General theory

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

Basics

• Ratios
  • Ratio math
• Cents
• Chords
• Scales
• Notation

Core Concepts

• JI
• Regular Temperaments
• Equal Temperaments
• Periods and Generators
• EDO
• EDT
• MOS Scales
• Periodic scale
• EDL (Equal divisions of length)
• Arithmetic irrational divisions
• ADO (Arithmetic rational divisions)
• Comma pump

How it Works

• Monzos
• Vals
• Mappings
• 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