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Table of Contents
Intro
Foreword
Preface
Acknowledgements
Contents
Abbreviations
List of Figures
List of Tables
1 Introduction
1.1 The Science of Musicology
1.2 Numerology and Bach
1.3 About This Book
2 An Information Theory Approach
2.1 Information and Communication
2.2 Measuring Information-The Bit
2.3 The Bit as Binary Digit
2.4 Signal, Noise, Redundancy and Encoding
2.5 Messages and Symbols
2.6 Throughput and Protocols
2.7 Gematria as Hash Coding
2.8 An Unambiguous Coding
2.9 Codings and References
3 Some Possible Codings in Music
3.1 Preamble
3.2 Number of Bars
3.3 Notes
3.4 Intervals
3.5 Note Lengths
3.6 Number of Notes
3.7 Number of Pieces, Movements or Sections
3.8 Sum of the G-Values of Notes
3.9 Key Signature
3.10 Accidentals
3.11 Occurrences of Words
3.12 Rests
3.13 Time Signature
3.14 Figured Bass
3.15 Entries of a Theme
3.16 Other Possibilities
3.16.1 Acrostics
3.16.2 More Subtle Ways
3.17 Beyond Bach
3.17.1 BWV Numbers
3.17.2 Frequencies
3.17.3 Morse Code
3.17.4 Colours and Shapes
3.17.5 Other Puzzles
3.18 Combined Codings
3.19 A Cryptographic Example
3.20 Summary
3.21 The Real Coding
3.22 Notes for Researchers
4 Ambiguity in Decoding
4.1 Preamble
4.2 Sources
4.3 Modern Dictionary
4.3.1 Method
4.3.2 Modern Dictionary with Latin Natural Coding
4.3.3 Modern Dictionary with Latin Milesian and Trigonal Coding
4.4 Historic Sources
4.4.1 Luther Bible
4.4.2 Cantata Texts
4.4.3 Combining Historic Sources
4.5 Summary
4.6 Notes for Researchers
5 Multiple Words and Partitioning
5.1 Partitioning and Permutations
5.2 Partitioning G-Values
5.3 Composers' Names
5.4 Notes for Researchers
6 Score Analysis
6.1 The Method
6.2 Counting Bars
6.3 Statistics
6.4 Further Applications
6.5 Summary
6.6 Other Representations and Tools
6.7 Notes for Researchers
7 Statistical Methods
7.1 Preamble
7.2 Probability and Distributions
7.3 Hypothesis Testing and Significance
7.4 Confidence Interval
7.5 Monte Carlo Simulation
7.6 Bayes Theorem
7.7 Notes for Researchers
8 Exploring Proportions
8.1 Preamble
8.2 Simple Proportions and Terminology
8.2.1 Sets and Pieces
8.2.2 Proportion
8.2.3 Combinations
8.2.4 Solutions, Targets, Opposites and Complements
8.2.5 Symmetries, Signatures and Patterns
8.2.6 Binary Signatures
8.3 Layers of Proportion
8.4 Summary of Terms
8.5 The Proportional Parallelism Explorer Program
8.5.1 Solution Search
8.5.2 Solutions Search Through Layers
8.5.3 Pattern Matching
8.5.4 Pattern Matching in Layers
8.5.5 Colour Coding for Visual Pattern Recognition
8.5.6 Monte Carlo Simulation
9 Applying the Methods to the Well Tempered Clavier Book 1 BWV 846-869
9.1 Preamble
9.2 Solutions
9.3 Probability
9.4 Monte Carlo Simulation
Foreword
Preface
Acknowledgements
Contents
Abbreviations
List of Figures
List of Tables
1 Introduction
1.1 The Science of Musicology
1.2 Numerology and Bach
1.3 About This Book
2 An Information Theory Approach
2.1 Information and Communication
2.2 Measuring Information-The Bit
2.3 The Bit as Binary Digit
2.4 Signal, Noise, Redundancy and Encoding
2.5 Messages and Symbols
2.6 Throughput and Protocols
2.7 Gematria as Hash Coding
2.8 An Unambiguous Coding
2.9 Codings and References
3 Some Possible Codings in Music
3.1 Preamble
3.2 Number of Bars
3.3 Notes
3.4 Intervals
3.5 Note Lengths
3.6 Number of Notes
3.7 Number of Pieces, Movements or Sections
3.8 Sum of the G-Values of Notes
3.9 Key Signature
3.10 Accidentals
3.11 Occurrences of Words
3.12 Rests
3.13 Time Signature
3.14 Figured Bass
3.15 Entries of a Theme
3.16 Other Possibilities
3.16.1 Acrostics
3.16.2 More Subtle Ways
3.17 Beyond Bach
3.17.1 BWV Numbers
3.17.2 Frequencies
3.17.3 Morse Code
3.17.4 Colours and Shapes
3.17.5 Other Puzzles
3.18 Combined Codings
3.19 A Cryptographic Example
3.20 Summary
3.21 The Real Coding
3.22 Notes for Researchers
4 Ambiguity in Decoding
4.1 Preamble
4.2 Sources
4.3 Modern Dictionary
4.3.1 Method
4.3.2 Modern Dictionary with Latin Natural Coding
4.3.3 Modern Dictionary with Latin Milesian and Trigonal Coding
4.4 Historic Sources
4.4.1 Luther Bible
4.4.2 Cantata Texts
4.4.3 Combining Historic Sources
4.5 Summary
4.6 Notes for Researchers
5 Multiple Words and Partitioning
5.1 Partitioning and Permutations
5.2 Partitioning G-Values
5.3 Composers' Names
5.4 Notes for Researchers
6 Score Analysis
6.1 The Method
6.2 Counting Bars
6.3 Statistics
6.4 Further Applications
6.5 Summary
6.6 Other Representations and Tools
6.7 Notes for Researchers
7 Statistical Methods
7.1 Preamble
7.2 Probability and Distributions
7.3 Hypothesis Testing and Significance
7.4 Confidence Interval
7.5 Monte Carlo Simulation
7.6 Bayes Theorem
7.7 Notes for Researchers
8 Exploring Proportions
8.1 Preamble
8.2 Simple Proportions and Terminology
8.2.1 Sets and Pieces
8.2.2 Proportion
8.2.3 Combinations
8.2.4 Solutions, Targets, Opposites and Complements
8.2.5 Symmetries, Signatures and Patterns
8.2.6 Binary Signatures
8.3 Layers of Proportion
8.4 Summary of Terms
8.5 The Proportional Parallelism Explorer Program
8.5.1 Solution Search
8.5.2 Solutions Search Through Layers
8.5.3 Pattern Matching
8.5.4 Pattern Matching in Layers
8.5.5 Colour Coding for Visual Pattern Recognition
8.5.6 Monte Carlo Simulation
9 Applying the Methods to the Well Tempered Clavier Book 1 BWV 846-869
9.1 Preamble
9.2 Solutions
9.3 Probability
9.4 Monte Carlo Simulation