User:Mousemambo/Workbench: Difference between revisions

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== Xenharmonic music: An introduction to 21st century tuning systems ==

This ~~[developing]~~ outline can be used as an introductory course through the Xenharmonic Wiki for people interested in understanding, playing or composing xenharmonic music. Although it consists entirely of links to Xen Wiki and some Wikipedia articles~~, without any text of its own~~, it's ordered to guide a growing conceptual understanding for ~~those~~ new to the subject. The intention is to help answer the question, "Where should I begin learning about xenharmonic music?" for those who wish to go deeper than the introductory texts provided by the ~~list of~~ [[Guides]].

This outline of links can be used as an introductory course through the [[Main Page|Xenharmonic Wiki]] for people interested in understanding, playing or composing what's termed microtonal or [[xenharmonic music]]. Although it consists almost entirely of links to Xen Wiki and some Wikipedia articles, it's carefully ordered to guide a growing conceptual understanding for people new to the subject. The intention is to help answer the question, "Where should I begin learning about xenharmonic music?" for those who wish to go deeper than the more introductory texts provided on the Xen Wiki [[Guides]] page.

This course 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 free online textbooks teaching Music Theory 101 [~~recommendations need to be provided~~]. ~~The 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~~.

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 ([https://musictheory.pugetsound.edu/mt21c/MusicTheory.html Music Theory for the 21st-Century Classroom], [https://viva.pressbooks.pub/openmusictheory/ Open Music Theory], [https://www.8notes.com/theory/ Music Theory]). If you work through one of those comprehensive courses, many of the links below to Wikipedia articles will be redundant.

This ~~"Introduction to xenharmonic music"~~ course begins by reintroducing some basic musicology 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 ~~[in progress]~~. However, some Wikipedia pages were created with a partly or entirely xenharmonic perspective (e.g. [[Wikipedia:Regular diatonic tuning|Regular diatonic tuning]])~~, although this can be difficult for beginners to recognize~~.

This course begins by reintroducing some basic musicology 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. [[Wikipedia:Regular diatonic tuning|Regular diatonic tuning]]).

Some of the articles linked to by 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 to decide when a useful depth of understanding has been reached, and then return to this outline. Revisiting deeper material at a later time is always ~~available.~~

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. 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 with a xenharmonic perspective.

Some of the articles linked to by 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 at a later time is always possible!

=== Foundations ===

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*[[Harmonic series]] and the [[Overtone scale]]. Wikipedia: [[Wikipedia:Harmonic series (music)|Harmonic series (music)]].

*[[Scale]]. Wikipedia: [[Wikipedia:Scale (music)|Scale (music)]].

**[[Mode~~]]. "[[Tonal center]]" redirects to here, but probably should redirect to [[Tonic~~]]. Wikipedia: [[Wikipedia:Mode (music)|Mode (music)~~]].~~

**[[Mode]]. Wikipedia: [[Wikipedia:Mode (music)|Mode (music)]].

**[[5L 2s]]. "[[Diatonic]]" has a link to here. Wikipedia: [[Wikipedia:Diatonic scale|Diatonic scale]], and [[Wikipedia:Regular diatonic tuning|Regular diatonic tuning]].

**[[Scale naming]]

**[[5L 2s]] (aka [[Diatonic]]). Wikipedia: [[Wikipedia:Diatonic scale|Diatonic scale]], and [[Wikipedia:Regular diatonic tuning|Regular diatonic tuning]].

**[[MOS scale|Moment of symmetry (MOS)]]

**[[Harmonic limit]]. This article badly needs a non-mathematical introductory summary paragraph. Wikipedia: [[Wikipedia:Limit (music)|Limit (music)]].

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*[[Comma]]. Wikipedia: [[Wikipedia:Comma|Comma]].

**[[Pythagorean comma]]. Wikipedia: [[Wikipedia:Pythagorean comma|Pythagorean comma]].

**[[81/80]] (aka Ptolemaic comma). Wikipedia: [[Wikipedia:Syntonic comma|Syntonic comma]].

**[[81/80]] (aka, Ptolemaic comma). Wikipedia: [[Wikipedia:Syntonic comma|Syntonic comma]].

*[[Temperament]]. Wikipedia: [[Wikipedia:Musical temperament|Musical temperament]].

**[[Equal temperament]]. Wikipedia: [[Wikipedia:Equal temperament|Equal temperament]].

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*[[Consonance and dissonance]]. Wikipedia: [[Wikipedia:Consonance and dissonance|Consonance and dissonance]].

*[[Diatonic functional harmony]]. Wikipedia: [[Wikipedia:Function (music)|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. Some ideas to include...

*[[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. Interval table analysis of an example 3-limit JI tuning (see provided table) 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 at this time was essentially ideological, reinforced by the strong human tendency to hear unfamiliar tunings as "wrong."

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**Melodic arpeggiation, ostinato, and the introduction of early basso continuo accompaniment, provided composers with an opening 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 [[Wikipedia:Meantone temperament|meantone temperaments]] in European Renaissance music expanded the number of acceptably consonant intervals ([[Wikipedia:List_of_meantone_intervals|List of meantone intervals]]), while listeners also became more accepting of less pure intervals as consonant (continuing into the 20th century [[Wikipedia:Emancipation of the dissonance|Emancipation of the dissonance]]). This allowed expansion and exploration of triadic and larger harmonies. These tempered tunings also permitted 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. Those familiar with the advantages of ubiquitous equal temperament may initially find that 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]]

*Harmony in specific tunings

@@ Line 73: / Line 73: @@
 == Xenharmonic music: An introduction to 21st century tuning systems ==
-This [developing] outline can be used as an introductory course through the Xenharmonic Wiki for people interested in understanding, playing or composing xenharmonic music. Although it consists entirely of links to Xen Wiki and some Wikipedia articles, without any text of its own, it's ordered to guide a growing conceptual understanding for those new to the subject. The intention is to help answer the question, "Where should I begin learning about xenharmonic music?" for those who wish to go deeper than the introductory texts provided by the list of [[Guides]].
+This outline of links can be used as an introductory course through the [[Main Page|Xenharmonic Wiki]] for people interested in understanding, playing or composing what's termed microtonal or [[xenharmonic music]]. Although it consists almost entirely of links to Xen Wiki and some Wikipedia articles, it's carefully ordered to guide a growing conceptual understanding for people new to the subject. The intention is to help answer the question, "Where should I begin learning about xenharmonic music?" for those who wish to go deeper than the more introductory texts provided on the Xen Wiki [[Guides]] page.
-This course 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 free online textbooks teaching Music Theory 101 [recommendations need to be provided]. The 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.
+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 ([https://musictheory.pugetsound.edu/mt21c/MusicTheory.html Music Theory for the 21st-Century Classroom], [https://viva.pressbooks.pub/openmusictheory/ Open Music Theory], [https://www.8notes.com/theory/ Music Theory]). If you work through one of those comprehensive courses, many of the links below to Wikipedia articles will be redundant.
-This "Introduction to xenharmonic music" course begins by reintroducing some basic musicology 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 [in progress]. However, some Wikipedia pages were created with a partly or entirely xenharmonic perspective (e.g. [[Wikipedia:Regular diatonic tuning|Regular diatonic tuning]]), although this can be difficult for beginners to recognize.
+This course begins by reintroducing some basic musicology 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. [[Wikipedia:Regular diatonic tuning|Regular diatonic tuning]]).
-Some of the articles linked to by 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 to decide when a useful depth of understanding has been reached, and then return to this outline. Revisiting deeper material at a later time is always available.
+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. 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 with a xenharmonic perspective.
+Some of the articles linked to by 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 at a later time is always possible!
 === Foundations ===
@@ Line 87: / Line 89: @@
 *[[Harmonic series]] and the [[Overtone scale]]. Wikipedia: [[Wikipedia:Harmonic series (music)|Harmonic series (music)]].
 *[[Scale]]. Wikipedia: [[Wikipedia:Scale (music)|Scale (music)]].
-**[[Mode]]. "[[Tonal center]]" redirects to here, but probably should redirect to [[Tonic]]. Wikipedia: [[Wikipedia:Mode (music)|Mode (music)]].
+**[[Mode]]. Wikipedia: [[Wikipedia:Mode (music)|Mode (music)]].
-**[[5L 2s]]. "[[Diatonic]]" has a link to here. Wikipedia: [[Wikipedia:Diatonic scale|Diatonic scale]], and [[Wikipedia:Regular diatonic tuning|Regular diatonic tuning]].
 **[[Scale naming]]
+**[[5L 2s]] (aka [[Diatonic]]). Wikipedia: [[Wikipedia:Diatonic scale|Diatonic scale]], and [[Wikipedia:Regular diatonic tuning|Regular diatonic tuning]].
 **[[MOS scale|Moment of symmetry (MOS)]]
 **[[Harmonic limit]]. This article badly needs a non-mathematical introductory summary paragraph. Wikipedia: [[Wikipedia:Limit (music)|Limit (music)]].
@@ Line 99: / Line 101: @@
 *[[Comma]]. Wikipedia: [[Wikipedia:Comma|Comma]].
 **[[Pythagorean comma]]. Wikipedia: [[Wikipedia:Pythagorean comma|Pythagorean comma]].
-**[[81/80]] (aka Ptolemaic comma). Wikipedia: [[Wikipedia:Syntonic comma|Syntonic comma]].
+**[[81/80]] (aka, Ptolemaic comma). Wikipedia: [[Wikipedia:Syntonic comma|Syntonic comma]].
 *[[Temperament]]. Wikipedia: [[Wikipedia:Musical temperament|Musical temperament]].
 **[[Equal temperament]]. Wikipedia: [[Wikipedia:Equal temperament|Equal temperament]].
@@ Line 150: / Line 152: @@
 *[[Consonance and dissonance]]. Wikipedia: [[Wikipedia:Consonance and dissonance|Consonance and dissonance]].
 *[[Diatonic functional harmony]]. Wikipedia: [[Wikipedia:Function (music)|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. Some ideas to include...
+*[[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. Interval table analysis of an example 3-limit JI tuning (see provided table) 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 at this time was essentially ideological, reinforced by the strong human tendency to hear unfamiliar tunings as "wrong."
@@ Line 156: / Line 158: @@
 **Melodic arpeggiation, ostinato, and the introduction of early basso continuo accompaniment, provided composers with an opening 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 [[Wikipedia:Meantone temperament|meantone temperaments]] in European Renaissance music expanded the number of acceptably consonant intervals ([[Wikipedia:List_of_meantone_intervals|List of meantone intervals]]), while listeners also became more accepting of less pure intervals as consonant (continuing into the 20th century [[Wikipedia:Emancipation of the dissonance|Emancipation of the dissonance]]). This allowed expansion and exploration of triadic and larger harmonies. These tempered tunings also permitted 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. Those familiar with the advantages of ubiquitous equal temperament may initially find that 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]]
 *Harmony in specific tunings