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This study deals with the processes of tonal counterpoint inherent in the songs of Schoenberg's Opus 15i "Book of the Hanging Gardens" and, by implication, in related works. Chapter I, "The Concept of Harmonic Voice", introduces the conceptual key to the manner of investigation presented herein. Simply stated, "harmonic voices" consist of the strongly-directed, predictable motions by semitone and whole-tone, and the common-tone connections which occur from one chord to the next in a tonal progression. Examples of strongly-directed motions are the rising of the leading-tone and falling of the minor seventh of a dominant-seventh chord, and the diverging motions present when an augmented sixth progresses to an octave on the dominant. To show how the harmonic voice concept may be applied in analysis, passages from Opus 6, Number k are examined. Chapter II, "Harmonic Procedures Which Minimize Diatonic-Chromatic Differences", deals with specific types of harmonic voice motion which are common to chromatic passages and simpler, more overtly tonal ones. The lack of importance which the harmonic voice concept attributes to the presence or absence of the root of a chord is emphasized. The harmonic procedures discussed come under the following subject headings: "The Tritone-Substitute", "The Minor-Seventh/Augmented-Sixth Potential of 'Whole-tone' Chords", "Double-Neighbor Pairs in 'Whole-tone' and Other Contexts", "The Minor-Third Relationship", and "The Minor-Second Relationship". Passages from songs of Opus 3i 6, 12, and 14 are analyzed. Chapter III is a detailed analysis of Opus 1$, Number 5$ which applies the harmonic voice concept and attempts to expose the harmonic devices dealt with in Chapter II. Chapter IV is a detailed analysis of Opus 15, Number 11. / Arts, Faculty of / Music, School of / Graduate

Issued also as inaugural dissertation, Basel. / "Notenbeispiele": 20 p. at end. "Literaturverzeichnis": p. 161-163.

Issued also as inaugural dissertation, Basel. / "Notenbeispiele": 20 p. at end. "Literaturverzeichnis": p. 161-163.

No description available.

The literature about the unfinished ending of J S Bach’s The Art of Fugue (Die Kunst der Fuga) BWV 1080 is in universal agreement that the work remained unfinished at Bach’s death; some texts go a step further to say that it is unfinished because he died. After giving a series of performances of the work, the author became convinced that this latter view must be incorrect, and that Bach left the work unfinished deliberately. This thesis explores this idea in detail and, by presenting a number of new theories, suggests not only that Bach left the work unfinished deliberately as an invitation to the reader, student or performer to work out his or her own completion, but also that he left a number of clues, hidden to a greater or lesser extent, to indicate that that was his intention and to supply vital information about the content of the missing bars. Divided into two parts, the thesis first considers some of the evidence contained within the manuscript itself, up to and including the final written bar, and then in the second part goes on to consider two essential aspects of the completion. By way of introduction, the first chapter surveys the controversial area of Bach’s use of numbers in his music and draws attention to the number of the final bar, which can be interpreted as a clue to the fact that Bach expects the music to be continued. Chapter Two invites a reconsideration of Christoph Wolff’s famous “Fragment X” theory, which suggests that the continuation of the final fugue was written on a separate, now lost, piece of paper. Many inconsistencies and details in the manuscript suggest strongly that Wolff’s theory is incorrect. As part of this theory, the author reports on his own examination of the original manuscript in Berlin. Chapter Three, through a detailed study of the architecture of the final fugue, makes the bold claim that the author has definitively proved the exact number of bars required to complete the music in accordance with Bach’s intentions: this theory develops and refines the work of Gregory Butler in this area, and, to corroborate the theory, presents a possible interpretation of the unusual markings at the end of Bach’s score and of a significant correction made by Bach in his manuscript. Finally, in Chapter Four, the question of the proposed inverted combination of all four fugue subjects is revisited – a combination that several writers have claimed to be impossible – and a new and convincing solution to this problem is presented and justified.

The literature about the unfinished ending of J S Bach’s The Art of Fugue (Die Kunst der Fuga) BWV 1080 is in universal agreement that the work remained unfinished at Bach’s death; some texts go a step further to say that it is unfinished because he died. After giving a series of performances of the work, the author became convinced that this latter view must be incorrect, and that Bach left the work unfinished deliberately. This thesis explores this idea in detail and, by presenting a number of new theories, suggests not only that Bach left the work unfinished deliberately as an invitation to the reader, student or performer to work out his or her own completion, but also that he left a number of clues, hidden to a greater or lesser extent, to indicate that that was his intention and to supply vital information about the content of the missing bars. Divided into two parts, the thesis first considers some of the evidence contained within the manuscript itself, up to and including the final written bar, and then in the second part goes on to consider two essential aspects of the completion. By way of introduction, the first chapter surveys the controversial area of Bach’s use of numbers in his music and draws attention to the number of the final bar, which can be interpreted as a clue to the fact that Bach expects the music to be continued. Chapter Two invites a reconsideration of Christoph Wolff’s famous “Fragment X” theory, which suggests that the continuation of the final fugue was written on a separate, now lost, piece of paper. Many inconsistencies and details in the manuscript suggest strongly that Wolff’s theory is incorrect. As part of this theory, the author reports on his own examination of the original manuscript in Berlin. Chapter Three, through a detailed study of the architecture of the final fugue, makes the bold claim that the author has definitively proved the exact number of bars required to complete the music in accordance with Bach’s intentions: this theory develops and refines the work of Gregory Butler in this area, and, to corroborate the theory, presents a possible interpretation of the unusual markings at the end of Bach’s score and of a significant correction made by Bach in his manuscript. Finally, in Chapter Four, the question of the proposed inverted combination of all four fugue subjects is revisited – a combination that several writers have claimed to be impossible – and a new and convincing solution to this problem is presented and justified.

The literature about the unfinished ending of J S Bach’s The Art of Fugue (Die Kunst der Fuga) BWV 1080 is in universal agreement that the work remained unfinished at Bach’s death; some texts go a step further to say that it is unfinished because he died. After giving a series of performances of the work, the author became convinced that this latter view must be incorrect, and that Bach left the work unfinished deliberately. This thesis explores this idea in detail and, by presenting a number of new theories, suggests not only that Bach left the work unfinished deliberately as an invitation to the reader, student or performer to work out his or her own completion, but also that he left a number of clues, hidden to a greater or lesser extent, to indicate that that was his intention and to supply vital information about the content of the missing bars. Divided into two parts, the thesis first considers some of the evidence contained within the manuscript itself, up to and including the final written bar, and then in the second part goes on to consider two essential aspects of the completion. By way of introduction, the first chapter surveys the controversial area of Bach’s use of numbers in his music and draws attention to the number of the final bar, which can be interpreted as a clue to the fact that Bach expects the music to be continued. Chapter Two invites a reconsideration of Christoph Wolff’s famous “Fragment X” theory, which suggests that the continuation of the final fugue was written on a separate, now lost, piece of paper. Many inconsistencies and details in the manuscript suggest strongly that Wolff’s theory is incorrect. As part of this theory, the author reports on his own examination of the original manuscript in Berlin. Chapter Three, through a detailed study of the architecture of the final fugue, makes the bold claim that the author has definitively proved the exact number of bars required to complete the music in accordance with Bach’s intentions: this theory develops and refines the work of Gregory Butler in this area, and, to corroborate the theory, presents a possible interpretation of the unusual markings at the end of Bach’s score and of a significant correction made by Bach in his manuscript. Finally, in Chapter Four, the question of the proposed inverted combination of all four fugue subjects is revisited – a combination that several writers have claimed to be impossible – and a new and convincing solution to this problem is presented and justified.

The literature about the unfinished ending of J S Bach’s The Art of Fugue (Die Kunst der Fuga) BWV 1080 is in universal agreement that the work remained unfinished at Bach’s death; some texts go a step further to say that it is unfinished because he died. After giving a series of performances of the work, the author became convinced that this latter view must be incorrect, and that Bach left the work unfinished deliberately. This thesis explores this idea in detail and, by presenting a number of new theories, suggests not only that Bach left the work unfinished deliberately as an invitation to the reader, student or performer to work out his or her own completion, but also that he left a number of clues, hidden to a greater or lesser extent, to indicate that that was his intention and to supply vital information about the content of the missing bars. Divided into two parts, the thesis first considers some of the evidence contained within the manuscript itself, up to and including the final written bar, and then in the second part goes on to consider two essential aspects of the completion. By way of introduction, the first chapter surveys the controversial area of Bach’s use of numbers in his music and draws attention to the number of the final bar, which can be interpreted as a clue to the fact that Bach expects the music to be continued. Chapter Two invites a reconsideration of Christoph Wolff’s famous “Fragment X” theory, which suggests that the continuation of the final fugue was written on a separate, now lost, piece of paper. Many inconsistencies and details in the manuscript suggest strongly that Wolff’s theory is incorrect. As part of this theory, the author reports on his own examination of the original manuscript in Berlin. Chapter Three, through a detailed study of the architecture of the final fugue, makes the bold claim that the author has definitively proved the exact number of bars required to complete the music in accordance with Bach’s intentions: this theory develops and refines the work of Gregory Butler in this area, and, to corroborate the theory, presents a possible interpretation of the unusual markings at the end of Bach’s score and of a significant correction made by Bach in his manuscript. Finally, in Chapter Four, the question of the proposed inverted combination of all four fugue subjects is revisited – a combination that several writers have claimed to be impossible – and a new and convincing solution to this problem is presented and justified.

Thesis (Ph. D.)--Eastman School of Music, University of Rochester, 1965. / Typescript. Vita. Includes bibliographical references (pt. 1, leaves 181-184).