Romantic Muse

Werckmeister’s Harmonies
 
Christensen notes that “the simple triadic theories of Lippius and his followers could not account for the increased complexity of dissonance treatment found in the more advanced Italian practice coming to be known in Germany at mid-century.”[1]  In the middle of the sixteenth century Zarlino had defined a dissonance as "that which causes the consonance which follows it to sound more agreeable.  The ear then grasps and appreciates the consonance with greater pleasure, just as light is more delightful to the sight after darkness....We daily have the experience that after the ear is offended by a dissonance for a short time, the consonance following it becomes all the more sweet and pleasant.  Therefore the musicians of older times held that compositions should include not only perfect and imperfect consonances, but also dissonances; for they realized that their work would achieve more beauty and charm with them than without them.  Had they composed solely with consonance, they might have produced agreeable effects, but nonetheless their compositions (being mixed with dissonance) would have been somehow imperfect; and this form the standpoint of singing as well as of composition, for they would have lacked the great grace that stems from these dissonances."[2]

The reference to grace in this last phrase is echoed in Mersenne’s Harmonie Universelle, in which the author writes: “‘Dissonances form part of compositions only incidentally, because music is principally comprised of consonances, and dissonances serve only to make them more graceful, and all the more excellent and pleasing...Consonances comprise the principal element of harmony, by which all music should be regulated; they should serve as a rule by which to judge dissonances.’”[3]  Among the seventeenth century musical trends, Christensen notes that “there were, particularly in Italy, ever bolder explorations and employment of dissonance for expressiveness that...was to some degree predicated upon a clearly-implied triadic tonality.”[4]  Albert Cohen describes one manifestation of this trend, the technique of supposition, whereby “a dissonant note is used in place of a ‘supposed’ consonance, which, being understood, need not (but could) be sounded.”[5]  The association by Zarlino, Mersenne, and others, of the resolution of dissonance and grace doubtless accounts for the term grace note to designate a species of supposition whereby one of the consonant tones of the triad is preceded by a dissonance located a step above or below.  Seventeenth century French theorist Danoville states that “‘the trill...is performed by means of the supposition.’”[6] 
Seventeenth century theorists recognized both melodic and harmonic forms of the cadence.  Concerning the former, Christensen notes: “a cadence could designate the specific ornamentation found at some melodic closing.  Since the penultimate note of such a closing was typically ornamented by a trill, the trill came to be called a ‘cadence.’”[7]
 
There was historical precedence for Rameau’s representation of dissonance as essential to music for Christensen observes: “many seventeenth-century musicians began to interpret dissonance as an essential component of musical structure.”[8]  This interpretation was characteristic of French Baroque theorists who formulated a type of dissonance known as the supposition.  Christensen notes that, “in the second edition of his important thorough-bass treatise, Denis Delair called the consonant triad the ‘accord fondamental.’  All other dissonant harmonies, he tells us, are ‘suppositions.’  Every non-triadic dissonant interval ‘supposes’ a consonant one: 4 supposes 3, 6 supposes 5 (!), and 7 and 9 suppose the octave.”[9]  According to Christensen, “the most ubiquitous example of supposition to be found in French Baroque music” was in “ornaments” which achieved expressiveness “because of the explicit consonant harmonies against which they sounded and ultimately resolved.”[10]  One such ornament is the trill, which Tartini would interpret as a metaphysical symbol in the following century.
 
Andreas Werckmeister (1645-1706) is the first theorist both to extend the relation between music and Christian metaphysics to include a musical analogy of the two natures of Christ and to discuss the seventh harmonic of the overtone series in the context of metaphysical symbolism.  These innovations appear in his On Allegorical and Moral Music, an appendix to a treatise published in 1686.  In this treatise Werckmeister acknowledges the human tension between ignorance and knowledge of the divine:
All arts and sciences in this mortal state fall far short of comparison with the holy and divine creations, inasmuch as nothing is more incomprehensible and occult than God, who dwells in darkness where no man can enter (I Kings 8:12; Isaiah 45:15).  Yet since the Almighty has revealed himself to us not only in the Holy Scriptures but also in Nature and the Arts (Romans 1:19-20; Wisdom 13), we have decided to present a parallel of the holy Creation in music for the admonition and edification of our fellowman.[11]
 
These Scriptural references justify Chiapusso’s remark: “the ultimate support for [Werckmeister’s] speculative theses comes from the Bible.”[12]  Accepting both Zarlino’s simile comparing “darkness” to “dissonance” [13] and Doppelbauer’s assertion that “the audible is similarly related to the inaudible,” [14] Werckmeister’s reference to the association in Scripture of God with darkness invites the association of God with dissonance.
 
In presenting a parallel between music and metaphysics Werckmeister, in a passage which recalls the Platonic language of Zarlino, adds to the parallel between Trinitrian theology and triadic harmony inherited from his predecessors discussed above the parallel between spiritual tension and tonal dissonance; this parallel qualifies the association of dissonance with God.
We know that all things have their origin from God as a perfect being, and that everything which comes forth from him strives to return thither, to the most perfect of all.  If we consider our music, it is also a mirror and an example through which we may recall the same perfect Being.  For all perfect harmony comes from the perfect unison and unity.  Now as God makes a good harmony and concord with those closest to him - we mean the holy angels and blessed Christ - so the unison makes a harmony with its own nearest neighbors, the octave, fifth, etc.  And just as the great God makes no harmony with those who depart from him and his holy Word - indeed, if they stray too far and too long, they can scarcely be accepted again, but are cast out - , so it is the case that those dissonances which depart too far from the unison can sometimes hardly be resolved or tolerated without upsetting the harmony.[15]
 
Werckmeister’s analogy between God’s relation to the angels and the harmony of the unison with “the octave, fifth, etc.” is contrary to the conjecture of Eric Peterson: “If those who resemble angels do not sing a polyphonic song, this arises from the angelic order itself, for the angels all sing with ‘one voice’.”[16]  This last statement, vaguely based on “ancient literature,”[17] is consistent with the musical representation of the Deity offered by seventeenth century Franciscan theorist Marin Mersenne that I will now contrast with that of Werckmeister.
 
Before developing parallels between spiritual exile and tonal dissonance Werckmeister first displays his indebtedness to early seventeenth century German theorists 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.”[18]  Werckmeister’s description of the triad as ‘unitrisonus’ betrays the particular influence of Lippius, to whom Werckmeister frequently refers in his works, and who describes the triad as unitrisonic.
 
In contrast to the interplay of the one and the many in the unitrisonus harmony of the threefold unison which Werckmeister recognizes as an analogy of “the threefold unity of God’s being”, Mersenne perceives “an eternal Unison in the Deity, for the three Persons are all of the same nature and all have a single will, power, and virtue, although they are in fact distinct.”[19]  In orthodox belief there are two wills within the Trinity, and this distinction surely makes the triad a more accurate tonal model of the Trinity than the monotonous unison.  Despite Mersenne’s ‘unisonic’ perception of the Deity, he acknowledges that “pieces end more often with the octave, fifth, third, or their inversions than with the unison”[20]; this observation accords with the fact recognized by both Schlick and Lippius that seventeenth century composers were regularly employing the triad.  It is puzzling that Mersenne would reject the triad as an analogy of the Trinity, for Christensen notes that “Mersenne had...noticed the correspondence between overtones and triadic harmony: ‘Strings and all other kinds of bodies make three or four different sounds at the same time which blend together...This is worthy of great consideration, for is seems that the harmony of chords is imprinted in the nature of each thing that is employed for the praise of its author’.”[21]  If traces of the Deity are to be found in nature one would expect the same triadic harmony to characterize the Deity.
 
Werckmeister offers two unique contributions to the development of ideas concerning music and metaphysics in mentioning the two natures of Christ in the context of musical analogies and in discussing the dissonant flat seventh tone derived from the seventh harmonic of the overtone series in the context of metaphysical symbolism.  “We know from our Christian symbolism that the two natures in Christ could not be entangled or confused with one another, for the divine and the human characters cannot exist together.  Now there follows in our natural sequence the seventh number.  This has no affinity within this octave, nor indeed with the whole of theoretical music, although on the trumpet the note Bb follows here.”[22]  The references to the seventh number and the note Bb suggest that Werckmeister has in mind the flat seventh tone, for it is the seventh harmonic of the overtone series and Bb is the flat seventh tone in the key of C.  Although Werckmeister does not directly associate the flat seventh with the natures of Christ, this association was suggested by eighteenth century theorist Georg Andreas Sorge, whom, Lester notes, “reflects the theism of his German predecessors such as Andreas Werckmeister...by invoking the ratio 1:7 as the origin of the minor seventh (Sorge [1745-1747], Vol. 3, Chapter 4).  This exemplifies for him how music reflects God: the chord seventh must resolve because false intervals like 1:7 represent depravity in need of redemption (ibid. Chapter 22).”[23]  Sorge’s metaphysical interpretation of “the chord seventh” (by which he indicates the dominant seventh chord, including the flat seventh tone relative to the fifth, rather than to the fundamental) influenced succeeding philosophers to further develop its association with redemption, albeit in an intellectual climate which proved to be rather hostile to Christian metaphysical ideas.
 
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.”[24]  Faulkner believes that this incursion spread throughout Europe in the following 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.”[25]  The collision of these two worldviews is vividly described in James R. Gaines’ Evening in the Palace of Reason, which chronicles the events surrounding J.S. 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. 
 
Faulkner’s view of the demise of neo-Platonist Christian thought 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.”[26]  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.”[27]  Although Faulkner and Spitzer’s views concerning the despiritualization of Enlightenment thought may hold true with regard to society, this did not prevent individual philosophers and theorists from continuing to advance metaphysical ideas of music.  Godwin recognizes this continuity of thought when referring to “an unbroken Platonic and Pythagorean tradition in the eighteenth century, preserving such doctrines as...the primacy of number and the spiritual power of tone.”[28]  Christoph Gottlieb Schroter preserved such doctrines in his recognition, noted by Lester, of  “the presence of the triad in instrumental resonance, explaining that we respond to the triad because God implanted it both there and in the human soul to represent the Trinity (Schroter 1772, probably completed by 1754, pp. 7-8).”[29]  Schroter is one of many exceptions to Chua’s erroneous claim that “by the eighteenth century...triads [lost] their resemblance to the Trinity.”[30]  This resemblance is also found in the principles of Rameau, Tartini and Saint-Martin.
 
Principles of Rameau and Tartini
 
That Rameau’s music theory is based on the harmonic triad suggests an indebtedness to the Baroque theorists we have looked at.  Rivera corroborates this suggestion in concluding: “Without a doubt Rameau’s eighteenth-century harmonic theory owes much to Lippius’ Synopsis.”[31]  Evidently this influence extended to the metaphysical significance of the triad, for eighteenth century theorist Jean le Rond d’Alembert wrote that Rameau claimed to have found “‘the Trinity in the triple resonance of the corps sonore’”, which he describes as “‘the Chord called Perfect, or Natural...C (1), G (1/3), E (1/5)...the Chord which affects us the most agreeably, toward which all our desires are directed, & after which we wish nothing more’.”[32]  D’Alembert’s statement accords with Christensen’s acknowledgement that “a number of critics and historians to this day continue to maintain” Rameau’s perception of a parallel between “the resonating partials of the corps sonore with the holy Trinity.”[33]  This view is supported by James Doolittle’s observation that Rameau came to regard the corps sonore as “the material manifestation of the mind of divinity; it is the spirit of God made flesh, the original principle of man’s knowledge.”[34]  Indeed, Rameau asserts that the corps sonore offers “‘striking images of an antecedent Creator.’”[35]  Rameau seems here to be echoing the metaphysical language of the Baroque theorists.  Therefore, Lester notes that Rameau “contended that not only mathematics and the sciences, but religion itself was revealed to man via the corps sonore.  This brought Rameau to a position commonly held by many devout theorists before him: ‘the entire basis of harmony consists of numbers and proportions, for God has set the measure and importance of everything in numbers because he himself is a God of order.  What God and Nature order, man must willingly imitate...When we consider the musical proportional numbers, they are nothing other than a proper order set by God and Nature’ (Werckmeister 1697, p. 2).”[36]
 
Whereas Lippius’ interest in the triad was based on compositional analysis and personal intuition, Rameau provided a scientific basis for adopting the triad as a tonal norm, which accounts for Isacoff’s perception of his work as marking the transition from Pythagorean to contemporary music theory:
The acoustics of antiquity and of the Middle Ages was ruled by Pythagoras.  The shift from the Greco-Medieval to the ‘new’ acoustics was slow and gradual, as it was in other scientific fields and in science at large...Jean-Philippe Rameau (1683-1764) marks a turning point: his first work, Traite de l’harmonie (1722) is still essentially arithmetical, but the Demonstration du principe de l’harmonie (1750) is already based on the natural phenomenon of the overtone series...Rameau’s delight with the natural overtone series was intense.  Because the series contains the major but not the minor triad, the domination of the latter by the former seemed proven beyond all doubt.  ‘That first burst of nature is so powerful, so brilliant, so virile - if I may call it thus - that it surpasses minor and shows itself to be the master of harmony,’ exclaims Rameau.  The scientific discovery of the major triad in the overtone series may well have been at least partly responsible for the exalted position of major over minor from the eighteenth century until practically our own time.[37]
 
That Rameau regarded the triad as a principle of multiplicity rather than unity is suggested by Alejandro Enrique Planchart, in his remark that “Rameau states that musical sound is not one but three.”[38]  However Rameau did not stop at the three tones of the triad, for he states that “‘harmony is contained in the two chords proposed: the perfect chord and the seventh chord.  All our rules are founded on the natural progression of these two sounds.’”[39]  Levy verifies Rameau’s assertion when stating that “two chords, triad and seventh chord, constitute the whole of the material of harmony.”[40]  According to Christensen, “Prior to Rameau, the seventh chord had not enjoyed any particularly important status as a dissonance.”[41]  Although harmonic material expands to encompass other dissonant chords, Rameau believed that “‘the seventh is the first and so to speak the source of all dissonances’”[42]  The reason for the special status which Rameau afforded the seventh is its function as a dissonance in the harmonic motion of what Joan Ferris observes were for Rameau “two fundamental chords, the perfect major triad and the chord of the seventh.  The most perfect progression of these two chords proceeds from the less perfect to the more perfect, from tension to repose.  One calls the first chord of this perfect cadence the dominant-tonic, ‘because it should always precede the final note, and therefore dominate it.’  One calls the final chord the tonic, ‘because everything begins and ends on it.’”[43]  This progression is known as a perfect cadence, which Neubauer notes “is in Rameau’s scheme the elementary and archetypal musical structure.”[44]  Rameau describes this structure as follows: “‘the perfect cadence alone is...the origin of the principal varieties introduced into harmony.  One inverts this cadence, interrupts it, imitates it, avoids it - this is what [harmonic] variety consists of’.”[45]
 
The influence of the archetypal harmonic structure of the perfect cadence is underscored in Lester’s observation that “Rameau’s ideas were the single greatest influence on harmony theory for following generations.... Rameau’s theories dominate both his own century and the following ones.  There is hardly an idea in later eighteenth-century, nineteenth-century, or much twentieth-century harmonic theory that does not have its origin in Rameau’s works.  And not until Schenker does a theorist articulate a significantly different musical perspective.”[46]  Despite the dominance of Rameau’s harmonic theory, its relation to metaphysics was swept under the carpet by many of his successors; Christensen notes: “few theorists bothered with the metaphysical implications Rameau attributed to the corps sonore.  The rhetoric Rameau employed in his late speculative writings explaining the powers of the corps sonore failed, so to speak, to resonate among his readers.”[47]
 
Fortunately there were exceptions to this last statement of Christensen.  One such exception was eighteenth century violinist, composer, and theorist Giuseppe Tartini (1692-1770), who was not exempt from Rameau’s influence, for Rameau’s principle of multiplicity was incorporated into Tartini’s principle of unity.  The success of this incorporation is suggested in Lester’s observation that “Tartini’s system was viewed by some as comparable in standing to that of Rameau as a path to understanding the origin and use of musical elements.”[48]  Concerning the philosophical background of Tartini’s system, Enrico Gatti recognizes that all of “Tartini’s writings issued from a Neoplatonic substructure that revived and deepened the speculations on the relationships that united music and the scientific disciplines.”[49]  Tartini bases the unity of his philosophical system upon the following law: “for the establishment of any physico-mathematical system, the two realms of physics and mathematics must be united in such a way that they are inseparable, and form from them a single principle.”[50]  This last phrase anticipates the “one grand physical principle” proposed by contemporary string theorists, which is, according to Greene, based on “the central fact” that “just as different vibrational patterns of a violin string give rise to different musical notes, the different vibrational patterns of a fundamental string give rise to different masses and force charges.”[51]  This “fact” of modern physics is consistent with Tartini’s claim, which he based on experiments involving the vibrations of a violin string, that “harmonic unity is the physical principle”, and that the “plainest example” of the unification of this physical principle with mathematics “is that of the string with three tones.”[52]  Godwin comments that here “Tartini refers to his discovery of the harmonics sounded by a string, which he heard as only three in number: the fundamental, third, and fifth harmonics” - the tones of the triad which he discovered while playing his violin.”[53]
 
Godwin notes that Tartini “believed himself to have rediscovered the lost key to the universal science of Antiquity: it had been lost, he thought, since the Greek philosophers, but this had not prevented composers from following it intuitively.  In the opening pages of Scienza Platonica he defines this lost science as the ‘Harmonics’ recommended by Plato (in Bk. VII of the Republic) as essential to philosophers.”[54]  In contrast to the musical key of antiquity, which was the tetractys, Godwin mentions Tartini’s discovery of the triad: “It was Tartini’s discovery...that every note we hear, unless extremely pure in timbre, contains as harmonics the common chord.”[55]  This distinction between tetractys and triad is suggested again in Alfred Rubeli’s reference to Tartini’s “‘idea that only the synthesis of the harmonic thought of Antiquity with the latest discoveries of physics could lead to the true understanding of all musical questions”[56]; “the harmonic thought of Antiquity” and “the latest discoveries of physics” are doubtless references to the tetractys and triad, respectively. 
 
Tartini seems to allude to the triad in the reference to music in the following passage: “‘The Harmony of the universe is the whole tree; music is one of its branches, and necessarily of the same nature and root.... One can see the possibility of discovering the tree from the branch, the whole from the part, as in fact the author has suc[c]eeded in doing.’”[57]  Having translated such passages (apparently without the aid of a spelling check) it is understandable that Godwin would describe “Tartini’s musico-mathematical theories” as being “complex” and “confused.”[58]  In spite of the apparent complexity and confusion of the above passage, I think what Tartini means by “discovering the tree from the branch” is discovering the universal principle of harmony from the “the string with three tones,”[59] the tones of the triad.
 
The triad was also the basis of Rameau’s theory, and therefore Planchart rightly states that, “in spite of Tartini’s polemic attitude towards Rameau and the attack on Tartini’s system by Rameau’s followers, the basic theoretical conclusions of both men are quite similar.”[60]  Planchart, however, notes a subtle distinction between their theoretical conclusions: “When Tartini states that the three sounds of the monochord string are harmonic monads, he does not place himself in direct opposition to Rameau since he considers multiplicity a function of unity and regards the division of unity into multiplicity and the resolution of multiplicity into unity as parts of a complete cycle.  Rameau’s emphasis on multiplicity would not contradict directly Tartini’s assumption of unity as the basic harmonic principle.”[61]
 
Shirlaw clearly favors Tartini’s conception when stating that it encompasses that of Rameau:
while Rameau makes it his principal endeavour to demonstrate that sound is in its nature not simple but complex, not uniform but multiform, Tartini’s object is to prove that harmony presents us, not with a diversity, but a uniformity; all must resolve itself into Unity: all is Unity.  Rameau has said that musical sound is not one but three; Tartini demonstrates that the sounds of harmony...are not three, but one.
But in doing this, Tartini does not set himself in opposition to the principle of Rameau.  He accepts it, and regards the two principles, that of Unity breaking itself up into a series of harmonic monads, and that of these monads resolving themselves into Unity, as complementary principles, of equal importance and of equal significance for the theory of harmony.  For him indeed they are one and the same. ‘Therefore,’ he remarks, ‘the harmonic system reduces diversity to uniformity, multiplicity to unity; and, given a simple Unity, this divides itself harmonically.  Then the harmonic system must, in every respect, be regarded as Unity; rather the harmonic system resolves itself into Unity, as into its principle.  This is a legitimate consequence, and is physically demonstrable; it is, indeed, independent of the human will’.[62]
 
Considering the analogous relation between triad and Trinity, it is unsurprising that replacing the phrases musical sound, sounds of harmony, and harmonic system with the Trinity results in an accurate description of the interpenetration of perichoresis and particularity within the Trinity; whereas Tartini’s principle corresponds to Trinitarian perichoresis,  Rameau’s principle corresponds to Trinitarian particularity.  This reconciliation of the seemingly contradictory principles of Rameau and Tartini anticipates the reconciliation of the opposing principles of Saint-Martin, to be explored below.
 
Shirlaw refers to Tartini’s Trattato di Musica, published in 1754, as “one of the most remarkable works ever written on the subject of harmony.”[63]  In this work Tartini bases the claim that his principle is physically demonstrable on his discovery that “‘the stretched string of the monochord, which in itself ought to produce a single sound, has clearly three sounds’.”[64]  The senarius from which the triad is derived is, therefore, not an arbitrary limitation for it isolates the only three tones which are audible overtones of a single tone; this can not be said of the next overtone in the series - the seventh.  For Tartini as for the Baroque theorists the chord derived from the major triad has metaphysical significance; Gatti notes that for Tartini the “complete chord” is the harmonic triad, “symbolizing the Divine Trinity.”[65] 
The Christian symbolism of the triad is consistent with the fact that Tartini wrote the Trattato as a “Christian author...to Christian philosophers” (from Harmony, 321).  Shortly before his death, however, he addressed
the class of those pretended philosophers who affect the name of strong spirits: ‘procul este profani.’ [“Hence, you profane!” (Vergil, Aeneid VI, 258)]  It is one of their foolishnesses if they presume to attain possession of this science by the sole power of their cleverness, because if the measure of their cleverness is not sufficient to make them know the One, the True and the Good in the spectacle of the universe, it suffices far less to make them understand the doctrine of the universe.  It is, moreover, one of their blasphemies if they presume that they are aided in the comprehension of this doctrine by that light to which they are directly opposed.  Here, in all truth, one may say ‘evanuerunt in cogitationibus suis.’ [“They have become futile in their thinking” (Romans 1:21)]  They remain in their blindness because they love it, either through pride in their intelligence or through depravity of will, or through both together.[66]
 
That such an antagonistic tone was also adopted for the same reasons and in the same century with “Rameau’s war on the philosophes”[67] and by Saint-Martin confirms my earlier statement that the intellectual climate of the Enlightenment was generally hostile to ideas concerning Christian metaphysics.  The metaphysical nature of the work of these philosophers brought them into a relationship with society which is comparable to Nietzsche’s description of the relation between the genius and society: “‘The genius must not fear to enter into the most hostile relationship with the existing forms and order if he wants to bring to light the higher order and truth that dwells within him.’”[68]  Saint-Martin illuminates this order by extending the metaphysical symbolism of the Trinity to include the dissonant seventh chord, which, although overlooked by Tartini, was an element of Rameau’s principle of multiplicity.
 
 
SAINT-MARTIN’S PRINCIPLES
 
In Search of the Lost Chord
 
The theoretical innovations of Werckmeister and the Principles of Rameau and Tartini are brought together by French Classical philosopher Louis-Claude de Saint-Martin (1743-1803).  According to Benz, German Romantic philosopher “Friedrich von Schlegel attested to the orthodoxy of Saint-Martin’s religious philosophy in his Geschichte der alten und neuen Literatur,” [69] where Schlegel describes Saint-Martin’s work as “Christian philosophy divinely revealed and based on an ancient sacred tradition.”[70]  The apologetic tone of Saint-Martin’s first work, Des erreurs et de la verite, published in 1775, justifies Spitzer’s assertion, referred to earlier, that leading Enlightenment thinkers were disposed to criticize and ridicule Christianity.  Thus Chua observes that, “in the Age of Reason, to tease out the resemblance between things was no longer an act of erudition but error” (78).  Saint-Martin, however, reverses this socially ascendant view of error when stating that he would not have written Des erreurs “if the errors by which the human sciences poison my kind had not forced me to take up my defense”[71]; therefore, he wrote partly because he “was indignant with the Philosophers so called.”[72]  This indignation recalls that of Tartini towards “those pretended philosophers.”  Arthur Waite offers a more detailed exposition of Saint-Martin’s literary motivation when mentioning that Des erreurs was written “to lead back the mind of his age to Christianity...but he judged, not altogether incorrectly, that the mind of the age was in no mood to tolerate an explicit defence of Christianity.  He ‘wrote for the rationalists and materialists who had possession of the literary world in France, who made ridicule of the Gospel’...He therefore placed a certain veil over his doctrine, referring, for example, to Christ only under the name of the Active and Intelligent Cause.” [73]
 
Saint-Martin confirms his apologetic motivation in employing such a veil when, at the close of Des erreurs, he confesses: “‘If I stripped off the veil which I have assumed, if I uttered the name of this beneficent Cause, on which I would direct the gaze of the entire universe, that utterance would move the majority of my readers to deny the virtues which I have attributed thereto, and to disdain my entire doctrine’” (228).  Concerning the name of this Cause, Waite states: “That Cause is incontestably the Word as it was understood by St. John, and by all the early Christian fathers - without whom ‘was not anything made that has been made [Jn. 1:3].’” [74] Waite’s view is consistent with that of M. Gence, who states of Saint-Martin that “‘all his writings rest more or less on [the] ground’” of the Christian Word.’”[75]
 
Acknowledging the Scriptural statement that the Word is “sustaining all things by his powerful command” (Heb. 1:2), Saint Martin concludes that, “if the Word did not sustain the action and display of all phenomena, the phenomenal would come immediately to its end” (from Waite, 231).  From this conclusion, Waite deduces that, for Saint-Martin, “the proper business and study of man is...the search for the lost Word” (239), which Saint-Martin regards as “‘the key of Nature’” (from Waite, 225).  This last phrase recalls Tartini’s claim to have “rediscovered the lost key”, which is, in Rameau’s phrase, the “perfect chord”.  Although Godwin states that Saint-Martin “transposes to the metaphysical level the theory of Rameau concerning the archetypal primacy of the triad,”[76] we have seen evidence in support of Thomas’ claim that Rameau expanded “music theory to the level of metaphysics.”[77] However, as Saint-Martin more fully expanded the metaphysical dimensions of triadic tonality, it does not seem off the mark to state that he regarded the study of man as the search for the lost chord.  Such a search was conducted against the current of humanism and rationalism epitomized in the opening couplet of Alexander Pope’s Essay on Man:
Know then thyself, presume not God to scan,
The proper study of mankind is Man.
“Epistle II”, i, 1-2.[78]
 
Contrary to Pope’s advice, Saint-Martin finds the key to the significance of the chord of nature, the triad, to be the lost Word, which “is the Great Name,” namely “Jesus....Apart from this Name we are in death and sterility.”[79] As the name of Jesus is the key of Nature, it is ironic that Saint-Martin did not use this name for reasons given above.  The use of the “veil” of abstract principles is extended in his references to the first and third persons of the Trinity.  Both the veiled references to metaphysical persons and Saint-Martin’s omission concerning the role of the Spirit in the Trinity result in difficulties in interpreting the Second Principle.
Saint-Martin describes music as “one of the productions of that true language whose conception I am trying to recall to mankind.”[80] The implication that music is a derivative language is consistent with Saint-Martin’s claim that the source of music “is the primal and universal language which indicates and represents things in their natural state: so one cannot doubt that music was once the true measure of things, just as writing and the word once expressed their meaning.”[81] In accordance with this claim, he urges his readers “to believe that, however perfect their musical compositions may be, others exist of another order and more perfect; and that it is only by reason of its greater or lesser conformity to these that artificial music touches us and causes us more or less emotion.”[82] This distinction between artificial and perfect music recalls Werckmeister’s more specific distinction between the “perfect music” of triadic tonality and the “perfect Being” of the Trinity, cited earlier.  These distinctions are developed in Saint-Martin’s recognition of the epistemological limitations of musical analogies of metaphysical principles: “One should not insist, in the sense-picture which I am presenting, on an entire uniformity with the Principle of which it is merely the image, for then the copy should be equal to the model.  All the same, although this sense-picture is inferior, and can moreover be subject to variation, it nevertheless exists in no less complete a manner, it nonetheless represents the Principle, because the instinct of the senses supplies the remainder.”[83] This epistemological ambiguity both recalls Werckmeister’s acknowledgment of the human tension between ignorance and knowledge of the divine, and anticipates the following lines of English Romantic poet John Keats:
Heard melodies are sweet, but those unheard
Are sweeter; therefore, ye soft pipes, play on;
Not to the sensual ear, but, more endeared,
Pipe to the spirit ditties of no tone.
“Ode on a Grecian Urn”, 11-14.[84]
 
While acknowledging Saint-Martin’s recognition of the epistemological limitations of musical analogies, let us learn what we can from their relation to metaphysical principles.
 
Saint-Martin’s Principles: Beyond Good and Evil
 
The fundamental idea of Des Erreurs is expressed by Saint-Martin in the following passage: “In the first place, that which we know in music under the name of the common chord [accord parfait] is, for us, the image of that first unity that embraces everything and from which everything comes forth.  This chord is single and unique, entirely self-contained without need of any note other than its own; in a word, it is unalterable in its intrinsic value, like unity.”[85] To this description of the triad, Saint-Martin adds the observation that, “Secondly, this common chord is the most harmonious of all; it is the only one that satisfies the human ear and leaves nothing else to be desired.”[86]
 
Contrary to this last statement, however, Saint-Martin goes on to suggest that the ear desires, not only to be satisfied, but also to be shocked: “if the ear were offered nothing but a series of common chords it would not be shocked, it is true; but aside from the monotonous boredom that would ensue, we would not find therein any expression, any idea.  It would not, in fact, be music for us, because music, and in general everything that is sensible, is as incompatible with unity of action as with the unity of agencies.
In thus acknowledging all the laws necessary for the constitution of musical works, we can still apply these same laws to verities of another level.”[87] Saint-Martin is suggesting what I earlier claimed when distinguishing the Platonic from the Christian model of Being, namely that, just as the triad considered as a static entity is not music, but rather the dynamic unfolding of a triad in a musical composition, so the Trinity considered as a static being is not God, but the dynamic interplay of perichoresis and particularity among the three divine persons.  Saint-Martin applies musical laws to his second metaphysical principle of separateness, when associating it with the dissonant seventh chord, following from the triadic image of a first principle of divine unity:
this chord of the seventh tires the ear, holds it in suspense, and demands (in aesthetic terms) to be saved.  It is therefore through the opposition between this dissonant chord and all those derived from it, and the common chord, that all musical works are born: for they are nothing other than a continuous play - not to say a combat - between the consonant common chord and the seventh chord, or all dissonant chords in general.
Why should not this law, thus shown us by nature, be for us the image of the univer[s]al production of things?  Why should we not find therein the Principle, as we have found above the assembly and the constitution in the order of intervals of the common chord?  Why, I say, should we not touch with finger and eye the cause, the birth, and the consequences of the universal temporal confusion, since we know that in this corporeal nature there are two Principles which are ceaselessly opposed, and since nature could not survive without the help of the two contrary actions from which proceed the combat and the violence that we see: a mixture of regularity and disorder which harmony represents to us faithfully by the assembly of consonances and dissonances of which all musical works consist?[88]

Saint-Martin’s reference to the “chord of the seventh” suggests the influence of Werckmeister, who described the “seventh” in the context of metaphysical symbolism.  Godwin describes the tonal manifestation of the second principle when stating that Saint-Martin “obviously has in mind the note which changes a perfect major chord into a ‘dominant seventh’, thereby disturbing its harmonic equilibrium and demanding a particular resolution.”[89] This description is consistent with Saint-Martin’s reference to the musical form of the first and second principles, above, as the common chord and the dissonant chord of the seventh, which Godwin describes as “the resolution of the dominant seventh to the common chord.”[90] Earlier I noted that Rameau refers to this resolution as a perfect cadence.  Thus, the seventh tone of Saint-Martin’s second principle refers to the seventh tone relative to the dominant chord and not the tonic chord.  This seventh tone (in the key of C it is F, the seventh tone relative to G, the dominant chord relative to C) should not be confused with the seventh tone, or leading tone, relative to the tonic (B in the key of C), which I earlier associated with the Spirit of the Son.

Although Godwin’s description of the musical representation of the second principle as a dominant seventh chord is well founded, his interpretation of the ethical and metaphysical representations of the second principle are more problematic.  Godwin describes the second principle in ethical terms when stating that “before the beginning of time it diverged, asserting its own will and separating itself from the First Principle to become the origin of all evil - which is likewise the forsaking one’s own Principle to run after an illusory separateness.”[91] Insofar as this interpretation associates dissonance with evil it is consistent with the Medieval ethical view indicated in Zuckerkandl’s reference to the association of tonality and morality by “the theologically minded musicians of the Middle Ages”, who “saw in the two states of consonant and dissonant sound the tonal counterpart of Good and Evil: That Which Should Be, and That Which Should Not Be.”[92] This view may derive from Ptolemy, who, Godwin notes, “was the major scientific authority for the medieval period”, after Aristotle.[93] In the third chapter of Book III of his Harmonics, Ptolemy writes: “Among tones, too, consonance is a virtue and dissonance an evil; and, mutatis mutandis, the same applies to the human soul: virtue is a kind of consonance of the soul, evil a dissonance.  What is common to both [tones and soul] is that a harmonically regulated ratio of parts is natural, and an unregulated one against Nature” (26).

 Saint-Martin’s ethical representation of his second principle is ambiguous. This ambiguity can, however, be resolved by distinguishing two species of this principle of opposition.  The first species of Saint-Martin’s second principle is an opposition that does not result in unity.  He describes this species of opposition in ethical terms when stating that the first principle “is the only real and the only true one.  How then was it possible for the second Principle to become evil?  How could evil have taken birth and appeared?  Was it not because the superior and dominant note of the common chord, namely the octave, was suppressed, and another note introduced in its place?”[94] A historical example of this type of opposition is found in Spitzer’s reference, cited earlier, to an opposition between the period of Christianity to the seventeenth century and the epoch of dechristianization, during which time the Christian Logos was suppressed.  A human example of this type of opposition in the work of Tartini is his reference, cited earlier, to “those pretended philosophers” who “are directly opposed” to divine “light” and have, therefore, “‘become futile in their thinking’ (Romans 1:21).”  In the same Epistle as that cited by Tartini Paul identifies spiritual opposition as part of the natural state of humanity when stating that “the outlook of disordered human nature is opposed to God.”[95] Ruland adds musical and metaphysical associations to this spiritual opposition when confessing that “the impulse of my untempered inner nature to realize itself in the outer world arrogantly and without undergoing transformation is one side of the devil.”[96] Accepting Doppelbauer’s addition of the audible with reference to the discussion concerning the general revelation of creation from Romans to which Tartini alludes, one could posit that ill-tempered human nature is dissonant in relation to divine harmony.

In addition to his ethical interpretation of the second principle Godwin offers a metaphysical interpretation when stating that Saint-Martin is “describing the rebellion of Satan against God and the consequent origin of evil.  But he does not use these names, speaking instead of First [God] and Second [Satan] Principles.”[97] Although Saint-Martin associates the second principle with evil, he never associates it with Satanic rebellion.  Part of the confusion concerning the metaphysical interpretation of Saint-Martin’s second principle is his avoidance of names  The only evidence I have found to support Godwin’s association of Saint-Martin’s second principle with Satanic rebellion is the association of the dissonances of the musical analogy of the second principle with the musical trill, which is employed in Tartini’s Sonata known as The Devil’s Trill.
 
In contrast to the first species of the second principle of Saint-Martin, the second species of this principle is an opposition that results in unity. Godwin’s interpretation is, however, inconsistent with Saint-Martin’s representation of his second principle, which he describes, not in ethical, but in metaphysical and aesthetic terms, when stating that it “demands (in aesthetic terms) to be saved”.  This metaphysical and aesthetic representation of tonal dissonance is consistent with the Ancient association of Dionysus with dissonance and ugliness, and of Apollo with consonance and beauty.  Perhaps Saint-Martin is justified in avoiding the ethical dimension of his second principle if metaphysics and aesthetics - religion and art - are, in some sense, beyond good and evil.  This proposition is supported by Gershom Scholem’s use of a musical simile to represent divine ethics, when describing “aspects of divine action that seem to us to be in conflict with each other, although they each have their place, like notes in a melody, in the dynamic oneness of the Godhead.  In these tensions are the ultimate foundation of what appears to human beings as evil.”[98] This last sentence is consistent with Frye’s reference to Isaiah’s suggestion “that God is above such distinctions as those that the knowledge of good and evil provides: I form the light, and create darkness; I make peace, and create evil: I the Lord do all these things. (Isaiah 45:7).”[99] This accords with seventeenth century writer John Heydon’s assertion: “What the ignorant call evil in this Universe, is but as the shadowy strokes in a fair picture; or the mournful notes in Music, by which the beauty of the one is more lively and express, and the melody of the other more pleasing and melting.”[100]
 
Whereas Ruland associated the first type of opposition with the devil, he associates this second type with Christ, when describing Werckmeister’s view that “‘spiritual tempering’ is associated with the deed of Christ, which guided what Lucifer had led astray into a[n] infinite nothingness back to unity in its original source in the Father.”[101]
My musical and metaphysical interpretation of Saint-Martin’s principles is consistent with Ruland’s description of tonal and spiritual tempering.  Ruland notes that “The word ‘temperature’ comes from the Latin for ‘correct mixture, right ordering, moderation.’  Within a musical tone system it has to do with the finding of a compromise between the demands of two diametrically opposed tonal laws or structuring forces, each of which has a full claim to realization.  Without tempering, only one of the laws can be purely realized - and only at the expense of the other, which then either is not realized at all or else is forced into a badly distorted, musically unpleasing form.”[102] We saw an example of the tempering of opposed tonal laws in the philosophy of Tartini, whereby Rameau’s principle of multiplicity is tempered with Tartini’s principle of unity.  In the philosophy of Saint-Martin the tempering of a tonal law with its opposite is the resolution of the discordant principle of multiplicity, represented by the dominant seventh chord, to the concordant principle of unity, represented by the tonic triad.
 
Devil’s Trill
 
Godwin’s observation that, although Saint-Martin was “a lover of music...he was not technically educated” accounts for some obscurities concerning Saint-Martin’s description of a trill.[103] His statement that “there is in the whole scale absolutely nothing but the second and the seventh”[104] is somewhat misleading as it suggests that he is referring to the second and seventh tones relative to a fundamental tone (the notes D and B relative to C in the key of C; if C is the first tone, D and B are the second and seventh tones, respectively), whereas it is evident that he is referring to the second and seventh tones relative to the dominant (the notes A and F relative to the G chord in the key of C), for, in the same work, Saint-Martin refers to “the second or seventh of the dissonant chord”, by which he means the dominant chord.[105] When added to the notes of the tonic and dominant triads, C, E, G, and G, B, D, the notes A and F complete the diatonic scale, as all the notes of this scale - A, B, C, D, E, F, G - are accounted for.  Therefore, in asserting that “there is in the whole scale absolutely nothing but the second and the seventh”, Saint-Martin appears to be saying that the whole diatonic scale can be accounted for by regarding it as a projection of the tonic triad and the dominant chord, including its second and seventh intervals.
 
I believe that Saint-Martin’s metaphysical interpretation of the use of the second and seventh tones in a trill is influenced by the work of Tartini.  Godwin’s recognition that “Saint-Martin was an amateur violinist and a lover of music”[106] suggests that he was cognizant of Tartini’s compositions for the violin, which illustrate the composer’s virtuosity.  In Pietro Denis’s “Introduction” to Tartini’s Treastise on the Ornaments of Music, Denis writes that Tartini is acclaimed “by all the academies of Europe as the greatest musician of his century.”[107] This Treatise was translated by Denis into French in 1771, four years before the publication of Des Erreurs, and is described by Sol Babitz as “the only book written on that subject in Italy at a time when all Europe was copying the Italian model in performance” (1).  Saint-Martin may well have derived his metaphysical idea of the trill from both this treatise and Tartini’s most famous composition, The Devil’s Trill (c. 1749).
 
Gatti mentions Tartini’s “use of ornaments used not as embellishments, but rather as functional ‘affective’ elements distilled from jealously guarded inner myths.”[108] One such ornament is the trill, which Tartini describes as “a perfect ornament of music....The trill is used at the ends of phrases where occur final cadences.”[109] Tartini is specifically referring to a cadential trill, which occurs on the last strong beat before the final chord of a phrase, in distinction to a passing trill, which is used in the middle of a phrase to ornament a melodic passage.  Cadential trills consist of alternations of dissonant tones with triadic tones a step away, such as the alternation of a seventh or second tone with a fundamental, a fourth with a third, and a sixth with a fifth.
 
The trill functions as a symbol of the devil in The Devil’s Trill.  Peter Holman describes the role of the devil in the composition of this Sonata:
Cartier wrote that Tartini ‘saw the Devil at the end of his bed playing the trill that appears in the last movement of the sonata’, and Tartini’s account of the circumstances that supposedly led to its composition appears in J G de Lalande’s Voyage d’un francois en Italie (Paris, 1769):
 
One night I dreamt that I had made a bargain with the Devil for my soul.  Everything went at my command - my novel servant anticipated every one of my wishes.  Then the idea struck me to hand him my fiddle and to see what he could do with it.  But how great was my astonishment when I heard him play with consummate skill a sonata of such exquisite beauty as surpassed the boldest flight of my imagination.  I felt enraptured, transported, enchanted; my breath was taken away; and I awoke.  Seizing my violin I tried to retain the sounds that I had heard.  But it was in vain.  The piece I then composed, the Devil’s Sonata, although the best I ever wrote, how far below the one I heard in my dream![110]
 
Holman adds that “The trill appears in the driving Allegro assai that repeatedly interrupts a gentle Andante - representing, presumably, the sleeping composer.”[111] Given that the trill is a species of supposition, the waking function of the trill in the Devil’s Trill parallels the function of the supposition, described by eighteenth century French theorist L’Abbé Drouyn, in his Abrege de musique: “‘the supposition is used’” primarily “‘in order to awake the attention of the listener, who would fall asleep to a music that is too sweet or too even.’”[112] That Tartini awoke to compose the Devil’s Trill suggests that he shared Luther’s opinion that “‘the devil should not have all the beautiful melodies for himself alone.’”[113]
Tartini’s use of the trill in the Devil’s Trill doubtless influenced Saint-Martin, who describes both the trill and its metaphysical significance when writing:
It is thus that we see that at the moment of termination of a piece of music there is ordinarily a confused beating, a trill, between one of the notes of the common chord and the second or seventh of the dissonant chord, which latter is indicated by the bass which usually holds its fundamental note in order then to restore the whole to the common chord or to unity.  One can see, moreover, that just as after this musical cadence one necessarily returns to the common chord which restores all to peace and order, it is certain that...applying the same to man, one must see how the true knowledge of music might preserve him from fear of death: for this death is only the trill which ends his state of confusion, and restores him.[114]
 
This passage is the first instance in which the consideration of tones derived from the harmonic series that have metaphysical significance is extended to include the second interval, which is the eighth harmonic of the overtone series.  More significantly, Saint-Martin extends Tartini’s association of the trill with the devil by associating the resolution of a cadential trill with the transition from the natural human fear of mortality to a restoration of life.  This transition is doubtless derived from the following passage of the Letter to the Hebrews: “Since all the children [of God] share the same human nature, he [Jesus] too shared equally in it, so that by this death he could set aside him who held the power of death, namely the devil, and set free all those who had been held in slavery all their lives by the fear of death.”[115] Both this reference to the Christian resurrection from the state of human nature and Tartini’s symbolic use of the trill seem to have been adapted by Saint-Martin into a metaphysical analogy of a cadential trill.  This adaptation invites an analogy between the tonal cadence and the human and divine natures of Christ as defined by Chalcedonian Christology, the subject of the following section.
 
Chalcedonian Christology and Cadential Tonality
 
Godwin’s reference to analogies between music and metaphysics in the work of Saint-Martin as steps “towards understanding how the musical system can be an intelligible symbol of the world of Ideas” suggests an analogy between Saint-Martin’s second principle and what Coleridge calls the Idea Idearum - the Trinity.[116] This analogy is consistent with both Saint-Martin’s assertions, cited earlier, that the dissonant dominant seventh chord is essential to music, to the musical expression of an idea, and to prevent “monotonous boredom”, and with his presumption that his readers
will not consider the dissonances as vices in regard to music, since it is from them that it draws its greatest beauties, but only as the sign of the opposition which reigns in all things.
They will also realize that within the harmony of which sensible Music is only the image there must be the same opposition between dissonances and consonances; but that, far from causing the least fault in it, they are its nourishment and its life; and intelligence will see there only the action of several different faculties which sustain one another even though they fight together, and which by their reunion give birth to a multitude of results, ever novel and striking.
This has been only a very much abbreviated account of all the observations of this sort I might make on music, and on the relationships which exist between it and important verities; but what I have said will suffice to give a glimpse of the reason of things, and to teach men not to isolate their different branches of knowledge: for we show that they all come from the same tree, and that the same imprint is everywhere.[117]
 
The metaphor of music as a branch of the tree of knowledge is yet another indication of the influence of Tartini, who refers to music as a branch of the tree of universal harmony.
More importantly, Saint-Martin’s description of dissonances as part of “the harmony of which sensible Music is only the image” and his statement that opposition which results in reunion is the life of this harmony indicate that the metaphysical interpretation of the second principle is the Son of God in his relation to the Father in the Trinity.  This interpretation is consistent with Voegelin’s insistence, cited earlier, that opposition is necessary to “the vitality of life as it has been experienced by the creators of the tensional symbols”.  Furthermore, this interpretation is supported by the parallels which exist between Saint-Martin’s conception of the first and second principles and von Balthasar’s conception of the relation of Father and Son within the Trinity, as both conceptions are characterized by a life-affirming opposition.  In spite of Schlegel’s attestation to the orthodoxy of Saint-Martin’s religious philosophy, cited earlier, Saint-Martin neglects to mention the unifying role of the Spirit, whereas von Balthasar is closer to Trinitarian orthodoxy when representing the Spirit as providing a love which replaces the opposition between Father and Son with unity.  Restating this point while employing the terminology of Bray’s summary of Lonergan’s conception of Trinitarian relations, Saint-Martin recognizes the two generational relations between the Father and the Son, but he omits the two processional relations involving the Spirit, who conceives the “reunion” mentioned by Saint-Martin.  Earlier I cited Bray’s reference to 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).  It is the Son, in particular, who represents the eternal reconciliation which extends beyond the Godhead, and is symbolized above all in crucified manhood of Christ, which he has united to himself”.[118] Bray’s description is consistent with von Balthasar’s perception of a “polarity in God”,[119] which is manifest in his recognition that “both life and death are images of God...if death is understood to mean the sacrifice of life, then the original image of that sacrifice is in God as the gift of life flowing between Father and Son in the Spirit...Jesus’ death, even his most bitter death in abandonment, is the pure expression of his eternal, trinitarian life.”[120] The polarity characteristic of the generational relations of Father and Son is expressed in the first prayer of Jesus in the garden of Gethsemane: “My Father, if it is possible, may this cup be taken from me.  Yet not as I will, but as you will.”[121] This metaphysical polarity is replaced by the love characteristic of the processional relations involving the Spirit, whose role is described by von Balthasar: “as the essence of love, he maintains the infinite difference between [Father and Son], seals it and, since he is the one Spirit of them both, bridges it.”[122] Both the triad and the Trinity, therefore, conform to Coleridge’s abstract observation concerning opposites: “All opposites, like the extreme points of all lines, must have a mid-term common to both.”[123]
Bray’s reference to the reconciliation of the Godhead with the manhood of Christ, cited above, characterizes the Definition of Chalcedon, which has, Grudem observes, “been taken as the standard, orthodox definition of the biblical teaching on the person of Christ since [451] by Catholic, Protestant, and Orthodox branches of Christianity alike.”[124] Voegelin describes this definition as being concerned to make “divine and human nature, which are supposed to be different, intelligible as copresent in the one person of Christ.”[125] That intelligibility is lacking in the definition of Chalcedon is suggested in Voegelin’s reference to “a sense of incongruity between the Christ of the dogma and the Son of God we meet in the Gospels and the letters of Paul.  One can admire the technical perfection of the Definition of Chalcedon under the conditions of philosophical culture in the fifth century A.D. and still refuse to use its language when speaking of ‘Christ,’ because the philosophical terminology of ‘natures’ has become inadequate in the light of what we know today about both classic philosophy and theophanic events.”[126] An adequate language for Christology is suggested in Morrissey’s statement that, for Voegelin, “creedal statements about the Christ are really a ‘love language.’”[127] Both Voegelin’s preference for the musical metaphor of attunement to characterize the relations between humanity and divinity and Overath’s belief that the primary language of divine love is music provide a basis for recognizing music as an adequate symbol of the creedal statement of the definition of Chalcedon.
 
The first reference to music as a representation of the human nature of Christ was actually made a century before the formulation of the Chalcedonian creed by Eusebius, whose analogy between the “human nature” of Christ and “a musical instrument” was cited earlier.  I also earlier mentioned Werckmeister’s references to “the two natures in Christ...the divine and the human characters” and to “the seventh number”.  An analogy between these metaphysical and musical entities is suggested in Saint-Martin’s doctrine that the opposition between the tonic triad and the dominant seventh chord, “and all those derived from it”, is applicable “to verities of another level”, an oblique reference to the opposition between the Godhead and the manhood of Christ.  Let us now consider how the dominant seventh chord is analogous to the human will and nature of Christ.
 
Grudem’s statement, cited earlier, that “no one person [of the Trinity] has any attributes that are not possessed by the others”, does not seem to account for the humanity of Christ, which Grudem acknowledges in his observation that “the great majority of the church throughout its history has said that Jesus had two wills and centers of consciousness, yet he remained one person.  Such a formulation is not impossible, merely a mystery that we do not now fully understand.”[128] The musical analogy of a perfect cadence, in which a dominant seventh chord moves to a tonic triad, can serve as an aid in comprehending this mystery.   Zuckerkandl distinguishes between the qualities of the four tones of the dominant seventh chord and of the three tones of the tonic triad: “As it contains four different tones, the seventh chord is necessarily dissonant; its sound state is always tension, not, as in the triad, balance.”[129] Zuckerkandl’s association of the four tones of the seventh chord with tension and of the three tones of the triad with balance is consistent with Peck’s more general observation of the intelligible significance of the numbers four and three: “4 is the corporeal, 3 the spiritual form...Three cannot be divided and thus designates the indissolvable and incorruptible.”[130] These characteristics are also evident in Jacques Ellul’s associations of three with God, “since God is the Trinity”, and of four with creation, “which was understood in antiquity according to a rhythm of fours."[131] Thus, Godwin states that “all traditional arithmology assigns the number four to the lower world (the place of the four elements, etc.), and the ternary to the higher word.”[132] In the following pages I will represent the three tones of the tonic triad in its second inversion and the four tones of the dominant seventh chord in its root position as analogies of the divine and human natures of Christ, respectively.
The divine will and center of consciousness of Christ is analogous to the will of the fifth tone of a tonic triad to accept the fundamental tone as its center of gravity.  The human will and center of consciousness of Christ is analogous to the will of the fifth tone to bear its own triad, of which it is the center.  Allen Forte refers to this tendency of a “fifth to manifest itself as a fundamental” as “the tonicization process.”[133] This process introduces a fourth tone, the flat seventh, which initially manifests the dependence of the consequent dominant seventh chord upon its original tonic triad and consequently manifests the original will of the fifth tone to submit to the fundamental tone.  Earlier I cited Jesus’ prayer, “not as I will, but as you will”;[134] these words are an expression of his human will and center of consciousness submitting to its divine counterpart, much as a dominant seventh chord resolves to a tonic chord in a cadence.  
 
Bettina Brentano refers to the seventh as "the divine leader, - the Mediator between sensual and heavenly Nature...and if it were not, all tones would remain in limbo....As it is with Christians, so is it with sounds: every Christian feels the Redeemer within himself, each tone can elevate itself to Mediator, or seventh, and thus perfect the eternal work of redemption from the sensual to the heavenly; as only through Christ we enter the kingdom of Spirit, so only through the seventh, the benumbed kingdom of tone is delivered and becomes Music...and as redemption extends itself to all, who, embraced by the living spirit of the Godhead, long after eternal life, so the flat seventh by its solution leads all tones, which pray to it for delivery, in a thousand different ways, to their source – divine spirit.[139]
 
Brentano interprets the role of the seventh tone of the dominant chord in relation to the tonic triad as an analogy of the role of Christ in the redemption of humanity to the kingdom of God.  This analogy is consistent with Zuckerkandl’s description of the function of the dominant (V) chord in relation to the tonic (I): "Since V is the only chord audibly directed towards I, it is by virtue of V only that I can effectively establish itself as the center of action.  Any harmonic motion, in order to express the rule of I, must be ultimately channeled through V.  In this role, then, as the chord that dominates the access to I as I, and on which I depends for the manifestation of its power, V seems quite appropriately called the dominant chord."[140] Zuckerkandl’s description of the function of the dominant chord in relation to the tonic chord is analogous to the function of the Son in the redemption of humanity to the Father.  Just as the dominant chord "dominates the access to I" in tonal music, so the Son is "the gate"[141] through which humanity must enter in order approach the Father.  Christians "come to God through" the "one mediator between God and men", Jesus; through him believers "have access to the Father."[142] Thus Jesus states: "I am the way...No one comes to the Father except through me."[143] This metaphysical interpretation of the perfect cadence has some affinity with the following statement of Luther: “In music, the leading tone is the Gospel, the other notes the law, and as the law is softened by the Gospel, so the Gospel dominates the other tones.”[144] The tonal analogy of the perfect cadence suggests that redeemed humanity relates to the Son in his human nature as distant harmonies relate to a dominant chord, and that the Son in his human nature relates to the Father as a dominant chord relates to a fundamental tone.  
 
Earlier I stated that the Son was analogous to the triad in its second inversion.  However, the theological distinction between the divine and human natures of the Son necessitates the following analogical distinctions.  The divine will of the Son is analogous to the triad in its second inversion, and the human will of the Son is analogous to the dominant seventh chord in root position.  Furthermore, the Spirit of the Son is analogous to the dominant seventh chord in its first inversion, and redeemed humanity is analogous to the dominant seventh chord in its second inversion.  The relation between fallen humanity and a chord built on the seventh interval of the dominant seventh chord - the diminished seventh chord, also know variously as the Bach, Samiel, and Tristan chord - will be developed in the following section.
 
Bach, Samiel, and Tristan Chord
 
The metaphysical interpretation of the dominant seventh chord as a musical analogy of the human nature of Christ is consistent with the use of a derivative of this chord, the diminished seventh, in the works of J.S. Bach.  Whereas the dominant seventh chord is based on the fifth tone of a diatonic major scale, the diminished seventh chord is based on the seventh tone.  In spite of this difference Forte observes that “the birthplace of the seventh lies in the chord built on the fifth rather than the fundamental tone of the key...the seventh chord stands for movement and calls forth movement.  Moreover, the movement produced leads backward; it points to the lower fifth.”[145] Thus the diminished seventh chord, which Forte calls “the seventh chord”, is a derivative of the dominant seventh chord, which Forte refers to as “the chord built on the fifth”.  In the key of C the seventh chord that points to the lower fifth is the B diminished seventh chord, which points to the G dominant seventh chord.  The diminished seventh chord functions much like a dominant chord in its pull to the tonic, but it has as its root the leading tone; therefore, in the key of C, b is both the leading note of c and the root of the diminished seventh chord b–d–f–ab.  Grave notes: “Vogler does not shirk from regarding a triad whose fifth is diminished, such as B-D-F in C major, as a legitimate triad.  He suggests that such a chord need not stand on its own acoustically.  Instead, it acquires its fundamental status from the key in which it originates.  Chords on all degrees of the scale, in other words, are understood as sovereign representatives of their key.  This is the path of reasoning that leads Vogler to invent the system for representing chords that has since become standard: each degree of the scale is assigned a Roman numeral, which designates its function as a chord root within a key” (Praise, 22-23).  Perhaps Vogler’s perception of the diminished chord founded on the seventh scale degree as a derivative of the tonic chord founded on the first scale degree accounts for Robert Wason’s description of Vogler as “the prophet of the romantic musical language.”[146] The metaphysical significance of these two chords is a recurring feature of romantic music.
 
Earlier I cited Ruland’s statement that, in the key of C, “b is the original leading-tone.  It precedes the tonic like a herald and announces him unmistakably as the ruling king” (146).  Ruland shows how the leading tone functions in a harmonic context when observing that “the diminished seventh chord provides each of the three tones of the major triad with its own ‘leading-tone herald.’”[147] With reference to the C major triad of c, e, and g, although b is the leading tone of c, f and ab are not leading tones of e and g, respectively, but they are perhaps ‘leading-tone heralds’, to use Ruland’s phrase, as they approach their respective ‘ruling king tones’, e and g, from a semi-tone above, rather than below, as does a leading tone proper.  Ruland describes the geometric significance of the diminished seventh chord: “Its tones mark the quadrants of the cycle of twelve.  With its double tritone relationships it forms a cross in the circle of twelve.”[148] The “cycle of twelve” is a reference to the cycle of fifths and the tritone is a reference to the interval of a diminished fifth or an augmented fourth.  In the key of C the double tritone relationships of the diminished seventh chord are those between f and b, and between ab and d, which form a cross in the cycle of fifths.  Ruland comments on the metaphysical significance of this harmonic structure in the works of Bach: “This tonal structure plays such a central role in the works of J.S. Bach that it could be called the Bach chord.  It is no accident that when this great musical mystic seeks to present the crucifixion on Golgotha musically in his two passions, his deepest and most individual works, he repeatedly employs the chord that forms the cross in the cyclic system.”[149] 
 
The diminished seventh chord, as it contains none of the tones of the tonic triad, may be regarded as analogous to the kenosis of Christ,[150] the emptying of his divine nature, which is analogous to the tonic triad in its second inversion.  Therefore, Werckmeister’s analogy, cited earlier, that, “just as the great God makes no harmony with those who depart from him and his holy Word...so it is the case that those dissonances which depart too far from the unison can sometimes hardly be resolved”, is applicable to the diminished seventh chord.  Just as fallen humanity, represented by the crucified Christ emptied of his divine nature and forsaken by God,[151] cannot approach the divine presence except through the mediation of the risen Christ, so the diminished seventh chord cannot be resolved to the tonic chord except through the mediation of the dominant chord.  
 
Earlier I cited Eger’s reference to an ancient Hebrew belief in an analogy between the Creator, the seven days of the Biblical account of creation, and the seven tones of the musical scale.  This analogy is similar to that made by Ruland between Christ and the seven tones of the scale, expressed in Ruland’s view that the significance of the number seven associated with John’s apocalyptic vision of Christ extends to “the seven musical intervals”[152] This analogy is evident in Ruland’s statement that “inner musical life”, by which he means the significance of music in relation to divine and human harmony, “depends on the Seven, which are embodied in the sevenfold tones and intervals of a tonality”, as well as on “the Seven as embodied in the ‘sacrificial lamb’ on the cross.”[153] Although Ruland does not specify how the harmony of the seven tones of a scale are analogous to the role of Christ in creating metaphysical harmony, Table 15 does offer such a conceptual analogy, if fallen humanity is identified with the crucified Christ in the metaphysical model, and if a, the major sixth of c, is altered to ab, the minor sixth of c, in the musical model of the harmonic motion of the seven notes of the C major scale.  This elaborate analogy is consistent with Faulkner’s conclusion that “the influence of metaphysical, speculative Christian theology” accounts for the complex formal structures characteristic of Western polyphonic music.”[154]
 
Bach’s use of the diminished seventh chord as a symbol of the cross has some affinities with Calvin Stapert’s recognition that “German composers of the Baroque also had a melodic symbol for the cross.  It consists of four notes (although it could be made more elaborate with additional notes) that go in a zigzag pattern - up, down, up, down (or the reverse).  If one imagines a line drawn between the first and fourth notes and another between the second and third notes, a cross appears.”[155] However, Stapert’s description of such symbols as mere “devices that were useful to give music a stronger rhetorical impact”[156] in the service of a sacred text would appear to strip music of its metaphysical significance, which would counter Schlick’s claim, cited earlier, that “the most outstanding musicians” of the Baroque era recognized a relation between music and metaphysics.  That Bach employed the diminished seventh chord 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 suggested in Eric 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.”[157] Commenting on this last phrase, Chafe notes that “this metaphysical tradition was largely a seventeenth-century phenomenon and was epitomized in the works of Andreas Werckmeister.”[158] A further link between Bach, Werckmeister, and the Lutheran baroque metaphysical tradition is found in Chafe’s observation that “Bach, like Werckmeister, produced a canon on the triad that affirmed its expression of universal harmony.”[159] More specifically, this observation suggests that Bach, like Werckmeister, affirmed the triad as an analogy of the Trinity, which is consistent with Chiapusso’s acknowledgement that Bach “deeply respected [Werckmeister’s] work in musical philosophy” and that “he was deeply imbued...with the musical speculation of...Werckmeister.”[160] Accepting Chafe and Chiapusso’s representations of Bach, I feel justified in representing Bach’s symbolic use of the diminished seventh chord as a metaphysical symbol, and more specifically as a musical representation of the second principle of Saint-Martin, who regards “the opposition between this dissonant chord [the dominant seventh] and all those derived from it [including the diminished seventh], and the common chord [the tonic triad]” as a representation of “the opposition which reigns in all things”, be they physical or metaphysical; this accounts for Saint-Martin’s reference to music as “one of the productions of that true language” of metaphysics.
 
The use of the diminished seventh chord in the sacred music of Bach was later adapted into the secular context of Romantic opera as a leitmotif, a recurring tonal element associated with a particular character, image, setting, or theme.  In the course of this adaptation Ruland notes that, “significantly, after Bach’s time the diminished seventh chord ceased being used to express a self-sacrificing cosmic being.  It became more the expression of the forces which led this cosmic being into death.  Thus in Weber’s Freischutz the diminished seventh chord appears as the satanic ‘Samiel’s chord.’”[161] The significance of Ruland’s comment lies in its relation to the trend, noted by Frye, that “with the Romantic movement there comes a large-scale renewal of sympathy for...tragic Biblical figures...Cain, Ishmael, Esau, Saul, even Lucifer himself, are all romantic heroes.”[162] Another example of this Romantic sympathy for the devil is the wild huntsman Samiel in Carl Maria von Weber’s opera Der Freischutz.  Considering that Vogler - who recognized the metaphysical significance of the triad as he “knew the works of Rameau” and “Tartini”[163] – was Weber's last music teacher,[164] it is unsurprising that Weber extended the metaphysical significance of music to his association of the diminished seventh chord with Samiel.
 
Although some German critics attribute the birth of German romantic opera to Der Freischutz, which was first performed in 1821, a majority credit Hoffman’s opera Undine, first performed in 1816, with this distinction.  Weber wrote an enthusiastic review of  Undine, concerning which Schafer notes:
Weber, however, had two minor complaints: ‘the predilection for little short figures which tend to lack variety and obscure the melody’ and ‘the partiality for … diminished-seventh chords’ – a valid criticism, though Weber was scarcely the one to point it out.
One interesting feature of the opera – perhaps what Weber was referring to as the ‘short figures’ – was the use of the recurring themes to identify characters or situations, a principle Weber was later to employ himself, and one which was to be fully developed into the leitmotif principle by another Hoffman admirer, Richard Wagner.[165]
 
This last comment is justified by Thomas Grey’s observation that “Wagner was perfectly well aware of Weber’s use of recurring ‘characteristic motives.’”[166] It is therefore unsurprising that Weber’s use of the unstable and ambiguous diminished seventh chord as a leitmotif for Samiel anticipates Wagner’s use of this chord as a leitmotif for Tristan in the opera Tristan und Isolde, on account of which the diminished seventh, according to Bryan Magee, “remains the most famous single chord in the history of music.”[167]
 
That Wagner employed the leitmotif of the diminished seventh chord, not merely as a rhetorical device, but as a metaphysical symbol, is suggested in Allan Bloom’s comment that Wagner’s audience “had the religious sense that Wagner was creating the meaning of life and that they were not merely listening to his works but experiencing that meaning.”[168] The nature of this religious meaning is indicated in both Wagner’s identification of the fundamental “‘Key’” with Christianity and his recollection when he was sixteen of having “had visions by day in semi-slumber in which the tonic, third, and dominant seemed to take on a living form and revealed a mighty significance to me……(‘Autobiographische Skizze’ in Gesammelte Schriften und ichtungen Leipzig  1907, 1: 6)”[169] The implication of these statements is that the meaning of the three notes of the triad is their analogous relation to the Christian Trinity.  Wagner’s visions were inspired by Hoffman’s first published story, Ritter Gluck, in which the composer Gluck has a synaesthetic perception of “the sun” as “the triad” and “rays of light” as “tones”, two of which, “the Tonic and the Dominant”, raise him as he is told: “’I know the reason for the longing which fills thy breast.  It is the longing for the Third, that tender youth, who now steps up between the two.’”[170]
 
Wagner develops the significance of tonality beyond the scope of the triad when representing the fundamental tone as conceiving “‘chief-tones’” which “‘are, in a sense, the adolescent members of the family, who yearn to leave its wonted surrounding for an unhindered independence.’”[171] This representation of the derivative tones of the fundamental is consistent with Wagner’s use of the Tristan chord, and it recalls Forte’s description of the tonicization process, which is developed in his interpretation of “the meaning of the cadence”, whereby the seventh tone of the dominant chord is represented “as a corrective, depriving V (the dominant) of its independence and pointing it back in the direction of its origin.”[172] In Tristan, however, this cadential motion is conspicuously delayed for nearly four hours until the final chords, on account of Wagner’s sympathetic attachment to his romantic hero.
Earlier I cited Novack’s description of the history of triadic tonality as an arch; Novack concludes this description by stating that the “apex of this arch occurs in the Classic era...a period of continuous development from Haydn to Brahms.  Somewhere during this period the arch begins to descend...because of other conditions in the nineteenth century.”[173] One of these conditions is what Schoenberg calls the “‘emancipating [of] the dissonance’”,[174] specifically in the form of what Robert Bailey refers to as “a double tonic complex.”[175] Before the composition of Tristan in the middle of the nineteenth century Western music was governed by monotonality, described by Schoenberg as a principle whereby “‘every digression from the tonic is considered to be still within the tonality’” and, therefore, “‘subordinate to the central power of a tonic.’”[176] Monotonal music is not monotonous, as there are key changes; however, Christopher Lewis describes changes in key as “merely prolonged chromatic elaborations of the fundamental diatonic progression that is prolonging the tonic triad.”[177] According to Lewis the Tristan Prelude is the first piece of music to break from monotonality and to feature “two tonics both successively and simultaneously”,[178] a description of Bailey’s double tonic complex.
 
The fact that the Teutonic Wagner first composed music with two tonics led the Teutonic philosopher Oswald Spengler to assert that Western music “died in Tristan.  This work is the giant keystone of Western music.”[179] Although Spengler is surely overstating the historical and cultural significance of Tristan, its inauguration of the double tonic complex does anticipate the annulment of what George Steiner calls a “contract”,  which “is broken for the first time, in any thorough and consequent sense, in European, Central European and Russian culture and speculative consciousness during the decades from the 1870s to the 1930s.  It is this break of the covenant between word and world which constitutes one of the very few genuine revolutions of spirit in Western history and which defines modernity itself.”[180] On account of this spiritual revolution Steiner divides Western history into two phases: “the first, which extended from the beginnings of recorded history and propositional utterance (in the pre-Socratics) to the later nineteenth century, is that of the Logos, of the saying of being.  The second phase is that which comes after”.  Ratzinger describes the musical consequences of this second phase: “when the religious ground is cut away from under music, then...music and indeed art itself are threatened.”[181]
 
Earlier I cited Ruland’s reference to the “experience of the third” as a conscious union of subject and object, the world and the Word.  Steiner’s perception of the modern obsolescence of this experience is also suggested in a chapter entitled “The Development of Western Third Consciousness and its Crisis”[182] in which Ruland, in a passage which doubtless influenced that which I cited from Dlugoszenski in the first chapter, states that contemporary music created without reference to a Logos
is experienced as having a strikingly close correspondence to our subjective, wholly personal experience.  All of music’s cosmic elevation is lost and the listener is thrown back upon his own feelings, sentiments and passions...all that remains is a subjective, hedonistic enjoyment of the [harmonic] alterations, and a music that expresses a feeling for life that is satisfied by ignoring its spiritual background and merely pursuing whatever brings personal enjoyment.  In consequence, all the cyclic forces - both those ‘dying out’ in the harmony of alterations and those that still are very much ‘alive’ in the cadence - degenerate into spiritless slang, an empty facade: neither are experienced with any artistic spirit.[183]
 
The cadence has truly degenerated into spiritless slang as it is no longer commonly employed with reference to spiritual regeneration, as it was in the time of Bach, Weber, and Wagner.  Goehr undermines this contemporary trend in her assertion, cited earlier, that “the claim regarding philosophy’s identity with music...carries as much weight today...as it carried in German Romanticism”.  This identity of philosophy with music originates with Pythagoras, whose perception of a musical cosmos is shared by contemporary physicists who, like Greene, regard elementary particles as being “all part of the same cosmic score.”[184] A musical cosmos, however, implies the existence of a cosmic composer, to whose key we may become attuned through the mediation of a philosophical Logos - the philosopher’s “stone.”[185] This metaphysical alchemy is analogous to the musical harmony of a perfect cadence, in which a dominant seventh chord leads willing discordant derivatives into harmonious participation with a tonic triad.

[1] Christensen, 45.

[2] Zarlino, 53-54. 

[3] II, 122, 129; from Cohen, 68.

[4] Christenson, 46. 

[5] Cohen, 65.

[6] from Cohen, 72.

[7] Christensen, 113.

[8] Chrsitensen, 64.

[9] Chrstensen, 66.

[10] Ibid., 66-67.

[11] From Godwin, Spheres, 293.

[12] Chiapusso, 132.

 [13] Zarlino, 53.

[14] Doppelbauer, 213.

[15] From Godwin, Harmony, 293-94. 

[16] Eric Peterson, 28.

[17] Ibid., note 33, 63.

[18] From Spheres, 297.

[19] Marin Mersenne, Harmonie Universelle (Paris, 1637); from Spheres, 253-54.

[20] Ibid., 259. 

[21] Christenson, Note 16, 138.

[22] From Spheres, 297.

[23] Lester, Compositional, 194.

[24] Faulkner, 131.

[25] Ibid., 199.

[26] Spitzer, 75-6.

[27] Ibid., 76. 

[28] Godwin, Music, 173.

[29] Lester, Compositional, 194.

[30] Chua, 77.

[31] From Lippius, Synopsis, i.

[32] From Thomas, 95, 92.

[33] Christensen, 298.

[34] Doolittle, 248.

[35] From Christensen, 297-98.

[36] Lester, Compositional, 48-9.

[37] Isacoff, 233-34.

[38] Planchart, 35. 

[39] From Tenney, 67.

[40] Levy, Theory, 181-82.

[41] Christensen, 111.

[42] From Wason, 37.

[43] Ferris, 243.

[44] Neubauer, 81.

[45] From Neubauer, 82.

[46] Lester, Compositional, 157.

[47] Christensen, 302.

[48] Lester, Compositional, 198.

[49] Enrico Gatti,  “Guiseppe Tartini”,  Tartini Concerti,  (Arles: Harmonia Mundi: 1995), Gatti, 14.

[50] Giuseppe Tartini, Trattato di Musica secondo la vera scienze dell’armonia (Padua, 1754), 21-22; from Spheres, 316. 

[51] Greene, Elegant, 143..

[52] Tartini, Trattato; from Spheres, 317, 316.

[53] Spheres, 464, note4.

[54] Ibid, 315.

[55]Ibid, 466, note3.

[56] Alfred Rubeli, Trattato, (Dusseldorf: Verlag der Gesellschaft zur Forderung der systematischen Muskwissenschaft, 1966), 84; from Spheres, 465, note 11.

[57] Giuseppe Tartini, Scienza Platonica fondata nel cerchio, edited by Anna Todeschini Cavalla (Padua: Cedam, 1977), 4; from Spheres, 315.

[58] Godwin, Spheres, 314.

[59] Ibid., 316.

[60] Planchart, 35.

[61] Ibid., 36.

[62] Shirlaw, 288-89.

[63] Ibid., 287.

[64] Trattato di Musica, Ch. I; from Shirlaw, 287. 

[65] Gatti, 15.

[66] Tartini, Scienza; from Spheres, 321.

[67] Neubauer, 78. 

[68] From Goehr, 226.

[69] Benz, 91.

[70] Ibid, 92.

[71] Des Erreurs et de la verite, par un Philosophe Inconnu,  Edinburgh [actually Lyon], 1775,  Reprinted Paris, Le Lis, 1979; from Spheres, 328. 

[72] From Arthur Waite,  The Unknown Philosopher.  (New York: Rudolph Steiner Publications,  1970) 441.

[73] Waite, 81.

[74] Ibid, 228.

[75] From Waite, 94.

[76] Godwin, Spheres, 466, note 2.

[77] Thomas, 96.

[79] From Waite, 242, 247, 244.

[80] From Spheres, 323.

[81] Ibid, 330.

[82] Ibid, 331.

[83] Ibid., 325.

[84] John Keats,  “Ode on a Grecian Urn”,  Norton Anthology of English Literature,  (Volume  II.  Fifth Editon.  Ed. M.H. Abrams.  New York: Norton, 1987). 

[85] From Spheres, 324.

[86] Ibid.

[87] from Spheres, 327.

[88] From Spheres, 326.

[89]Godwin,  Harmonies, 186.

[90] Spheres, 466, note 7.

[91] Des Erreurs, p. 512ff, from Harmonies, 186.

[92] Zuckerkandl, Sense, 152.

[93] Godwin, Spheres, 21.

[94] From Spheres, 326.

[95] Rom. 8:7, New Jerusalem Bible.

[96] Ruland, 96.

[97] Des Erreurs, p. 27ff, from Harmonies, 186.

[98] Gershom Scholem, On the Mystical Shape of the the Godhead,  (New York: Schocken Books, 1991), 61.

[99] Frye, Code, 111.

[100] The Harmony of the World, London, 1662, p. 239; from Music, 162).

[101] Ruland, 181.

[102] Ibid., 24.

[103] Spheres, 323.

[104] Ibid., 327.

[105] Des Erreurs, 518f; from Occult, 22).

[106] Spheres, 323.

[107] Pietro Denis,  “Introduction”;  Giuseppe Tartini,  Treatise on the Ornaments of Music,  (Los Angeles: Early Music Laboratory, 1970) 3 

[108] Gatti, 13.

[109] Tartini, 7, 9 

[110] Peter Holman,  Guiseppe Tartini,  “The Devil’s Trill and Other Sonatas”,  The Locatelli Trio, (London: Hyperion Records, 1991), 4-5.

[111] Ibid., 5.

[112] From Cohen, note 38, 71.

[113] From Luther, 111.

[114] Des Erreurs, 518f; from Occult, 22.

[115] Heb. 2:14-15; New Jerusalem Bible.

[116] Godwin, Harmonies, 188.

[117] From Spheres, 329.

[118] Bray, 187-88 

[119] Theo-Drama, III, 510.

[120] Theo-Drama, V, 251-52.

[121] Mt. 26:39; New International Version.

[122] Theo-Drama, IV, 324.

[123] Coleridge, Logic, 129-30.

[124]Grudem, 556.

[125] Ecumenic, 329.

[126] Ibid, 329-30.

[127] Morrissey, 232.

[128] Grudem, 253, 561. 

[129] Zuckerkandl, Sense, 181.

[130] Peck, 76.

[131] Jacques Ellul,  The Meaning of the City, (Grand Rapids: William B. Eerdmans, 1970), 197-98.

[132] Godwin, Occult, 21.

[133] Allen Forte,.  “Schenker’s Conception of Musical Structure”,  Schenker Studies,  (Cambridge: Cambridge UP, 1990), 32.

[134] Mt. 26:39; New International Version.

[135] Ruland, 24.

[136] John Hollander,  The Untuning of the Sky,  (Princeton: Princeton UP, 1961), 25.

[137] Ibid., 96.

[138] Ibid., 181.

[139] Bettina Brentano,  Goethe’s Correspondence with a Child,  (Boston: James R. Osgood and Company, 1872), 143.

[140] Zuckerkandl, Sense, 195-96.

[141] Jn. 10:9; New Jerusalem Bible.

[142] Heb. 7:25; 1Tim. 2:6; Eph. 2:18; New Jerusalem Bible. 

[143] Jn. 14:6.

[144] From Söhngen, Luther, 95.

[145] Forte, 19.

[146] Robert Wason,  Viennese Harmonic Theory from Albrechtsberger to Schenker and
Schoenberg, (Ann Arbor: UMI Research Press, 1985), 28.

[147] Ruland, 147.

[148] Ibid., 146.

[149] Ibid., 147.

[150] see Phil. 2:5-7, Grudem 550.

[151] Phil. 2:7; Mt. 27:46.

[152] Ruland, 175.

[153] Ruland, 176. 

[154] Faulkner, 151. 

[155] Calvin R. Stapert,  My Only Comfort,  (Cambridge: William B. Eerdmans Publishing  Company, 2000), 16.

[156] Ibid., 12.

[157] Eric Chafe,  Tonal Allegory in the Vocal Music of J.S. Bach,  (Berkeley: University of California Press, 1991),  8. 

[158] Ibid., note 25, 8.

[159] Ibid., 117.

[160] Chiapusso, 132, 137-38.

[161] Ruland, 148.

[162] Frye, Code, 182.

[163] Lester, Compositional, 209.

[164] Grout, 741.

[165] Schafer, 180

[166] Thomas S. Grey,  Wagner’s Musical Prose,  (Cambridge: Cambridge University Press, 1995), 229.

[167] Bryan Magee,  The Tristan Chord,  (New York: Henry Holt and Company, 2000),

208. 

[168] Allan Bloom, 68.

[169] Prose, 288, 291; from Jones, 42, 44; from Schafer, 185.

[170] From Schafer, 154.

[171] From Jones, 44.

[172] Forte, 23.

[173] Novack, 71.

[174] Style and Idea, 104; from Norton, 239.

[175] From Lewis, 19.

[176] Structural Functions of Harmony, 19; from Lewis, 17.

[177] Christopher Lewis,  “Mirrors and Metaphors: On Schoenberg and Nineteenth-Century Tonality.”  Music at the Turn of the Century,  (Berkeley: U of California P, 1990), 17.

[178] Ibid., 18.

[179] Spengler, 155.

[180] George Steiner,  Real Presences,  (London: Faber, 1989), 93.

[181] Ratzinger, Problems, 216.

[182] Ruland, 136.

[183] Ibid., 150.

[184] Greene, Fabric, 428. 

[185] Mt. 21:44, New Jerusalem Bible.