General theory

Here are some links to some of the key ideas underlying tuning:

Basics

• Ratio
  • Ratio math
• Cent
• Chords
• Scales
• Notation

Core Concepts

• Just intonation
• Regular temperaments
• Equal-step tuning
• Periods and generators
• EDO
• EDT
• MOS scale
• Periodic scale
• EDL (Equal divisions of length)
• AID (Arithmetic irrational divisions)
• ADO (Arithmetic rational divisions)
• Comma pump

How it Works

• Monzo
• Val
• Mapping
• Patent val
• Tempering out
• Rank and codimension

Personal Explanations

• Mike's Lectures On Regular Temperament Theory
• Keenan's explanation of vals

Javascript tools

• Interval calculator – a nice online interval calculator tool, shows linear fraction and EDO fraction expansions, too
• An animated Javascript Moment of Symmetry (MOS) ring demo, another untwelve.org creation
• An excellent Firefox browser tuning demo synthesizer, 'Wicksynth'

Additional Stuff

• Benedetti height
• Kees height
• Tenney height
• ABC, High Quality Commas, and Epimericity
• Graham complexity
• Generator complexity
• Lumma stability
• Chord of nature
• Modal UDP Notation
• Cluster temperament
• Consonant class scale
• Maximum variety
• Distributional Evenness
• Essential tempering commas

Advanced Theory

• Mathematical Theory