Tetrachord - Revision history

TallKite: /* Dividing the perfect fourth into more parts */ added an alternate generalization of tetrachord in a non-heptatonic context

2026-11-03T12:04:30Z

Dividing the perfect fourth into more parts: added an alternate generalization of tetrachord in a non-heptatonic context

← Older revision		Revision as of 12:04, 3 November 2026
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	== Dividing the perfect fourth into more parts ==		== Dividing the perfect fourth into more parts ==
	While tetrachords are useful for classifying heptatonic scales, in larger scales, such as the decatonic scales of [[pajara]] temperament, a scale segment spanning a perfect fourth often contains more than 4 notes~~. A segment with 5 notes is called a '''pentachord''', a segment with 6 notes a '''hexachord''', etc~~.		While tetrachords are useful for classifying heptatonic scales, in larger scales, such as the decatonic scales of [[pajara]] temperament, a scale segment spanning a perfect fourth often contains more than 4 notes.

	For example, the ''pentachordal'' pajara decatonic scale contains two equal pentachords and a 9/8 interval split into two semitones.		There are two ways to name such a scale segment. One way is to name it after the number of notes it contains. A segment with 5 notes is called a '''pentachord''', a segment with 6 notes a '''hexachord''', etc. For example, the ''pentachordal'' pajara decatonic scale contains two equal pentachords and a 9/8 interval split into two semitones.

			Another way is to name the scale segment after the interval it spans. The logic is that the "tetra" in tetrachord refers both to 4 notes and to a 4th, since these are identical in a heptatonic context. With this usage, the pajara decatonic scale contains two 5-note tetrachords and a 3-note '''dichord'''. For precedent for this usage, and for a discussion of its advantages, see [[Kite's thoughts on generalizing the term tetrachord]].

	== Dividing other-than-perfect fourths ==		== Dividing other-than-perfect fourths ==

BudjarnLambeth at 02:30, 30 October 2026

2026-10-30T02:30:07Z

← Older revision		Revision as of 02:30, 30 October 2026
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	== See also ==		== See also ==
	* [[Gallery of Wakalixes#Divisions of the Tetrachord\|Wakalix tetrachords]]		* [[Gallery of Wakalixes#Divisions of the Tetrachord\|Wakalix tetrachords]]
			* [[Kite's thoughts on generalizing the term tetrachord]]

	[[Category:Tetrachords\| ]] <!-- main article -->		[[Category:Tetrachords\| ]] <!-- main article -->

ArrowHead294 at 13:30, 30 January 2026

2026-01-30T13:30:19Z

Show changes

Overthink: /* Dividing the perfect fourth into more parts */ mention tetrachords in section

2026-01-15T23:26:06Z

Dividing the perfect fourth into more parts: mention tetrachords in section

← Older revision		Revision as of 23:26, 15 January 2026
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	== Dividing the perfect fourth into more parts ==		== Dividing the perfect fourth into more parts ==
	A scale segment spanning a perfect fourth ~~can also contain~~ more than 4 notes~~; for example, a~~ segment with 5 notes is called a '''pentachord''', a segment with 6 notes a '''hexachord''', etc. ~~These are useful in larger scales, such as the decatonic scales of [[pajara]] temperament. In particular~~, the ''pentachordal'' decatonic scale contains two equal pentachords and a 9/8 interval split into two semitones.		While tetrachords are useful for classifying heptatonic scales, in larger scales, such as the decatonic scales of [[pajara]] temperament, a scale segment spanning a perfect fourth often contains more than 4 notes. A segment with 5 notes is called a '''pentachord''', a segment with 6 notes a '''hexachord''', etc.

			For example, the ''pentachordal'' pajara decatonic scale contains two equal pentachords and a 9/8 interval split into two semitones.

	== Dividing other-than-perfect fourths ==		== Dividing other-than-perfect fourths ==

Overthink: Add section on larger divisions

2026-01-15T23:21:25Z

Add section on larger divisions

← Older revision		Revision as of 23:21, 15 January 2026
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	If you'd like to wrestle some tetrachords out of an equal temperament, please consider making a page for them and linking to that page from here!		If you'd like to wrestle some tetrachords out of an equal temperament, please consider making a page for them and linking to that page from here!

			== Dividing the perfect fourth into more parts ==
			A scale segment spanning a perfect fourth can also contain more than 4 notes; for example, a segment with 5 notes is called a '''pentachord''', a segment with 6 notes a '''hexachord''', etc. These are useful in larger scales, such as the decatonic scales of [[pajara]] temperament. In particular, the ''pentachordal'' decatonic scale contains two equal pentachords and a 9/8 interval split into two semitones.

	== Dividing other-than-perfect fourths ==		== Dividing other-than-perfect fourths ==

Dummy index: /* Ptolemy's catalog */ fix cent value order

2025-11-07T16:34:36Z

Ptolemy's catalog: fix cent value order

← Older revision		Revision as of 16:34, 7 November 2025
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	\|-		\|-
	\| 16/15, 9/8, 10/9		\| 16/15, 9/8, 10/9
	\| 112 + 182 ~~+ 204~~		\| 112 + 204 + 182
	\| intense diatonic		\| intense diatonic
	\|-		\|-

FloraC: +interwiki

2024-12-18T08:21:25Z

+interwiki

← Older revision		Revision as of 08:21, 18 December 2024
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			{{Interwiki
			\| en = Tetrachord
			\| ja = テトラコード
			}}
	{{Distinguish\| Tetrad }}		{{Distinguish\| Tetrad }}
	{{Wikipedia}}		{{Wikipedia}}

FloraC: Rework the intro; + category

2024-11-15T10:00:57Z

Rework the intro; + category

← Older revision		Revision as of 10:00, 15 November 2024
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	{{Wikipedia}}		{{Wikipedia}}

	~~The word~~ '''tetrachord''' usually ~~refers to~~ the interval of a [[perfect fourth]] (~~just or not~~) ~~divided~~ into three subintervals by the interposition of two additional notes.		A '''tetrachord''' is a four-note segment of a [[scale]] or tone row, usually spanning the interval of a [[perfect fourth]] (possibly tempered). It can be formed by dividing the perfect fourth into three subintervals by the interposition of two additional notes.

	[[John Chalmers]], in [~~http~~://eamusic.dartmouth.edu/~~%7Elarry~~/published_articles/divisions_of_the_tetrachord/index.html Divisions of the Tetrachord], tells us:		Tetrachords are fundamental to many musical traditions around the world. [[John Chalmers]], in [https://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/index.html ''Divisions of the Tetrachord''], tells us:

	''Tetrachords are modules from which more complex scalar and harmonic structures may be built. These structures range from the simple heptatonic scales known to the classical civilizations of the eastern Mediterranean to experimental gamuts with many tones. Furthermore, the traditional scales of much of the world's music, including that of Europe, the [[Arabic, Turkish, Persian\|Near East]], the Catholic and Orthodox churches, Iran and India, are still based on tetrachords. Tetrachords are thus basic to an understanding of much of the world's music.''		<blockquote>
			Tetrachords are modules from which more complex scalar and harmonic structures may be built. These structures range from the simple heptatonic scales known to the classical civilizations of the eastern Mediterranean to experimental gamuts with many tones. Furthermore, the traditional scales of much of the world's music, including that of Europe, the [[Arabic, Turkish, Persian\|Near East]], the Catholic and Orthodox churches, Iran and India, are still based on tetrachords. Tetrachords are thus basic to an understanding of much of the world's music.
			</blockquote>

	== Ancient Greek genera ==		== Ancient Greek genera ==
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	[[Category:Scale]]		[[Category:Scale]]
	[[Category:Terms]]		[[Category:Terms]]
			[[Category:Ancient Greek music]]
	[[Category:Arabic music]]		[[Category:Arabic music]]
	[[Category:Historical]]		[[Category:Historical]]

BudjarnLambeth at 03:15, 8 November 2024

2024-11-08T03:15:35Z

← Older revision		Revision as of 03:15, 8 November 2024
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	[[Category:Scale]]		[[Category:Scale]]
	[[Category:Terms]]		[[Category:Terms]]
	[[Category:Arabic]]		[[Category:Arabic music]]
	[[Category:Historical]]		[[Category:Historical]]

BudjarnLambeth: Categories

2024-11-08T03:15:09Z