User:Mousemambo/Introduction to xenharmonic music terminology

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This page introduces xenharmonic music theory through the terminology used by its practitioners. This outline of links can be used as a self-guided introductory course through the Xenharmonic Wiki for beginners interested in understanding, playing or composing microtonal or xenharmonic music.

About this course

Although it consists only of links within an outline, the structure is intentionally ordered to help guide people new to this subject toward a growing conceptual understanding. The purpose is to open one doorway (among many possible others) to answering the question "How can I begin learning about xenharmonic music?" Other doorways include listening to or playing music.

This course overlaps and extends from a prerequisite of Music Theory 101, a ubiquitous first-semester college course whose material is also commonly taught to high school piano, guitar and jazz musicians. There are several excellent free online comprehensive textbooks teaching conventional Music Theory 101 (Music Theory for the 21st-Century Classroom, Open Music Theory, Music Theory). If you work through at least the first half of one of those comprehensive courses, many of the links below to Wikipedia articles will be redundant, or you may prefer the Wikipedia readings.

Using this introduction

This course begins by reintroducing some basic music theory terms but in a xenharmonic context. That may mean they have unusual definitions, or that they're explained in a way that points toward how they're understood and used in xenharmonic musicology and music. If there is corresponding English Wikipedia page, a link is provided here to help contrast the xenharmonic perspective with the one more commonly taught in conventional music theory. However, some Wikipedia pages were created with a partly or entirely xenharmonic perspective (e.g. Regular diatonic tuning).

This course draws a somewhat arbitrary line between "beginner" material that is included, and "intermediate" material that is not. A guideline for that distinction is that the material presented might fit within a one-semester college course. People who already have significant xenharmonic theory understanding may feel this course remains too superficial, and that much more could be added to the "Tuning system analysis and design" section (possibly a few items could be added). Unfortunately, hardly any standard introductions to music theory go deeply enough into tuning systems and temperament to provide enough of a foundation for exploring xenharmonic music theory. Therefore, this course recapitulates many introductory topics but from a xenharmonic perspective.

Some of the articles offered in this outline start with useful introductory material but then go deeper than the level intended by this course. In these cases, readers are encouraged to use their judgement as they read to decide when a useful depth of understanding has been reached, and then return to this outline. Revisiting deeper material later is always possible! However, at the time of this writing (Sept. 2023) some of the Xen Wiki articles lack much of a basic introduction at all (i.e. one without college math). In those cases, if there is a Wikipedia link provided you're encouraged to visit there. But one reason for developing this outline is to identify and remedy those articles, so perhaps by the time you read this some helpful wiki editors will have addressed the problem.

Other doorways to understanding

Although there is no "listening guide" for this course, you will find links to YouTube videos that provide some of that valuable experience. But note that links in the "Other Articles" and "Videos" sections are related and supporting, but outside the flow of the course. If you play or wish to learn an musical instrument capable of microtonality, you may find opportunities to play along as you progress here.

Finally, some people prefer to "learn microtonal music" mostly by listening to music, so this outline will probably not be useful for them. That's OK! There are other resources for you. For many of us, though, a progressive structure like this outline is very helpful.

Next level terminology

An "Intermediate xenharmonic terminology" outline is being compiled, which could follow this introduction. If you have suggestions for that page, or for this developing beginner terminology outline, please add them to this page's Discussion page or post them to the #wiki channel of the Xen Discord server.

Foundations

• What is microtonal or xenharmonic music? Wikipedia: Microtonal music.
  • Why use alternative tunings?
  • Scott McCormick. Microtones: the notes between the notes.
  • Michael W. Dean. Making microtonal music is easier than you’d think. Also archived at the Xen wiki.
  • Dave Tremblay. Beyond the veil: Behold the xenharmonic, or, understanding microtonal music.
  • Philip Mantione. Intro to microtonality (+ Interview with Brendan Byrnes).
  • Misconceptions about xenharmony
  • Kyle Gann. Combatting anti-just-intonation propaganda.
  • Kyle Gann. My idiosyncratic reasons for using just intonation.
  • What is microtonal music
  • Why microtonality? And some responses.
• Glossary
• Interval. Wikipedia: Interval (music).
• Interval region
• Ratio
• Ratio math
• Interval size measure
• Harmonic series. Wikipedia: Harmonic series (music).
• 2-limit, 3-limit & 5-limit. Wikipedia: Limit (music).
• Scale. Wikipedia: Scale (music).
  • Mode. Wikipedia: Mode (music).
  • Scale naming
  • EDO
  • Equal-step tunings. Wikipedia: Equal temperament.
  • 5L 2s (aka Diatonic). Wikipedia: Diatonic scale and Regular diatonic tuning.
  • MOS scale (Moment of Symmetry)
  • Mosstep & Mosdegree
  • Periods and generators
  • Equave (aka Equivalence interval), contrast with Period and Periodic scale.
• Tonic
• Videos
  • Brendan Byrnes. Microtonal Music Tutorial (Xenharmonic). YouTube.
  • dolomuse. PolyChromatic Music Theory. YouTube.
  • Hear Between The Lines. You've never heard (of) these chords. YouTube.
  • John Moriarty. Tuning Theory 0: A Primer ("Microtonal" Theory). YouTube.
  • TEDx Talks. Polychromatic music | Dolores Catherino | TEDxSacramento. YouTube.
  • Sevish. Learn about microtonal music. YouTube (300+ videos playlist).

Tuning systems and temperament

• Tuning system. Wikipedia: Musical tuning § Tuning systems.
• Harmonic limit (aka p-limit).
• Just intonation. Wikipedia: Just intonation.
• Comma. Wikipedia: Comma.
  • Pythagorean comma. Wikipedia: Pythagorean comma.
  • 81/80 (aka, Ptolemaic comma). Wikipedia: Syntonic comma.
• Gallery of just intervals
• Temperament. Wikipedia: Musical temperament.
  • Rank
  • Regular temperament. Wikipedia: Regular temperament.
  • Linear temperament
  • Support
  • Tempering out
  • EDO vs ET
  • Temperament naming
  • Temperament families and clans
• Notable historical and common tuning systems
  • Pythagorean tuning. Wikipedia: Pythagorean tuning.
  • Meantone family. Wikipedia: Meantone temperament.
    • Wikipedia: Ptolemy's intense diatonic scale.
    • Quarter-comma meantone. Wikipedia: Quarter-comma meantone.
  • 12edo. Wikipedia: 12 equal temperament.
• Other Articles
  • Kyle Gann. Just intonation explained.
  • Kyle Gann. An introduction to historical tunings.
  • Pierre Lewis. Understanding temperaments.
  • Chris Morda. Microtonal guitar tutorial overview.
  • Margo Schulter. Pythagorean tuning and Medieval polyphony.
  • Tall Kite. Alternative tunings: Theory, notation and practice.
  • Paul Erlich. A middle path between just intonation and the equal temperaments.
  • Links § Educational websites
• Videos
  • Alice M. Chuaqui Baldwin. Meantone Temperament and Other Historical Tuning Systems, Part 2. YouTube.
  • Classical Nerd. Tuning: An Introduction. YouTube.
  • Early Music Sources. Tuning and Temperaments in the Renaissance - PART I. YouTube.
  • John Moriarty. Tuning Theory 1: Just Intonation ("Microtonal" Theory). YouTube.
  • John Moriarty. Tuning Theory 2: Temperament ("Microtonal" Theory). YouTube.
  • Xotla Music. Intro To Microtonal Terminology. YouTube.

Tuning system analysis and design

• Tuning system design. This needed article would explain some of the (sometimes conflicting) qualities that make a tuning system attractive to some people, e.g. many consonant intervals, attractive harmonies, easy modulation to other keys, similarity to existing popular tunings, etc. [See the discussion page for more thoughts about this.]
• Harmonic lattice diagram (aka tuning lattice)
• Tonality diamond. [Unfortunately, the current (2023-09-04) Xen Wiki page doesn't present the common meaning of the term. See the discussion page for more thoughts about this.]
• Generator
• Monzo
• Val
• Mapping
• Harmonic class
• Rank-2 temperament
• TAMNAMS
• Ups and downs notation
• Glossary of scale properties
• Notable xenharmonic tuning systems for beginners: Exemplars to get you started.
  • 19edo. Wikipedia: 19 equal temperament.
  • 24edo (aka, quarter tone scale). Wikipedia: Quarter tone.
  • 31edo. Wikipedia: 31 equal temperament.
  • 53edo. Wikipedia: 53 equal temperament.
  • Porcupine
  • Bohlen-Pierce scale
• Collection of EDO impressions
• Families of scales
• Collections of temperaments: A wide survey.
  • Tour of regular temperaments
  • Category:Lists of temperaments
• Collections of scales: A wide survey.
  • Scale index
  • Gallery of 12-tone just intonation scales
  • Gallery of 12-tone tempered scales
  • Category:12-tone scales
• Other Articles
  • Alex Zorach. Why 31-tone equal temperament?
  • Mike Sheiman's Very Easy Scale Building From The Harmonic Series Page
  • Siggy. A Trivial Knot (blog). Xenharmonic music theory part 1: Perception of microtones, part 2: Dissonance Theory, part 3: Tuning theory
  • Kraig Grady. Introduction to Erv Wilson's moments of symmetry.
  • Dave Keenan & Douglas Blumeyer's guide to RTT (multi-part guide; math intensive; advanced)
  • Mike's lectures on regular temperament theory
  • Aura's music theory: Introduction
• Videos
  • 12tone. How Many Notes Are There? The Theory of Quarter Tones. YouTube.
  • HEHEHE I AM A SUPAHSTAR SAGA. Exploring 19-TET. YouTube (7 videos playlist)
  • John Moriarty. Tuning Theory 3: Moment of Symmetry ("Microtonal" Theory). YouTube.
  • John Moriarty. Porcupine Temperament Tutorial (Microtonal/Xenharmonic theory). YouTube.
  • John Moriarty. Bohlen-Pierce Temperament Tutorial (Microtonal Theory). YouTube.
  • Sevish. Making microtonal scales with Scale Workshop. YouTube.
  • Sketching_Fox. 22 TET Music Theory: Tone Sizes. YouTube.
  • uethanian. 19 tone equal temperament. YouTube.

Xenharmonic harmony

• Dyad. Wikipedia: Dyad (music).
• Interval quality
• Consonance and dissonance. Wikipedia: Consonance and dissonance.
• Chord
• Dyadic chord
• Diatonic functional harmony. Wikipedia: Function (music).
• Just intonation harmony (or Harmony in just intonation). This needed article would present an introduction to creating harmony in just intonation (JI) tunings. It would introduce ideas and strategies for harmony that also apply to other uneven tunings, describe some historical developments within Western music, and provide a foundation for understanding more extended xenharmonic harmonization. [See the discussion page for more thoughts about this.]
• Other Articles
  • Margo Schulter. Pythagorean tuning and Medieval polyphony § Pythagorean tuning and Gothic polyphony.
  • Aura's Ideas on functional harmony‎‎
  • FloraC's Overview on functional harmony
• Videos
  • Hear Between The Lines. How to use microtones to harmonise? | Ep. 3. YouTube.
  • John Moriarty. 31-Tone Meantone Tutorial. YouTube.
  • Levi McClain. What If We Had 31 Notes Instead of 12? YouTube.
  • Listening In. Jacob Collier: Moon River - Harmonic Analysis. YouTube.
  • Lumi - Music & Theory. What Makes Gleam Great? - Microtonal Music Analysis. YouTube.
  • mannfishh. Microtonal Comma Chords and an Explanation of 5-Limit Just Tuning Lattices. YouTube.
  • Quartertone Harmony. Harmonic Functions of Quartertones. YouTube.
  • Zheanna Erose. 31-EDO Music Theory. YouTube (12 video playlist).
  • Zheanna Erose. Rare Chord: Maj7‡11‡15‡19 (harmony in 31-edo). YouTube.