4, 5, 7, 6 8, or 9 semitones. That is, they are major and minor thirds or sixths, perfect 7 fourths or fifths, and their enharmonic equivalents, which are notes that are 8 written differently (such as A flat and G sharp) but sound the same in the 9 tempered scale, the size of which deviates by more than one syntonic comma 10 (about 21.5 cents) from the corresponding, justly intonated interval. In the 12- 11 note Pythagorean division of the musical canon, all tones are separated by 12 intervals of perfect fifths with the higher frequency at exactly 3/2 times that of 13 the lower ones.20 Number, ratio and proportion define the notes and hence all 14 subsequent music that partakes of that tradition. 15 This mathematical division results in at least one note on the scale always 16 being out of tune or ‘dissonant’, and usually more than one. It has been a well- 17 attested issue for musicians and composers since antiquity. And a more 18 dissonant note from such a scale has been sometimes denoted as the ‘wolf 19 tone’ due to its resembling the sound made by a howling wolf (sometimes 20 referred to as the ‘flatted fifth’ as well as ‘the Devil’s interval’), especially 21 when played on a pipe organ. The earliest demonstrable use of the term appears 22 to derive either from very late antiquity or from the Middle Ages.21 Even so, 23 there is ample room for Tolkien to have become acquainted with the concept 24 and likely even the later term applied to it. Indeed, the character of Melkor is 25 also specifically associated with werewolves and wargs (along with wolves 26 more generally), which were his creation and serve him in his evil deeds.22 And 27 it seems to beg the question as to whether the author was deliberately invoking 28 the so-called ‘wolf tone’ with such pointed associations. 29 Tolkien’s education and background are helpful in terms of pointing 30 toward some possible epistemological connections. It is known that he studied 31 Latin and ancient Greek from as early as 1904, along with Finish, modern and 32 ancient Gothic. In the autumn of 1911, he attended Exeter College, Oxford 33 where he initially read the Classics, Old English, the Germanic languages 34 (especially Gothic), Welsh and Finnish, until 1913. Tolkien obtained second- 35 class degree in Honour Moderations, which was the ‘midway’ stage of a 4-year 36 Oxford ‘Greats’ (i.e. Classics) course, although he received an ‘alpha plus’ in

19K. R. Moore, “Pythagoras and the (Were)Wolf” in the Athens Journal of History, 2.4, 2016, 227-238. See too W. Hawkins, Pythagoras, The Music of the Spheres, and the Wolf Interval. Accessed 14 December 2015. http://philclubcle.org/papers/Hawkins,W20111115.pdf; see too Kennedy, The Musical Structure, passim. 20W. A. Sethares, Tuning, Timbre, Spectrum, Scale. Madison, WI: University of Wisconsin Press, 2005, 163. 21See R. W. Duffin. A Performer's Guide to Medieval Music. Bloomington, IN: Indian University Press, 2000, 547. It is thought that the name might have originated when the wolf fifth was being played on Gothic organs and it reminded listeners of howling wolves; but, this is not to say that the term was not used earlier. 22Tolkien, Silmarillion, Quenta Silmarillion, chapter XIX: “Of Beren and Lúthien”.

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1 philology, which would be a defining feature of his later, academic career. In 2 consequence, he changed from the Classics to the more agreeable English 3 Language and Literature course. He would receive a first-class honours degree 4 in June of 1915, prior to joining up for the War. One of the poems that he 5 discovered in the course of his Old English studies was the Crist of Cynewulf, 6 which evidently intrigued him with its use of the term middangeard, which he 7 translated as “Middle Earth”.23 8 What emerges from most any detailed biography or scholarship on Tolkien 9 is that he despised modernism and industrialisation and that he railed against 10 the horrors of modern, industrial warfare, with which he had considerable 11 personal experience. These become allegorised in the villains of his various 12 books—such as Melkor, Sauron and Saruman. Though a trained classicist and 13 firmly rooted in the Classical tradition, he is perhaps best described as a 14 medievalist, with perhaps his own Catholicism urging him toward medieval 15 Christian philosophy including the likes of St. Augustine (13 November A.D. 16 354 - 28 August 430), Boethius (c. A.D. 477–524) and St. 17 (1225 – 7 March 1274).24 These facts do not necessarily clarify the 18 epistemological journey from Pythagoras to Tolkien but seem to suggest that 19 his Neo-Platonic/Pythagorean roots derive more so out of the later, Christian 20 writers of late antiquity and the Middle Ages. His medievalism might also 21 point to a source for his incorporation of Pythagorean tuning and the apparent 22 association between discordant tones and wolves, and so thus the ‘wolf tone’ 23 identified above, as well as Melkor’s obvious connections with the Christian 24 Devil. 25 Neo-Platonic influences and themes are numerous in Tolkien. This has 26 been well-documented and it is not the aim of this article to rehash them all 27 here. However, some do bear mention as they are highly relevant to this topic. 28 The concept of cosmic harmony adopted by Tolkien in the song of the Ainur, 29 for example, may be seen to derive almost directly from Plato’s Timaeus (29b- 30 42), and especially from St. Thomas Aquinas’ discussion of it in the Ethics 31 (15). These reflect ancient Greek ideas of the ratios in musical structure (noted 32 above), equated by the Pythagoreans, Plato and later, in their own unique way, 33 Christian scholars such as Aquinas, Augustine and Boethius with the ‘World 34 Soul’ and the non-static nature of creation.25 A link with Plotinus (A.D. 204/5 – 35 270) may be noted through his influences on Augustine and, as Halsall has 36 observed, “Tolkien allies himself to this received inheritance of the 37 Augustinian Neoplatonic tradition in terms of goodness and evil in a pre- 38 lapsarian state”.26 There are obvious links with Augustine and especially his de 39 Musica which is replete with Neo-Platonic and Pythagorean elements. Speech 40 and light, for example, are taken together by Augustine as “intellectual 41 illumination”, exemplified in his interpretation of Genesis. Although, if

23D. Doughan MBE, “J.R.R. Tolkien: A Biographical Sketch”, The Tolkien Society, https:// www.tolkiensociety.org/author/biography/ (accessed 13/04/20). 24Halsall, Creation, 10-13 et passim. 25Halsall, Creation, 22-23. 26Halsall, Creation, 28.

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1 Tolkien was acquainted with Augustine’s views on creation, then they were 2 worked into his cosmogony very “astutely”, with some notably “stylized” 3 departures from that philosophy.27 The Ainur acting as sub-creators differ from 4 Augustine’s view which regarded God as the sole creator, through the agency 5 of logos.28 And there is an additional variance. Tolkien himself has indicated in 6 his own letters that he does not accept the idea of “Absolute Evil”, noting that 7 Melkor’s fall, unlike that of Lucifer, transpired “before Creation of the physical 8 world”.29 This is more in keeping with the old Anglo-Saxon concept of ‘doom’ 9 (overarching law or judgement), which is apt considering Tolkien’s interests; 10 although, it also resonates well with Pythagorean tuning and the discordant 11 tones inasmuch as Melkor’s fall is effectively a feature of the musical theme 12 prefigured by Illúvatar. 13 It has been observed that the cosmogony of the Ainulindalë fits neatly 14 “among the real cosmogonies known to early Western medieval Europe”.30 15 Christian thinkers inherited two distinct traditions of this kind, reflecting those 16 which had originated in Jerusalem and Athens: the Hexameron (Ἡ Ἑξαήμερος 17 Δημιουργία), which included the ex nihilo creation myth of Genesis and the 18 other being some combination of the Hesiodic cosmogony mingled with that 19 found in Plato’s Timaeus, referred to above, which had been translated into 20 Latin and was widely read by medieval scholars.31 The Hexameron genre of 21 theological treatise elucidates the Judeo-Christian God’s activities during the 22 biblical six days of creation, usually in the form of commentaries on Genesis I, 23 and hexameral literature was popular in the early and medieval periods of 24 Christian history. This kind of commentary is to be found amongst the Latin 25 ; St. Basil composed works on the topic, as did St. (c. 26 A.D. 340 - 397), St. Augustine and, later, St. Thomas Aquinas.32 Alongside 27 these, the early medieval thinkers had access to numerous pagan commentaries 28 on Plato’s Timaeus—all of which, to one extent or another, bore a significant 29 influence from the Neo-Platonist philosopher Plotinus. It was St. Augustine’s 30 reflections on both these and on interpretations of Genesis that dominated 31 medieval theological thought about creation.33 In fact, it has been observed that 32 the double-creation (first the idea/song, then the world) of Tolkien’s 33 Ainulindalë would have likely been regarded by medieval scholars “as 34 reassuringly easy to fit into the schema of Augustine’s Christian Neoplatonist 35 synthesis, and the writings of others such as Pseudo-Dionysius and Dante”.34

27Halsall, Creation, 56. 28J. W. Houghton, “Augustine in the Cottage of Lost Play: the Ainulindalë as Asterisk Cosmogony”, in J. Chance ed., Tolkien the Medievalist. London: Routledge, 2003, 171-82, 173-5. “Sub-creation” and “sub-creators”, are Tolkien’s own terms, see Letter 153, to Peter Hastings (draft, not sent), in Carpenter, Letters, 1981. 29H. Carpenter, J.R.R. Tolkien: A Biography. London: Allen and Unwin, 1977, 243. 30Houghton, “Augustine”, 171. 31Ibid. 32See F.E. Robbins. The Hexaemeral Literature: A Study of the Greek and Latin Commentaries on Genesis. Chicago: University of Chicago Press, 1912. 33Halsall, Creation, 53. 34Ibid.

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1 This is particularly observable in Augustine’s refutation of the dualist beliefs 2 within the Manichaean heresy. Even so, Tolkien has not provided us with any 3 direct statement to the effect that his work was directly influenced by these 4 sources. 5 In keeping with this theme, if we are to trace the epistemological roots of 6 Tolkien’s Pythagoreanism, it is worthwhile to consider some additional, 7 specific Neo-Platonist influences such as those identified by Collins and others 8 here.35 As we have seen, they are intrinsically interwoven into early Christian 9 thought thanks to Plotinus by way of Augustine. A key source identified by 10 both Collins and Halsall above is Pseudo-Dionysius. He was a Christian Neo- 11 Platonist writing in the late 5th or early 6th centuries A.D. who transposed, in a 12 thoroughly unique manner, the whole of Pagan Neo-Platonism from Plotinus 13 (A.D. 204/5 – 270) to Proclus (A.D. 412–485), but particularly that of Proclus 14 and the Platonic Academy of Athens, into an idiosyncratically novel Christian 15 framework. His works were written as if they were composed by St. Dionysius 16 the Areopagite, a member of the Athenian judicial council (the Areopagus) in 17 the 1st century A.D., who had been converted to Christianity by St. Paul. This 18 was clearly with the intent of giving its author a greater claim to veracity. So, 19 these works might be considered a ‘successful’ forgery insofar as the author 20 was not really St. Dionysius the Areopagite but nonetheless contributed greatly 21 to Christian thinking, injecting key elements of Neo-Platonism into it and 22 thereby Pythagoreanism as well. Pseudo-Dionysius’ view of the visible, 23 created universe was to exert a prominent influence for two major reasons. 24 Firstly, this was due to his vivid sense of the “aesthetic and imaginative beauty 25 of the sensible universe”, which derived from the perspective of divine beauty 26 by its “interrelatedness and harmony”.36 Such notions came to inspire Abbot 27 Suger’s (Sugerius; c. 1081 – 13 January 1151) program for a new architecture, 28 notably the Gothic cathedral. Secondly, Pseudo-Dionysius also took account of 29 “ugliness, defect, resistance and evil” according to his principle of evil as 30 “privation and non-being”, which was a theory adopted directly from Plotinus 31 (with major theological changes further adapting it to Christianity) and Proclus. 32 Psuedo-Dionysius interest in “non-being” as associated with evil here seems 33 virtually synonymous with Tolkien’s Nameless Void, with which Melkor, we 34 are told, is also obsessed and intrinsically connected.37 35 The views put forth by Psuedo-Dionysius would exert a further influence 36 upon the likes of St. Thomas Aquinas (1225 – 7 March 1274) in medieval 37 times and Marsillio Ficino, the noted Platonist scholar and alchemical 38 researcher, in 15th century Renaissance Florence.38 Ficino was also responsible 39 for translating the complete works of Plato, obtained from Constantinople, into

35See Drout, Enyclopedia, 19. He too identifies the probable influence but without being able to pinpoint a definitive connection to Tolkien. 36See esp. On the divine names (DN) (περί θείων ονομάτων) VII. 37Tolkien, Silmarillion, 16, 32. 38K. Corrigan, and L. M. Harrington, “Pseudo-Dionysius the Areopagite”, The Stanford Encyclopedia of Philosophy (Winter 2019 Edition), Edward N. Zalta (ed.), URL = https://pla to.stanford.edu/archives/win2019/entries/pseudo-dionysius-areopagite/ (last accessed 13/03/ 20).

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1 Latin. In Pseudo-Dionysius, Harmony is always associated with goodness. And 2 he likewise comments on disharmony or discord, saying: 3 4 But if they should say that it does not make baseness in souls, but that they are 5 dragged to it, how will this be true? For many of them look towards the good; and 6 yet how did this take place, when matter was dragging them entirely to the Evil? 7 So that the Evil in souls is not from matter, but from a disordered and discordant 8 movement. But, if they say this further, that they invariably follow matter, and 9 unstable matter is necessary for those who are unable to stand firmly by 10 themselves, how is the Evil necessary, or the necessary an evil?39 11 12 He also adds, “so far as, if anything should have been led astray to discord 13 and disorder, and should suffer any diminution of the perfection of its own 14 proper goods, even this it [Divine Justice] redeems from passion and 15 listlessness and loss”.40 One can readily observe in these quotes, following 16 Collins above, a view that appears to resonate quite strongly with Tolkien’s 17 song of the Ainur and particularly Melkor’s dissonant contribution to it, along 18 with his subsequently villainous behaviour in his role which, as stated, was the 19 equivalent in many ways to that of Milton’s Lucifer and, more broadly, the 20 Judeo-Christian Satan. Pseudo-Dionysius too subordinates discord to Divine 21 Justice much as Tolkien subordinates Melkor’s dissonant notes to the ultimate 22 will and plan of Illúvatar.41 Was Tolkien acquainted with Pseudo-Dionysius? It 23 seems more than possible but specific evidence to that effect is lacking. 24 The author too has offered some tantalising revelations on this subject in a 25 letter which, for whatever reasons, he never sent but which is included in the 26 compendium of his surviving correspondences. He writes: 27 28 The Ainur took part in the making of the world as ‘sub-creators’: in various 29 degrees, after this fashion. They interpreted according to their powers, and 30 completed in detail, the Design propounded to them by the One. This was 31 propounded first in musical or abstract form, and then in an ‘historical vision’. In 32 the first interpretation, the vast Music of the Ainur, Melkor introduced alterations, 33 not interpretations of the mind of the One, and great discord arose. The One then 34 presented this ‘Music’, including the apparent discords, as a visible ‘history’.42 35 36 This harmonises (if the reader will pardon the wordplay) well with other 37 topics already discussed here. But note Tolkien’s repeated use of the term “the 38 One” to refer to the supreme creator Illúvatar. And he does so not only in this 39 letter alone but in multiple of them, using the term to refer alternately to both 40 Illúvatar and the Christian God. The phrase appears to leap straight out of the 41 pages of Plato, echoing the teachings of Parmenides and the Pythagoreans. And 42 it is not only in his correspondences that he uses the term. In the very opening

39DN, Caput IV.XXVIII. 40DN, Caput X.IX. 41See Halsall, Creation, 37-39, he references Job 38:6-7 here. 42Letter no. 212, draft of a continuation of letter 211 To Rhona Beare (no. 212), dated 14 October 1958, (not sent) in Carpenter, Letters, 1981.

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1 paragraph of the Silmarillion is stated: “There was Eru, the One, who in Arda 2 is called Ilúvatar; and he made first the Ainur, the Holy Ones, that were the 3 offspring of his thought, and they were with him before aught else was made”. 4 That they are the “offspring of his thought” emphasises the likeness with 5 Plato’s Theory of Forms, itself quite probably of Pythagorean origin. Even if 6 Tolkien has not directly alluded to any specific Pythagorean or Neo-Platonist 7 source within his correspondences, the draft letter and the opening lines of the 8 Silmarillion itself appear to substantially confirm just such a connection. 9 Tolkien’s unsent letter also underscores the Christian adaptations of 10 Pythagoreanism as observed in the writings of Pseudo-Dionysius and 11 elsewhere. The discords are only “apparent”, as Tolkien writes, not an actual 12 rebellion in the true sense, because they are inherently integral to Illúvatar’s 13 plan, much as the dissonant notes must be included in the Pythagorean division 14 of the musical canon in order for the scale to exist at all. 15 The other Pythagorean link indicated by Collins, whose ideas appear to be 16 present in Tolkien, is the Neo-Platonic poet Aurelius Prudentius Clemens, a 17 Romano-Christian from Tarraconensis (Northern Spain), 348-c.413. He is also 18 identified as a probably influence by Drout in his compendious encyclopaedia 19 of Tolkien scholarship, but without definitive proof that the author was familiar 20 with that source.43 Prudentius’ allegorical Psychomachia (The Battle of the 21 Psyche) was his most prominent work, incorporating elements of Classical epic 22 in order to explore aspects of internal, psychological struggle.44 Unsurprisingly, 23 within it we can clearly observe notions of harmony and discord adapted to a 24 Christian context. Consider the following lines from the poem spoken by 25 Discord personified: 26 27 I am called Discord, and my other name is Heresy; God to me is variable, now 28 lesser, now greater, now double, now single; when I please he is insubstantial, 29 merely an apparition, or again the soul within us, when I chose to ridicule his 30 divinity. My teacher is Belial, my home and country is the world—45 31 32 Discord here could almost be speaking the words of Tolkien’s Melkor. 33 And like Tolkien in the 20th century, Prudentius was marrying neo-Platonic and 34 Pythagorean ideas with Christian ones, in keeping with the likes of 4th and 5th 35 century scholars such as Eusebius and St. Augustine.46 Prudentius was also 36 appropriating epic tropes from Virgil.47 And that is fitting for Tolkien too, 37 given the epic nature of his own works. The reference to Belial in the

43M. D. C. Drout, ed. J.R.R. Tolkien Encyclopedia: Scholarship and Critical Assessment. New York: Routledge, 2007, 346. 44See G. Highet. Juvenal the Satirist. OUP, 1960, 184 ff. 45“Discordia dicor, cognomento Heresis, deus est mihi discolor,” inquit, “nunc minor aut maior modo duplex et modo simplex, cum placet, aerius et de fantasmate uisus, aut in nata anima est, quotiens uolo ludere numen; praeceptor Bella mihi, domus et plaga mundus.” (700-14). 46See M. Mastrangelo. The Roman Self in Late Antiquity: Prudentius and the Poetics of the Soul. Baltimore: the Johns Hopkins University Press, 2008, passim. 47Contrast Psych. 902 with Aeneid VI.86 and VII.41.

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1 Psychomachia is additionally striking as this name occurs in the Hebrew Bible 2 and is later considered synonymous with the Devil.48 3 Is it that Tolkien had an eye on Pseudo-Dionysius, Prudentius as well as 4 Augustine? Perhaps that is the case and these may well have been part and 5 parcel of his reading lists during his student days; although, we have no explicit 6 evidence to support such a view apart from Collins’ speculation that such 7 material might have been covered in the philosophical lectures that Tolkien 8 attended at Oxford. However, it has been suggested that another source, even 9 more in keeping with Tolkien’s Catholic religious background is at play here, 10 and one that subsumes many or all of the others. Halsall has argued that 11 Tolkien’s Neo-Platonism in the Ainulindalë derives more from the musical 12 theory and theology of St. Thomas Aquinas than from Augustine or Boethius, 13 even if it appears to reflect Pseudo-Dionysius and Prudentias, as Collins and 14 McIntosh have implied. And Aquinas’ theological interpretations of musical 15 theory have been regarded as having an observable impact on Tolkien and his 16 contemporaries.49 Furthermore, when Tolkien was a youth, it is known that he 17 was given an annotated copy of the Summa Theologica by his guardian, Father 18 Francis Morgan.50 19 St. Thomas Aquinas was well aware of Pythagorean ideas and especially 20 those concerning music, which he derived in no small part from Augustine’s de 21 Musica. He even devoted quite a few passages to discussion of “the One” in his 22 Summa Theologica, as he understood it to have been expressed by Plato and 23 Pythagoras.51 Frequently referencing Aristotle, Plato, Empedocles, Augustine 24 (especially his de Musica) and Pythagoras throughout, he declares that music is 25 derived “from principles established by arithmetic”.52 Pointedly, in his 26 discourse on music, he talks about it as having being per se, since it has a 27 cause, and he contrasts it with the colour white, or ‘whiteness’, which too has 28 being, also having a cause (L.115.7). It may be merely coincidence, but the 29 Pythagoreans considered the colour white to have special, metaphysical 30 symbolism/properties.53 Empedocles (444-443 B.C.) had worked out a theory 31 of light and colour which was innately connected with musical harmony. 32 Colour theory in general was important to the Pythagoreans, as well as to Plato, 33 and it formed part of the theoretical framework of both his and their philosophy

48See The Ascension of Isaiah 1:8-9, 2:4, 3:11-13, 4:2, 4:14-18, 5:1, 5:15; this is pseudepigraphical Jewish-Christian text, ranging anywhere between the final decades of the 1st century to the early decades of the 3rd century and certainly known to Prudentius. 49See J. Maritain, trans. J.W. Evans. Art and Scholasticism and the Frontiers of Poetry. New York: Scribner’s Sons, 1962 and J. Maritain, trans. F.J. Sheed. Theonas: Conversations of a Sage. London: Sheed and Ward, 1923. 50A. B. Robertson. Voices in Tolkien: Aquinas, The Lord of the Rings, and True Myth in the Twenty-First Century. A Thesis Submitted to Atlantic School of Theology, Halifax, Nova Scotia in partial fulfilment of the Requirements for the Degree of Masters of Arts (Theology and Religious Studies). Halifax, Nova Scotia: April 2017, 4 et passim. 51St. Thomas Aquinas, Summa Theologica, II.2, especially in his Reply to Objection 1, “It seems that ‘one’ adds something to ‘being.’” 52Summa Theologica I.3 and see too I.6. 53K.R. Moore, “The Pythagorean Symbolism in Plato’s Philebus” in the Athens Journal of History, 2.2, 2016, 83-95.

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1 about music.54 Whether Aquinas was aware of this, making it a conscious 2 selection for him to place ‘whiteness’ alongside music as things that have 3 being, is not possible to affirm with any certainty; but it is an interesting choice 4 on his part. 5 Again, in his Summa Theologica, discussing the metaphysics of music, 6 Aquinas delineates three objective characteristics of beauty: integrity, 7 proportion and clarity.55 Integrity refers to the ‘completeness’ and formal 8 structure of a thing, in keeping with Tolkien’s vision of the Ainur as sub- 9 creators based on Illúvatar’s sonata. Proportion is a fundamentally Pythagorean 10 concept; ‘qualitative proportion’ produces harmony and beauty and refers 11 explicitly to the mathematical qualities of the division of the musical canon 12 noted above. Clarity is the “shining forth of form”, which Tolkien inserts into 13 the Ainulindalë when the Ainur first observe the created world.56 Aquinas was 14 heavily influenced by Neo-Platonism and if, as some sources noted above have 15 suggested, Tolkien was intimately acquainted with Aquinas’ views on the 16 metaphysics of music, then there appears to be a clear link which may account 17 for the author’s use of such concepts in the Silmarillion. 18 Even so, Halsall has argued that having the Ainur as co-creators runs 19 contrary to the Neo-Platonist principle of “diminution and decline” 20 (exemplified by Plato’s ‘Nuptial Number’ of the Republic, VIII.546b), adding 21 that “even the rebellious and discordant music of Melkor is an opportunity on 22 the part of the Ainur for ‘theodicy’”.57 And that is more in keeping with 23 Aquinas’ theological positions that those of Pythagoras or Plato. Theodicy 24 refers to the vindication of divine providence in view of the existence of evil, 25 or why a ‘good’ God would permit evil to exist at all. This is a topic with 26 which Christian theology has grappled for centuries. Halsall addresses the issue 27 of evil and free will in his work with much recourse to Catholic doctrine and 28 Aquinas in particular. Tolkien himself has added his own views on this subject 29 in his letters, writing: 30 31 That Sauron was not himself destroyed in the anger of the One is not my fault: 32 the problem of evil, and its apparent toleration, is a permanent one for all who 33 concern themselves with our world. The indestructibility of spirits with free wills, 34 even by the Creator of them, is also an inevitable feature, if one either believes in 35 their existence, or feigns it in a story.58 36

54See G. Comotti, Music in Greek and Roman Culture (trans. R. V. Munson). Baltimore and London: Johns Hopkins University Press, 1989, 110-20; See too Meno 76c-d, Theætetus 153e- 154aff., both referencing Empedokles and Pythgaorean theories of colour; Lysis 217d, Timaeus 67c ff., Euthydemus 303d, the Republic’s myth of Er 617a, Laws 947b. 55Summa Theologica, I.5-6. 56Tolkien, Silmarillion, 21. See Halsall, Creation, 68-8; and see too R.E. Wood. Placing Aesthetics: Reflections on Philosophic Tradition. Athens, IL: Ohio University Press, 1999, 109. 57Halsall, Creation, 72. 58Letter no. 211, in response to a letter of Rhona Beare, dated 14 October 1958, (the one to which 212 was originally written as a further reply but was not sent) in Carpenter, Letters, 1981.

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1 Indeed, Melkor’s ‘free will’ is clearly subordinated to the divine plan of 2 Illúvatar and, in that regard at least, it is highly compatible with Aquinas’ and 3 Prudentius’ views. Yet, as has been demonstrated, the dissonance of Melkor’s 4 musical theme is not merely a discordant element that reflected the zeitgeist of 5 Tolkien’s era following the First World War, figuring prominently into the 6 music of composers at the time, as stated, it is also absolutely essential for the 7 Pythagorean division of the musical canon. Tolkien, of course, as he himself 8 has written, is not obliged to follow any single philosophical or religious 9 tradition in his fiction writing and we would therefore not expect his theology 10 to be one hundred percent compatible with either Neo-Platonism or 11 Christianity, however influenced by both of them. The discord of Melkor 12 resonates with Christian debates and discourses over evil and free will going 13 back to the Latin Fathers but it is also a distinctly Pythagorean element and a 14 deliberate choice on Tolkien’s part. 15 In terms of the secondary scholarship availed here, some further caveats 16 need to be levied. Collins seems to overplay the role of modern philosophy, 17 though not without due recourse to ancient and medieval, in his interpretation 18 of the Ainulindalë. And this position has some merit though it depends on 19 precisely which philosophical influences affected Tolkien and whether we can 20 know them. By contrast, Halsall is clearly more immersed in medieval Catholic 21 philosophy, undertaking some very fine analysis of Aquinas in particular, and 22 relating it reasonably well in his exegesis of Tolkien’s Silmarillion. The author 23 was, by all accounts, a devout Catholic and Halsall may not be remiss in 24 drawing just such connections. Both of these sources, as with others, have their 25 own agendas. And they run the risk of depicting Tolkien perhaps less correctly 26 than he really was and more as they would have him be. Not unlike Alexander 27 the Great, such epic figures, as Tolkien has become in our own age, tend to 28 take on a distorted nachleben (afterlife) of their own in the writings of their, 29 albeit well-intentioned, interpretive biographers; although, all usually entail 30 elements of truth to varying degrees. The ‘real’ man and his thoughts 31 nevertheless remain more elusive. 32 What we can know with relatively certainty is that Tolkien read Aquinas at 33 an early stage in his life, and that he was living in an era and a cultural context 34 steeped in that theologian’s philosophies. And Aquinas was well-versed in 35 Pythagorean musical theory. Tolkien studied the Classics too, during which 36 time he was almost certainly exposed to Plato and other ancient philosophers, 37 especially those whose ideas were more compatible with Catholic doctrine. Did 38 he also read Prudentius and Pseudo-Dionysius? This is not certain but the 39 apparent connections with Neo-Platonist views regarding music, and discord in 40 particular, seem reasonable and well-supported by the scholarship on the 41 Ainulindalë. Even so, as this article has tried to demonstrate, Tolkien evinces a 42 keen grasp of Pythagorean tuning and has incorporated this in a specific and 43 unique way within his writing—a subject that, apart from its allegorical 44 manifestations, has been widely unknown outside specialist studies of 45 Pythagoreanism and musical theory. And he has deployed it in a manner that is

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1 apt to both the allegorical and the wider metaphysical ramifications of those 2 approaches. 3 No doubt some would find it thrilling for this article to conclude by 4 asserting that J.R.R. Tolkien was in fact some kind of secret Pythagorean who 5 was fully aware of their division of the musical canon, with its dissonant notes, 6 along with the wider, more cosmic implications thereof, embedding these ideas 7 into his narrative. Melkor’s discordant additions to the song of the Ainur, as 8 with the song of the Ainur itself, are compelling evidence in and of themselves. 9 And Tolkien’s multiple references to “the One” in both the Silmarillion and in 10 his letters, sent and un-sent, are very interesting indeed. However, the evidence 11 available does not unequivocally sustain such an assertion. What appears to be 12 a more solid a conclusion is that Tolkien was manifestly influenced by a series 13 of thinkers, spanning through a virtually unbroken chain from Pythagoras 14 himself up to Aquinas, by way of Augustine and others, and beyond, from 15 which the general pattern of the Ainulindalë’s Pythagorean elements may be 16 epistemologically deduced to a point, as they have been here. This article’s 17 particular inquiry into Tolkien’s apparent awareness of rather nuanced 18 elements of Pythagorean tuning has disclosed a range of possible and probable 19 links. However, it shall conclude on a ‘sour note’, not unlike the so-called wolf 20 tone howling out for attention, but without revealing its more arcane mysteries. 21 The final words must go to Tolkien himself and, in those words, we may take 22 some small consolation: “For (partly to redress the evil of the rebel Melkor, 23 partly for the completion of all in an ultimate finesse of detail) the Creator had 24 not revealed all.”59 25 26 27 Bibliography 28 29 Agan, C. “Hearkening to the Other: A Certeauvian Reading of the Ainulindale”, in 30 Mythlore: A Journal of J.R.R. Tolkien, C.S. Lewis, Charles Williams, and Mythopoeic 31 Literature, 34.1 (10), 2015, Available at: https://dc.swosu.edu/myth 32 lore/vol34/iss1/10 (accessed 17/04/20) 33 Carpenter, H. J.R.R. Tolkien: A Biography. London: Allen and Unwin, 1977. 34 Carpenter, H. ed., with the assistance of Christopher Tolkien. The Letters of J. R. R. 35 Tolkien: A Selection. Boston & Sidney: George Allen & Unwin, 1981. 36 Chance, J. ed. Tolkien the Medievalist. London: Routledge, 2003. 37 Corrigan, K. and L. M. Harrington, “Pseudo-Dionysius the Areopagite”, The Stanford 38 Encyclopedia of Philosophy (Winter 2019 Edition), Edward N. Zalta (ed.), URL = 39 https://plato.stanford.edu/archives/win2019/entries/pseudo-dionysius-areopagi te/ 40 (accessed 02/04/20). 41 Collins, R. A. “‘Ainulindale’: Tolkien’s Commitment to an Aesthetic Ontology”, in 42 Journal of the Fantastic in the Arts, 11.3 (43) 2000, 257-265. (https://www.jstor. 43 org/stable/43308458?read-now=1&seq=1#page_scan_tab_contents) (accessed 07/ 44 04/20). 45 Comotti, G., trans. R. V. Munson. Music in Greek and Roman Culture. Baltimore and 46 London: Johns Hopkins University Press, 1989

59Letter no. 131, to Milton Waldman in Carpenter, Letters, 1981.

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1 Doughan, D. MBE, “J.R.R. Tolkien: A Biographical Sketch”, The Tolkien Society, 2 https://www.tolkiensociety.org/author/biography/ (accessed 13/04/20). 3 M. D. C. Drout, ed. J.R.R. Tolkien Encyclopedia: Scholarship and Critical Assessment. 4 New York: Routledge, 2007. 5 Duffin, R. W. A Performer's Guide to Medieval Music. Bloomington, IN: Indian 6 University Press, 2000. 7 Halsall, M. J. Creation and Beauty in Tolkien’s Catholic Vision: A Study in the Influence 8 of Neoplatonism in J.R.R. Tolkien’s Philosophy of Life as “Being and Gift”. Eugene, 9 OR: Pickwick Publications, 2020. 10 Hawkins, W. Pythagoras, The Music of the Spheres, and the Wolf Interval. Accessed 14 11 December 2015. http://philclubcle.org/papers/Hawkins,W20111115.pdf (accessed 12 12/03/20). 13 Hensler, K. R. “God and Ilúvatar: Tolkien’s Use of Biblical Parallels and Tropes in His 14 Cosmogony” in Mythmoot II: Back Again, Proceedings of the 2nd Mythgard Institute 15 Mythmoot Conference Center at the Maritime Institute, Linthicum, Maryland, 16 December 13-15, 2013. 17 Highet, G. Juvenal the Satirist. Oxford: Oxford University Press, 1960. 18 Houghton, J. W. “Augustine in the Cottage of Lost Play: the Ainulindalë as Asterisk 19 Cosmogony”, in J. Chance ed., Tolkien the Medievalist. London: Routledge, 2003, 20 171-82. 21 Kennedy, J. B. The Musical Structure of Plato’s Dialogues. London: Acumen, 2011. 22 J. Maritain, trans. F.J. Sheed. Theonas: Conversations of a Sage. London: Sheed and 23 Ward, 1923. 24 J. Maritain, trans. J. W. Evans. Art and Scholasticism and the Frontiers of Poetry. New 25 York: Scribner’s Sons, 1962. 26 Mastrangelo, Marc. The Roman Self in Late Antiquity: Prudentius and the Poetics of the 27 Soul. Baltimore: the Johns Hopkins University Press, 2008. 28 McIntosh, J. “Tolkien’s Pythagorean ‘inversion’: reality isn’t ‘like’ music, it ‘is’ music”, 29 in The Flame Imperishable, https://jonathansmcintosh.wordpress.com/20 30 12/07/30/tolkiens-pythagorean-inversion-reality-isnt-like-music-it-is-music/1/1 31 (accessed 12/03/20). 32 Milton, J., ed. by A. W. Verity. Paradise Lost. Vol. II. Cambridge: Cambridge University 33 Press, 1929. 34 Moore, K. R. “Pythagoras and the (Were)Wolf” in the Athens Journal of History, 35 2.4, 2016 227-238. 36 ------, “The Pythagorean Symbolism in Plato’s Philebus” in the Athens Journal of 37 History, 2.2, 2016, 83-95. 38 Robertson. A. B. Voices in Tolkien: Aquinas, The Lord of the Rings, and True Myth in the 39 Twenty-First Century. A Thesis Submitted to the Atlantic School of Theology, 40 Halifax, Nova Scotia in partial fulfilment of the requirements for the degree of 41 Masters of Arts (Theology and Religious Studies). Halifax, Nova Scotia: April 2017. 42 Robbins, F.E. The Hexaemeral Literature: A Study of the Greek and Latin Commentaries 43 on Genesis. Chicago: University of Chicago Press, 1912. 44 Sethares, W. A. Tuning, Timbre, Spectrum, Scale. Madison, WI: University of Wisconsin 45 Press, 2005. 46 Tolkien, J. R. R., C. Tolkien ed. The Silmarillion. London: George Allen and Unwin, 47 1977. 48 Whittall, A. “The Study of Britten: Triadic Harmony and Tonal Structure”, in Proceedings 49 of the Royal Musical Association, 106 (1979 - 1980), 27-41. 50 Wood, R.E. Placing Aesthetics: Reflections on Philosophic Tradition. Athens, IL: Ohio 51 University Press, 1999. 52 53

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