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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.

Although it consists only of links, the outline 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, but you may prefer the Wikipedia route.

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 "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 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.

Foundations

Tuning systems and temperament

Tuning system analysis and design

Xenharmonic harmony

  • Dyad. Wikipedia: Dyad (music).
  • Interval quality
  • Consonance and dissonance. Wikipedia: Consonance and dissonance.
  • 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 introduces ideas and strategies for harmony that also apply to other uneven tunings, and provides a foundation for understanding more extended xenharmonic harmonization. It should emphasize the important explicit and implicit harmonic qualities of arpeggiation, counterpoint, and dyadic harmony in JI and other non-regular tunings. Some ideas to include...
    • In ancient music, "pure" tunings based on lower harmonic series overtones (e.g. Pythagorean, aka 3-limit) were understood to mostly support only limited dyadic harmony, because few intervals in any purely JI tuning were considered acceptably consonant. Singing and playing in unison was typical. Interval table analysis of an example 3-limit JI tuning (see table; to be added) reveals how many of that tunings' dyadic intervals are unusable for harmony. Triads that are consonant — by traditional measure — are unavailable in ancient JI tunings.
    • However, many traditional cultural musics successfully integrated dyadic harmony, e.g. ancient Greek music and its early European descendants, traditional Middle Eastern music, traditional classical Chinese music, and some traditional African music. The commitment to 3-limit tunings of this time was essentially ideological, reinforced by the strong human tendency to hear unfamiliar tunings as "wrong."
    • The expansion of JI tunings from 3-limit (Pythagorean) to 5-limit (e.g. Ptolemaic) increased the number of intervals considered consonant, and therefore the harmonic possibilities in these tunings. Although options for triadic harmony were still limited compared to later developments, the strongly consonant Ptolemaic just major triad and some other consonant triads became available. Nevertheless, harmony through the European Medieval period remained mostly limited to fifths and fourths in parallel motion, with some experimentation.
    • Melodic arpeggiation, ostinato, and the introduction of early basso continuo accompaniment, provided composers with a conceptual doorway to more sophisticated harmonic ideas in early European JI music, without the more obvious dissonance of nearby-pitched notes sounded simultaneously. The developing popularity of counterpoint in Medieval melody also encouraged considering more complex harmony.
    • Subsequently, the abandonment of pure intonation for newly developed meantone temperaments in European Renaissance music greatly enlarged the set of acceptably consonant intervals (e.g. List of meantone intervals), while listeners also became more accepting of less pure intervals as consonant (continuing into the 20th century Emancipation of the dissonance). This allowed expansion and exploration of triadic and larger harmonies. These tempered tunings also permitted some key modulation on fixed-pitch instruments like piano.
    • Some contemporary composers have been rediscovering the attractive tonality of pure harmony and its deeply consonant quality. People only familiar with the advantages of ubiquitous equal temperament may initially find composing in just intonation is notably constrained because many intervals are unavailable due to dissonance, reducing its harmonic possibilities. However, constraints in artistic work can also inspire creative solutions. One of the charms of composing in a new tuning system is learning what works well in it, and expresses its tonality with enough beauty that the listener doesn't realize what the composer has worked to avoid. It's also worth considering that humans have composed music in just intonation for thousands of years, although nearly all of it has been lost.
  • Dyadic chord
  • Articles
  • Videos
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