| Canons & Fugues | Well-Tempered Clavier |
Well-Tempered Clavier:
Index of Contrapuntal Operations,
Learning Objects, and Concepts
|Contrapuntal Operations|Objects & Concepts|
Contrapuntal Operations
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Book I No. 1: C No. 2: cm No. 3: C# No. 4: c#m No. 5: D No. 6: dm No. 7: Eb No. 8: d#/ebm No. 9: E No. 10: em No. 11: F No. 12: fm No. 13: F# No. 14: f#m No. 15: G No. 16: gm (a) No. 17: Ab No. 18: g#m No. 19: A No. 20: am No. 21: Bb No. 22: bbm No. 23: B No. 24: bm Book II No. 1: C No. 2: cm No. 3: C# No. 4: c#m  No. 5: D No. 6: dm No. 7: Eb No. 8: d#m No. 9: E No. 12: fm No. 13: F# No. 14: f#m No. 15: G No. 16: gm No. 18: g#m No. 19: A No. 20: am No. 21: Bb No. 22: bbm No. 23: B No. 24: bm |
Style demonst. moderno passion demonst. dance antico ricercar moderno canon dance verset moderno antico concerto verset verset verset verset competit. character antico verset? passion Style character verset verset dance verset improv. ricercar canzona antico dance galant passion partimento moderno verset chorale fughetta dance moderno moderno dance |
Voices 3 3 5 4 3 3 3 3 2 3 4 3 4 3 3 4 4 3 4 3 5 4 4 Voices 3 4 3 3 4 3 4 4 4 3 3 3 3 4 3 3 3 3 4 4 3 |
Subject Entries 8 12 31 11 17 9 36 10 9 13 10 8 9 14 17 15 12 14 38 8 22 12 13 Subject Entries 8 23 45 15 25 9 11 16 38 9 11 30 6 17 12 10 8 11 24 14 9 |
Tonal/ Real tonal tonal real tonal real tonal tonal real real tonal tonal tonal real real tonal tonal tonal tonal real tonal tonal tonal tonal Tonal/ Real tonal tonal tonal real either real tonal real either tonal real tonal tonal tonal real real tonal tonal real tonal tonal |
Stretti - - moderate moderate moderate - extreme - - moderate - - - moderate moderate - - moderate extreme - extreme moderate - Stretti - extreme extreme - extreme moderate moderate slight extreme - - - - moderate - - - - extreme - - |
Counter Subject 6 11 - - 5 7 - 9 10 4 8 11 7 - 12 - 7 - - 7 - 5 11 Counter Subject 6 - 14 - - 4 - 7 13 - 9 - 5 15 3 - 7 7 9 5 4 |
2nd Ctr * - - - - - - - - - * - - - - - * - - * - - - 2nd Ctr - - - - - - - - - - * - * - - - - * * * * |
Mel Inv * * * - * - * - - * - * * * - - - - * * - * * Mel Inv - * * * - * - * * - - * - - - - - - * - - |
Inv Ctpt * * * - * * - - * - * * * - * - * * - * - * * Inv Ctpt * - - * - - * * * - * * * 10/12 * - * 10/12 * 12 * |
Aug - - - * - - * - - - - - - - - - - - - - - - - Aug - * * - - - - - - - * - - - - - - - - - - |
Double Triple - - Triple - - - - - - - - - - - - - - Double - - - - - Double Triple - - - Double - - - - Triple - - Triple - - Double - - - - Double - |
BACH - - * - - - - - - - - - - - - - * - - - * - * BACH - - - - - - - - - - - - - - - * - - - - * |
Crown - - * - - - - - - - - - * - - - - - - - - - - Crown - - - - - - - * - - - * - - * * - - - - * |
| Book I | Contents |
| No. 1: C | Prelude: streaming audio link Topics: stretto and expositional architecture (tonal/real) Key concepts: Prelude and fugue thematically linked; stretto, subject, answer, false subject defined; subject accompanies itself and inherently develops in certain ways. Interpretation: Korevaar performance notes included. Questionnaire: Students can answer ten questions online. |
| No. 2: cm | Topics: figural structure of subject, countersubject, invertible counterpoint, melodic inversion, sequence, palindrome Key concepts: Subject represents an economy of means; two countersubjects require triple counterpoint; sequence likened to stairs, functions to connect related keys. Interpretation: Korevaar performance notes included. Questionnaire: Students can answer ten questions online. |
| No. 3: C# | Topics: structure of subject, countersubject, melodic inversion, sequence, enharmonicism, well-tempered, re-exposition Key concepts: Disjunct subject outlines compound melody; countersubject melodically inverted; sequence likened to engine; enharmonics justified; well-tempered intonation defined; exposition repeated at conclusion of fugue; similarity of fugue to Italian concerto grosso. Interpretation: Korevaar performance notes included. |
| No. 4: c#m | Topics: Lutheranism, chiasmus, lamento, triple fugue, Bach symbols, retrogradation, melodic inversion, passion music Key concepts: Shortest subject in WTC is chiastic; triple fugue is passion music with which artist identified by authorial inclusion; BACH motive/numbers/monogram Interpretation: Korevaar performance notes included. Questionnaire: Students can answer ten questions online. |
| No. 5: D | Topics: structure of subject, French manier Key concepts: Subject contains two motives, one of which is developed by augmentation; influence of French music; performance practice of dotted rhythms Interpretation: Korevaar performance notes included. |
| No. 6: dm | Topics: structure of subject/countersubject, melodic inversion, rounded binary, Fortspinnung Key concepts: Subject fragmented into three motives and undergoes inversion for 1st time in WTC; countersubject motivically related to subject; fugue likened to big bang; form is rounded binary Interpretation: Korevaar performance notes included. Questionnaire: Students can answer ten questions online. |
| No. 7: Eb | Prelude: streaming audio link Topics: modulating subject, bridge passage, ritornello Key concepts: Prelude is a double fugue; following fugue has unusual tonal relationship between subject and answer; bridge passage receives extraordinary development; ritornello principle is likened to boomerang. |
| No. 8: d#/ebm | Topics: inversion, augmentation, Dostoevsky Brothers K. Key concepts: Classic example of subject inversion and augmentation; fugue like polyphonic novel, Brothers Karamazov. Interpretation: Korevaar performance notes included. |
| No. 9: E | Topics: structure of subject/countersubject, melodic inversion, retrogradation, augmentation, DNA Key concepts: Motives in subject/countersubject analyzed at figural level; unusual variation of countersubject; atomized figures undergo inversion, retrogradation, augmentation; generative tendency of fugue likened to DNA. |
| No. 10: em | Topics: counterfugue, double counterpoint, canon, Möbius Key concepts: Only two-voiced fugue is canon comprised of two parts (fugue/counterfugue) in double counterpoint; fugue likened to Möbius strip. |
| No. 11: F | Topics: structure of subject, counterexposition, canon, melodic inversion Key concepts: Subject fragmented into three motives; counterexposition and developments repeat structures in new voice order; canonic episodes; fugue like building blocks. |
| No. 12: fm | Topics: countersubject, chromaticism, wohltemperirt, triple counterpoint Key concepts: Second most chromatic subject in Book I provides occasion to reference wohltemperirt, Werckmeister, Kircher, and Kirnberger |
| No. 13: F# | Topics: invention, false sequence Key concepts: Episodes develop material not derived from the subject; like a fugue with three-part invention. Interpretation: Korevaar performance notes included. |
| No. 14: f#m | Topics: countersubject, stile antico, chromaticism, melodic inversion Key concepts: Chromatic subject is complemented by sighing countersubject in the inverse of the subject's arched shape; fugue is an amalgam of opposites, stile antico with moderno; discussion weaves themes from O'Brien on James Joyce, and Ciardi. Questionnaire: Students can answer ten questions online. |
| No. 15: G | Topics: structure of subject, scale, proportionality Key concepts: Rhythmic symmetry of the subject; scalar material developed by economical means; fugue likened to Palladio villa with ensuing discussion of geometric and harmonic means, Zarlino, and "music of the spheres." Questionnaire: Students can answer ten questions online. |
| No. 16: gm (a) | Topics: structure of subject/countersubject, melodic inversion, double counterpoint Key concepts: Countersubject is derived from the subject by melodic inversion and reordering of head/tail; fugue likened to fractal. Questionnaire: Students can answer ten questions online. |
| No. 16: gm (b) | Topics: Paul Celan, Imre Kertész, the Holocaust, Bach's funeral music Key concepts: fugal purpose, character, and essence. It is the fugue's essence to reveal the likeness of seemingly unlike things. This alternate study of the gm fugue, asks why Paul Celan titled his poem on the Holocaust a "fugue" (Todesfuge). It compares Celan's work with the axial fugue of BWV 106, which uses the same subject as the gm fugue of WTC Book I. An analogue is suggested of the Jewish- Christian experience, with lessons of the fugue and Holocaust applied to contemporary life. Features the paintings and poetry of Holocaust survivor, Tamara Deuel. |
| No. 17: Ab | Topics: Heinrich Schenker, prolongation, fundamental structure Key concepts: Schenkerian analysis briefly explained and applied to fugue. Questionnaire: Students can answer ten questions online. |
| No. 18: g#m | Topics: structure of subject, tritone, modulation, harmonic cycle, wohltemperirt, tonal functions Key concepts: Subject's head exposes a melodic tritone above tonic, modulation to dominant results; subject's tail implies tritone between predominant and dominant; tonic- predominant-dominant-tonic cycle explained and related to the Canon super Fa Mi (BWV 1078); explanation of well-tempered intonation; includes Index of Harmonic Variations Questionnaire: Students can answer ten questions online. |
| No. 19: A | Topics: double fugue, imbrications of motive, Dante, Milton Key concepts: Double fugue's disjunct subject developed by imbrications of motives; stepwise 2nd subject flies; etymology of fugue considered in Divine Comedy and Paradise Lost. Questionnaire: Students can answer ten questions online. |
| No. 20: am | Topics: melodic inversion, stretto, canon, counterexposition, design, Gerhardt Niedt, Lutheranism, Bach symbols, S.D.G. and J.N.J. Key concepts: Longest fugue in WTC I has the most iterations of subject, half inverted; symbolism of 14 canonic stretti; fugue compared to kinetic sculpture; theological implications of purposefulness and design; Soli Deo Gloria after WTC I |
| No. 21: Bb | Topics: permutation fugue, countersubject, pattern & metapattern Key concepts: Contrapuntal texture with two countersubjects inverted in a pattern with one anomaly; rotation of polyphonic voices; fugue likened to Amish quilt, poetry, and folk art. Interpretation: Korevaar performance notes included. |
| No. 22: bbm | Prelude: streaming audio link Topics: hyperstretto, stile antico counterpoint, Fux Key concepts: Second of two fugues for five voices in the stile antico; counterpoint likened to choreography by Balanchine; Fux Gradus; dramatic leap (9th), largest of any subject; 2nd of three instance of the BACH motive in WTC Book I. Theories about the affective connotation of b-flat minor. |
| No. 23: B | Topics: melodic inversion, tonal and modal variation, invertible counterpoint, Affekt, Monet Key concepts: Fugue is like Monet series paintings of poplars; techniques that unite composition and painting. Questionnaire: Students can answer ten questions online. |
| No. 24: bm | Prelude: streaming audio link Topics: chromaticism, Lutheranism, chiasmus, Cranach, passion music Key concepts: Most chromatic of subjects in WTC employs twelve tones; outlines three crosses; 25 iterations of BACH motive; intertextual associations of passion music with Weimar painting by Lucas Cranach the Elder; motivic connotations of prelude. |
| Book II | Contents |
Topics: structure of subject/countersubject, sequence, Voyager spacecraft, Carl Sagan |
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| No. 2: cm | Topics: structure of subject, stretto, augmentation, melodic inversion, retrogradation Key concepts: Second half of subject retrogrades contour of first half; improvisatory character of fugue likened to migrating geese. |
Topics: Hofstadter's Gödel Escher Bach, Polanyi |
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Topics: Metalanguage, Metacognition, Metaphor, and Metamorphosis |
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| No. 5: D | Topics: Stockhausen, Adorno, Cage, universals, nominalism Key concepts: Subject borrows rhythm and melody from canzona; "naturally" lends itself to stretto; tail motive consumes 3/4 of fugue; plagal exposition; perception of exposition in the "right" key; tonal "perspective"; Bach's music realistic vs. nominalistic; modern commitment to nominalism exemplified in Cage and Adorno; conclusion of nominalism in Stockhausen and World Trade Center tragedy. |
| No. 6: dm | Topics: rhetoric, word painting Key concepts: Bach's conception of fugue as rhetoric; fugal invention; Aristotle's topoi, Mattheson's loci topici; exposition equivalent to thesis; development involves antithesis; connotations of specific word paintings including the lamento; Affekt and the relationship of (Prout's) words to music. Questionnaire: Students can answer ten questions online. |
| No. 7: Eb | Topics: Nietzsche, Wagner, philosophy, nihilism, St. Matthew Passion Key concepts: Mendelssohn's revival of the St. Matthew Passion stimulates interest in Bach's music; Schumann and the Bach Gesellschaft; 19th century reception of Bach as "healing force"; compared with Wagner; Nietzsche's nihilism, friendship with Wagner, and 1878 criticism of Bach in Aphorism 149, Human, All-Too-Human. Questionnaire: Students can answer ten questions online. |
| No. 8: d#m | Topics: Scheibe, Mattheson, rhetoric, word painting Key concepts: Scheibe's criticism of Bach's music and Mattheson's challenge; Bach responds by demonstrating mastery of musical rhetorical techniques: gradation, paronomasia, peroration, tmesis, and antithesis; implications of canzona rhythm, suspiratio, and chiastic motives as word paintings; discussion of rhetorical "meaning"; fugue compared with BWV 4. |
| No. 9: E | Topics: wave theory, quantum mechanics Key concept: fugue is like a wave Fugue has three subjects plus a countersubject; counterexposition treats subject and countersubject separately, in stretto; perceptual challenge of this type of fugue to maintain distinction between motives; fugue likened to waves of all kinds: ocean, sound, light, electromagnetic; review of quantum physics from Niels Bohr and Werner Heisenberg; Bohr contra Einstein debates; contemporary revolution in physics; Carver Mead's Collective Electrodynamics; fugue as intelligent design; the "Uncreated Wave" |
| No. 10: em | Not yet available |
| No. 11: F | Not yet available |
| No. 12: fm | Topic: reconstruction of Bach's likeness by forensic anthropologists at the University of Dundee, Scotland Key concept: surreal comparison of fugal composition and analysis to forensic reconstruction, with analogies to Lamarckian Darwinism. Critique of scientific methods vs. humanistic ways of understanding what is "authentic" and "real." Questionnaire: Students can answer ten questions online. |
| No. 13: F# | Topics: time, tempo, perception of time, definition of time Key concepts: Fugal time is neither circular nor linear, but epochal and spiraled. Meaning in the fugue is dependent upon relationships between the past, present, and future. The intensity of conscious cognitive processing required in listening to a fugue protracts (and compresses) the passage of time: the fugal future is in its past, and its past is in its future. |
| No. 14: f#m | Topics: Lutheranism, chiasmus, lamento, triple fugue, Bach symbols, melodic inversion, passion music Key concepts: definitive triple fugue of the cycle; two of its subjects borrowed from earlier works in the WTC; each subject receives its own exposition, followed by development with subjects prior to it; third of three "passion fugues" contains many symbols, both of the composer and his faith. |
| No. 15: G | Topics: absolute expressionism, modern art, Kandinsky, Schoenberg Key concepts: Kandinsky's 1914 painting, Fuga, provides occasion to explore the aesthetic ideal of expressionism and the historical roots of modern art, both in reaction to impressionism and as a continuation of the western aesthetic. Bach's legacy to Schoenberg and Kandinsky can be found in the principle of affect coupled with motivic development and economy of means. The spiritual quest of each artist also finds "expression" in his unique style and medium. |
| No. 16: gm | Topics: Grand Canyon, geology, double counterpoint Key concepts: The fugue's subject and countersubject are heard in its various "voices." This analysis is primarily concerned with how the composer notates fugal voices so that they can be aurally and visually distinguished from each other. Analogy is made to the sedimentary layers of Grand Canyon, Arizona, with many allusions to its geology and history. This particular fugue is famous for its double counterpoint at the octave, 10th, and 12th--structures that are illustrated and explained. Questionnaire: Students can answer ten questions online. |
| No. 17: Ab | Not yet available |
| No. 18: g#m | Topics: Bach's Bible, Calov, Frederick the Great, Musical Offering, Enlightenment Key concept: Bach's commitment to the preaching purpose of music. The narrative begins with Bach in the Weimar jail, by some counts beginning his composition of the Well-Tempered Clavier, and ends with his 1747 encounter with Frederick the Great. The discussion is threaded with references to Bach's many underlinings and annotations in the Calov Bible. His Lutheran understanding of music's purpose is contrasted with the galant style preferred by Frederick, as well as the philosophical assumptions of Aufklärung and what would come to be known as the Enlightenment. |
| No. 19: A | Topics: Architecture, Christopher Alexander, Milton Babbitt Key concepts: Art = beauty, beauty = life, life = relationships. This aesthetic philosophy, articulated by Berkeley professor of architecture in The Nature of Order, is applied to the fugue and contrasted with Milton Babbitt's article, "Who Cares if You Listen?" |
| No. 20: am | Topics: Humor in music, self-similar structures, matryoshka doll Key concepts: Dr. Ledbetter offers three reasons why this fugue should be interpreted as parody. Nevertheless, there are some serious ideas here, mainly in the self-similar contours and rhythms of the subject's head and tail. The fugue likened to a Russian "babushka" doll. |
| No. 21: Bb | Topics: Invariance, Permutation, Syllogism, Plato and Meno's Square Key concepts: The brilliance of Bach's fugues lies in his understanding of process and invention. Unlike "book fugues" that mimic form, Bach understood that the fugal complex must have the capacity to generate new material from old. In this fugue Bach interrupted a process of permutation. The analysis asks why, concluding with analogies from astronomy, philosophy, and the words of C. S. Lewis |
| No. 22: bbm | Topics: Schweitzer, Sartre, Nietzsche Key concepts: This fugue, the most logocentric of the cycle, provides an opportunity to compare theistic and atheistic existentialism, as exemplified in the writings of Bach biographer/editor/performer, Albert Schweitzer, and his cousin, Jean-Paul Sartre. Thematically, the analysis focuses on the Stoic concept of logos and its etymological derivatives. The logos of Bach's counterpoint demands recognition as purposeful and meaningful, not merely a display of contrapuntal process. Questionnaire: Students can answer ten questions online. |
| No. 23: B | Topics: Triads, Tonality, Trinitarianism Key concepts: Bach's music is the way it is because other things are the way they are. The power of Bach's music is proportional to the power of those other things. This fugue gives opportunity to consider how Trinitarian dogma has shaped musical structure. There is a brief discussion of the changing attitudes toward musical meaning and purpose during Bach's lifetime. This is contextualized in the dispute between Buttstett (representing the cantoral tradition) and Mattheson (representing the Enlightenment view). |
| No. 24: bm | Topics: Dance, Relationship of the bm fugues |