Twelve-tone TonalityIn this classic work, George Perle argues that the seemingly disparate styles of post-triadic music in fact share common structural elements. These elements collectively imply a new tonality as "natural" and coherent as the major-minor tonality that was the basis of a common musical language in the past. His book describes the foundational assumptions of this post-diatonic tonality and illustrates its compositional functions with numerous musical examples.The second edition of "Twelve-Tone Tonality" is enlarged by eleven new chapters, some of which are "postscripts" to earlier chapters--clarifying, elucidating, and expanding upon concepts discussed in the original edition. Others discuss new developments in the theory and practice of twelve-tone tonality, including voice-leading implications of the system and dissonance treatment. |
Contents
Introduction | 1 |
Inversionally Complementary Cycles | 5 |
Symmetrical Chords and Progressions | 10 |
Dyadic Sums and Differences | 16 |
The Cyclic Set of Interval 7 | 18 |
Cognate Sets | 20 |
Verticalization in TwelveTone Music | 23 |
Cyclic Chords and AxisNote Dyads | 25 |
Derived Sets | 69 |
The Remaining Cyclic Sets | 73 |
Alban Bergs Master Array of the Interval Cycles | 76 |
Sum and Difference Scales | 80 |
The Master Modes | 82 |
The Master Keys | 95 |
Composing With Sum Tetrachords | 107 |
Modulation Through Tonic Cyclic Chords and Tonic Sum Tetrachords | 123 |
Difference Tables | 29 |
Composing With 12Tone Modes | 31 |
The Odd and Even Modes | 43 |
Sum Tables | 45 |
Tonic and Resultant Set Forms | 47 |
Sum Tetrachords | 51 |
The Cyclic Set of Interval 1 | 55 |
Larger Implications of Tonic Set Forms | 59 |
The Interval1 and Interval7 Sets Combined | 65 |
Imitative Counterpoint | 133 |
LargeScale Pregression | 137 |
The Three Tonalities | 143 |
Triadic Arrays | 152 |
Conclusion | 162 |
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Common terms and phrases
adjacency sums axis dyads axis notes axis of symmetry axis-dyad chords axis-interval bars Béla Bartók Berg's cell column component cyclic intervals cyclic set derived set forms Diff difference scales difference-scale dyadic array dyadic sums dyads of sum equivalent example 20 Galaxy Music Corporation given hexachords intersect interval cycles interval numbers interval system interval-7 inversional complementation inversional equivalence inversionally complementary inversionally related Master Mode neighbor-note dyads Opus original array P/I dyads paired set forms paired sum-scales partition perfect fifth Perle pitch level pitch-class number Pop7 precompositional primary sum couple represented respective row forms Schoenberg's secondary interval couple secondary sums semi-equivalent array semitonal scale shift Sum 9 sum array sum of complementation sum scales sum table sum tetrachords symmetrically related tetrachordal segments tetrachordal sum tion tonal tone row tonic cyclic chords tonic derived set tonic set forms tonic sum tonic sum-tetrachords triadic set tritone transposition twelve-tone unfold whole-tone Wozzeck