Contents

• Contents
• Introduction
  • The Role of Intonation in Music
  • Intonation Theory
  • Digital Instruments and Intonation
  • Overview
  • Document Conventions
  • Review of Key Background Topics
    • Pitch Names
    • Interval Names and Abbreviations
    • The Harmonic Model of Tones
    • Frequency Ratios as Doublings
    • Modulo and Integer Division
• Related Work
  • Tuning Theory
    • Helmholtz and Ellis
    • Blackwood
    • Lindley and Turner-Smith
    • Regener
  • Dynamic Intonation Systems
    • Sethares
    • Waage
    • McCoskey (FasTrak)
    • Justonic, Inc.
• Tuning Theory
  • Models of Tunings
    • Absolute Tunings
    • Relative Tunings
    • Transposable Tunings
    • Register-Doubling Tunings
  • The Choice of a Model for Diatonic Tunings
  • Diatonic Pitches as Fifth-Register Vectors
  • Converting Pitches to FRV
  • Fifth Tunings
  • Beatless (Just) M3 and P5
    • Beating
    • Beating and Dissonance
    • The Derivation of Beatless M3 and P5
  • Evaluations of Fifth Tunings
  • Discussion of Specific Diatonic Tunings
    • Regular Tunings
    • Just P5 and M3 Impossible in Diatonic Tunings
    • The Size of Regular Diatonic Tunings
    • Truncated Tunings
    • Wolf Intervals in Truncated Tunings
    • Enharmonic Expectations
    • Well Temperaments
    • Review of Diatonic Tunings
  • Triadic Tunings
    • The Representation of Triadic Pitch
    • Just Triadic Tuning
    • Other Triadic Tunings
• Intonation Software
  • The Score Description Language
  • MIDI Tuning Technique
  • SMF Mode
  • Score Following Mode
• Conclusions
• Future Directions
  • Extensions to the Software
  • Extensions to the Theory
  • Tuning and Synthesis
• References