3. The first official effort to depart from the Bach's well-tempered C=256, to the Russian bandmaster's A=440, was ordered by agents of the Holy Alliance powers, in the setting of the Congress of Vienna. Later, a more insidious effort to enforce what mere decree had failed to bring about, occurred with the redesign of wind instruments, and also keyboard instruments, with a built-in registration which was shifted away from the natural registration of the bel-canto-trained human singing voice. This latter change gained momentum under the conditions provided by Palmerston's 1848-1849 revolutions. Those "Young Europe" revolutionaries, as typified by the cases of Richard Wagner and his bomb-throwing crony, and fellow-Beethoven-hater, N. Bakunin, also marked the unleashing of a more concerted effort to supplant the Classical tradition of Bach, Haydn, Mozart, Beethoven, et al., with the irrationalist Romanticism of Carl Czerny's Franz Liszt, et al. back

 4. At a recent time, even after hearing sundry Furtwängler recorded performances many times, this writer was taken by surprise once again, recapturing the same kind of "Furtwängler effect" which he had experienced on the referenced 1946 occasion. This time it was a first hearing of the Furtwängler direction of the Franz Schubert Ninth Symphony, as performed at Berlin's Jesus-Christus-Kirche, in December 1951 [Polydor International GmbH, Germany: Mono 427 405-2]. back

 5. The alternative expression is "... from behind the notes." In the interest of reaching for greater conceptual transparency, the present writer's own choice, would be performing from behind (var., beneath) the intervals. For the functional significance of such distinctions, see below. back

 6. In defense of Leibniz's arguments in his writing which was posthumously published as the Monadology. back

 7. The present writer employs the term "type" in the sense provided to mathematics by Georg Cantor's notion of the ontologically transfinite; the writer reads Cantor's usage from the vantage-point of what Leibniz identified as Analysis Situs (see note below). A type is a species of those orderings which lie outside the bounds of any deductive/inductive method, as, for example, outside, and above, the virtual-reality domain of today's generally-accepted classroom mathematics. Typical is the distinction, in the domain of experimental physics, between entropic and anti-entropic, non-linear ordering of deductively, mutually incongruent states of a continuing process. The distinction between a living and a no-longer-living process, belongs to this domain of Analysis Situs. back

 8. An evolutionary sequence of mutually distinct species, is typical of such orderings in general. The notion that sequences of physical systems might be ordered in such a way that the sequence is either entropic, or anti-entropic, lying within what Leibniz defined as the domain of Analysis Situs, is exemplary of topics beyond the scope of deductive forms of analysis. To locate the historical origins of the writer's approach to the subject of the essential role of the concept of time-reversal in understanding the compositional method of motivic thorough-composition, see Gottfried Wilhelm Leibniz: Philosophical Papers and Letters, ed. by Leroy E. Loemker, 2nd ed. (Dodrecht, Netherlands: Kluwer Academic Publishers, 1989); "Studies in a Geometry of Situation" (1679), pp. 248-257. The writings which most influenced the present writer's adolescent thought on the subject of Leibnizian Analysis Situs are, as provided in the same current location: "The Monadology," pp. 643-653, and, from the Leibniz-Clarke correspondence, Leibniz's 3rd (pp. 682-684), 4th (pp. 687-691), and 5th reply (696-721). See, also, Gottfried Leibniz, Monadology and Other Philosophical Essays, trans. by Paul and Anne Martin Schrecker (Engelwood Cliffs, N.J.: MacMillan Publishing Co., 1965). For the related writings of Bernhard Riemann which were the most crucial of the present writer's readings during 1952, see Bernhard Riemanns Gesammelte Mathematische Werke, trans. by H. Weber (New York: Dover Publications, 1953); see "Über die Hypothesen, welche der Geometrie zu Grunde liegen (On the Hypotheses Which Underlie Geometry)" (1854), pp. 272-287; see, also, "Lehrsätze aus der analysis situs für die Theorie der Integrale von zweigliedrigen vollständigen Differentialien (1857). Among the present writer's subsequent readings of Riemann which are relevant to the notions of applied Leibnizian Analysis Situs, see, most emphatically, the collection of posthumously published fragments from work of the year 1853 (I. Zur Psychologie und Metaphysik, II. Erkenntnistheoretisches, III. Naturphilosophie), pp. 507-538, and, with aid of the preface supplied by M. Noether and W. Wirtinger (pp. iii-vi of the same volume's appended Nachträge), Riemann's celebrated (1858-1859) "Vorlesungen über die hypergeometrische Reihe" (pp. 69-93) points to the kinds of mathematical implications of musical memory's act of "time-reversal," which the writer locates as central to the efficiency of Mozart's discoveries in motivic thorough-composition. back

 9. Leibniz identified this as the method of "necessary and sufficient reason." This is the same notion represented by the fundamental discoveries for physics by Bernhard Riemann, respecting the characteristic "curvature" of a specific physical space-time, among an orderable series of what are, from a deductive standpoint, mutually inconsistent such physical space-times. [Bernhard Riemann, "Über die Hypothesen, welche der Geometrie zu Grunde liegen," loc. cit.] back

10. The first effort to institutionalize A=440 was a conference organized in 1939 by Nazi Propaganda Minister Joseph Goebbels, who had standardized A=440 as the official Nazi German pitch. Professor Robert Dussaut of the National Conservatory of Paris told the French press that, "by September 1938, the Acoustic Committee of Radio Berlin requested the British Standard Association to organize in London a congress to adopt internationally the German Radio tuning of 440 periods. The congress was held in London, a very short time before the War, in May-June 1939. No French composer was invited. The decision to raise the pitch was thus taken without consulting French musicians, and against their will." A Manual On the Rudiments of Tuning and Registration, op. cit., p. 15. back

11. See Mindy Pechenuk, "Mozart's Ave Verum Corpus: A Crucial Proof of Mozart's Discovery, and a Short Pedagogical Exercise in Musical Memory," Fidelio, Winter 1996 (Vol. V, No. 4), pp. 34-45. back

12. On this specific matter, see Lyndon H. LaRouche, Jr., "Musical Memory and Thorough-Composition, Executive Intelligence Review, Sept. 1, 1995 (Vol. 22, No. 35), and "Norbert Brainin on Motivführung," Executive Intelligence Review, Sept. 22, 1995 (Vol. 22, No. 38) [also Fidelio, Winter 1995, (Vol. IV, No. 4)]. back

13. The writer employs the term "cognitive" to signify that feature of human mental processes which sets man absolutely apart from, and above all other living species: the quality which Immanuel Kant relegates to his poorly defined purgatory of synthetic judgment a priori, the quality of reason which exists entirely outside the narrow realm of Kant's understanding. back

14. E.g., Plato, Republic, Book II: The difference in definition of the passion for justice (and, truth) among Socrates, Glaucon, and Thrasymachus. back

15. In the discussions which occurred on the matter of selecting content for the composition of this Book II, the present writer had proposed an editorial plan in which the presentation of the modern instrumental palette, would adopt, as a point of departure, the difference in methods of composition of ensembles, which are best typified by comparing the work of C.P.E. Bach with that of a dedicated student of C.P.E. Bach's work, Josef Haydn. In response to hearing of this proposal, Norbert Brainin exclaimed, "Motivführung!," and pinpointed Haydn's six string quartets, Opus 33 (the "Russian Quartets"), as the more than likely prompting for Mozart's own, subsequent discovery and development of what became, from approximately 1782-1783 onward, the Bachian approach to motivic thorough-composition of Mozart, Beethoven, Brahms, et al. See footnote 12, above. back

16. See footnotes 8 and 9, above. back

17. The contrary, irrationalist view, is at the center of the pervasive dogma of I. Kant's Critiques. Kant's irrationality is heavily underscored, respecting art as such, in his Critique of Judgment. This is the crucial point on which Friedrich Schiller warned his followers, such as Wilhelm von Humboldt, against the perniciousness of Kant's influence. Schiller's warning against Kant, is echoed prophetically by the anti-Romantic Heinrich Heine, in his Religion and Philosophy in Germany. During the Nineteenth century, G.W.F. Hegel's chief political ally, Professor Karl Friedrich von Savigny, took Kant's irrationalist dogma in aesthetics as a point of departure for decreeing a hermetic separation of Geisteswissenschaft (e.g., art) from Naturwissenschaft, science. Savigny's neo-Kantian irrationalism [of Geisteswissenschaft versus Naturwissenschaft] became the widespread premise for the apologies made in defense of Nineteenth-century, anti-Classical Romanticism, such as that of Franz Liszt, erstwhile pupil of [Ludwig van Beethoven: "that criminal!"] Carl Czerny, and also, later, the apologies for virulent, anti-Beethoven irrationalism of Richard Wagner. back

18. Norbert Wiener, Cybernetics (New York: John Wiley, 1948). Wiener, a radical positivist in the tradition of Ernst Mach and Bertrand Russell, adapted the H-theorem, ironically, from the statistical mechanics of the anti-Mach, anti-positivist Ludwig Boltzmann, purporting, thus, to derive human thought and its communication from the kinetic theory of gases. Wiener relied upon the fact [see Morris Levitt,"Linearity and Entropy: Ludwig Boltzmann and the Second Law of Thermodynamics," Fusion Energy Foundation Newsletter, Sept. 1976], that Boltzmann's ("H-theorem") formulations allow for a relatively improbable, local reversal of entropy; this served Wiener's purpose, of providing a seemingly rational (e.g., mathematical-physical) basis for measuring human ideas as a relative increase in order in a purely local aspect of a kinematic domain, thus measurable in terms of negative values for Boltzmann's H-theorem. There are weaknesses in Boltzmann's own work, when it is extended beyond the bounds of its axiomatically assumed special case; these fallacies arise from accepting the hereditary assumption of "linearity in the extremely small," of Rudolf Clausius' and J.C. Maxwell's relevant dogmas; but, the fallacies imposed upon Boltzmann, posthumously, after 1906, by such among his radical-positivist adversaries, and survivors, are entirely the concoction of the latter. It is notable, that the conception of the universe inhering in the relevant work of Wiener and Von Neumann, is traced, without interruption, from the "kinetic" social theory of Hobbes' Leviathan, via that Hobbesian "hedonistic calculus," of Giammaria Ortes and Pierre-Louis Maupertuis, on which Bentham relied in his Introduction to The Principles of Morals and Legislation, his In Defense of Usury, and his In Defense of Pederasty. Thomas Malthus' plagiarizing of the same Giammaria Ortes' 1790 publication on population, is part of the same set. It should be noted that Wiener's "information theory," and Von Neumann's theory of the brain, are each copies of the argument demanding the ban of metaphor from the English language, in Hobbes' Leviathan. back

19. The credit for showing Mozart's Das Veilchen as a breakthrough in the application of motivic thorough-composition to song, was the joint work of several collaborators, notably prompted by the argument of Kathy Wolfe, the co-editor of Book I. Mozart's Abendempfindung is an exquisite example of the same principle; his Ave Verum Corpus, as noted elsewhere, embodies the principle in an advanced way, and to relative perfection. back

20. For example, Hamlet's Act III, Scene I soliloquy: "... But that dread of something after death,— / The undiscover'd country, from whose bourn / No traveller returns—puzzles the will, / And makes us rather bear those ills we have / Than fly to others that we know not of? / Thus conscience does make cowards of us all; / And thus the native hue of resolution / Is sicklied o'er with the pale cast of thought; / And enterprises of great pith and moment, / With this regard, their currents turn awry, / And lose the name of action." This soliloquy, set in the context provided by the closing soliloquy of the preceding act, expresses Shakespeare's central, motivic germ, upon which the derivation of the entirety of that play's composition depends. This is to be compared with Friedrich Schiller's notion of this principle of composition of tragedy. The apparently unbridgable distinction between the contending two, each ostensibly truthful principles, exemplies the absolute degree of irony on which the composition of great Classical tragedy pivots; the inability of the Hamlets, is the lack of will to muster that specific quality of emotion, through which breakthroughs to a new, higher, resolving order of comprehension, may be secured. That failure to force through an intellectual resolution of the conflict, through attaining a higher level of comprehension of the contradiction itself, is the defining, underlying subject-matter of all great Classical tragedy, from its root in the Homeric epics, through the compositions of Aeschylos, Shakespeare, and Schiller. back

21. In bad reviews, great Classical musical compositions are degraded to products of symbolism. That is the vantage-point of the worst apologists for the Romantic school, and for the still more decadent effluvia produced in the course of the present century. In metaphor, there is no symbolism, a distinction which separates metaphor absolutely from certain less rigorous forms of irony. All metaphor represents a well-defined paradox; the most important metaphors, in science and in Classical art, present an ontological paradox. The essence of motivic thorough-composition, is of the form of ontological paradox. back

22. The "agency" referenced here, echoes implied solutions to the principle of ontological paradoxes set forth in Plato's Parmenides. Plato's Timaeus is of crucial relevance in this connection. back

23. For an introduction to the notion of potential relative population-density, see Lyndon H. LaRouche, Jr., So, You Wish To Learn All About Economics?, 2nd ed. (Washington, D.C.: EIR News Service, 1995) back

24. Op. cit. back

25. The case of the consummate work establishing modern arithmetic, Carl F. Gauss' Disquisitiones Arithmeticae, is the proverbial exception which proves the rule. This is the entry into what Gauss identifies as "higher arithmetic," by means of creating, repeatedly, the type of contradictions, within arithmetic, which we have identified in the preceding paragraphs. The mind of the author of that most remarkable work, thinks in the language of higher geometry. Riemann's references to the precedents in Gauss, upon which he himself relied for developing higher, Riemannian geometries, underscore the approach which must be employed. back

26. A.-M. Legendre, the author of the comprehensive work in geometry, composed as the basis for the mathematics education program of Gaspard Monge's famous Ecole Polytechnique. Legendre, the teacher of Riemann's sponsor, Lejeune Dirichlet, was, together with Gauss, a principal current leading into Riemann's revolutionary, 1854 habilitation dissertation. back

27. Euler was a key figure among those Leibniz-haters imposed upon the Berlin Academy of Science by King Frederick "The Great" of Prussia. Together with his accomplice, Pierre-Louis Maupertuis, Euler participated as a leading figure in several hoaxes against the memory of Leibniz. One was the notorious "least action" hoax, in which Euler gave witting support to hoaxster Maupertuis, in a matter which led, subsequently, to Maupertuis' leaving Berlin in disgrace. Maupertuis, together with Giammaria Ortes, were the original authors of the "hedonistic calculus," whose development leads directly into the "systems analysis" hoaxes of John Von Neumann, et al. The idea that a mathematics for physics could be premised adequately upon infinite series, was the product of a hoax concocted by Euler himself, in his attacks on the work of Leibniz posthumously published under the title Monadology. This Euler hoax led into the Ninteenth-century efforts, of Clausius, Maxwell, Hermite, et al., to impose upon mathematical physics the arbitrary, false assumption, that physical relations could be represented adequately by functions of series, which assume linear extension, axiomatically, into the extremely small. Cf. B. Riemann, habilitation dissertation, on the matter of the extremely small. back

28. Op. cit. back

29. Christian Huyghens, The Pendulum Clock, trans. by Richard Blackwell, (Ames, Iowa: Iowa State University Press, 1986). Jean Bernouilli, in David E. Smith, A Source Book in Mathematics (New York: Dover Publications, 1959), pp. 644-655. Poul Rasmussen, "Ole Roemer and the Discovery of the Speed of Light," 21st Century Science & Technology, Spring 1993 (Vol. 6, No. 1). back

30. Following the period of that Mediterraean "dark age" which bridges the end of the Second Millenium b.c. and the opening centuries of the First, Egypt emerged as the center of a kind of renaissance of civilization within the Mediterranean littoral and adjoining areas. Against Egypt's traditional enemies, Babylon and Caananite Tyre, Egypt extended its sympathies to the Ionian Greeks, in the eastern Mediterranean, and to the Etruscans, in the western Mediterranean. This becomes visible to scholars for the period of the Eighth and Seventh centuries b.c. The crushing of Tyre and Babylon (Persian Empire) by Cyrenaica-allied Alexander the Great, is the predominantly happy, if imperfect outcome of this process. For the competent understanding of European civilization today, the crucial feature of superiority of the Classical Greek culture, is that centered in the work and heritage of Plato, in the notion of ideas. The hegemony of Classical Greek thought, and language-culture, in the eastern Mediterranean, following Alexander's conquests, is exemplified by the role of the Platonic Academy's great Eratosthenes, in Egypt, and Archimedes in Magna Grecia. The cultural superiority of these Greeks, over the Egyptian culture of that time, is centered in the development of the notion of the idea by Classical Greeks, Plato most notably. back

31. This development of deductive method to its highest level, by means of attacks upon the fallacies of the archetypical sophists of the Eleatic strain, is represented by the construction of the ontological paradox central to Plato's Parmenides. back

32. Inverted, that becomes a reflection of Leibniz's notion of necessary and sufficient reason: the hypothesis which coincides with the characteristic form of extension of the domain in which the relevant occurrences are situated. back

33. In no way, does this fact justify the fatalism of those sundry, gnostic doctrines of history peddled by the notorious G.W.F. Hegel, the irrationalist dogmas of neo-Kantian Friedrich K.Savigny, or the "objective," deterministic "theories of history" of the Social Democrats, et al. The history of the human species is based upon a voluntary principle: one may do anything it is physically possible for one to do, and the universe may react even more freely in its response. The "dark ages" in human existence, for example, do not occur because of any inevitably cyclic character of history; each occurs because the relevant, extant culture has violated the principles of reason, either with such violence, or persistence, this to the effect, that the continued existence of the human species requires that mankind be purged of that offensive, or simply degenerate culture. The order of ideas to which we refer here, the epistemological ordering, is the resource from which men, women, and societies, select, or evade, voluntarily, those choices of behavior which determine the pathways history will follow. back

34. As stated in other locations, a formal Analysis Situs must be organized on the basis of a nine-celled array, constructed as follows. The subject-matter of human knowledge as such, appears to be organized as sets or relations among the elements of a three-by-three table. We must assort the evidence among three domains: astrophysical, microphysical, and macrophysical; we must assort processes among three types: ostensibly non-living, living but not cognitive, and cognitive. All possible permutations of those nine cells exist; all possible permutations are subsumed by a general principle. The principled topic of such an array is the characteristic ordering found within and among the cells, for which the distinction between entropic and anti-entropic orderings is paradigmatic. See, Lyndon H. LaRouche, Jr., "The Essential Role of 'Time-Reversal' in Mathematical Economics," Executive Intelligence Review, Oct. 11, 1996 (Vol. 23, No. 41); this also appeared in Fidelio, Winter 1996 (Vol. V, No. 4). back

35. As referenced earlier, Immanuel Kant, Critique of Judgment (1790). back

36. By no accident, Savigny's Volksgeist doctrine laid the foundations for legalizing the "Nuremberg rally" form of populist dictatorship represented by Adolf Hitler's regime in Germany. Every effort to substitute the ever-capricious popular will (real or fictional), for a principle of law which defends the individual right against the popular will to violate that right, tends toward the worst forms of tyranny. A tyranny based upon that principle of capriciousness which, once it had seized the popular whim, then moved onward and upward, as in the procession of ancient Rome, through the Civil Wars of the Republic, to its more perfect incarnation of populist irrationalism, as the imperial Pontifex Maximus of a Tiberius, Nero, and Caligula. back

37. On Scalia et al., see, Lyndon H. LaRouche, Jr., "The U.S. Constitution's New Life," Executive Intelligence Review, March 14, 1997 (Vol. 24, No. 12). back

38. In the relevant dogmas of Nineteenth-century German Romanticism, the terms are Volksgeist or Zeitgeist. back

39. Lyndon H. LaRouche, Jr., "The Essential Role of 'Time-Reversal' in Mathematical Economics," loc. cit., and "Return to the Machine-Tool Principle," Executive Intelligence Review, Feb. 7, 1997 (Vol. 24. No. 7). back

40. Thus: let is be said, of the pervasively corrupt present U.S. system of justice, that such judges shall be judged for, and by their own judgments. back

41. The high relief sculpture of singing children, in the choir of Florence's Santa Maria del Fiore Cathedral, is indelible evidence that the choir was the product of vocal training and singing in the mode known today as Florentine bel canto. Thus, with respect to the discovery of principle embodied in Brunelleschi's design and construction of the cupola of that cathedral, this sculpture attests to the fact that the 1439-1440 sessions of the great ecumenical Council at Florence, were, among other accomplishments, not only the setting for Nicolaus of Cusa's founding of modern science, and the shaping of what was to become the first, modern sovereign nation-state, that of France's Louis XI, but also a crucial bench-mark for the modern history of music, as of painting. back

42. Op. cit. back

43. Mozart's realization of this significance of the Lydian interval, is the crucial distinction of his K.475, as compared with the K.457 keyboard sonata to which he prefixed that Fantasy. The Lydian interval, as the most characteristic feature—the virtual "Pythagorean"—of the domain of well-tempered polyphony, is most commonly associated with the C-major/C-minor modality of Bach's A Musical Offering. This bears upon the relevant register-shifts of the soprano and tenor voice-species. It appears to be a relatively commonplace error, to regard the appearance of that interval there as a peculiarity of the C-major/C-minor modality; in fact, the Lydian interval is a pervasive characteristic of well-tempered counterpoint, especially so with the appearance of the so-called "late Beethoven" compositions, his Missa Solemnis and his last string quartets most notably. As Mindy Pechenuk stresses, the role performed by the Lydian interval in the Mozart Ave Verum Corpus, both within voices, and intervals across voices, is a characteristic of the most agapic musical compositions. back

44. Once again, the values of the well-tempered tones are not algebraically exact. They are singularities, each a small, but finite region of discontinuity within the extent of the octave-scale. The values are determined, not only by the fact that there must be the obvious coincidence of the tones among all scales; but, that each local interval must be peformed, as Furtwängler's referenced motto implies, from the standpoint of a musical memory of the composition as that unified process which is manifested as a completed process of continuous, coherent development, in the immediate "aftertaste" of its concluding tones. This must take into account avoidance of the "wolf-tone" potential in the vicinity of each register-shift, of each and all of the voice-species represented in well-tempered polyphony as a whole. The region of singularity, within which the enunciation of the well-tempered tone, may lie within the range defined by the application of each and all of the inversions imposed by the function of "time-reversal" in performing, according to that view of each interval as apprehended in the mirror of the perfected, whole composition being completed. back

45. A few years back, baritone William Warfield demonstrated to a master class, the role of the principle of motivic thorough-composition's applicability to the performance of a Negro Spiritual. This writer was not present during that class, but the Meastro recapitulated his presentation of the point during a later event, where the writer was present, that same evening. The genius which sometimes appears in folk-song, as Antonin Dvor[HACHEK]ak demonstrated Johannes Brahms' principle for the case of the American Negro Spiritual, is not accidental. The great compositions of a Bach, Mozart, Beethoven, and Brahms, are the outgrowths of a great, agapic yearning for such qualities of musical expression. The best performers, once they have mastered the most advanced products of Classical composition, are best equipped for recognizing the same yearning expressed in the noblest attempts of relatively less developed musical media and forms. In the sea of anonymity, in which the African-American slaves were as if buried alive, a cry reaches out to us, from across the generations, by means of Dvorak's and Harry Burleigh's grasp of the Negro Spiritual. One hears the beautiful yearning from the souls of those crushed bodies, cheating thus the satanic vigilance of the slave-master class. Those Spirituals remind us, that it was from similar kinds of social conditions, in ancient and medieval Europe, that the germ of the best Classical motivic thorough-composition also lived, and grew. See Dennis Speed, op. cit. back