Let's calculate Bach : applying information theory and statistics to numbers in music / Alan Shepherd.

Format:

Book

Author/Creator:

Shepherd, Alan, author.

Series:

Quantitative methods in the humanities and social sciences.

Quantitative methods in the humanities and social sciences

Language:

English

Subjects (All):

Bach, Johann Sebastian, 1685-1750.

Bach, Johann Sebastian.

Physical Description:

1 online resource (372 pages)

Place of Publication:

Cham, Switzerland : Springer, [2021]

Summary:

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 . "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

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

9.5 Hypothesis Testing and Significance

9.6 Bayes Theorem

9.7 Patterns

9.8 Preludes and Fugues Separately

9.9 Ariadne Musica

10 Consolidated Observations

10.1 Preamble

10.2 The Effect of the Number of Pieces

10.3 Works Which Could Have More Than One Layer

10.4 Probability

10.5 Types of Distribution

10.6 Real Works Versus Single-Layer Simulations

10.7 Accuracy

10.8 Proportions and Other Structures

10.9 Proportions in Durations

10.10 Works with No Proportions

10.11 The Impossible Proportions

10.12 Reverse Engineering and the Art of Fugue BWV 1080

10.13 Combining Works

10.14 Summary of Main Statistics

10.15 Notes for Researchers

11 Magic Squares

11.1 The Dieben Rectangle.

11.1.1 Deriving Proportions from Dieben's Rectangle

11.2 Use by Modern Composers

12 Psychological Fallacies

12.1 Preamble

12.2 Story Bias or Narrative Fallacy

12.3 Confirmation Bias

12.4 Neglect of Probability

12.5 Halo Effect

12.6 Conjunction Fallacy

12.7 Notes for Researchers

13 Bach, Science and Technology

13.1 Mathematics and Philosophy in Bach's Time

13.2 Models

13.3 Computers

13.4 Artificial Intelligence

13.5 Quantz and Hi-Fi

13.6 Summary

14 Conclusion

Appendix A More Parallel Proportion Results

A.1 Preamble

A.2 Mass in B Minor BWV 232

A.3 Brandenburg Concertos BWV 1046-1051

A.4 Canonic Variations on "vom Himmel Hoch" BWV 769

A.5 Cello Suites BWV 1007-1012

A.6 Clavierübung I-Partitas BWV 825-830

A.7 Clavierübung II-Italian Concerto BWV 831 and French Overture BWV 971

A.8 Clavierübung III-Organ Mass BWV 669-689, 552, 802-805

A.9 English Suites BWV 806-811

A.10 French Suites BWV 812-817

A.11 Goldberg Variations BWV 988

A.12 Great Fifteen Organ Preludes BWV 651-665

A.13 Inventions and Sinfonias BWV 772-801

A.14 Musical Offering BWV 1079

A.15 Schübler Chorales BWV 645-650

A.16 Sei Soli for Violin BWV 1001-1006

A.17 Transcribed Concertos BWV 972-980, 592, 981-982

A.18 Trio Sonatas for Organ BWV 525-530

A.19 Violin Sonatas BWV 1014-1019

A.20 Well Tempered Clavier Book 1-See Chap. 9

Appendix B Proportional Parallelism Explorer Program User Manual

B.1 Installing the Program

B.1.1 Download

B.1.2 Prerequisite

B.1.3 Caveats

B.1.4 Installing the Program

B.1.5 Removing the Program

B.2 Running the Program

B.2.1 From the Downloaded File

B.2.2 Running the Program from the Command Prompt

B.2.3 Running Multiple Instances

B.2.4 Starter Script

B.2.5 CSV Separator

B.2.6 Mixed Languages

B.2.7 Error Messages.

B.3 File Processing

B.3.1 File Processing Data Flow

B.3.2 Input File-General

B.3.3 Input File-Pieces

B.3.4 Input File-Patterns: Overview

B.3.5 Input File-Patterns: BinaryTemplate

B.3.6 Input File-Patterns: Count

B.3.7 Input File-Patterns: Built in Functions

B.3.8 Solutions Output File

B.3.9 Patterns Output File

B.3.10 File Processing Summary

B.4 Monte Carlo Simulation

B.4.1 Monte Carlo Processing Data Flow

B.4.2 Results Output File

B.4.3 Monte Carlo Summary

B.4.4 Lengths Histogram Output File

B.4.5 Results Histogram Output File

B.5 Further Processing with Other Programs

B.5.1 Import to Excel

B.5.2 Formatting Histograms with Excel

B.5.3 Text Processors

B.6 Main Window

B.7 Program Menu

B.8 Preferences

B.5.4 General Tab

B.5.5 Monte Carlo Tab

B.5.6 Output Tab

B.9 Close

B.10 File Menu

B.11 Open File

B.12 Start from File

B.13 Pause File

B.14 Resume File

B.15 Cancel File

B.16 Monte Carlo Menu

B.17 Start Monte Carlo

B.18 Pause Monte Carlo

B.19 Resume Monte Carlo

B.20 Cancel Monte Carlo

B.21 Help Menu

B.22 Use Cases

B.23 Try Various Proportions

B.24 Try Various Inputs

B.25 Performance

B.26 Large Files

Appendix C Tabular History

Appendix D Alphabet Tables

D.1 Numeric Alphabets

D.2 G-Values for Notes with Sharps and Flats

Appendix E Interval Proportions

Appendix F Excel Functions

F.1 Factors of a Number

F.2 G-Value

Literature

General Index

Index of Names.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

3-030-63769-7

OCLC:

1260344026