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E-raamat: Let's Calculate Bach: Applying Information Theory and Statistics to Numbers in Music

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Let's Calculate Bach: Applying Information Theory and Statistics to Numbers in MusicSuurem pilt
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This book shows how information theory, probability, statistics, mathematics and personal computers can be applied to the exploration of numbers and proportions in music. It brings the methods of scientific and quantitative thinking to questions like: What are the ways of encoding a message in music and how can we be sure of the correct decoding? How do claims of names hidden in the notes of a score stand up to scientific analysis? How many ways are there of obtaining proportions and are they due to chance?

After thoroughly exploring the ways of encoding information in music, the ambiguities of numerical alphabets and the words to be found “hidden” in a score, the book presents a novel way of exploring the proportions in a composition with a purpose-built computer program and gives example results from the application of the techniques. These include information theory, combinatorics, probability, hypothesis testing, Monte Carlo simulation and Bayesian networks, presented in an easily understandable form including their development from ancient history through the life and times of J. S. Bach, making connections between science, philosophy, art, architecture, particle physics, calculating machines and artificial intelligence. For the practitioner the book points out the pitfalls of various psychological fallacies and biases and includes succinct points of guidance for anyone involved in this type of research.

This book will be useful to anyone who intends to use a scientific approach to the humanities, particularly music, and will appeal to anyone who is interested in the intersection between the arts and science.

With a foreword by Ruth Tatlow (Uppsala University), award winning author of Bach’s Numbers: Compositional Proportion and Significance and Bach and the Riddle of the Number Alphabet

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“With this study Alan Shepherd opens a much-needed examination of the wide range of mathematical claims that have been made about J. S. Bach's music, offering both tools and methodological cautions with the potential to help clarify old problems.”
Daniel R. Melamed, Professor of Music in Musicology, Indiana University

 

1 Introduction
1(6)
1.1 The Science of Musicology
1(1)
1.2 Numerology and Bach
2(1)
1.3 About This Book
3(4)
2 An Information Theory Approach
7(12)
2.1 Information and Communication
7(1)
2.2 Measuring Information---The Bit
8(1)
2.3 The Bit as Binary Digit
9(1)
2.4 Signal, Noise, Redundancy and Encoding
9(2)
2.5 Messages and Symbols
11(2)
2.6 Throughput and Protocols
13(1)
2.7 Gematria as Hash Coding
13(2)
2.8 An Unambiguous Coding
15(1)
2.9 Codings and References
16(3)
3 Some Possible Codings in Music
19(20)
3.1 Preamble
19(1)
3.2 Number of Bars
20(1)
3.3 Notes
21(1)
3.4 Intervals
22(1)
3.5 Note Lengths
22(1)
3.6 Number of Notes
23(1)
3.7 Number of Pieces, Movements or Sections
24(1)
3.8 Sum of the G-Values of Notes
25(1)
3.9 Key Signature
25(2)
3.10 Accidentals
27(1)
3.11 Occurrences of Words
27(1)
3.12 Rests
27(1)
3.13 Time Signature
28(1)
3.14 Figured Bass
29(1)
3.15 Entries of a Theme
29(1)
3.16 Other Possibilities
29(2)
3.16.1 Acrostics
29(1)
3.16.2 More Subtle Ways
30(1)
3.17 Beyond Bach
31(3)
3.17.1 BWV Numbers
31(1)
3.17.2 Frequencies
31(1)
3.17.3 Morse Code
31(1)
3.17.4 Colours and Shapes
32(1)
3.17.5 Other Puzzles
33(1)
3.18 Combined Codings
34(1)
3.19 A Cryptographic Example
34(1)
3.20 Summary
35(1)
3.21 The Real Coding
36(2)
3.22 Notes for Researchers
38(1)
4 Ambiguity in Decoding
39(12)
4.1 Preamble
39(1)
4.2 Sources
40(1)
4.3 Modern Dictionary
40(4)
4.3.1 Method
40(1)
4.3.2 Modern Dictionary with Latin Natural Coding
41(1)
4.3.3 Modern Dictionary with Latin Milesian and Trigonal Coding
42(2)
4.4 Historic Sources
44(2)
4.4.1 Luther Bible
44(1)
4.4.2 Cantata Texts
45(1)
4.4.3 Combining Historic Sources
45(1)
4.5 Summary
46(3)
4.6 Notes for Researchers
49(2)
5 Multiple Words and Partitioning
51(6)
5.1 Partitioning and Permutations
51(1)
5.2 Partitioning G-Values
52(3)
5.3 Composers' Names
55(1)
5.4 Notes for Researchers
55(2)
6 Score Analysis
57(16)
6.1 The Method
57(3)
6.2 Counting Bars
60(5)
6.3 Statistics
65(2)
6.4 Further Applications
67(3)
6.5 Summary
70(1)
6.6 Other Representations and Tools
71(1)
6.7 Notes for Researchers
72(1)
7 Statistical Methods
73(14)
7.1 Preamble
73(1)
7.2 Probability and Distributions
74(3)
7.3 Hypothesis Testing and Significance
77(2)
7.4 Confidence Interval
79(1)
7.5 Monte Carlo Simulation
80(2)
7.6 Bayes Theorem
82(3)
7.7 Notes for Researchers
85(2)
8 Exploring Proportions
87(30)
8.1 Preamble
87(6)
8.2 Simple Proportions and Terminology
93(7)
8.2.1 Sets and Pieces
93(1)
8.2.2 Proportion
94(1)
8.2.3 Combinations
95(2)
8.2.4 Solutions, Targets, Opposites and Complements
97(1)
8.2.5 Symmetries, Signatures and Patterns
98(1)
8.2.6 Binary Signatures
99(1)
8.3 Layers of Proportion
100(2)
8.4 Summary of Terms
102(1)
8.5 The Proportional Parallelism Explorer Program
103(14)
8.5.1 Solution Search
103(4)
8.5.2 Solutions Search Through Layers
107(1)
8.5.3 Pattern Matching
107(3)
8.5.4 Pattern Matching in Layers
110(1)
8.5.5 Colour Coding for Visual Pattern Recognition
111(1)
8.5.6 Monte Carlo Simulation
111(6)
9 Applying the Methods to the Well Tempered Clavier Book 1 BWV 846--869
117(36)
9.1 Preamble
117(1)
9.2 Solutions
117(1)
9.3 Probability
118(5)
9.4 Monte Carlo Simulation
123(4)
9.5 Hypothesis Testing and Significance
127(1)
9.6 Bayes Theorem
128(5)
9.7 Patterns
133(8)
9.8 Preludes and Fugues Separately
141(8)
9.9 Ariadne Musica
149(4)
10 Consolidated Observations
153(52)
10.1 Preamble
153(1)
10.2 The Effect of the Number of Pieces
153(14)
10.3 Works Which Could Have More Than One Layer
167(1)
10.4 Probability
167(5)
10.5 Types of Distribution
172(2)
10.6 Real Works Versus Single-Layer Simulations
174(5)
10.7 Accuracy
179(2)
10.8 Proportions and Other Structures
181(1)
10.9 Proportions in Durations
182(3)
10.10 Works with No Proportions
185(1)
10.11 The Impossible Proportions
185(1)
10.12 Reverse Engineering and the Art of Fugue BWV 1080
186(4)
10.13 Combining Works
190(6)
10.14 Summary of Main Statistics
196(7)
10.15 Notes for Researchers
203(2)
11 Magic Squares
205(8)
11.1 The Dieben Rectangle
205(7)
11.1.1 Deriving Proportions from Dieben's Rectangle
209(3)
11.2 Use by Modern Composers
212(1)
12 Psychological Fallacies
213(4)
12.1 Preamble
213(1)
12.2 Story Bias or Narrative Fallacy
213(1)
12.3 Confirmation Bias
214(1)
12.4 Neglect of Probability
214(1)
12.5 Halo Effect
215(1)
12.6 Conjunction Fallacy
216(1)
12.7 Notes for Researchers
216(1)
13 Bach, Science and Technology
217(16)
13.1 Mathematics and Philosophy in Bach's Time
217(3)
13.2 Models
220(6)
13.3 Computers
226(2)
13.4 Artificial Intelligence
228(2)
13.5 Quantz and Hi-Fi
230(1)
13.6 Summary
231(2)
14 Conclusion
233(2)
Appendix A More Parallel Proportion Results 235(48)
Appendix B Proportional Parallelism Explorer Program User Manual 283(36)
Appendix C Tabular History 319(4)
Appendix D Alphabet Tables 323(2)
Appendix E Interval Proportions 325(2)
Appendix F Excel Functions 327(4)
Literature 331(8)
General Index 339(10)
Index of Names 349
Alan Shepherd obtained a degree in electrical engineering and electronics from Brunel University, UK and has had a successful career as a computer programmer and IT management and governance professional. In retirement he has returned to one of his spare time interests, the music of J.S. Bach, to bring his technological and scientific knowledge to the exploration of numbers in music.
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