## 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. |

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### Contents

Introduction | 1 |

Inversionally Complementary Cycles | 5 |

Symmetrical Chords and Progressions 1 o 4 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 |

g Difference Tables | 29 |

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 |

77i Master Keys | 95 |

Composing With Sum Tetrachords | 107 |

Modulation Through Tonic Cyclic Chords and Tonic Sum Tetrachords 12 3 | 120 |

Composing With 12Tone Modes | 31 |

The Odd and Even Modes | 43 |

Sum Tables | 45 |

Tonic and Resultant Set Forms | 47 |

Sum Tetrachords | 51 |

77 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 |

173 | |

174 | |

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### Common terms and phrases

adjacency sums axis dyads axis notes axis of symmetry axis-dyad chords axis-dyad sum axis-interval bars Berg's cell column component cyclic intervals derived set forms Diff difference scales difference-scale dyadic array dyadic sums dyads of sum elements equivalent example 20 George Perle given hexachords intersect interval cycles interval system interval-7 inversion 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 semi-equivalent array semitonal scale set complex shift slide-rule Sum 9 sum array sum of complementation sum table sum tetrachords sum-scales Sums and Intervals symmetrically related tetrachordal segments tetrachordal sum thematic idea tion tonal tone row tonic cyclic chords tonic derived set tonic set forms tonic sum tonic sum-tetrachords transposed tritone transposition twelve-tone unfold whole-tone Wozzeck