General theory

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

If you are new to tuning theory looking for an overview, see Xen concepts for beginners and various others in our collection of guides.

If you are looking for tools to start playing microtonal music, see List of music software, but we would like to highlight these, which will aid your study of tuning theory:

• Scale Workshop – scale-creation site by Lumi Pakkanen. Allows playing via QWERTY computer keyboard. Can also export .scl and .kbm files.
• Xenpaper – text-based microtonal sequencer, like a notepad. Write down musical ideas and share the link around.
• xen-calc – interval calculator that translates to/from ratios, cents, FJS and color notation, much more too.

Basics

• Interval
• Ratio
  • Ratio math
• Cent
• Chord
• Scale
• Mode
• Musical notation
• Terminology
  • Glossary
  • Acronyms

Core concepts

• Just intonation
• Harmonic series
  • Chord of nature
• Equal division of the octave
  • Equal-step tuning (edt, edf, …)
  • Well temperament
• Regular temperaments
  • Diatonic, chromatic, enharmonic, subchromatic
• MOS scale
  • Periods and generators
• Hexany
• Delta-rational chord

Regular temperament theory (RTT)

• Monzo
• Val
• Mapping
• Patent val
• Tempering out
• Rank and codimension
• Keenan's explanation of vals
• Comma pump
• Comma basis
• Saturation, torsion, and contorsion
• Dyadic chord
• Essential tempering comma
• Graham complexity

Advanced theory

Main article: Mathematical theory