TOLKIEN'S UNIQUE RECEPTION OF PYTHAGOREAN ‘DISSONANCE’ IN THE AINULINDALË OF THE SILMARILLION

This article is about J. R. R. Tolkien's adaptation of Pythagorean musical elements in the ‘Song of the Ainur’ of the Silmarillion. It details Tolkien's use of Pythagorean dissonance, along with what that amounts to in terms of musical theory, and explores the epistemological origins of the concept and how it found its way into this work of fiction. On the latter point, Platonism, Neoplatonism, and early Christian theology are considered. This includes the likes of Prudentius, pseudo-Dionysius, Augustine, and Aquinas, among others. The article observes that Tolkien has deliberately chosen a somewhat esoteric element of Pythagorean musical theory, albeit highly relevant to his own historical context, in order to explore concepts of morality along with the traditional, Christian conundrum of predestination vs. free will.

considering the impact of several ancient and medieval sources.The question is scarcely one of whether or not Tolkien was influenced by, and deliberately incorporated, Pythagorean elements into his Silmarillion.This is well known and, in this regard, scholars have tended to focus on the Harmony of the Spheres and Plato's Theory of Forms.The question here is this: why did he choose to incorporate Pythagorean dissonance in such a significant manner and how and by what epistemological routes did this and other related elements find their way into his thinking?It seems that Tolkien intentionally borrowed this fundamental feature of ancient musical theory, generally overlooked in the scholarship, and extensively wove it into his tale.That he did so was not merely the influence of early Christian adaptations of Pythagorean ideas present in Tolkien's Catholic context, as some sources seem to imply.It was certainly derived in no small part from his education and background but also clearly chosen by him for a purpose.The route of transmission seems most likely to have been by way of Augustine and Aquinas, as will be presently considered.
In Tolkien's creation mythos at the beginning of the Silmarillion, the divine beings, referred to as the Ainur, are summoned before their creator, Ehru Illúvatar (referred to also as 'the One'), to sing a song composed by that deity and from which, in a likeness of it, the world, Arda, would be created.Immediately, one can detect a parallelism with Plato's Theory of Forms in Tolkien's cosmogenic narrative.This is a double creation myth that is both like and unlike others with which Tolkien would have already been familiar.In fact it appears to have much in common with the Hesiodic cosmogony in some notable contrast to the creation narrative found in Genesis.This can be observed in the process of order being formed out of chaos (the Void), with the agency of the divine will of Illúvatar infusing every creation, which is strikingly similar with the Stoic and Neoplatonic concept of logos ('Ultimate Logic or Reason', 'Universal Ordering Principle'). 1 It very much recollects Plato's Theory of Forms, where the 'Song of the Ainur' is the pattern/Form/Idea of the world, which comes first, and then the actual, physical creation comes next and inquiry; although it necessarily figures into it, given Tolkien's religious and philosophical influences.
Melkor differs markedly from the other gods (the Ainur or Valar, as those that would go into Arda would be called) in the Silmarillion.And he aptly illustrates Pythagorean elements, with conspicuously Christian overtones, incorporated into the narrative.Melkor is the greatest in power amongst the other created divinities and, like Milton's fictionalized archangel Lucifer, he has his own plans, which he seems to think are at variance with those of the Supreme Being.Akin to Milton's Lucifer, Tolkien writes: 'To Melkor among the Ainur had been given the greatest gifts of power and knowledge.' 6He is described in comparison to the other divine beings as follows: . ..of these Melkor was the chief. ..and he meddled in all that was done, turning it if he might to his own desires and purposes; and he kindled great fires.When therefore Earth was yet young and full of flame Melkor coveted it, and he said to the other Valar: 'This shall be my own kingdom; and I name it unto myself!' 7 Clearly, in the first instance, Melkor is meant to recollect the Christian Devil, in both biblical traditions and in fiction.And we can virtually pin down Tolkien's narratological links with the Bible to chapter and verse.
When, for example, Illúvatar summons the Ainur before him to sing his song, it reflects Job 1:6 (KJV): 'Now there was a day when the sons of God came to present themselves before the Lord, and Satan came also among them.'The descent of Melkor into Arda to work his mischief following the creation too recalls Isaiah 14:12 (KJV): 'How art thou fallen from heaven, O Lucifer, son of the morning!How art thou cut down to the ground, which didst weaken the nations!' Melkor will stir up serious strife among the elves, firstly, and then among men and other creations, stealing the Silmarills (gems of power made from the magic of creation found in the Two Trees, Telperion and Lorien), ultimately destroying the Two Trees themselves, which were the only source of light in the world before the sun and moon were made, causing wars and other violent upheavals.He will eventually be cast into the Nameless Void (not unlike the pit of Hell), though his evil would live on through his protégé, the lesser deity known as Sauron.What is more, like Milton's Lucifer, Melkor adopts an uglier, darker aspect when he goes into Arda to work his evil: 'Lucifer [i.e.Satan] was so illuminated that he far surpassed the brightness of the sun, and all the stars. ..this brightness was dimmed after Satan's fall'. 8And Melkor too dwells in darkness, obsessed with the Void even before being cast into it, and concealing his deeds through a cloak of shadows cast by one of his monstrous servants, the giant spider-thing called Ungoliant.
The parallels are too many to be coincidence; more could certainly be enumerated but will be omitted for want of space here.Indeed, we have Tolkien's own words on the matter which attest his position with relative clarity: In the cosmogony there is a fall: a fall of Angels we should say.Though quite different in form, of course, to that of Christian myth.These tales are 'new', they are not directly derived from other myths and legends, but they must inevitably contain a large measure of ancient wide-spread motives or elements.After all, I believe that legends and myths are largely made of 'truth', and indeed present aspects of it that can only be received in this mode; and long ago certain truths and modes of this kind were discovered and must always reappear.There cannot be any 'story' without a fall-all stories are ultimately about the fall at least not for human minds as we know them and have them. 9t that is not a subject of dispute here.And there are many other mythic features present in the work.Collins rightly calls Tolkien's approach 'syncretic', combining Indo-European (Sanskrit) and Latin linguistic and religious elements and, in terms of literary/philosophical influences, he alludes to authors such as Sydney, Milton, Spenser, and Plato.The character of Melkor, in particular, reflects aspects of the Judeo-Christian Satan, as indicated, as well as Norse and other mythological figures such as the Scandinavian Loki and the Celtic Bilé.Notably, though, Collins identifies a Pythagorean feature in the 'Song of the Ainur', adding that many 'of the Valar inhabit the orbs of the heavenly spheres, like the celestial intelligences of the pseudo-Dionysius, and their heavenly music recalls that of Pythagoras, while the essential dichotomies, particularly the emphasis of Concord versus Discord, reflect exactly the personified polarities of the Neoplatonist Prudentius'. 10The role of discord is fundamental to this analysis and it is this Pythagorean connection in particular that this article is exploring in some further detail here, as well as presently adding an observation about it that has largely gone unnoticed by other scholars.
The musical aspects of the Ainulindalë are numerous and sophisticated.Collins points out that the 'Song of the Ainur', with Melkor's discordant blasts, has been identified as a three-part piece consistent with traditional sonatas and cantatas, themselves having Classical roots.11He identifies Melkor's dissonant tones as an 'aesthetic challenge' for the supreme deity Illúvatar, alongside a discussion of free will in the Christian context, as well as recollecting some points made by Geoffrey Chaucer (reflecting Boethius) 12 and others on some of the central problems inherent in Western, Christian theology.These points are observable in the quotes above.And Collins associates the harmony/disharmony of the song with Hegelian Dialectics: thesis, antithesis, synthesis, as well as being in some ways analogous to the Christian paradox of the 'fortunate fall'.Indeed, as indicated, Illúvatar adapts Melkor's dissonance into the music, suggesting that an interpretation based on Hegelian synthesis carries some weight.Consequently, the narrative structure of the Lord of the Rings itself follows the pattern prefigured in the 'Song of the Ainur' in the Silmarillion, keeping true to the theme of Plato's Forms, as already noted.But apart from the brief mention of Pythagorean influences, Collins mainly focuses on literary, religious (modern and other), philosophical, and structural elements playing out through the 'Song of the Ainur'.13Do Melkor's tumultuous additions then represent an actual 'challenge' to the will of Illúvatar?Halsall, for example, has pointed out that Melkor's dissonance not only merges with the 'Song of the Ainur', perhaps reflecting some kind of Christianized version of Hegelian synthesis, arguing that it is clearly part of Illúvatar's divine plan from the onset. 14cIntosh has identified the relevant philosophical background behind the Ainur's Music as ultimately being derived from the mathematician and philosopher Pythagoras (sixth century BC) and indicates that this has naturally received frequent mention in discussions of the subject. 15We shall see that it does indeed appear to be derived from Pythagorean musical theory, likely transmitted through Christian re-interpretations and particularly that of Aquinas by way of Augustine.Scholars have mainly focused on the obvious homage to the Harmony of the Spheres, which has been traditionally ascribed to the Pythagoreans.On this, Aristotle has written that 'they took the elements of number to be the elements of all things, and the whole cosmos to be harmony and number' and that, according to them, 'the movement of the stars produces a harmony, that is to say, the sounds they make are concordant'. 16Yet, within both the 'Song of the Ainur' as well as in Pythagorean tuning, any continuous concord is broken by one or more dissonant notes.The very musical scale itself, along with any harmonious concord it may produce, is mathematically impossible without also generating some dissonant notes.
Consonance and dissonance are features of harmony, as observed by the Pythagoreans, who also extended this mathematical understanding to broader, 'cosmic' phenomena, as Aristotle has observed.Almost any mathematical division of the musical canon will produce some notes that are more harmonious and some that are less so.The dissonant notes might be omitted from the range chosen by a composer, or used in differently effective ways. 17The twentieth-century composer Benjamin Britten, for example, a contemporary of Tolkien, utilized dissonance very effectively to convey in his music the disruptive upheavals of the First World War. 18In relation to Tolkien and the 'Song of the Ainur', it is the 'dissonance' of Melkor that stands out and which 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.
15 J. McIntosh, 'Tolkien's Pythagorean "inversion": reality isn't "like" music, it "is" music', in The Flame Imperishable, <https://jonathansmcintosh.wordpress.com/2012/07/30/tolkienspythagorean-inversion-reality-isnt-like-music-it-is-music/1/1>,accessed 20 November 2023.For other references to Pythagoreanism in Tolkien, see also Collins (n.10), 257-65. 16Aristotle, Metaphysics I.5.986a; and see the section usually titled 'On the Heavens', in Metaph.II.9.290b12. 17 principally connects to Pythagorean musical theory and its subsequent reception by the Neoplatonists and Neoplatonist Christians in particular.I have discussed these 'wolf intervals' or 'wolf tones' (the more dissonant notes) in detail in another article. 19However, Pythagorean tuning may be briefly summarized here.The musical scale, or chromatic scale, is operationally defined through intervals composed of 3, 4, 5, 7, 8 or 9 semitones.That is, they are major and minor thirds or sixths, perfect fourths or fifths, and their enharmonic equivalents, which are notes that are written differently (such as A flat and G sharp) but sound the same in the tempered scale, the size of which deviates by more than one syntonic comma (about 21.5 cents) from the corresponding, justly intonated interval.In the twelve-note Pythagorean division of the musical canon in particular, all tones are separated by intervals of perfect fifths with the higher frequency at exactly 3/2 times that of the lower ones. 20Number, ratio, and proportion define the notes and hence all subsequent music which partakes of that tradition.
This mathematical division results in at least one note on the scale always being out of tune, or 'dissonant', and usually there will be more than one.It has been a well-attested issue for musicians and composers since antiquity.And a more dissonant note from such a scale has been sometimes referred to as the 'wolf tone' due to it resembling the sound made by a howling wolf (sometimes referred to as the 'flatted fifth' as well as, rather pointedly, 'the Devil's interval'), especially when played on a pipe organ.The earliest demonstrable use of the term 'wolf tone' appears to derive either from very late antiquity or from the Middle Ages. 21Even so, there is ample room for Tolkien to have become acquainted with the concept and likely even in terms such as 'wolf tone' and 'Devil's interval'.As we have already seen, the character of Melkor recollects the Christian Devil.As it turns out, he is also specifically associated with werewolves and wargs (along with wolves more generally), which were his creation and serve him in his evil schemes and deeds. 22And it seems to beg the question as to whether the author was deliberately invoking the so-called 'wolf tone' with such seemingly explicit associations.
Tolkien's education and background are helpful here in terms of pointing toward some possible epistemological connections.It is known that he studied Latin and ancient Greek from as early as 1904, along with Finnish and modern and ancient Gothic.In the autumn of 1911 he attended Exeter College, Oxford, where he initially read the Classics, Old English, the Germanic languages (especially Gothic), Welsh, and Finnish until 1913.Tolkien obtained a secondclass degree in Honour Moderations, which was the 'midway' stage of a four-year Oxford 'Greats' (i.e.Classics) course, although he received an 'alpha plus' in philology, which would be a defining feature of his later, academic career.In consequence, he changed from the Classics to the English Language and Literature course, which he evidently found to be more agreeable with his interests.He would receive a first-class honours degree in June of 1915, prior to joining up for the War.One of the poems that he discovered in the course of his Old English studies was the Crist of Cynewulf, which clearly intrigued him with its use of the term middangeard, which he translated as 'Middle Earth'. 23hat emerges from most any detailed biography or scholarship on Tolkien is that he despised modernism and industrialization and that he railed against the horrors of modern, industrial warfare, with which he had considerable personal experience.These become allegorized in the villains of his various books, such as Melkor, Sauron, and Saruman.Though a trained classicist and firmly rooted in the Classical tradition, he is perhaps best described as a medievalist, with perhaps his own Catholicism urging him toward medieval Christian philosophy including the likes of St. Augustine (13 November AD 354-28 August 430), Boethius (c.AD 477-524), and St. Thomas Aquinas (1225-7 March 1274). 24These facts do not necessarily clarify the epistemological journey from Pythagoras to Tolkien but seem to suggest that his Neoplatonic/Pythagorean roots derive more so out of the Christian writers of late antiquity and the Middle Ages.His medievalism might also point to a source for his incorporation of Pythagorean tuning and the apparent association between discordant tones and wolves, and so thus the 'wolf tone' identified above, as well as Melkor's obvious connections with the Christian Devil.Even so, the subject of dissonance also figures prominently into Plato's depiction of the tripartite psyche ('soul/mind') in the Republic, especially when it is 'disordered' (439b-432a), which Tolkien almost certainly read, and which would also be adapted into the works of later, Christian thinkers. 25Indeed, given the ubiquitous operation of something like the Theory of Forms in the Silmarillion, along with the later, but much more apparent, appropriation of Plato's story of the Ring of Invisibility (the myth of the ancestor of Gyges) in Book II of the Republic (359a-360d), he must have read at least that dialogue if not also the Timaeus and Phaedrus as well.
Neoplatonic influences and themes are numerous in Tolkien.This has been well-documented, and it is not the aim of this article to rehash them all here.However, some do bear mention as they are highly relevant to this topic.The concept of cosmic harmony adopted by Tolkien in the 'Song of the Ainur', for example, may be seen to derive almost directly from Plato's Timaeus (29b-42), and especially from St. Thomas Aquinas' discussion of it in the Ethics (15).These reflect ancient Greek ideas of the ratios in musical structure (noted above), equated by the Pythagoreans, Plato, and later, in their own unique way, Christian scholars such as Aquinas, Augustine, and Boethius with the 'World Soul' and the non-static nature of creation. 26A link with Plotinus (AD 204/5-270) may be noted through his influences on Augustine and, as Halsall has observed, 'Tolkien allies himself to this received inheritance of the Augustinian Neoplatonic tradition in terms of goodness and evil in a pre-lapsarian state'. 27There are obvious links with Augustine and especially his de Musica (On Music), which is replete with Neoplatonic and Pythagorean elements.Speech and light, for example, are taken together by Augustine as 'intellectual illumination', exemplified in his interpretation of Genesis.Although, if Tolkien was acquainted with Augustine's views on creation, then they 25  26 Halsall (n.14), 22-3. 27Ibid., 28.
were worked into his cosmogony very 'astutely', with some notably 'stylized' departures from that philosophy. 28The Ainur acting as sub-creators differ from Augustine's view, which regarded God as the sole creator, through the agency of logos. 29And there is an additional variance.Tolkien himself has indicated in his own letters that he does not accept the idea of 'Absolute Evil', noting that Melkor's fall, unlike that of Lucifer, transpired 'before Creation of the physical world'. 30This is more in keeping with the old Anglo-Saxon concept of 'doom' (or Wyrd, 'overarching law, judgement, or personal destiny'), which is apt considering Tolkien's interests; although, it also resonates well with Pythagorean tuning and the discordant tones inasmuch as Melkor's fall is effectively a feature of the musical theme prefigured by the will of Illúvatar.
The result is that Tolkien has created a plausible, alternative version of Genesis, in the sense of internal consistency and external comparability with existing systems of belief.Houghton has observed that the cosmogony of the Ainulindalë fits neatly 'among the real cosmogonies known to early Western medieval Europe', albeit also differing from them. 31Christian thinkers inherited two distinct traditions of this kind, reflecting those which had originated in Jerusalem and Athens: on the one hand, the Hexameron (Ἡ Ἑξαήμερος Δημιουργία), which included the ex nihilo creation myth of Genesis and, on the other hand, some combination of the Hesiodic cosmogony mingled with that found in Plato's Timaeus, referred to above, which had been translated into Latin and was widely read by medieval scholars in the West. 32The Hexameron genre of theological treatise elucidates the Judeo-Christian God's activities during the biblical six days of creation, usually in the form of commentaries on Genesis I, and hexameral literature was popular in the early and medieval periods of Christian history.This kind of commentary is to be found among the Latin Church Fathers; St. Basil composed works on the topic, as did St.Ambrose (c.AD 340-397), St. Augustine, and later St. Thomas Aquinas. 33Alongside these, the early medieval thinkers had access to numerous pagan commentaries on Plato's Timaeus, all of which, to one extent or another, bore a significant influence from the Neoplatonist philosopher Plotinus.It was St. Augustine's reflections on both these commentaries and on interpretations of Genesis that dominated medieval theological thought about creation. 34n fact, it has been observed that the double creation (first the idea/ song, then the world) of Tolkien's Ainulindalë would have likely been regarded by medieval scholars 'as reassuringly easy to fit into the schema of Augustine's Christian Neoplatonist synthesis, and the writings of others such as Pseudo-Dionysius and Dante'. 35This is particularly observable in Augustine's refutation of the dualist beliefs within the Manichaean heresy.Even so, Tolkien himself has not provided us with any definitive statement to the effect that his work was directly influenced by these sources.
In keeping with this theme, if we are to trace the epistemological roots of Tolkien's Pythagoreanism, it is worthwhile to consider some additional, specific Neoplatonist influences such as those identified by Collins and others already noted above. 36As we have seen, they are intrinsically interwoven into early Christian thought thanks to Plotinus by way of Augustine.A key source identified by both Collins and Halsall above is pseudo-Dionysius.He was a Christian Neoplatonist writing in the late fifth or early sixth century AD who transposed, in a thoroughly unique manner, the whole of pagan Neoplatonism from Plotinus (AD 204/5-270) to Proclus (AD 412-485), but particularly that of Proclus and the Platonic Academy of Athens, into an idiosyncratically novel Christian framework.His works were written as if they were composed by St. Dionysius the Areopagite, a member of the Athenian judicial council (the Areopagus) in the first century AD who had been reportedly converted to Christianity by St. Paul.This was clearly with the intent of giving the author a greater claim to veracity.So, these works might be considered a 'successful' forgery insofar as the author was not really He also adds, 'so far as, if anything should have been led astray to discord and disorder, and should suffer any diminution of the perfection of its own proper goods, even this it [Divine Justice] redeems from passion and listlessness and loss'. 41One can readily observe in these quotes, following Collins above, a view that appears to resonate quite strongly with Tolkien's 'Song of the Ainur' and particularly Melkor's dissonant contribution to it, along with his subsequently villainous behaviour in his role which, as stated, was the equivalent in many ways to that of Milton's Lucifer and, more broadly, the Judeo-Christian Satan.Pseudo-Dionysius too subordinates discord to Divine Justice, much as Tolkien subordinates Melkor's dissonant notes to the ultimate will and plan of Illúvatar. 42Was Tolkien acquainted with pseudo-Dionysius?It seems more than possible but specific evidence to that effect is lacking.
Tolkien too has offered some tantalizing revelations on this subject in a letter which, for whatever reasons, he never sent but is included in the compendium of his surviving correspondences.He writes: The Ainur took part in the making of the world as 'sub-creators': in various degrees, after this fashion.They interpreted according to their powers, and completed in detail, the Design propounded to them by the One.This was propounded first in musical or abstract form, and then in an 'historical vision'.In the first interpretation, the vast Music of the Ainur, Melkor introduced alterations, not interpretations of the mind of the One, and great discord arose.The One then presented this 'Music', including the apparent discords, as a visible 'history'. 43is harmonizes (if the reader will pardon the wordplay) well with other topics already discussed here.But note Tolkien's repeated use of the term 'the One' to refer to the supreme creator Illúvatar.And he does so not only in this letter alone but in multiple such communications, using that term to refer alternately to both Illúvatar and the Christian God.The phrase appears to leap straight out of the pages of Plato, echoing the teachings of the Eleatic Parmenides along with similar language used by the Pythagoreans.And it is not only in his correspondences that he has recourse to that term.In the very opening paragraph of the Silmarillion is stated: 'There was Eru, the One, who in Arda is called Ilúvatar; and he made first the Ainur, the 41 Ibid., 10.9. 42See Halsall (n.14), 37-9, where he references Job 38:6-7. 43See letter 212, draft of a continuation of letter 211 to Rhona Beare, dated 14 October 1958 (not sent), in Carpenter (n.9).
Holy Ones, that were the offspring of his thought, and they were with him before aught else was made.'That they are the 'offspring of his thought' emphasizes the likeness with Plato's Theory of Forms, itself quite probably of Pythagorean origin, as well as confirming that Melkor's dissonance is likewise derived from the thoughts of 'the One'.Even if Tolkien has not directly alluded to any specific Pythagorean or Neoplatonist source within his correspondences, the draft letter and the opening lines of the Silmarillion itself appear to substantially confirm just such a connection.Tolkien's unsent letter also recollects Christian adaptations of Pythagoreanism as observed in the writings of pseudo-Dionysius and elsewhere.The discords are only 'apparent', as Tolkien writes, not an actual rebellion in the true sense, because they are inherently integral to Illúvatar's plan, much as the dissonant notes must be included in the Pythagorean division of the musical canon in order for the scale to exist at all.
The other Pythagorean source indicated by Collins, whose ideas appear present in Tolkien, is the Neoplatonic poet Aurelius Prudentius Clemens, a Roman Christian from Tarraconensis (Northern Spain), who lived from AD 348 to 413.He is also identified as a probable influence by Drout in his compendious encyclopaedia of Tolkien scholarship, but without definitive proof, that the author was familiar with that source. 44Prudentius' allegorical Psychomachia (The Battle of the Psyche) was his most prominent work, incorporating elements of Classical epic in order to explore aspects of internal, psychological struggle. 45Unsurprisingly, within it we can clearly observe notions of harmony and discord adapted to a Christian context.Consider the following lines from the poem spoken by Discord personified: I am called Discord, he said, and my other name is Heresy; God to me is variable, now lesser, now greater, now double, now single; when I please he is insubstantial, merely an apparition, or again the soul within us, when I chose to ridicule his divinity.My teacher is Belial, my home and country is the world. 46scord here could almost be speaking the words of Tolkien's Melkor (or Milton's Lucifer).Like Tolkien in the twentieth century, 44 Drout (n.36), 346. 45See G. Highet, Juvenal the Satirist (Oxford 1960), 184 ff. 46'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 Belia mihi, domus et plaga mundus' (709-14).
Prudentius was marrying Neoplatonic and Pythagorean ideas with Christian ones, in keeping with the likes of fourth-and fifth-century scholars such as Eusebius and St. Augustine. 47Prudentius was also appropriating epic tropes from Virgil. 48And that is fitting for Tolkien too, given the epic nature of his own works.The reference to Belial in the Psychomachia is additionally striking, as this name occurs in the Hebrew Bible and is later considered synonymous with the Devil. 49ould it be that Tolkien had an eye on pseudo-Dionysius and Prudentius when composing the Silmarillion?Perhaps that is the case, and these may well have been part and parcel of his reading lists during his student days; although, we have no explicit evidence to support such a view apart from Collins' speculation that this material might have been covered in the philosophical lectures that Tolkien attended at Oxford.However, it has been suggested that another source, even more in keeping with Tolkien's Catholic religious background, is at play here, and one that subsumes many or all of the others here discussed.Halsall has argued that Tolkien's Neoplatonism in the Ainulindalë derives more from the musical theory and theology of St. Thomas Aquinas than from Augustine or Boethius, even if it appears to reflect pseudo-Dionysius and Prudentius, as Collins and McIntosh have implied.And Aquinas' theological interpretations of musical theory have been regarded as having an observable impact on Tolkien and his contemporaries. 50Furthermore, when Tolkien was a youth, it is known that he was given an annotated copy of the Summa Theologica (Summary of Theology) by his guardian, Father Francis Morgan. 51t. Thomas Aquinas was well aware of Pythagorean ideas and especially those concerning music, which he derived in no small part from Augustine's de Musica.He even devoted quite a few passages to 47 See M. Mastrangelo, The Roman Self in Late Antiquity.Prudentius and the Poetics of the Soul (Baltimore, MD, 2008), passim.
48 Contrast Prudent.Psychomachia 902 with Aeneid 6.86 and 7.41. 49See also the Ascension of Isaiah 1:8-9, 2:4, 3:11-13, 4:2, 4:14-18, 5:1, 5:15; this is a pseudoepigraphical Jewish-Christian text, ranging anywhere from the final decades of the first century AD to the early decades of the third century and certainly known to Prudentius. 50See J. Maritain (trans.),J. W. Evans, Art and Scholasticism and the Frontiers of Poetry (New York, 1962) and J. Maritain (trans.),F. J. Sheed, Theonas.Conversations of a Sage (London, 1923).discussion of 'the One' in his Summa Theologica, as he understood it to have been expressed by Plato and Pythagoras. 52Frequently referencing Aristotle, Plato, Empedocles, Augustine (especially his de Musica), and Pythagoras throughout, he declares that music is derived 'from principles established by arithmetic'. 53Pointedly, in his discourse on music, he talks about it as having being per se, since it has a cause, and he contrasts it with the colour white, or 'whiteness', which too has being, also having a cause (L.115.7).It may be merely coincidence, but the Pythagoreans considered the colour white to have special, metaphysical symbolism and properties. 54Empedocles (444-443 BC) had worked out a theory of light and colour which was innately connected with musical harmony.Colour theory in general was important to the Pythagoreans, as well as to Plato, and it formed part of the theoretical framework of both his and their philosophy about music. 55Whether Aquinas was aware of this, making it a conscious selection for him to place 'whiteness' alongside music as things that have being, is not possible to affirm with any certainty; it is nevertheless an interesting choice on his part.
Again, in his Summa Theologica, discussing the metaphysics of music, Aquinas delineates three objective characteristics of beauty: integrity, proportion, and clarity. 56Integrity refers to the 'completeness' and formal structure of a thing, in keeping with Tolkien's vision of the Ainur as sub-creators based on Illúvatar's sonata.Proportion is a fundamentally Pythagorean concept; 'qualitative proportion' produces harmony and beauty and refers explicitly to the mathematical qualities of the division of the musical canon noted above.Clarity is the 'shining forth of form', which Tolkien inserts into the Ainulindalë when the Ainur first observe the created world. 57Aquinas was heavily influenced by Neoplatonism and if, as some sources noted above have suggested, Tolkien was intimately acquainted with Aquinas' views on the metaphysics of music, then there appears to be a clear link which may account for the author's use of such concepts in the Silmarillion.
Even so, Halsall has argued that having the Ainur as co-creators runs contrary to the Neoplatonist principle of 'diminution and decline' (exemplified by Plato's 'Nuptial Number' in the Republic, 8.546b), adding that 'even the rebellious and discordant music of Melkor is an opportunity on the part of the Ainur for "theodicy"'. 58And that is more in keeping with Aquinas' theological positions than those of Pythagoras or Plato.Theodicy refers to the vindication of divine providence in view of the existence of evil, or why a 'good' God would permit evil to exist at all.This is a topic with which Christian theology has grappled for centuries.Halsall addresses the issue of evil and free will in his work with much recourse to Catholic doctrine and Aquinas in particular.Tolkien himself has added his own views on this subject in his letters, writing: That Sauron was not himself destroyed in the anger of the One is not my fault: the problem of evil, and its apparent toleration, is a permanent one for all who concern themselves with our world.The indestructibility of spirits with free wills, even by the Creator of them, is also an inevitable feature, if one either believes in their existence, or feigns it in a story. 59lkor's 'free will' is clearly subordinated to the divine plan of Illúvatar and, in that regard at least, it is highly compatible with Aquinas' and Prudentius' views.Yet, as has been demonstrated, the dissonance of Melkor's musical theme is not merely a discordant element that reflected the zeitgeist of Tolkien's era following the First World War, figuring prominently into the music of composers at the time, as stated, it is also absolutely essential for the Pythagorean division of the musical canon.Tolkien, of course, as he himself has written, is not obliged to follow any single philosophical or religious tradition in his fictionwriting and we would therefore not expect his constructed theology or cosmology to be 100 per cent compatible with either Neoplatonism or Christianity, however influenced by both of them.The discord of Melkor resonates with Christian debates and discourses over evil and free will going back to the Latin Fathers, but it is also a distinctly Pythagorean element and a deliberate choice on Tolkien's part.
In terms of the secondary scholarship availed here, some further caveats need to be levied.Collins seems to overplay the role of modern philosophy, though not without due recourse to ancient and medieval, in his interpretation of the Ainulindalë.And this position has some merit though it depends on precisely which philosophical influences affected Tolkien and whether we can know them.By contrast, Halsall is clearly more immersed in medieval Catholic philosophy, undertaking some very finely focused analysis of Aquinas in particular and relating it reasonably well in his exegesis of Tolkien's Silmarillion.The author was, by all accounts, a devout Catholic, and Halsall may not be remiss in drawing just such connections.Both of these scholars, as with others, have their own agendas.And they run the risk of depicting Tolkien perhaps less correctly than he really was and more as they would have him be.Not unlike Alexander the Great, Tolkien has become in our own age such an epic figure that his reception has taken on a distorted Nachleben (afterlife) in the writings of, albeit well-intentioned, interpretive biographers; although, all usually entail elements of truth to varying degrees.The 'real' man and his thoughts nevertheless remain more elusive.
What we can know with relative certainty is that Tolkien read Aquinas at an early stage in his life and that he was living in an era and a cultural context steeped in that theologian's philosophies.And Aquinas was well versed in Pythagorean musical theory.Tolkien studied the Classics too, during which time he was almost certainly exposed to Plato and other ancient philosophers, especially those whose ideas were more compatible with Catholic doctrine.Did he also read Augustine, Prudentius, and pseudo-Dionysius?This is not certain, but the apparent connections with Neoplatonist views regarding music, and discord in particular, seem reasonable and well supported by the scholarship on the Ainulindalë.Even so, as this article has tried to demonstrate, Tolkien evinces a keen grasp of Pythagorean tuning and has incorporated this in a specific and unique way within his writinga subject that, apart from its allegorical manifestations, has been widely unknown outside specialist studies of Pythagoreanism and musical theory.And he has deployed it in a manner that is apt to both the allegorical and the wider metaphysical ramifications of those approaches.

TOLKIEN'S RECEPTION OF PYTHAGOREAN DISSONANCE
No doubt some would find it thrilling for this article to conclude by asserting that J. R. R. Tolkien was in fact some kind of secret Pythagorean who was fully aware of their division of the musical canon, with its dissonant notes, along with the wider, more cosmic implications thereof, embedding these ideas into his narrative.Melkor's discordant additions to the 'Song of the Ainur', as with the 'Song of the Ainur itself', are compelling evidence in and of themselves.And Tolkien's multiple references to 'the One' in both the Silmarillion and in his letters, sent and unsent, are very interesting indeed.However, the evidence available does not unequivocally sustain such an assertion.
What appears to be a more solid a conclusion is that Tolkien was manifestly influenced by a series of thinkers, spanning through a virtually unbroken chain from Pythagoras himself up to Aquinas, from which the general pattern of the Ainulindalë's Pythagorean elements may be epistemologically deduced to a point, as they have been here.This article's particular inquiry into Tolkien's awareness of rather nuanced elements of Pythagorean tuning has disclosed a range of possible and probable links.Most scholars have missed this unique reception of Pythagorean dissonance in Tolkien or only obliquely noted it in the context of other agendas.Collins alluded to the potential influence of pseudo-Dionysius and Prudentius.And, while their impact is evident, it has been demonstrated that they formed only links in the chain of transmission and that there is no evidence that Tolkien ever read them, although he did read sources influenced by them.Like Collins, Halsall noted the discord of Melkor but focused more on its subordination to the divine will of Illúvatar, drawing parallels with the Christian Fall and questions of free will.This article has argued that Tolkien purposefully selected the notion of Pythagorean dissonance almost certainly from Augustine, by way of Aquinas, and potentially from his reading of Plato's Republic as well, pointedly implementing it in order to prefigure the narrative structure of his fictional universe.However, there are limits to what we can know of Tolkien's thoughts, and one runs the risk of concluding on a 'sour note' here, not unlike the so-called wolf tone howling out for attention, but without revealing the details of its arcane mystery.Such discord may perhaps yet be harmonized by permitting the closing lines to Tolkien himself and, in those words, we can perhaps take some small consolation: 'For (partly to redress the evil of the rebel Melkor, partly See J. B. Kennedy, The Musical Structure of Plato's Dialogues (London 2011), 37-8. 18A. Whittall, 'The Study of Britten: Triadic Harmony and Tonal Structure', Proceedings of the Royal Musical Association 106 (1979-80), 27-41.TOLKIEN'S RECEPTION OF PYTHAGOREAN DISSONANCE See D. H. Rice, 'Plato on Force: The Conflict Between His Psychology and Political Sociology and His Definition of Temperance in the Republic', HPTh 10.4 (Winter 1989), 569, for Plato's use of dissonance in the Republic.
51 A. 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, in partial fulfilment of the requirements for the degree of Masters of Arts in Theology and Religious Studies (Halifax, Nova Scotia, April 2017), 4 et passim.