Welcome to


Journey to the Heart of Music

(fourth revised edition)


Picture of Cover



Table of Contents

Chapter 00 Preface and Introduction 14 pages
Meter - X
Synopsis - XI
Acknowledgements - XII
Notes - XII
Chapter 01 The Heart of the Matter -- Harmony and Mutable Numbers 32 pages
Positional Notation - 01.2
The Harmonic Series - 01.6
Oscillation and Numbers - 01.8
Number Patterns - 01.11
Mutable Base Numbers - 01.13
Multiple Digit Sequences - 01.17
The Minor Chord - 01.22
Prelude No.1 - J. S. Bach - 01.23
Conclusions - 01.28
Chapter 02 The Piano Tuner's Tale -- Scales and Keys 24 pages
Graphs - 02.1
Scales - 02.7
Tonal Centers (Keys) - 02.13
The Language of Music - 02.20
Chapter 03 Numbers in the Material World -- Computation, Information and Entropy 24 pages
Information and Structure - 03.2
Algorithms and Computation - 03.12
Mutable Numbers, Energy and Entropy - 03.19
Chapter 04 Three Domains of Music? -- Pitch, Duration and Timbre 24 pages
Domain of Pitch - 04.3
Domain of Duration - 04.11
Domain of Timbre - 04.18
Chapter 05 Little Worlds -- Algorithms and Nested Patterns 22 pages
New Perspectives - 05.8
Chapter 06 The Full Cadence -- The Algorithm of Symmetrical Exchange 16 pages
Beyond the Full Cadence - 06.12
Chapter 07 Nested Harmonic Series -- The Format of Computation 26 pages
Patterns in the Table of Harmonic Series - 07.7
Primes, Factors and Divisors - 07.18
Chapter 08 The Tonal Era -- A Short History of Music and Music Theory 28 pages
Medieval Period 08.5
Renaissance - 08.8
Baroque Period - 08.10
Classical Style - 08.16
Romantic Period - 08.18
Twentieth Century - 08.23
Chapter 09 Identity and Change -- Modulating Oscillatory Systems 30 pages
Table of Harmonic Series - 09.3
Modulation, Meter and Time Signatures - 09.17
The Integration of Major and Minor - 09.22
Conclusions - 09.28
Chapter 10 Chords and Meters -- Numbers in Music 32 pages
Chords of the Augmented and Neapolitan Sixth - 10.12
Chord Progression - 10.23
Meters - 10.25
Chapter 11 The Minor Mode -- Dualism and the Root of the Minor Triad 28 pages
The Perception of Tonal Music - 11.8
Aggregation and the Minor Triad - 11.13
Chapter 12 Prelude by J.S.Bach -- MOS/MBN Examples 18 pages
Mutable Number Digit Sequences - 12.9
Prelude No.1 in C major - 12.10
Mozart Piano Sonata K545 - 12.12
Chapter 13 Mathematical Miscellany -- Geometry, Symmetry and Computation 32 pages
The Union of Pitch and Duration - 13.5
Sets, Groups and Mutable Numbers - 13.12
Computation with Mutable Numbers - 13.25
Study: The Divisors of Seventy-two - 13.29
Chapter 14 Reflection -- Harmonic Inversion 24 pages
Integrating the Arithmetic Principle into Traditional Harmony - 14.11
Symmetry and Negative Numbers - 14.20
Chapter 15 Wider Horizons -- From Particles to Planets 28 pages
Elements of Music? - 15.9
Conclusion - 15.24
Appendix A Music Theory Toolkit 12 pages
Harmonic Analysis - 16.7
Appendix B Fractional Mutable Base Numbers 06 pages
Appendix C Glossary 12 pages
Appendix D Examples, AWK Scripts, Cellular Automata, etc... 33 files, zipped
Appendix E Quick Start Outline 18 pages
Appendix F Introduction to the MOS Examples 28 pages
Guide to Constructing a MOS Analysis - 21.4
Index
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13 pages
Examples of Reflection
Example A Air from 'Giulio Cesare' - G.F.Handel -- Score and MIDI file 06 pages
Example B Gavotte - Jean-Philippe Rameau -- Score and MIDI file 04 pages
Example C Gavotte - H. Thornowitz -- Score and MIDI file 09 pages
Example D Fugue VII, Book II - J.S.Bach -- Score and MIDI file 06 pages
Example E La Follia - A. Corelli -- Score and MIDI file 56 pages
Example F Ricecar dopo il Credo - G. Frescobaldi -- Score and MIDI file 06 pages
Examples of MOS/Mutable Number Analysis
Introduction Guide to the MOS Examples 04 pages
Example G Prelude No.3, Op28 - F. Chopin -- Score and Analysis 17 pages
Example H Chanson: Adieu m'amour et ma Maistresse - G. Binchois -- S & A 08 pages
Example I Chorale: Christus, der ist mein Leben - J.S. Bach -- Score and Analysis 06 pages
Example J Intermezzo, Op119, No.3 - J. Brahms -- Score and Analysis 20 pages
Example K Waldstein Sonata, Op53 - L. van Beethoven -- Score and Analysis 33 pages
Example L Motet: Ave Maria - Josquin des Prez -- Score and Analysis 06 pages
Example M Courante - Johann Jakob Froberger -- Score and Analysis 10 pages
Example N Heinrich Schenker's Ursatz Reduction of Prelude No.1 - J. S. Bach 02 pages
Example O Study based on Prelude No.1 in C by J. S. Bach -- Score and MIDI file 06 pages
Example P The II-V-I Cadence 17 pages
Example Q Cadences in the MOS Model 23 pages
Example R Study: The Divisors of Seventy-Two 16 pages
Example R2 Rondo: The Divisors of Seventy-Two -- Score and MIDI file 07 pages
Example S MOS/MBN Analysis: Prelude No.1 by J.S. Bach 18 pages
Example S2 Computer Generated MOS/MBN Analyses: Prelude No.1 by J.S. Bach 40 pages
Example T Chorale: Ach Gott und Herr - J.S. Bach -- Score and Analysis 09 pages
Example T2 Computer Generated MOS/MBN Analysis: Ach Gott und Herr - J.S. Bach 10 pages