Foreword

The following presentation is for anyone curious about the pitch parameter of music (pitch and interval comprehension, just intonation, temperament, microtonality, etc.). It provides background for the H-System, which is the basis for Tonal Plexus keyboards and the MegaScore notation. This presentation is oriented towards seeing and hearing, and requires no previous experience with music theory. Historical information is included only when it is both relevant and logical, and some historical facts are simplified for the sake of clarity. The following basic concepts are assumed to be understood:

• the idea of high and low pitches, derived from the untrained human voice which physically raises and lowers in the throat when producing pitches which we call higher or lower
• whole numbers in counting order, as learned at an early age: 1, 2, 3, 4, etc.
• multiplication and division of whole numbers by 2, stated as fractions or ratios; i.e. 2/1 or 1:2
• the first seven letters of the Latin alphabet, in order: ABCDEFG

This work is dedicated with gratitude and respect to those whose writings have inspired and influenced mine, most notably Harry Partch (Genesis of a Music), Dr. Martin Vogel (On The Relations of Tone), and Dr. Patrick Ozzard-Low (21st Century Orchestral Instruments)  — Aaron Andrew Hunt

Contents

    SYSTEMATIC MUSIC THEORY

    CHAPTER 1 · Naturals  ≡  Boundaries ⊕ 3 Tones ⊕ 5 & 7 Tones ⊕ Letters & Notation

    CHAPTER 2 · Intervals  ≡  Melodic Modes ⊕ Melodic & Harmonic Intervals ⊕ Harmonic Modes ⊕ Interval Qualities

    CHAPTER 3 · Accidentals  ≡  Origins ⊕ Tritone Correction ⊕ Leading Tones ⊕ Halfsteps ⊕ From 7 to 13 Tones

    CHAPTER 4 · Measurement  ≡  Tone Rulers ⊕ Cents ⊕ Other Units

    CHAPTER 5 · Triads  ≡  Harmonic Mediant ⊕ Major Triad ⊕ Harmonic Submediant ⊕ Minor Triad ⊕ Lattice of Fifths & Thirds

    CHAPTER 6 · Superscales  ≡  13 Tones ⊕ 19 Tones ⊕ 31 Tones ⊕ 43 Tones ⊕ 55 Tones ⊕ Equal Divisions

    CHAPTER 7 · H-System  ≡  Overview ⊕ Scale ⊕ Pitches ⊕ Intervals ⊕ Notation ⊕ Keyboard ⊕ Chroma ⊕ Online H-System Calculators