Notes on Microtonality

Articles are added from the top down as they are brought to my attention.

  • Several articles
  • The Middle Path by Paul Erlich
  • The Forms of Tonality by Paul Erlich
  • Mathematics and Music
  • Rick Tagawa's 72 note equal temperament
  • Max Meyer's Diamond
  • Tuning & temperament bibliography
  • Paul Erlich on Tuning, Tonality, and 22 Tone Equal Temperament
  • Tuning History
  • Deriving the Musical Scale
  • A summary of historical temperaments
  • mbira tuning
  • mande jeli balafon tuning
  • Intonate your saxophone
  • Mathematics and Music (dis da bomb!)
  • The pentadecaphonic system
  • The Musical Octave
  • McLaren on composition
  • The Microtonal Activist
  • The complete writings of Ivor Darreg
  • A hard day's night in the microtonal studio
  • Tunings for 19 Tone Equal Tempered Guitar
  • Bach's tuning
  • Why I hate Vallotti (or is it Young?)
  • Why seven notes?
  • A Study in Musical Acoustics
  • an interview with Ben Johnson
  • Peter Frazer's notes on tuning
  • Just Triadic Tuning
  • Low Energy and Equal Spacing
  • A list archive
  • Another list archive
  • Tuning, temperaments and the traverso
  • Xenharmonic Bulletin #10
  • Xenharmonic Bulletin #11
  • John Allen on keyboard design
  • Tabla tuning
  • Tabla tuning
  • Tabla tuning
  • Defects of Equal Temperaments
  • The Enharmonic Genus
  • Golden Meantone Tuning
  • Comparison of Regular Temperaments
  • Just Tunings
  • About 31-tone Equal Temperament
  • Development of a 53-tone Keyboard Layout
  • The Family of Equal-interval Tunings
  • The Equal Tempered Scale and Some Peculiarities of Piano Tuning
  • Searching Small Intervals
  • 13 tones in the 3rd harmonic
  • Persian intervals
  • Lattices of some Arabic scales
  • Microtonal Tools Today
  • Just Intonation Primer
  • An essay by Johnny Reinhard
  • 24 Tone Equal Temperament
  • The continuum fingerboard
  • An interview with Kraig Grady
  • Intonatsiia and the Politics of Expression
  • appendix to Tuning the qin
  • Alternative Tuning and How We Hear
  • An Introduction to Historical Tunings
  • Intonation of embedded intervals
  • Temperament: A Beginner's Guide
  • Meantone and Temperament in Bach's Time
  • Distributing Commas
  • A Note on the Naming of Musical Intervals
  • Alternate Tunings for the Harmonica
  • Schismic Temperaments
  • An Interesting Result in the Theory of Well-Temperaments
  • A Beginners Guide to Temperament
  • Paul Erlich on Folker Periodicity Blocks
  • Music Theory Online
  • Fret Choices for Just Intonation Guitars
  • Pleng: Composing for a Justly Tuned Gender Barung
  • 72 Tone Equal Temperament
  • Three 22-tone Scales
  • Microtonal, meantone and equal tuning
  • The Mathematics of Tuning and Temperament with Audio Examples
  • Understanding Temperaments
  • Music Theory Online
  • One Octave in 31 Steps
  • Microtonal Tools Today
  • Microtonal Music on the ESQ-1/SQ-80
  • Tuning for Sound
  • EPS for JI
  • A Simple Way to Play Microtonal Music
  • Ratiotonic Temperament
  • Harmonic Theory and Just Intonation
  • Mathematics in Music
  • "The" Dominant Seventh Chord
  • "Wet/Dry" Sound and Tuning
  • An Atlas of Consonance
  • Xian shi yue Tuning
  • La Musique traduite en Mathématiques: Leonhard Euler
  • The microtonal wave
  • Articles by David Canright
  • A strange 9-limit temperament by Dave Keenan
  • Paul Erlich's notes
  • Dante Rosati's JI links
  • A microtonal font
  • String divisions and harmonics
  • Harmonic Errors in Open Tunings
  • A generalized keyboard
  • Articles by John S. Allen
  • Notes on the Bohlen-Pierce scale
  • John Dowland's lute fretting
  • Ric Carter
  • Distinctions Between Just-tuned Key Areas Within Musical Contexts
  • Erv Wilson archive
  • Monzo on the Hendrix chord
  • Harmonic Lattice Diagrams
  • JustMusic Notation
  • Relating Tuning and Timbre
  • Harmonic errors in equal tempered musical scales
  • Lydia Ayres course notes
  • Comparison of tuning systems
  • The zoomoozophone
  • McLaren's posts
  • Margo Schulter on Pythagorean tuning
  • The Bohlen-Pierce scale
  • A McLaren post
  • Ken Wauchope's Allotonality
  • Steel guitar tunings and more
  • Graham Breed's notes
  • Ed Foote on historical tunings
  • Tuning by Ratios
  • Just Intonation Explained
  • How to Refret Your Guitar
  • Bill Cooper on microtuning
  • Tuning and Temperament by Neil Midkiff
  • Wim Verheyen on microtonality
  • Analysis of a Neanderthal Flute
  • Automatic Just Intonation
  • Barbershop Forum Tuning Discussion
  • Kyle Gann's Reviews
  • Microtonality on Roland GS Synths
  • A Short History of Western Tuning
  • Scarlatti's Tunings
  • The JI System of Nicola Vicentino
  • Pianos and Continued Fractions
  • Historical Notes by Brian Mclaren
  • On Building Barbershop Windchimes
  • Pygmy Polyphony
  • r.l.reid's notes on microtonal composition