| 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 | -- | 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 | Original 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 S3 | Most Recent MOS/MBN Analysis: Prelude No.1 by J.S. Bach | 26 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 |
| Example U | Bach Chorale: O Jesulein Suss - The Math of Exchange | 18 pages |
| Example V | Chopin: Prelude 20 - Harmonic trends in 19th century | 16 pages |
| Example W | Per non mi dir ch'io moia - M. Rossi, Just Intonation & MBN model | 14 pages |
| Example X | Prelude No.1 - Claude Debussy, Diffuse tonality & MBN model | 27 pages |
| Example Y | Polonaise - A Straightforward Mutable Number Analysis | 9 pages |
| Example Z | the ‘Tristan Chord’ - A Mutable Number Interpretation | 15 pages |
