User:Mousemambo/Workbench: Difference between revisions

Line 91:

**[[Scale naming]]

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

**[[Harmonic limit]]. This article badly needs a non-mathematical introductory summary paragraph~~, to go with its~~ Wikipedia ~~link to~~ [[Wikipedia:Limit (music)|Limit (music)]].

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

*[[Tonic]]

Line 100:

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

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

*[[Temperament]]

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

**[[Equal temperament]]

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

**[[Equal-step tuning]]

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

Line 146:

=== Xenharmonic harmony ===

*[[Dyad]]

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

*[[Interval quality]]

*[[Consonance and dissonance]]

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

*[[Diatonic functional harmony]]

*[[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...

**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.

**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."

**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 became available.

**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, and the introduction of ~~ostinato in~~ early basso continuo accompaniment, provided an opening to harmonic ideas in early European JI music, without the more obvious dissonance of notes sounded simultaneously.

**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.

**~~Later~~, the ~~development~~ of [[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.

**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.

*[[Dyadic chord]]

*Harmony in specific tunings

@@ Line 91: / Line 91: @@
 **[[Scale naming]]
 **[[MOS scale|Moment of symmetry (MOS)]]
-**[[Harmonic limit]]. This article badly needs a non-mathematical introductory summary paragraph, to go with its Wikipedia link to [[Wikipedia:Limit (music)|Limit (music)]].
+**[[Harmonic limit]]. This article badly needs a non-mathematical introductory summary paragraph. Wikipedia: [[Wikipedia:Limit (music)|Limit (music)]].
 *[[Tonic]]
@@ Line 100: / Line 100: @@
 **[[Pythagorean comma]]. Wikipedia: [[Wikipedia:Pythagorean comma|Pythagorean comma]].
 **[[81/80]] (aka Ptolemaic comma). Wikipedia: [[Wikipedia:Syntonic comma|Syntonic comma]].
-*[[Temperament]]
+*[[Temperament]]. Wikipedia: [[Wikipedia:Musical temperament|Musical temperament]].
-**[[Equal temperament]]
+**[[Equal temperament]]. Wikipedia: [[Wikipedia:Equal temperament|Equal temperament]].
 **[[Equal-step tuning]]
 **[[Regular temperament]]. Wikipedia: [[Wikipedia:Regular temperament|Regular temperament]].
@@ Line 146: / Line 146: @@
 === Xenharmonic harmony ===
-*[[Dyad]]
+*[[Dyad]]. Wikipedia: [[Wikipedia:Dyad (music)|Dyad (music)]].
 *[[Interval quality]]
-*[[Consonance and dissonance]]
+*[[Consonance and dissonance]]. Wikipedia: [[Wikipedia:Consonance and dissonance|Consonance and dissonance]].
-*[[Diatonic functional harmony]]
+*[[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...
 **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.
+**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."
-**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 became available.
+**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, and the introduction of ostinato in early basso continuo accompaniment, provided an opening to harmonic ideas in early European JI music, without the more obvious dissonance of notes sounded simultaneously.
+**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.
-**Later, the development of [[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.
+**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.
 *[[Dyadic chord]]
 *Harmony in specific tunings