Axis system - Revision history

Kili: diaglam

2026-05-07T19:38:58Z

diaglam

← Older revision		Revision as of 19:38, 7 May 2026
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	=== Compositional Use ===		=== Compositional Use ===
			[[File:Eighteenedoaxissystemsplitcycles.jpg\|thumb\|An Axis Diagram for 18edo, conceptualized as 3 Trees of 6edo, corresponding to the same 3 Axis of the 6edo Tree]]
	The Axis System can greatly simplify functional harmonic composition, as it does not prescribe specific orders and contexts chords are meant to be used in, only their colors and relation to the Tonic (or any note.) The one misconception that might derail an Axis-aware composer is that a chord of only Tonic-Axis notes is not a completely at rest chord. The conception that the model is flawed because it calls an out-of-key "diminisht seven" chord the most Tonic is ignoring the contexts through which you would use the theory. While conventional common practice harmony would have you play all the tonic notes at rest, the Axis conception of Tonic notes is not there for use all in one instance, rather it shows how a resolution to the Original Tonic can just as easily land on any Tonic-Axis chord, providing a framework for dynamic key changes and novelty cadences. When constructing a chord for restfullness, it is important to balance colors from all Axis to provide the illusion that there is no where left to resolve. It is also important to note that while Common Practice Harmony uses the Dominant Chord as the highest point of tension, and the Subdominant Chord as something that must go before it, in Axis Harmony with those Axis, the "Dominant" Axis and "Subdominant" Axis are mirror images of each other, and may be considered equally tense (or Subdominant more tense) depending on the composers preference.		The Axis System can greatly simplify functional harmonic composition, as it does not prescribe specific orders and contexts chords are meant to be used in, only their colors and relation to the Tonic (or any note.) The one misconception that might derail an Axis-aware composer is that a chord of only Tonic-Axis notes is not a completely at rest chord. The conception that the model is flawed because it calls an out-of-key "diminisht seven" chord the most Tonic is ignoring the contexts through which you would use the theory. While conventional common practice harmony would have you play all the tonic notes at rest, the Axis conception of Tonic notes is not there for use all in one instance, rather it shows how a resolution to the Original Tonic can just as easily land on any Tonic-Axis chord, providing a framework for dynamic key changes and novelty cadences. When constructing a chord for restfullness, it is important to balance colors from all Axis to provide the illusion that there is no where left to resolve. It is also important to note that while Common Practice Harmony uses the Dominant Chord as the highest point of tension, and the Subdominant Chord as something that must go before it, in Axis Harmony with those Axis, the "Dominant" Axis and "Subdominant" Axis are mirror images of each other, and may be considered equally tense (or Subdominant more tense) depending on the composers preference.

	=== In Prime Edos ===		=== In Prime Edos ===
	Prime Edos will always lack the multiple factors required to construct Axis, however they may contain approximations of 1\2, 1\3, 1\4, or 1\5 such that their effects and uses for substition and analogy may still be possible.		Prime Edos will always lack the multiple factors required to construct Axis, however they may contain approximations of 1\2, 1\3, 1\4, or 1\5 such that their effects and uses for substition and analogy may still be possible.

Kili: /* Compositional Use */ typos

2026-05-06T13:38:01Z

Compositional Use: typos

← Older revision		Revision as of 13:38, 6 May 2026
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	=== Compositional Use ===		=== Compositional Use ===
	The Axis System can greatly simplify functional harmonic composition, as it does not prescribe specific orders and contexts chords are meant to be used in, only their colors and relation to the Tonic (or any note.) The one misconception that might derail an Axis-aware composer is that a chord of only Tonic-Axis notes is not a completely at rest chord. The conception that the model is flawed because it calls an out-of-key "diminisht seven" chord the most Tonic is ignoring the contexts through which you would use the theory. While conventional common practice harmony would have you play all the tonic notes at rest, the Axis conception of Tonic notes is not there for use all in one instance, rather it shows how a resolution to the ~~Originally~~ Tonic can just as easily land on any Tonic-Axis chord, providing a framework for dynamic key changes and novelty cadences. When constructing a chord for restfullness, it is important to balance colors from all Axis to provide the illusion that there is no where left to resolve. It is also important to note that while Common Practice Harmony uses the Dominant Chord as the highest point of tension, and the Subdominant Chord as something that must go before it, in Axis Harmony with those Axis the "Dominant" Axis and "Subdominant" Axis ~~one~~ mirror images of each other, and may be considered equally tense (or Subdominant more tense) depending on the composers preference.		The Axis System can greatly simplify functional harmonic composition, as it does not prescribe specific orders and contexts chords are meant to be used in, only their colors and relation to the Tonic (or any note.) The one misconception that might derail an Axis-aware composer is that a chord of only Tonic-Axis notes is not a completely at rest chord. The conception that the model is flawed because it calls an out-of-key "diminisht seven" chord the most Tonic is ignoring the contexts through which you would use the theory. While conventional common practice harmony would have you play all the tonic notes at rest, the Axis conception of Tonic notes is not there for use all in one instance, rather it shows how a resolution to the Original Tonic can just as easily land on any Tonic-Axis chord, providing a framework for dynamic key changes and novelty cadences. When constructing a chord for restfullness, it is important to balance colors from all Axis to provide the illusion that there is no where left to resolve. It is also important to note that while Common Practice Harmony uses the Dominant Chord as the highest point of tension, and the Subdominant Chord as something that must go before it, in Axis Harmony with those Axis, the "Dominant" Axis and "Subdominant" Axis are mirror images of each other, and may be considered equally tense (or Subdominant more tense) depending on the composers preference.

	=== In Prime Edos ===		=== In Prime Edos ===
	Prime Edos will always lack the multiple factors required to construct Axis, however they may contain approximations of 1\2, 1\3, 1\4, or 1\5 such that their effects and uses for substition and analogy may still be possible.		Prime Edos will always lack the multiple factors required to construct Axis, however they may contain approximations of 1\2, 1\3, 1\4, or 1\5 such that their effects and uses for substition and analogy may still be possible.

Inthar: Inthar moved page Axis harmony to Axis system without leaving a redirect: as in Wikipedia

2026-05-05T22:57:40Z

Inthar moved page Axis harmony to Axis system without leaving a redirect: as in Wikipedia

← Older revision	Revision as of 22:57, 5 May 2026
(No difference)

Inthar at 22:57, 5 May 2026

2026-05-05T22:57:23Z

← Older revision		Revision as of 22:57, 5 May 2026
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	The ~~Axis System of functional harmony~~ was first described by Ernő Lendvai in his analysis of Béla Bartok, a ~~somewhat xenharmonic~~ composer. Primarily organizing chords, it describes a new complete system of chord relations / substitutions for the full system of ~~12 edo~~, rather than a ~~meantonic~~ approach, such that notes separated by 1\2 are primarily connected and notes separated by 1\4 are secondarily connected. It is notable for its elegance, and its ~~popular~~ power in analyzing complex jazz (or punk) in situations where no other system seems to work.		The '''axis system''' was first described by Ernő Lendvai in his analysis of Béla Bartok, a 20th-century avant-garde composer. Primarily organizing chords, it describes a new complete system of chord relations or substitutions for the full system of 12edo, rather than a Meantone-based approach, such that notes separated by 1\2 are ''primarily connected'' and notes separated by 1\4 are ''secondarily connected''. It is notable for its elegance, and its power in analyzing complex jazz (or punk) in situations where no other system seems to work.
	[[File:Placeholderaxisharmony.png\|thumb]]		[[File:Placeholderaxisharmony.png\|thumb]]

	The purest form of Axis harmony is immediately applicable to all multiple of 12 edos, simply with additional cycles. Most conservatively, Axis Harmony is applicable to all edos which share a 1\4 tetrad, by considering the functions of all the notes in that tetrad as the same rather than individually. All multiple of 2 edos as well will be able to symmetrize functions across the tritone. In addition, all multiple of 3 edos will be able to benefit from the secondary component of the theory, the division of functions into 3 types of contrasting effect, for harmonic use. Furthermore, the principles of Axis Harmony by drawing the cycles of relationships along the lines of the edos natural symmetries will expand easily to any composite edo. It has even been postulated that the equivalences based on the intervals of 1\4 and 1\3 function even without a closed loop to the octave, allowing for unlimited expansion to ji.		The purest form of Axis harmony is immediately applicable to all multiple of 12 edos, simply with additional cycles. Most conservatively, Axis Harmony is applicable to all edos which share a 1\4 tetrad, by considering the functions of all the notes in that tetrad as the same rather than individually. All multiple of 2 edos as well will be able to symmetrize functions across the tritone. In addition, all multiple of 3 edos will be able to benefit from the secondary component of the theory, the division of functions into 3 types of contrasting effect, for harmonic use. Furthermore, the principles of Axis Harmony by drawing the cycles of relationships along the lines of the edos natural symmetries will expand easily to any composite edo. It has even been postulated that the equivalences based on the intervals of 1\4 and 1\3 function even without a closed loop to the octave, allowing for unlimited expansion to ji.

Inthar: Inthar moved page Axis Harmony to Axis harmony without leaving a redirect: Styling

2026-05-05T22:53:31Z

Inthar moved page Axis Harmony to Axis harmony without leaving a redirect: Styling

← Older revision	Revision as of 22:53, 5 May 2026
(No difference)

Kili: /* Co add add addmpositional Use */

2026-05-05T19:08:10Z

Co add add addmpositional Use

← Older revision		Revision as of 19:08, 5 May 2026
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	=== Compositional Use ===		=== Compositional Use ===
	The Axis System can greatly simplify functional harmonic composition, as it does not prescribe specific orders and contexts chords are meant to be used in, only their colors and relation to the Tonic (or any note.) The one misconception that might derail an Axis-aware composer is that a chord of only Tonic-Axis notes is not a completely at rest chord. The conception that the model is flawed because it calls an out-of-key "diminisht seven" chord the most Tonic is ignoring the contexts through which you would use the theory. While conventional common practice harmony would have you play all the tonic notes at rest, the Axis conception of Tonic notes is not there for use all in one instance, rather it shows how a resolution to the Originally Tonic can just as easily land on any Tonic-Axis chord, providing a framework for dynamic key changes and novelty cadences. When constructing a chord for restfullness, it is important to balance colors from all Axis to provide the illusion that there is no where left to resolve.		The Axis System can greatly simplify functional harmonic composition, as it does not prescribe specific orders and contexts chords are meant to be used in, only their colors and relation to the Tonic (or any note.) The one misconception that might derail an Axis-aware composer is that a chord of only Tonic-Axis notes is not a completely at rest chord. The conception that the model is flawed because it calls an out-of-key "diminisht seven" chord the most Tonic is ignoring the contexts through which you would use the theory. While conventional common practice harmony would have you play all the tonic notes at rest, the Axis conception of Tonic notes is not there for use all in one instance, rather it shows how a resolution to the Originally Tonic can just as easily land on any Tonic-Axis chord, providing a framework for dynamic key changes and novelty cadences. When constructing a chord for restfullness, it is important to balance colors from all Axis to provide the illusion that there is no where left to resolve. It is also important to note that while Common Practice Harmony uses the Dominant Chord as the highest point of tension, and the Subdominant Chord as something that must go before it, in Axis Harmony with those Axis the "Dominant" Axis and "Subdominant" Axis one mirror images of each other, and may be considered equally tense (or Subdominant more tense) depending on the composers preference.

	=== In Prime Edos ===		=== In Prime Edos ===
	Prime Edos will always lack the multiple factors required to construct Axis, however they may contain approximations of 1\2, 1\3, 1\4, or 1\5 such that their effects and uses for substition and analogy may still be possible.		Prime Edos will always lack the multiple factors required to construct Axis, however they may contain approximations of 1\2, 1\3, 1\4, or 1\5 such that their effects and uses for substition and analogy may still be possible.

Kili: pirme iprmiee edos

2026-05-05T18:57:22Z

pirme iprmiee edos

← Older revision		Revision as of 18:57, 5 May 2026
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	=== Compositional Use ===		=== Compositional Use ===
	The Axis System can greatly simplify functional harmonic composition, as it does not prescribe specific orders and contexts chords are meant to be used in, only their colors and relation to the Tonic (or any note.) The one misconception that might derail an Axis-aware composer is that a chord of only Tonic-Axis notes is not a completely at rest chord. The conception that the model is flawed because it calls an out-of-key "diminisht seven" chord the most Tonic is ignoring the contexts through which you would use the theory. While conventional common practice harmony would have you play all the tonic notes at rest, the Axis conception of Tonic notes is not there for use all in one instance, rather it shows how a resolution to the Originally Tonic can just as easily land on any Tonic-Axis chord, providing a framework for dynamic key changes and novelty cadences. When constructing a chord for restfullness, it is important to balance colors from all Axis to provide the illusion that there is no where left to resolve.		The Axis System can greatly simplify functional harmonic composition, as it does not prescribe specific orders and contexts chords are meant to be used in, only their colors and relation to the Tonic (or any note.) The one misconception that might derail an Axis-aware composer is that a chord of only Tonic-Axis notes is not a completely at rest chord. The conception that the model is flawed because it calls an out-of-key "diminisht seven" chord the most Tonic is ignoring the contexts through which you would use the theory. While conventional common practice harmony would have you play all the tonic notes at rest, the Axis conception of Tonic notes is not there for use all in one instance, rather it shows how a resolution to the Originally Tonic can just as easily land on any Tonic-Axis chord, providing a framework for dynamic key changes and novelty cadences. When constructing a chord for restfullness, it is important to balance colors from all Axis to provide the illusion that there is no where left to resolve.

			=== In Prime Edos ===
			Prime Edos will always lack the multiple factors required to construct Axis, however they may contain approximations of 1\2, 1\3, 1\4, or 1\5 such that their effects and uses for substition and analogy may still be possible.

Kili: compositional euse

2026-05-05T18:53:27Z

compositional euse

← Older revision		Revision as of 18:53, 5 May 2026
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	[[File:16edoaxisdingbat.jpg\|thumb\|An example of Axis Notation overlaying a 16edo circle of fifths, with little pictures replacing note-name-letters. Treating the top-most snowflake as the Tonic, the bottom-most green note is the Tonic Antipole. Additional colours yellow and blue are the secondary Pole Set for this leaf/branch. Addional Pole Dyad red and purple show one possible Pole Set that would addionally be treated tonically if the Axis was expanded to include 1\8. ]]		[[File:16edoaxisdingbat.jpg\|thumb\|An example of Axis Notation overlaying a 16edo circle of fifths, with little pictures replacing note-name-letters. Treating the top-most snowflake as the Tonic, the bottom-most green note is the Tonic Antipole. Additional colours yellow and blue are the secondary Pole Set for this leaf/branch. Addional Pole Dyad red and purple show one possible Pole Set that would addionally be treated tonically if the Axis was expanded to include 1\8. ]]

			=== Compositional Use ===
			The Axis System can greatly simplify functional harmonic composition, as it does not prescribe specific orders and contexts chords are meant to be used in, only their colors and relation to the Tonic (or any note.) The one misconception that might derail an Axis-aware composer is that a chord of only Tonic-Axis notes is not a completely at rest chord. The conception that the model is flawed because it calls an out-of-key "diminisht seven" chord the most Tonic is ignoring the contexts through which you would use the theory. While conventional common practice harmony would have you play all the tonic notes at rest, the Axis conception of Tonic notes is not there for use all in one instance, rather it shows how a resolution to the Originally Tonic can just as easily land on any Tonic-Axis chord, providing a framework for dynamic key changes and novelty cadences. When constructing a chord for restfullness, it is important to balance colors from all Axis to provide the illusion that there is no where left to resolve.

Kili at 18:36, 5 May 2026

2026-05-05T18:36:57Z

← Older revision		Revision as of 18:36, 5 May 2026
Line 14:		Line 14:
	[[File:Byonesixteenthispink.jpg\|thumb\|Example of harmonic color seemlessly changing through telephone of substitution]]		[[File:Byonesixteenthispink.jpg\|thumb\|Example of harmonic color seemlessly changing through telephone of substitution]]

	[[File:16edoaxisdingbat.jpg\|thumb\|An example of Axis Notation overlaying a 16edo circle of fifths, with little pictures replacing note-name-letters. Treating the top-most snowflake as the Tonic, the bottom-most green note is the Tonic Antipole. Additional colours yellow and blue are the secondary Pole Set for this ~~Leaf~~/~~Branch~~. Addional Pole Dyad red and purple show one possible Pole Set that would addionally be treated tonically if the Axis was expanded to include 1\8. ]]		[[File:16edoaxisdingbat.jpg\|thumb\|An example of Axis Notation overlaying a 16edo circle of fifths, with little pictures replacing note-name-letters. Treating the top-most snowflake as the Tonic, the bottom-most green note is the Tonic Antipole. Additional colours yellow and blue are the secondary Pole Set for this leaf/branch. Addional Pole Dyad red and purple show one possible Pole Set that would addionally be treated tonically if the Axis was expanded to include 1\8. ]]

Kili: capiiltol lettor

2026-05-05T18:36:51Z

capiiltol lettor

← Older revision		Revision as of 18:36, 5 May 2026
Line 14:		Line 14:
	[[File:Byonesixteenthispink.jpg\|thumb\|Example of harmonic color seemlessly changing through telephone of substitution]]		[[File:Byonesixteenthispink.jpg\|thumb\|Example of harmonic color seemlessly changing through telephone of substitution]]

	[[File:16edoaxisdingbat.jpg\|thumb\|An example of Axis Notation overlaying a 16edo circle of fifths, with little pictures replacing note-name-letters. Treating the top-most snowflake as the Tonic, the bottom-most green note is the Tonic Antipole. Additional colours yellow and blue are the secondary Pole Set for this ~~leaf~~/~~branch~~. Addional Pole Dyad red and purple show one possible Pole Set that would addionally be treated tonically if the Axis was expanded to include 1\8. ]]		[[File:16edoaxisdingbat.jpg\|thumb\|An example of Axis Notation overlaying a 16edo circle of fifths, with little pictures replacing note-name-letters. Treating the top-most snowflake as the Tonic, the bottom-most green note is the Tonic Antipole. Additional colours yellow and blue are the secondary Pole Set for this Leaf/Branch. Addional Pole Dyad red and purple show one possible Pole Set that would addionally be treated tonically if the Axis was expanded to include 1\8. ]]