Nicholas of Cusa (1400-1464) was a late Medieval/early Renaissance German cardinal, best known as a philosopher. Today he is probably best known because of Umberto Eco’s novel, The Name of the Rose, which seems to be based on Nicholas’ discovery, noted by Bett, of “a manuscript of Plautus, containing twenty comedies, twelve of which had been unknown in the Middle Ages.” In The Name of the Rose this discovery symbolizes the necessity for the fusion of comedy and tragedy, a synthesis of opposites into a higher unity, which Spitzer refers to as the “Cusian idea of coincidentia oppositorum.” The archetype of this idea is found in the dynamics of the Christian Trinity, which Bray describes when noting von Balthasar’s recognition “that the mutual relation of the Father and Son is a coincidence of opposites, in which opposition (conflict) is replaced by self-determination in love (Spirit).” A union of polarized forces is also characteristic of triadic tonality, which operates according to principles similar to those articulated by Nicholas.
Although Nicholas does not discuss music in his writings, Bett mentions the “constant emphasis upon number” in Nicholas’ thought, which is consistent with the “high regard for what he knew of Pythagorean doctrine.” Giordano Bruno reportedly said of Nicholas that if he had not been hindered by his priest’s vestment, he would have even been greater than Pythagoras. I’m not convinced that the priesthood was a hindrance to Nicholas, for his thought is characterized by a blending of Trinitarian theology, which was surely nurtured by his priestly office, and the Pythagorean emphasis on number, noted by Aristotle in the following comment: “For as the Pythagoreans say, the All and all things are defined by threes; for end and middle and beginning constitute the number of the All, and also the number of the Triad.”
Nicholas reconciled the Pythagorean doctrines of participation and the triad with the Christian doctrine of the Trinity. The reconciliation of these last two doctrines is suggested in his assertion that “‘in every creature we find the one and threefold God present by some sort of participation; for the more similar a creature is to God the more threefold and one it is.’” For Nicholas, the Trinity reveals Itself through metaphysical, epistemological, and physical triads: “the loving Love, the love-worthy Love, and the uniting act of Love; as that which knows, that which is known, and the uniting act of knowledge…and in many mundane triads, as centre, diameter, and circumference; as beginning, middle, and end; as the spring, the river, and the lake; and so forth.”
The relation between the first mundane triad and the specific persons of the Trinity was later described by Johannes Kepler, who states that “in the sphere, which is the image of God the Creator and the Archetype of the world…there are three regions, symbols of the three persons of the Holy Trinity – the centre, a symbol of the Father; the surface, of the Son; and the intermediate space, of the Holy Ghost.” With the Renaissance revival of interest in the liberal arts, including music, and the gradual acceptance of the harmonic principle of the triad, it was a logical progression to include the tonal triad among “the many mundane triads” referred to by Nicholas; with reference to the triad of the sphere, the tonal center of the harmonic triad is analogous to the center, the fifth tone, as it is farthest removed from the tonal center, is analogous to the surface, or circumference, and the third tone is analogous to the intermediate space. Earlier I mentioned de Muris’ precedent for including music – which he claims “takes its origin from the ternary number” – among the mundane images of the Trinity.
It is curious that so many German philosophers since the Renaissance have been concerned with music. One reason for this national tendency may be due to the fact that the German educational system “was strongly colored by Greek Paideia,” in which music assumed a prominent role. An additional reason is undoubtedly the influence of sixteenth century reformer Martin Luther (1483-1546). Westermeyer notes: “the Lutheran tradition has stimulated a string of composers who created choral and instrumental materials.” It is possible that this tradition also stimulated a series of German philosophers who embraced music theory as central to their ideas. Such a possibility is suggested in Faulkner’s observation that “from its earliest days, German Lutheran Protestantism approved and supported the practice of complex art music as a fitting way to praise God in worship…Such music maintained a close relationship to Lutheran liturgical life throughout the sixteenth and seventeenth centuries. Indeed, seventeenth-century central Germany (through the time of Bach’s childhood), a bastion of conservative Lutheran orthodoxy, seems to have been one of the last places where Christian life and worship flourished free from the serious incursion of more modern, self-conscious modes of thinking.”
Let us now consider how Luther’s love of music fostered an environment in which ideas concerning music and metaphysics could flourish. Many of Luther’s comments regarding music are found in his “Preface” to Georg Rhau’s Symphoniae iucnedae (Delightful Symphonies, 1538). In this Preface, Luther writes:
I would certainly like to praise music with all my heart as the excellent gift of God which it is and to commend it to everyone. But I am so overwhelmed by the diversity and magnitude of its virtue and benefits that I can find neither beginning nor end or method for my discourse. As much as I want to commend it, my praise is bound to be wanting and inadequate. For who can comprehend it all? And even if you wanted to encompass all of it, you would appear to have grasped nothing at all. First then, looking at music itself, you will find that from the beginning of the world it has been instilled and implanted in all creatures, individually and collectively. For nothing is without sound or harmony [literally, ‘sounding number.’ (editor)].
From this last sentence Faulkner concludes: “Luther adhered in some measure to the medieval neo-Platonic worldview and its accompanying conception of music.” Faulkner qualifies the philosophical adherence imputed to Luther when adding: “Yet Luther never promoted the ideas that grow from that worldview, since he was at heart a pragmatist…Luther represented a judicious balance of traditional Christian and more popular, progressive attitudes. He embodied this balance (as well as the contradictions that result from it) in his very personality, and the church that rose in his wake continued to embody it for the following two centuries. Although his involvement with music extended only superficially to speculation, his sympathy for the medieval worldview allowed room for tolerance of and interest in speculative inquiry in the church that issued from his reforming work. Lutheran musical practice, however, did not suffer under the repressive aspects of patristic or neo-Platonic doctrine. Thus as the Lutheran Church evolved in Germany, the practice of music blossomed freely in all forms, based on a love of the art and its gifts, and not necessarily on speculative premises.”
Luther’s balanced attitudes may, however, have leaned more in the direction of the medieval neo-Platonic worldview, for Gaines observes that “Martin Luther sided with the Platonic idea of music as evidence of divine order, and he set out to rehabilitate Pythagoras as a servant of God. In his commentary on Genesis he laments the fact that ‘we have become deaf toward what Pythagoras aptly terms this wonderful and most lovely music coming from the harmony of the spheres.’” Although these statements counter Oskar Söhngen’s opinion that Luther “swept aside the mediaeval attitude to music,” Luther did sweep aside Pope John XXII’s ban on the liberty to compose ecclesiastical melodies with “discanti” and “tripla”; Luther describes as “singularly marvelous…the manner in which a simple melody is set against three, four, or five other voices – these play and leap around this simple melody as if in jubilation, and adorn and decorate the same melody with all kinds of art and sound, and perform as it were a heavenly round dance, fondly greeting, soon embracing, and pleasantly surrounding each other.” Just as I suggested a relation between the compositional and doctrinal intolerance of John XXII, so there may be a relation between the zeal for both contrapuntal polyphony and doctrinal reformation expressed by Luther; in both instances there is a parallel between the desired musical and ecclesiastical forms.
That Luther continued to exert an influence on succeeding generations of theorists who promoted the traditional Christian recognition of the harmonic ratios is evident in both Lippius’ reference to “blessed Luther” and in the following passage from Andreas Werckmeister’s Musicalische Paradoxal-Discourse (1707): “the late Mr. Luther also says, ‘Anyone who loves music is of good stuff, and adept at all things; anyone who despises it is a coarse clod.’ Such contempt arises from a confused spirit that is not anchored and formed according to the harmonic ratios in the order of its wise Creator.” Such a confused spirit seems to have characterized the generations following those of Lippius and Werckmeister, during which time Luther’s balance of traditional and progressive Christian attitudes was upset, and music was based on subjective values of freedom rather than on objective ratios.
Söhngen clearly favors the liberal and progressive side of Luther, when writing: “Music was to him a metaphor for the freedom of the Gospel. If a man has no feeling for the ‘evangelical’ character of music and rejects it, then his theology cannot be correct.” In endorsing such freedom, however, Söhngen should not forget Paul’s warning: “do not use your freedom as an opening for self-indulgence.” That such an opening characterized subsequent Lutheran music and liturgy is evident in Faulkner’s recognition that “the potential for abuse inherent in the freedom to base music on personal taste instead of divine precept became evident only after the seventeenth century, when clergy and musicians no longer exercised that freedom so responsibly. What Friedrich Blume has observed about the Lutheran liturgy also holds true for its music: ‘…the history of the Lutheran service is justly called a history of its decline.’ (Protestant Church Music, p. 5)”
The phrase “divine precept” is presumably a reference to the musical ratios derived from the harmonic series. What Faulkner refers to as the irresponsible exercise of “freedom” to base music on personal taste without reference to these ratios parallels Dlugoszenski’s repudiation of Logos and subsequent degeneration into a “personal aestheticism where no two people can agree.” Christine Ammer describes the result of a nineteenth century trend to exercise the so-called “freedom” mentioned by Faulkner by repudiating musical Logos, or ratio: “the…freedom not to be established firmly in a key…led to the destruction of a common tonal language and prepared the world for tonal modernism.”
I mentioned earlier the contrast between this so-called “freedom” to abandon the order of harmonic ratios and the liberty of late medieval composers to base music on these ratios. As musical reforms of the past have tended to accompany metaphysical reforms, it is not surprising that the abuse accompanying liturgical “freedom” from the musical ratios derived from the harmonic series parallels the human “freedom” from metaphysical ratio, which was, according to Voegelin, “deformed by what Hegel has called the ‘Protestant principle’ of relocating the world of divine intellect (die Intellektual-Welt) in the mind of man, so that ‘one can see, know, and feel in one’s own consciousness everything that formerly was beyond.’” This ‘Protestant deformation’ encouraged a shift from participation to identification with the divine, which accompanied what Voegelin calls an “ideological rebellion” against both “predogmatic noesis” and “dogmatic ‘metaphysics.’” While Voegelin endorses the latter rebellion, he laments the former for the following reasons: “For when noesis is put into the same basket as ‘metaphysics,’ we lose the reality of knowledge of the noetic experience and also the differentiated material structure of the ratio, which means that we have no noetic science of order any more. This loss did indeed occur and has become the problem of all attempts of rational thought since the eighteenth century.”
That such an irresponsible exercise of musical freedom as that mentioned above by Faulkner was antithetical to Luther’s aesthetics is suggested in his statement that, only when musical learning is combined with “artistic music which corrects, develops, and refines the natural music, then at last it is possible to taste with wonder (yet not to comprehend) God’s absolute and perfect wisdom in his wondrous work of music.” Luther’s parenthetical comment suggests what we have found in other writers examined so far – that a relation between music and metaphysics is naturally intuitive to man, and yet difficult to explain. This difficulty perhaps explains why Luther bases his evaluation of music on practical experience rather than theory, for he claims that “experience confirms…that next to the Word of God, music deserves the highest praise”; this experiential focus explains Christhard Mahrenholz’s omission of the theory of music in his reference to Luther’s educational ideal of “the training of man toward God as the consequence of the practice of music to the glory of God.”
Luther’s perception of music as the penultimate expression of divine revelation is evident in Hosler’s note that “Luther placed music next to theology in the curriculum of the schools he instituted: ‘Ich gebe nach der Theologia der Musik den nähesten locum und höchste Ehre.’” However, Westermeyer’s observation that Luther envisioned “music in its own right as a parallel to preaching” indicates the Reformation shift away from the Medieval perception of music as a manifestation of metaphysics, which Odo defended when referring to music as an element of the general revelation of creation mentioned by Paul in Rom. 1:19, and towards the practical application of music as a rhetorical device in the service of theological texts. As this shift did not hinder the philosophers and theorists who continued to develop the metaphysical significance of music after the Reformation, I will not concern myself with it.
The Reformation focus on the rhetorical efficacy of music led most Protestants to ignore the metaphysical significance of music on account of their rejection of the Greek philosophical infrastructure, which had provided Catholic theology with a basis for making analogies between music and the Logos. Frye recognizes this rejection, in his statement that “with the Lutheran and Calvinist movements there came a renewed emphasis on the Old Testament as the sole basis for Christian doctrine, and something close to an abandoning of all attempts at an integrated philosophical infrastructure.” Had Protestantism not abandoned this philosophical basis, Frye surmises that it “would doubtless not have translated the ‘Logos’ in the Gospel of John as ‘Word,’ but would rather have tried to assimilate it to the philosophical Logos in Greek thought from Heraclitus onward, where it is more like a principle of order in the mind that recognizes a corresponding order in the physical world. Most Protestantism, however, turned to history rather than metaphysics as an infrastructure for revelation.” Although this rejection of the Greek philosophical infrastructure doubtless has much to do with “the antimetaphysical taboo” referred to by Voegelin, which blurs the distinction between “predogmatic philosophizing” and its dogmatic deformation, it left Protestantism with no basis for making analogies between music and the Logos, which has therefore come to be interpreted solely in verbal terms.
The Protestant rejection of the Greek philosophical infrastructure, which provided a basis for a theology of music, has resulted in a theological tragedy, as it occurred a century before the greatest musical advance since Pythagoras’ experiments on the monochord – the acceptance of triadic tonality. Although Zarlino provided a scientific basis for the recognition of the triad, he abandoned it, as Rameau observed, and therefore Isacoff credits William Noble and Thomas Pigot with this provision in 1673, when they observed “that a single string tuned to a particular musical tone produces a whole series of soft, ancillary tones,” known as harmonics, overtones, or harmonic overtones. Isacoff describes these tones in greater detail: “They sound above the original note with tones corresponding to the octave (2:1), the fifth (3:2), and the major third (5:4). Thus, they whisper their support for those theorists who for centuries had declared these to be the purest, most natural, and most perfect harmonies of all.” This last statement accords with the intuition concerning a triadic basis for music found in the work of the seventeenth century German music theorists to whom we will now turn.
Lippius’ Triad and Baroque Music Theory
Godwin notes the recognition by “the older German theorists of the likeness of the Holy Trinity in the common chord or major triad (harmonics 4, 5, 6).” This recognition is echoed in Eric Chafe’s representation of the triad: “Often called triunitas by theorists of the Lutheran metaphysical tradition, the triad seems to mirror the Deity as no other element can.” The following survey of German Baroque music theorists who based their theories on the analogy between triad and Trinity draws mainly upon English translations of their works by Benito Rivera. Although Rivera’s research is useful to my thesis, I find some of his opinions to be contradictory. For example, I am in agreement with Rivera’s view that “Rudolph Schlick’s oration on music, published in Speyer, 1588…possesses great historical significance, however, because perhaps for the first time in music theory it announces a direct link between the musical triad and the Holy Trinity.” Schlick’s publication is indeed of “great historical significance,” as the “link between the musical triad and the Holy Trinity” would prove to be a common thread in music theory up to the present. Rivera’s opinion of Schlick’s work, however, contradicts his statement that, “to the modern theorist, comparing the triad to the Holy Trinity will seem a rather amusingly pious way of viewing music.” This statement is misleading, however, for this comparison is entirely consistent with the theories of Rameau and Schenker, which have dominated tonal music theory from the eighteenth to the twentieth centuries. Thus, Lester observes: “Rameau’s theories dominate both his own century and the following ones…not until Schenker does a theorist articulate a significantly different musical perspective.” The influence of Schenker in the Anglo-American world is evident in William Rothstein’s description, sixteen years ago, of Schenkerism as having “become the dominant American theoretical tradition where tonal music is concerned,” and in Jonathan Dunsby’s assertion: “If you consider yourself an analyst of tonal music in Britain now, you are assumed to be a Schenkerian.”
Another contradiction concerning Schlick’s work is Rivera’s opinion that, “from the tenor of his argumentation, Schlick appears to suggest that his recognition of the theological symbolism of the triad is totally an original idea of his.” In Schlick’s treatise, however, he presents this recognition as a universal truth, for he claims that the triad “so represents the works and might of the Holy Trinity, that it bears an affinity to them; and all men are moved to declare with unanimous consent that this combination originated from the same fountain source.” This last phrase is perhaps an allusion to the Pythagorean reference to the tetractys as “the fountain which has its source in ever-flowing nature.” Schlick’s declaration of universal consent is consistent with his claim that “the most outstanding musicians, even those who have hardly mastered the first rudiments of this discipline of composing melodies can easily see the vestiges and marks of the Holy Trinity, albeit obscurely, radiating from these [three notes].”
To be fair to Rivera, the contradiction between regarding the analogy of triad and Trinity as a universally intelligible phenomenon and also as an individual discovery could originate from Schlick’s own writings, for the same contradiction is found in the writings of Lippius, to be explored below. Regardless of the origin of the contradiction, it is evident from these statements of Schlick that the analogy of Trinity and triad was ‘in the air’ during the Baroque era in Germany. Such a musical and spiritual zeitgeist accounts for several references to this analogy in theoretical works of succeeding decades.
A relative of Luther, Cyriacus Schneegass, in his Isagoge musicae libri duo, published in 1591, and Joachim Burmeister, in his Musica autoschediastike, published in 1601, also mention the analogy between the musical triad and the Christian Trinity found in Schlick’s work. Burmeister eloquently expresses this analogy in his “Epigram on the Origin of Music,” which begins:
That from the one godhead of the triad who would deny
that you derived your beginning, O divine music?
You represent the mysteries of the divine triad;
like the nourishing triad you celebrate the uneven number.
From this “Epigram” Burmeister claims to express how music “manifestly represents the mystery of the Holy Trinity.”
Early seventeenth century German philosopher, theologian, and musician Johannes Lippius (1585-1612) further developed ideas of his predecessors concerning the relation between the musical triad and the Christian Trinity, in treatises in which he sought to synthesize philosophy, theology, and music “for the glory of the eternal Geometrician and Musician.” Lester notes the unprecedented achievement of Lippius, in that he “for the first time presented a unified harmonic conception of music, in which the triad was the basis.” Rivera confirms the preeminence of Lippius among his contemporaries, stating that, among theorists of the late sixteenth and early seventeenth centuries, “Lippius undoubtedly stands foremost because of his clear and insistent reference to the three-note chord as the basis of all harmony. It was he who coined the term ‘trias harmonica,’ which quickly won approval and dissemination by subsequent writers like Johann Heinrich Alsted, Johannes Cruger, Abdias Trew, Lampertus Alard, Johannes Michael Corvinus, Conradus Matthaei, Wolfgang Caspar Printz, Johann George Ahle, Andreas Werckmeister, and Johann Gottfried Walther.” This term was not incidental to Lippius’ thought, for George Buelow rightly recognizes that the most important component of Lippius’ theory “was the triad, the trias harmonica, rooted in theological symbolism as the musical equivalent of the Trinity.” Lester is well founded in stating that “the role of theology in his thinking cannot be underestimated,” for Lippius presents the theological symbolism of the triad as the central concept in his Synopsis, published in 1612, both for the practice of music and for its theological significance.
I have mentioned Lippius’ inclusion of a third analogy, the syllogism, among the triad and Trinity; Lippius also extends the significance of the triad to the area of psychology, for he writes: “just as…the body [has] three dimensions (this remarkable and clearly divine phenomenon was revered by the ancient Pythagoreans, as Aristotle recounts in De coelo, Bk. I, chap. 1, and Scaliger in De causis linguae latinae, Bk. III, chap. 78), so also the harmonic root has three sounds. Behold the semblance of that great mystery of the divine and solely adorable Tri-unity.” Incidentally, this perception of a correspondence between harmony and psychology counters McClary’s view that “the tendency to deny the body and to identify with pure mind underlies virtually every aspect of patriarchal Western culture. Thus, it is not surprising to find that this fundamental mind/body split likewise informs classical music as well as its institutions.” Contrary to McClary’s claims, the triadic tonality which informs classical music provides a model of harmony rather than duality. In contrast to the ‘divine phenomena’ of the tripartite psyche and Godhead, the harmonic triad is a natural phenomenon, which functions as the basis of a philosophical synthesis for Lippius. In the following summary of his thought I will confine myself to Lippius’ musical and theological ideas, leaving aside his ideas of logic and psychology.
Consistent with Schlick’s view of the universal comprehension of the relation of triad and Trinity is Lippius’ assertion that, if the musical triad does not proclaim the triune Creator, “then in the name of Christ I do not know what the Doctor of the Gentiles [St. Paul] means by proclaiming God in His works.” Lippius specifies the Pauline proclamation he has in mind when stating: “That the most wise and excellent God has through all things divulged his gracious fame, is known by those who seek Him, as Saint Paul points out in his letter to the Romans, chap. 1, verses 19-20.” Although Paul suggests a visual focus in the verses alluded to, through his use of the phrase “by things seen,”
Doppelbauer extends this focus to include things heard: “In the Epistle to the Romans Paul says that the invisible is revealed in the visible, in other words that both are related to each other. To this we might add that the audible is similarly related to the inaudible.” Lippius anticipates Doppelbauer’s addition when adapting Paul’s discussion into an aural context: “This becomes especially clear when the book of Scripture, known beforehand, is compared with the book of Nature…One will surely esteem music more, if as a composer he does not spurn its true and basic causes, or if as a listener he feels and experiences its divine, powerful, pleasing, and constant driving force, thus celebrating with all his strength its thrice blessed Author.” Lippius’s comparison between the books of Scripture and Nature was later echoed in Coleridge’s reference to “the other great Bible of God, the book of nature.”
Despite acknowledging the universal accessibility concerning the spiritual significance of the triad, Lippius describes it as a secret peculiar to himself:
The triad is the image of that great mystery, the divine and solely adorable Unitrinity (I cannot think of a semblance more lucid). All the more, therefore, should theologians and philosophers direct their attention to it, since at present they know fundamentally little, and in the past they knew practically nothing about it. Recently some have had intimations of it in a somewhat confused manner, although (very strangely) it is much employed in practice, and, as will soon be seen, stands as the greatest, sweetest, and clearest compendium of musical composition. It draws a happy limit to other musicians’ almost infinite and loosely scattered considerations regarding complete harmony. This triad I have observed since boyhood (with only God and nature as my guides), I now study it by way of a pastime, and I hope to see it perfected with God’s help, to whom praise forever.
Lippius specifies how he studied the triad “by way of pastime” when commenting that he “observed the harmonic triad and the rules of progression by analyzing vocal and instrumental harmonies.” His representation of the triad as a “compendium of musical composition” was reaffirmed by succeeding theorists, for William Mickelsen notes that “Heinrich Albert states in the preface to Part II of his Arien (1640): ‘It is taken for granted (!) that all musical harmony, even that of a hundred simultaneously sounding voices, consists of only three sounds.’ (Matheson echoes this in his Das neu eroffnete Orchestre , p. 109: ‘And even if there were a hundred or more musicians in concert, all of them together could not bring forth any form of harmony other than these three tones.’)”
I have mentioned Kepler’s perception of the three regions of a sphere as an image of the three persons of the Trinity. Although he describes the tones of the triad as “the smallest of the consonances,” Kepler does not grant the triad the metaphysical status of the sphere, for he rejects those who seek the cause of the triad “in the revered Trinity itself of the Divinity.” Thus, E.J. Alton notes: “Kepler rejected the idea of a theological significance in the unity of musical triads in terms of the Trinity, held by Cyriacus Schneegass and Johann Lippius among others, and insisted that the unity was only a mental concept based on the understanding.” Kepler rejected Lippius’ universalist view of the triad in favor of a conceptualist view. That Kepler was wrong and Lippius right on this point is suggested by the following statements of Alton: “The second stage” of the “development of the modern idea of musical chords…began with Johann Lippius, who introduced the idea of chord inversion. Kepler contributed nothing to this second stage, for he always regarded the base note as the reference note, a fact which to some extent restricted his concept of major and minor tonality.” Just as Lippius’ introduction of chordal inversion was fruitfully developed by theorists in succeeding centuries, so was his perception of the triad as an image of the Trinity.
That the unity of the triad is not merely a mental concept, as Kepler assumed, is more explicitly evident in the following assertion of Levarie and Levy: “Among the many theories, there is hardly any disagreement concerning the inherent consonance of the triad. The senarius and the overtone series both point to the same conclusion.” Schenker reaffirms this assertion when stating: “The spaces available to melodic motion are the spaces of the octave, fifth and third offered by Nature,” in the form of the harmonic series. Thus, the unity of the triad exists as a natural phenomena independent of the mind, as eighteenth century theorist Giuseppe Tartini recognizes in his assertion that the unity of the harmonic system is both “physically demonstrable” and “independent of the human will.”
I stated earlier that, although succeeding philosophers have heeded Lippius’ advice to direct their attention to the divine idea contained within the triad, theologians have not. I also noted the Protestant rejection of the Greek philosophical infrastructure, which resulted in a purely verbal conception of theology void of musical significance. In contrast to this Protestant trend, Frye recognizes that the redemption of Hellenic culture by Catholicism has resulted in an emphasis upon “Hellenic philosophical conceptions rather than the Old Testament as the basis of Christian teachings.” In the field of thought, however, the Scholasticism of the Counter-Reformation was not very fruitful. In the speculative field the Counter-Reformation was content with the thought of Aristotle and remained isolated from the development of modern philosophy.
Faulkner notes that the sixteenth century Council of Trent established a “direction for Catholic policy and practice that was to endure for the next four centuries.” In a document written two years prior to the convocation of this Council, a bishop states that ecclesiastical songs must be “serious in tone without exciting laughter.” A preliminary report of this Council endorses “singing in musical modes” in order that “the hearts of the listeners be drawn to the desire of heavenly harmonies.” Although triadic harmony gained acceptance in the practice of liturgical music, these comments suggest that the Medieval church modes and the consonances of the tetractys, derived from the quaternarius, were preserved as theoretical models at the expense of adopting theoretical developments concerning triadic tonality and its relation to Trinitarian theology. This rift is suggested in Lester’s observation: “in the Catholic countries, modal plainchant was a body of centuries-old music increasingly divorced from contemporary [seventeenth century] compositional styles. The Council of Trent in 1565 had intensified this separation by expunging many of the more modern elements from the official body of chants.” Thus, the Catholic Church at the time of the Council of Trent seems not to have advanced in its views concerning music theory beyond those expressed by Pope John XXII, cited earlier. Ratzinger’s comment that “the Council of Trent confirmed and deepened” the provisions of the Docta sanctorum patrum of Pope John XXII is consistent with the final decree of the Council, which recommends that sacred music conform to “the norm which Pope John XXII prescribed” in this bull; therefore Alec Robertson seems quite justified in describing it as being “as severe as any proposed at the Council of Trent.”
As Catholic theologians since the Counter-Reformation have not integrated developments in music theory within the Hellenic philosophical infrastructure, Lippius’ advice has gone unheeded by them. Douglas summarizes the aftermath of the Council of Trent: “During the centuries which followed little attention was paid to the spirit in which church music was composed and performed, until the work of the Benedictines of Solesmes began to have its influence at the close of the nineteenth century.” This monastic work influenced Pius X, who wrote more encyclicals on music than all of his papal predecessors combined, to issue the motu proprio ‘Tra le sollecitudini’ on November 22, 1903. Winfried Schulz notes that this work, “which is regarded as the Magna Carta of church music, includes under the heading ‘Musica sacra’ Gregorian chant, classical polyphony and ecclesiastical compositions in modern style, to the extent that they harmonise with the spirit of the liturgy. Subsequent official documents made no changes.” This last sentence is evident in Overath’s comment that “in his  encyclical ‘Mediator Dei’ Pope Pius XII stressed that ‘the music of our own day and modern choral music are not to be excluded from Catholic worship…since they can contribute in no small way to the splendour of the sacred ceremonies, can lift the mind to higher things and foster true devotion of soul. One would be straying from the straight path were he to disdain and reject polyphonic music or singing in parts.’” In this last sentence Pius XII implies that John XXII was in error when imposing a ban on the liberty to compose ecclesiastical melodies with “discanti” and “tripla.”
Despite the admission by twentieth century Popes of modern and polyphonic music to the Catholic liturgy, Faulkner’s claim, cited earlier, that “no important theological movement, either in the nineteenth or twentieth century, has concerned itself in any profound way with the significance of harmony” may be validated by considering that the profound significance of the relation between triadic tonality and Trinitarian theology has yet to be recognized by the Catholic church. The profundity of this relation can be discerned in the metaphysical significance of two pioneering triadic concepts of Lippius mentioned by Rivera: “The concept of triadic generation and invertibility, so clearly and firmly established by Johannes Lippius in 1610 [Disputatio musica tertia], and then again in 1612 [Synopsis musicae novae], constitutes a milestone in the history of harmonic theory.” Let us now consider how these two theoretical concepts can aid in comprehending Trinitarian theology.
Trinitarian and Triadic Generation and Inversion
Rivera notes: “theology played a profound role in the birth of the theory of chord ‘generation.’ One clearly had to be a theologian-musician like Lippius to arrive at such a synthesis. Granted, he may not have been fully aware of its far-reaching implications in music theory, but great ideas are sometimes first conceived without full awareness.” The theological role in the theory of chord generation is evident in Lippius’ use of the language of Trinitarian theology to describe the triad as, “first of all, the two extremities, namely, the prima or ima basis, and the ultima or summa, which is ‘begotten’ by the prima. These two lie a fifth apart from each other in a 3:2 proportion. They ‘co-spirate’ in a perfect and masculine sonority, and then one media ‘proceeds’ from them and connects them with its milder sweetness, lying a major third away from one end in a 5:4 proportion, and a minor third away from the other in a 6:5 proportion.”
Rivera recognizes the Trinitarian basis of Lippius’ description of the triad: “In his analogy between the musical triad and the divine Triad, Lippius does not limit himself to pointing out the obvious three-in-oneness found in both analogues. A close analysis of his remark, that the ultima  is ‘begotten’ or generated by the basis (ab illa genita) , and that the media  ‘proceeds’ (procedens) from the ‘co-spiration’ (conspirantes) of the basis and the ultima, reveals a mode of thought that is replete with Trinitarian allusion.” Rivera offers some insight into this mode of thought when stating that Lippius “adopted the symbolism of the Holy Trinity or Triad, the perfect union of three Persons in one God, the one Source of all manifold reality. As the Father begets (generates) the Son, and as the Holy Spirit proceeds from the Father and the Son, so also the basic note (basis) of the musical triad begets or generates the fifth, and from them proceeds the intervening third.”
Rivera traces Lippius’ conception of the Trinity to scholastic theology: “According to scholastic theology, the Father ‘begets’ the Son, and the Spirit ‘proceeds’ from the Father and the Son through ‘spiration.’ One will find this terminology in St. Thomas Aquinas, Summa theologiae, Part 3, Question 27, Articles 2, 3, and 4.” In order that the integrity of the synthesis of scholastic theology and chord generation may be more fully appreciated, I present to the reader the above-mentioned articles of Thomas.
It is said (Ps. 2:7): “This day have I begotten Thee.”
I answer that, The procession of the Word in God is called generation.
The Holy Ghost proceeds from the Father (Jn. 15:26); and He is distinct from the Son, according to the words, “I will ask My Father, and He will give you another Paraclete” (Jn. 14:16). Therefore in God another procession exists besides the procession of the Word.
I answer that, There are two processions in God; the procession of the Word, and another. In evidence whereof we must observe that procession exists in God, only according to an action which does not tend to anything external, but remains in the agent itself. Such an action in an intellectual nature is that of the intellect, and of the will. The procession of the Word is by way of an intelligible operation. The operation of the will within ourselves involves also another procession, that of love, whereby the object loved is in the lover; as, by the conception of the word, the object spoken of or understood is in the intelligent agent. Hence, besides the procession of the Word in God, there exists in Him another procession called the procession of love.
That the Holy Ghost Who proceeds as love, would proceed as begotten; which is against the statement of Athanasius: “The Holy Ghost is from the Father and the Son, not made, nor begotten, but proceeding.”
So what proceeds in God by way of love, does not proceed as begotten, or as son, but proceeds rather as spirit; which name expresses a certain vital movement and impulse, accordingly as anyone is described as moved or impelled by love to perform an action.
In these articles Thomas develops two analogies derived from Augustine, the analogies of human thought and love. The analogy of human thought is found in Augustine’s comparison of the relations of the three persons of the Trinity to the mental faculties of memory, intellect, and will, found, for example, in the following stanza of seventeenth century poet John Davies of Hereford.
For as we hold there’s but one God alone
But yet three persons in the Deity:
So the soul’s parted, though in substance one,
Into understanding, will, and memory.
These powers or persons make one Trinity,
Yet but one substance indivisible;
Which perfect Trinity in unity,
Both being spiritual and invisible,
Do make the soul her God so right resemble.”
Fourteenth century theorist Jacques de Liege invites a musical analogy of the resemblance between the Deity and the soul when, in his encyclopedic treatise, The Mirror of Music, he comments on Boethius’ description of the psychological form of music: “Music must also investigate the organization of the powers of the soul…which are parts of the image by which man is capable of acts of blessedness (such as memory, which corresponds to the Father; intelligence, to the Son; will, to the Holy Spirit).”
The analogy of love is found in Augustine’s comparison of the relations of the three persons of the Trinity to “he that loves, and that which is loved, and love.” This latter analogy is based in part on the Father’s love towards the Son, who assumes the subordinate role of beloved: “it is the Father, living in me, who is doing his works.” The role of sacrificial love assumed by the Spirit within the Trinity is suggested in Gunton’s reference to Augustine’s conception of the Spirit as “the unifying link between Father and Son,” which is consistent with Augustine’s statement that the Father and Son are “harmonious because of the Holy Spirit”; therefore Augustine represents the Spirit as “One who cleaves to One by a harmony so great that through this harmony both are one.”
Gerald Bray’s summary of neo-Thomist philosopher-theologian Bernard Lonergan’s conception of Trinitarian relations provides a useful framework to make specific analogies between Trinitarian and triadic relations and generations. Bray states that
two processions in God produce three persons but four relations…Lonergan understands the four relations as follows:
(A) Two relations of the first procession (generation):
– understanding forming conception;
– conception formed (i.e. recognizing its begetter).
(B) Two relations of the second procession (procession):
– understanding evincing love in accordance with conception;
– love evinced (i.e. responding to its source/s).
To apply triadic analogies to this description, one could say that the two generational relations – the Father generating the Son and the Son recognizing the Father as his begetter – are analogous to 1 generating 5 and 5 recognizing 1 as its source. The two processional relations – the Spirit proceeding from the Father to the Son and the Spirit leading the Son to respond to the Father – are analogous to 3 proceeding from 1 as a harmonious bridge between 1 and 5, and the 3 of 5, which is the 7 of 1, leading 5 to unity with 1. This tonal analogy of the second processional relation, involving the Spirit of the Son, necessitates an understanding of both Chalcedonian Christology and the dynamics of a cadence, which I hope to offer in a further work.
Although it might be argued that analogies involving divine persons are inconsistent with the nature of tones, the conception of the biological and volitional nature of tones invites such an analogy. Christensen notes: “only with the notion of a chord fundamental could one begin to speak of inversions as somehow consanguineous [blood-related] by virtue of having been generated by an identical source.” Such a notion was advanced by Lippius, who uses the verbs generate and proceed – also used by theologians with reference to divine persons – with reference to the fundamental chord. Generation and procession are also characteristic of Schenker’s description of tones as analogous to creatures: “We should get accustomed to seeing tones as creatures. We should learn to assume in them biological urges as they characterize living beings.” This analogy is based on the fact that each tone insists “on its right to its own perfect fifth and major third; in other words, its right to procreate its own descendant generations.” Considering that biological procreation is analogous to mathematical multiplication, seventeenth century metaphysical poet George Herbert indicates this tonal “right” in his observation that
music is based upon a triad
Schenker indicates a hierarchy among the procession of tones when stating that, because the fifth precedes the third in the overtone series, it is “more potent than the third. The fifth enjoys among the overtones, the right of primogeniture, so to speak.” The tonal primogeniture of the fifth is analogous to the theological conception of Christ as the first-born in the resurrection. Von Cube betrays a Schenkerian influence when referring to the fundamental tone as “the progenitor of the overtones, in the sense that it sends them forth like a series of human generations, so to speak. Just as the likeness of the forefathers becomes ever more distant and foreign in the grandsons and great-grandsons, the relation of the overtones to the fundamental diminishes as the series ascends toward pronounced dissonance.” This analogy of a hierarchical continuum recalls the Platonic language of Zarlino, cited earlier.
Likewise, the verbs recognize and lead, also used by theologians with reference to divine persons, are characteristic of tones. Ernst Oster interprets the title of Schenker’s Der Tonwille as a suggestion that “the tones have a ‘will’ of their own, to which even the composer must submit.” This suggestion is echoed in both Zuckerkandl’s earlier reference to “the will of the tone” and his description of a composer as one who is “intent only on discovering the hidden will of the tones.” Schoenberg’s Schenkerian phrase, “the will of the fundamental tone,” cited earlier, is not surprising, given Schoenberg’s description of Schenker as “a first-rate mind, a man of insight and imagination.” Luther, however, betrays his musical ignorance when praising his favorite composer, Josquin des Pres, as “a unique master of the notes. They must do as he wills, whereas other masters are forced to do as the notes will.” Accepting my earlier postulation of a relation between Luther’s zeal for both contrapuntal polyphony and doctrinal reformation, his admiration for compositional mastery over the will of notes – which he apparently understood as a revelation of divine order – is perhaps symptomatic of a desire to assert his own will in ecclesiastical matters independently of the Divine will.
It is evident that the ‘will’ of the triadic tones is to remain a unity, when recalling Singer’s description of the triad, cited earlier: “if the three tones did not appear as a unity…the actual playing of a triad would be unbearable to the ear, since it would hear in these three components the most jarring dissonances. For example, with the triad CEG sound CEG, EG#B, and GBD; yet for all that, the ear hears only the tones CEG, evident proof that the complete, perfectly tuned triad sounds like a single perfect tone.” In this example, the will of the tones E and G, the third and fifth intervals of the C major triad, is to deny their right to procreate their own descendant generations, to use Schenker’s phrase. More specifically, the will of G to accept C as its fundamental is analogous to Jesus’ prayer to his heavenly Father in Gethsemane: “not as I will, but as you will.” The tension between dual wills of both the fifth interval of a triad and the Son of God appears to conform to Coleridge’s assertion, cited earlier, that “all symbols of necessity involve an apparent contradiction.” Music and metaphysics must be considered exempt from this rule, however, for they contain within themselves the innate potential for resolution, through the mediation of harmony and Spirit, respectively.
A second objection may be raised that, whereas the Trinity is one God, the musical triad is three distinct notes. This objection can be countered by considering Rivera’s representation of Lippius’ perception of the triad as a complete harmonic unit: “Lippius explains that unlike the dyad or two-note interval, which lacks a third pitch to complete its sonority, the triad needs nothing more to improve its essence. It satisfies all the requirements for perfect harmony. It also comprises a unified entity to the extent that it mirrors the oneness of the Holy Trinity.” These explanations can be substantiated by the acoustical research conducted by Vogler, who was enabled by his Tonmaass to accurately determine several theoretical principles of music, including the principle that any complex chord can be reduced to a major triad, the discovery of which he regarded “as an all-important landmark in the advancement of musical knowledge.” That this principle was the foundation of musical knowledge for Vogler is evident in Grave’s assertion that Vogler
drew the conclusion that musical knowledge was indeed founded on the natural resonance of the sounding string. When a string was caused to vibrate, it produced not only the octave of the fundamental and the double octave (1:2, 1:4) but a fifth (1:3) and major third (1:5) as well. A three-fold harmonious unity emerged, and in this manifold sonority lay the controlling source of all musical diversity. Thus the basis of musical understanding was fundamentally simple. It rested on irrefutable scientific foundations, and its principles were readily accessible to anyone with an unprejudiced mind, a sharp ear, and an elementary knowledge or arithmetic…It was central to Vogler’s purposes to show that the science of musical organization, far from being arcane, was universally accessible.
This universal accessibility is consistent with Paul’s statement from Romans 1:19-21, which is cited by Odo, Lippius, and later by Werckmeister and Tartini, with reference to music.
Singer validates the musical discoveries of Vogler and relates them to the archetypal triad of the Trinity:
The harmonic triad has already been called by that deep thinker the Abbe Vogler the ‘trinitarian harmony,’ because in it three different tones sound like a single one. In its whole musical existence, this triad seems to us an unmistakable and most impressive picture of the harmony of God the Trinity, resting eternally in itself, which is at the same time the ground of all creation and its goal and end. This triad, this original trinitarian harmony, consists of three tones, of which the first appears as the root, grounding the whole harmony; the second as manifesting the first as root and as characterizing the whole harmony; and the third as the tone that unites the first two in a complete harmonic whole. Indeed, on perfect instruments one can perceive that every first tone, played alone, brings forth the other two out of itself.
Singer offers evidence for this last sentence in the following passage:
The acute ear can observe this in all perfect tones, but it is easiest with deep ones, especially with the low tones of a harmonium [Physharmonika], because at low pitch the vibrations are slower, and consequently the perception of the substratum that makes up a perfect tone is easier. Abbe Vogler has made the same observation with deep organ pipes. This would also explain why on large organs every tone is accompanied by a complete triad, i.e. a third and a fifth beside the predominant tone.”
Vogler’s conception of the triad as a “three-fold harmonious unity” is analogous to the perichoresis of the Trinity. In terms of deity, then, the persons of the Trinity are equal, although the fact that the second and third persons generate and proceed, respectively, from the first person suggests that they have subordinate roles, as Wayne Grudem confirms when stating: “The Son and Holy Spirit are equal in deity to God the Father, but they are subordinate in their roles.” This subordination is also characteristic of the third and fifth tones of the triad when it is inverted.
The theoretical concept of chordal inversion is a second instance of the theological significance of the triad in the music theory of Lippius; its theological significance lies in its relation to what von Balthasar refers to as “trinitarian inversion.” Chordal inversion refers to the position of a chord when the fundamental is not the lowest note. When the fundamental is the lowest note the chord is in root position, whereas when the third interval of the chord is the lowest note the chord is in first inversion and when the fifth interval of the chord is the lowest note the chord is in second inversion. Rivera observes that Lippius makes an “important remark that implies he has arrived at a concept of triadic inversion: ‘And always more pleasing, more full, and more perfect is the triad whose prima basis lies in the lowest position with the others above it.’” This reference to the root position of the triad implies that this position may be inverted. Lippius confirms this implication when stating: “The bass voice may on rare occasions use the ultima or media of the unitrisonic root.” A bass voice using the ultima results in a triad in second inversion, and a bass voice using the media of the root results in a triad in first inversion.
Rivera explains the theological significance of the theory of triadic inversion when stating that, for Lippius, “Just as the tri-une God is the ‘root, source, foundation, beginning, middle, and end of all things,’ so also the simple triad is the ‘root’ from which all other triadic combinations originate, and to which they all return. This expresses clearly the fact that the triad retains its identity even when it is ‘diffused,’ inverted, or ‘enlarged.’” This triadic phenomenon is analogous to Grudem’s recognition that, despite the differing roles within the Trinity, “each person of the Trinity has all of the attributes of God, and no one person has any attributes that are not possessed by the others.” Bringing Trinitarian theology to bear on triadic inversion, one could say that the Father is analogous to the triad in root position, the Spirit is analogous to the triad in first inversion, and the Son is analogous to the triad in second inversion; these analogies are represented in the following table.
TRIADIC AND TRINITARIAN INVERSION
Root Position First Inversion Second Inversion
one three five
three five one
five one three
Root Position: Father First Inversion: Spirit Second Inversion: Son
Father Spirit Son
Spirit Son Father
Son Father Spirit
This representation of trinitarian inversion has some affinity with Coleridge’s description of the Trinity as “a triad of triads, or an ennead. 1. Father – Son – Holy Ghost. 2. Son – Father – Holy Ghost. 3. Holy Ghost – Son – Father.” An instance of trinitarian inversion is specified by von Balthasar in his reference to a
‘trinitarian inversion’ during the earthly span of Jesus’ earthly mission: if he is to be obedient to the Father, he must allow the Father’s Spirit to take an active, leading role, while at the same time letting the Spirit who proceeds from him, the Son, be in complete harmony with the Father’s will. The latter is essential if his obedience as Yahweh’s ‘Suffering Servant’ is to be always spontaneous, filial obedience and if his Yes to the Father is ultimately, that is, at the divine level, to rest on the equal-ranking initiative, now transformed into an indifference that is ready to embrace whatever the Father wills.”
While heeding von Balthasar’s advice that “only with great caution should we adduce analogies for the Trinity from outside Christianity,” his use of the word harmony to describe the relations among the persons of the Trinity in the context of this trinitarian inversion invites the following tonal analogy. Given the leading role of the Spirit of the Father during the earthly mission of Jesus, one could say that the Trinity was in first inversion during this period. Von Balthasar distinguishes the Spirit of the Father from the Spirit of the Son. The Spirit proceeding from the Son is analogous to the third interval proceeding from the dominant chord, which is also the seventh interval relative to the fundamental, and is called the leading tone, as it leads the dominant chord into harmony with the tonic triad. Vogler notes the indispensable role of the leading tone in the motion of a cadence: “A harmony becomes capable of producing a cadence through the major third; without it the harmony will never be decisive, and always remain noncadential.” Vogler is referring to the major third of the dominant chord, which is the leading tone, without which the cadence will be indecisive. In the key of C Ruland notes that “b is the original leading-tone. It precedes the tonic like a herald and announces him unmistakably as the ruling king.” The role of the third in the cadence is analogous to von Balthasar’s description of the role of the Spirit in the earthly mission of the Son. This musical analogy is consistent with Kevin Mongrain’s reference to von Balthasar’s belief “that the Father – the divine pedagogue – can use the risen Christ ‘like an alphabet or a keyboard’ to express customized sacraments of divine love uniquely suited to the educational needs of all his human pupils.”
The concept of chordal inversion is analogous to Grudem’s conception of relations among the persons of the Trinity:
Within the one being of God the ‘unfolding’ of personality must allow for the existence of three distinct persons, while each person still has the whole of God’s being in himself. The difference in persons must be one of relationship, not one of being, and yet each person must really exist. This tri-personal form of being is far beyond our ability to comprehend. It is a kind of existence far different from anything we have experienced, and far different from anything else in the universe.”
These last two sentences are consistent with an earlier statement of Grudem’s that, “although the Bible uses many analogies from nature and life to teach us various aspects of God’s character (God is like a rock in his faithfulness, he is like a shepherd in his care, etc.), it is interesting that Scripture nowhere uses any analogies to teach the doctrine of the Trinity.” In spite of this analogical absence in Scripture, Grudem indirectly alludes to an analogy that was unavailable to Biblical authors when likening the work of the Trinity in “the history of redemption” to “a great symphony.” It is significant that Grudem, like so many others, intuitively employs a musical analogy to describe the intricacy and complexity of the spiritual world, for music is truly a key to revealing metaphysical mysteries. In 1962 Pope John XXIII – in a simile that would undoubtedly not have met the approval of his predecessor John XXII, who implicitly resisted triadic, and therefore, in theory, symphonic music – likens the life of the Church to “a living symphony, an image of the heavenly Jerusalem and a kind of echo of the divine harmonies.” This analogy is expressed with the more direct trope of the metaphor in the title of von Balthasar’s book Truth is Symphonic. Ratzinger uses a similar trope in his reference to “attempts made in theology to depict the inner harmony upon which the relationship of the Trinity rests.”
The history of redemption is comparable to Godwin’s description of the archetypal form of a symphony: “As far as tonality is concerned, all classic movements tell the same story of leaving the home key, exploring other key areas, and returning. It is an archetypal tale one never tires of hearing, whether in its simplest form as the binary dance (minuet, waltz, etc.) or in the epic complexity of a symphonic movement by Beethoven or Brahms.” This last sentence is echoed in Schenker’s recognition that “great artists have moulded their symphonies according to precisely the same rules by which the people have given expression through folksong.” The primary role of the triad in the rules referred to by Schenker is evident in his recognition that “the unfurling of a triad is music – it is music’s sum and substance”; this first phrase recalls Grudem’s reference to “the unfolding” of the three persons of the Trinity. Schenker correctly regards all music, whether symphonic or folk music, as moulded by the tonal norm of the triad, which Levarie and Levy describe as “a harmonic archetype.” Schenker’s opinion accords with Christensen’s summary of Rameau’s musical thought: “Rameau’s conclusion is simple. Since all music seems to be an elaboration of the basic proportions contained in the corps sonore [major triad], this natural phenomenon is the unique source and generator of music.” These statements of Rameau and Schenker are not idiosyncratic, for their theories dominated music theory from the eighteenth to the twentieth centuries. Thus Rudhyar observes that “tonality took the form of a harmonic system providing order, direction, and the resolution of tension into the ‘perfect chord,’ the major triad (C, E, G),” which is a reflection of “the divine Trinity, Father, Holy Spirit, and Son.” Therefore, if we take Grudem’s analogy literally, we could say, in the form of a syllogism, that, if the work of the Trinity is analogous to a symphony, and if a symphony is the unfolding of a triad, therefore the work of the Trinity is analogous to the unfolding of a triad. These last two phrases are consistent with Lippius’ perception of the triad, cited earlier, as both the “compendium of musical composition” and “the image of that great mystery, the divine and solely adorable Unitrinity.”
Lester describes the unfortunate result of Lippius’ untimely death at the age of twenty seven: “Lippius’s theories never had the opportunity to be expounded as they might have been by Lippius himself had he lived longer and attained the stature in the musical community that he had seemed destined to achieve.” Despite this lack, Rivera justifies his characterization of Lippius’ harmonic theory as a ‘milestone’ when noting its widespread influence on the following generation of German theorists:Lippius’ concept of the triad enjoyed wide dissemination during the entire seventeenth century. Johann Alsted grafted the doctrine onto his Encyclopaedia of 1620 and 1630. Also in 1630, Henricus Baryphonus expanded the earlier version of his treatise, Pleiades musicae, to include a substantial discourse on chordal structure and on the proper method of successively connecting one chord to another. His description of triadic generation clearly descends from that of Lippius. Again also in 1630, Johannes Cruger, the highly revered composer and music director in Berlin, joined the ranks of Lippius’ followers, spreading the word about the harmonic triad by writing his own Synopsis musica for students of composition. In 1654 he revised the treatise and included a chapter on General-Bass, continuing to apply principles related to the triad. Whether directly or indirectly, whether the theological and numerological accouterments were retained or eliminated, Lippius’ teaching grew in prestige through the writings of Johann Andreas Herbst, Wolfgang Caspar Printz, and Johann Georg Ahle.
One may very well say that the movement reached its highest point in Andreas Werckmeister’s Harmonologia of 1702. With renewed zeal and thoroughness, Werckmeister set out to demonstrate the interaction between music and number.Eric Chafe affirms Rivera’s lofty view of Werckmeister’s work when stating that the Lutheran “metaphysical tradition was largely a seventeenth-century phenomenon and was epitomized in the works of Andreas Werckmeister.” Werckmeister, however, displays his indebtedness to Lippius in associating the musical triad with the revelation of the Christian Trinity: If we proceed to the third octave, which exhibits our natural sequence of numbers as 4.5.6-8., there we have a symbol of the New Testament in which God revealed himself further to us. For 4.5.6 point to the complete triad or threefold unison [Drey-Ein-stimmigkeit], in that when we hear it, it is nothing but a unison – yet it is also a three-note chord; it is indeed ‘unitrisonus.’ Could any clearer likeness be imagined, in which the threefold unity of God’s being were better mirrored than in this? Would to God that all good Christians understood music thus; they would find heartfelt joy in this symbol.” Werckmeister’s description of the triad as ‘unitrisonus’ betrays the influence of Lippius, to whom Werckmeister frequently refers in his works, and who describes the triad as unitrisonic. Calvin Stapert’s description of musical symbols such as the triad as mere “devices that were useful to give music a stronger rhetorical impact” in the service of a sacred text would appear to strip music of its metaphysical significance, which counters Schlick’s claim, cited earlier, that “the most outstanding musicians” of the Baroque era recognized a relation between triad and Trinity. Among these musicians was J.S. Bach, whom, Chafe observes, “like Werckmeister, produced a canon on the triad that affirmed its expression of universal harmony.” More specifically, it would seem that Bach followed Werckmeister in affirming the triad as an analogy of the Trinity, for Chiapusso acknowledges that Bach “deeply respected [Werckmeister’s] work in musical philosophy” and that “he was deeply imbued…with the musical speculation of…Werckmeister.” That Bach employed the triad as a metaphysical symbol – in accordance with Paul’s perception of the general revelation of creation in Rom. 1:19 – rather than as a rhetorical symbol – that is, as an arbitrary and artificial device void of any intrinsic metaphysical significance – is further suggested in Chafe’s description of Bach: “As a believing Christian, however, who was very close to a Lutheran baroque metaphysical tradition in musical thought, he would have seen music, and the other arts, as having theological significance. The Enlightenment no doubt weakened the ties between theology and music; still, Bach’s music more than any other fulfills the ideals of this metaphysical tradition.” The collision of this tradition with the Enlightenment is vividly described in Gaines’ Evening in the Palace of Reason, which chronicles the events surrounding Bach’s performance of A Musical Offering in 1747, three years before his death, at the Potsdam palace of Frederick the Great, King of Prussia. In contrast to this cultural collision of the past, contemporary American poet Adrienne Rich responds sympathetically to the metaphysical music of Bach when writing:
This antique discipline, tenderly severe,
Renews belief in love yet masters feeling,Asking of us a grace in what we bear.
Form is the ultimate gift that love can offer –
The vital union of necessityWith all that we desire, all that we suffer.
A too-compassionate art is half an art.
Only such proud restraining purityRestores the else-betrayed, too-human heart. “At a Bach Concert,” 4-12
The effect of the music on the poet is comparable to the salvific and cathartic function of music for Pythagoreans. A similar effect is attributed to the music of Bach by Rudhyar, who states: “perhaps more than any other European composer [Bach] has become the symbol of a highly intellectualized sense of formalized order….Individuals who have suffered from chaotic situations and emotional passions long to experience in music like Bach’s what the psychologist C. G. Jung called a ‘symbol of salvation.’ The message of such a symbol is that at the root of existence there is order, reason, and perfect form.”
Earlier I quoted Faulkner’s statement that seventeenth century Germany “seems to have been one of the last places where Christian life and worship flourished free from the serious incursion of more modern, self-conscious modes of thinking.” This incursion doubtless accounts for Ruland’s view that “musical people of our century often reach back into the paradise of Renaissance and Baroque music, times before ‘the tones fall from grace,’ in order to preserve their musical experience,” by which he means an experience imbued with metaphysical significance; such an experience is described in Rich’s lines, cited above, which lend credence to Ruland’s view. Manfred Bukofzer notes that in the Baroque era “the physical science of music..derived its meaning only from metaphysical speculation. Only if we realize this spiritual unity of matters physical and metaphysical do we understand how [Baroque composer Angelo] Berardi could seize on such concrete technical terms as cantus firmus and cantus figuratus and interpret them abstractly as symbols of divine and human law respectively. The symbolism of music was seen and actually experienced as the direct reflection of the parallelism between divine and human order.”
Faulkner maintains that the incursion of modern secularism spread throughout Europe in the eighteenth century: “The advance of views associated with the Enlightenment in Europe coincided with the demise of the last remnants of the neo-Platonist Christian worldview.” Faulkner’s view of the demise of this worldview during the Enlightenment is shared by Spitzer, who states: “the Enlightenment was at heart a denial of the mystical, spiritual dimension of existence. Leading thinkers were disposed to consider religion, especially the Christian religion, as superstition, and in criticizing, indeed, ridiculing it they hastened the evaporation not only of superstition, but also of spirituality.” As a consequence of the denial of spirituality Spitzer states that, “to the two periods, pagan antiquity and Christianity (the latter goes from the first century to the seventeenth, with the subdivisions: Middle Ages, Renaissance, Baroque), we should oppose the epoch of dechristianization.”
 Henry Bett, Nicholas of Cusa (New York: Richwood, 1976), 8.
 Spitzer, 129.
 Bray, 187-88.
 Bett, 107-18.
 Aristotle, On the Heavens, i. 1; 268 a 10; quoted in Fideler, 300.
 Nicholas, Opera III; quoted in German, 125.
 Quoted in Bett, 147.
 Johannes Kepler, Epitome of Copernican Astronomy, Great Books of the Modern World, Vol. 16. ed. Robert Maynard Hutchins (Chicago: Encyclopedia Britannica, Inc.,1939), 853-54.
 Fischer, 81.
 Westermeyer, 149.
 Faulkner, 131.
 Martin Luther, “Preface to Georg Rhau’s ‘Symphoniae iucnedae,’” Luther’s Works, Volume 53. ed. Ulrich S. Leupold (Philadelphia: Fortress Press, 1965), 321.
 Faulkner, 139.
 Gaines, 49.
 Oskar Söhngen, Martin Luther (Bonn: Inter Nationes, 1983), 40.
 Quoted in Hosler, 40.
 Lippius, Synopsis, 4; quoted in Faulkner, 101-02.
 Söhngen, Martin, 35-36.
 Gal. 5:13 NJB (New Jerusalem Bible).
 Faulkner, 140.
 Christine Ammer, Harper Collins Dictionary of Music (New York: Harper Perennial, 1995), 268.
 Voegelin, Ecumenic, 231.
 Voegelin, Anamnesis, 194.
 Luther, Preface, 324.
 Quoted in Gunther Stiller, Johann Sebastian Bach and Liturgical Life in Leipzig (St. Louis: Concordia Publishing House, 1984), 209.
 Hosler, note 20, 254.
 Westermeyer, 146.
 Frye, Vision, 66.
 Ibid., 68-69.
 Isacoff, 179.
 Godwin, Harmonies, 185.
 Eric Chafe, Tonal Allegory in the Vocal Music of J.S. Bach (Berkeley: University of California Press, 1991), 117.
 Rivera, German, 138.
 Ibid., 124.
 Lester, Compositional, 157.
 William Rothstein, “The Americanization of Heinrich Schenker,” Schenker Studies (Cambridge: Cambridge UP, 1990), 196; Jonathan Dunsby, “Schenkerian theory in Great Britian: developments and responses,” Schenker Studies, (Cambridge: Cambridge UP, 1990), 183.
 Rivera, German, 139.
 Quoted in Ibid., 140.
 Joachim Burmeister, Musical Poetics, trans. Benito Rivera (London: Yale UP, 1993), 213.
 Ibid., 217.
 Quoted in Rivera, German, 24.
 Joel Lester, Between Modes and Keys (Stuyvesant, New York: Pendrragon Press, 1989), 21.
 Rivera, Isagoge, 43.
 George Buelow, “Johannes Lippius,” The New Grove Dictionary of Music and Musicians, Vol. 14 (New York: Macmillan Publishers Limited, 2001), 739.
 Lester, Modes, 50.
 Quoted in German, 126, 227.
 McClary, 54.
 Quoted in German., 126.
 Ibid., 228.
 Rom. 1:20 NJB (New Jerusalem Bible).
 Doppelbauer, 213.
 Quoted in Rivera, German, 228.
 Coleridge, Lectures II, 541.
 Lippius, Synopsis, 41.
 Ibid., 3.
 Quoted in Hugo Riemann, History of Music Theory, Book III, trans. William C. Mickelsen (London: University of Nebraska Press, 1977), note 12, 174.
 Kepler, World, 168, 169.
 Ibid., note 66, 169.
 Ibid., note 65, 168-69.
 Levarie and Levy, Tone, 208.
 Schenker, Masterwork II, 8.
 Tartini, Trattato di Musica, Cap. I, p.13; quoted in Shirlaw, 289.
 Frye, Vision, 68.
 Faulkner, 140.
 Quoted in Hayburn, 26.
 Quoted in Faulkner, 140, note 15.
 Lester, Modes, 50.
 Ratzinger, “Problems”, 222; quoted in Hayburn, 27; Alec Robertson, 68.
 Douglas, 224.
 Winfried Schultz, “Church Music and Copyright Law Protection in the Federal Republic of Germany,” Crux et Cithara: Selected Essays on Liturgy and Sacred Music (Altötting: Verlag Alfred Coppenrath, 1983), 247.
 Overath, “Church,” 35.
 Rivera, “Seventeenth,” 63.
 Rivera, German, 122-23.
 Lippius, Synopsis, 41.
 Rivera, German, 122.
 Ibid., 121-22.
 Quoted in Lippius, Synopsis, 61-62, note 11.
 Saint Thomas Aquinas, Summa Theologica (Chicago: Encyclopaedia Britannica, 1955), 337-38.
 Quoted in C.S. Lewis, Discarded Image, 89.
 Speculum musicae, Vol. I. ed. R. Bragard (Rome: American Institute of Musicology, 1955), pp. 50-54; quoted in Godwin, Music, 104-05.
 Augustine, Trinity, 787.
 Mt. 3:17 NJB (New Jerusalem Bible).
 Ibid., Jn. 14:10.
 Quoted in Gunton, One, 190; Augustine. On Christian Doctrine, trans. John J. Gavigan, 2nd ed. (Washington: Catholic UP, 1966), I, 5, 5; Augustine, Trinity, Book 6, Chapter 9.
 Gerald Bray, The Doctrine of God (Illinois: Intervarsity Press, 1993), 186-87.
 Christensen, 70.
 Schenker, Harmony, 6-7.
 Ibid., 30.
 George Herbert, “Resurrection,” The Norton Anthology of English Literature, Vol. I, eds. M.H. Abrams, et al. (Norton: New York, 1986).
 Schenker, Harmony, 26.
 1 Cor. 15:23 NJB (New Jerusalem Bible).
 Von Cube, 17.
 Quoted in Schenker, Composition, 35.
 Zuckerkandl, Man, 328.
 Schoenberg, 318.
 Quoted in Söhngen, Luther, 20.
 Mt. 26:39 NIV (New International Version).
 Rivera, “Seventeenth,” 64.
 Quoted in Grave, 44.
 Ibid., 16-17.
 Singer; quoted in Godwin, Spheres, 363-364.
 Ibid., note 1, 470.
 Wayne Grudem, Systematic Theology: An Introduction to Biblical Doctrine (Grand Rapids, Zondervan, 1994), 249; see 1 Cor. 15:28.
 Von Balthasar, Theo-drama III, 521-22.
 Rivera, German, 119.
 Ibid., 122-23.
 Grudem, 253.
 Coleridge, Remains, 206.
 Von Balthasar, Theo-drama III, 521-22.
 Ibid., 508.
 Quoted in Wason, 14.
 Ruland, 146.
 Kevin Mongrain, The Systematic Thought of Hans Urs Von Balthasar (New York: Crossroads Publishing Company, 2002), 90.
 Grudem, 255.
 Ibid., 241.
 Ibid., 257.
 Quoted in Hayburn, 541.
 Joseph Ratzinger, God and the World, trans. Henry Taylor (San Francisco: Ignatius Press, 2000), 268.
 Godwin, Harmonies, 107.
 Schenker, Masterwork II, 116.
 Schenker, Masterwork I, 104.
 Levarie and Levy, Morphology, 71.
 Christensen, 218.
 Rudhyar, 98.
 Lester, Modes, 52.
 Rivera, “Seventeenth,” 65-6.
 Eric Chafe, Tonal Allegory in the Vocal Music of J.S. Bach (Berkeley: University of California Press, 1991), note 25, 8.
 Quoted in Godwin, Spheres, 297.
 Calvin R. Stapert, My Only Comfort (Cambridge: William B. Eerdmans Publishing Company, 2000), 12.
 Chafe, 117.
 Chiapusso, 132, 137-38.
 Chafe, 8.
 Adrienne Rich, “At a Bach Concert,” Poems: Selected and New, 1950-1974 (New York: Norton, 1975), 7.
 Rudhyar, 94.
 Faulkner, 131.
 Ruland, 50.
 Manfred F. Bukofzer, Music in the Baroque Era (New York: Norton, 1947), 392
 Faulkner, 199.
 Spitzer, 75-6.
 Ibid., 76.