Tetrachord - Revision history

Vector at 21:20, 16 May 2026

2026-05-16T21:20:52Z

← Older revision		Revision as of 21:20, 16 May 2026
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	== Modern xenharmonic interpretation ==		== Modern xenharmonic interpretation ==
	Tetrachords were historically used in largely monophonic music, so that additional structural constraints didn't become relevant until additional harmonic complexity entered the scene, and music switched primarily to using diatonic. Therefore, tetrachord-based scales, especially chromatic and enharmonic ones, remain useful in a monophonic or homophonic context, where the harmonic relations between notes do not matter as much. One can think of tetrachordal music as entirely "degree-based", whereas modal music is to an extent "interval-based".		Tetrachords were historically used in largely monophonic music, so that additional structural constraints didn't become relevant until additional harmonic complexity entered the scene, and music switched primarily to using diatonic. Therefore, tetrachord-based scales, especially chromatic and enharmonic ones, remain useful in a monophonic or homophonic context, where the harmonic relations between notes do not matter as much. One can think of tetrachordal music as entirely "degree-based", whereas modal music is to an extent "interval-based".

			Enharmonic tetrachords may be described as having a "shimmery" sound due to the two adjacent quarter tones.

	However, tetrachords are often still theoretically relevant in discussing the construction of modern scales, for example in the examination of the conventional framing of the melodic minor scale, where the upper tetrachord varies when ascending vs. when descending; additionally the Ionian major scale can be thought of as a M2-M2-m2 tetrachord stacked into an octave-repeating scale.		However, tetrachords are often still theoretically relevant in discussing the construction of modern scales, for example in the examination of the conventional framing of the melodic minor scale, where the upper tetrachord varies when ascending vs. when descending; additionally the Ionian major scale can be thought of as a M2-M2-m2 tetrachord stacked into an octave-repeating scale.

Vector at 19:51, 16 May 2026

2026-05-16T19:51:44Z

← Older revision		Revision as of 19:51, 16 May 2026
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	== Modern xenharmonic interpretation ==		== Modern xenharmonic interpretation ==
	'~~'Complete section''~~		Tetrachords were historically used in largely monophonic music, so that additional structural constraints didn't become relevant until additional harmonic complexity entered the scene, and music switched primarily to using diatonic. Therefore, tetrachord-based scales, especially chromatic and enharmonic ones, remain useful in a monophonic or homophonic context, where the harmonic relations between notes do not matter as much. One can think of tetrachordal music as entirely "degree-based", whereas modal music is to an extent "interval-based".

			However, tetrachords are often still theoretically relevant in discussing the construction of modern scales, for example in the examination of the conventional framing of the melodic minor scale, where the upper tetrachord varies when ascending vs. when descending; additionally the Ionian major scale can be thought of as a M2-M2-m2 tetrachord stacked into an octave-repeating scale.

			==== Other polychordal structures ====

			===== Trichord =====
			Scales may also be constructed from trichords (3-note segments spanning a perfect fourth); these scales will be pentatonic and vary entirely on what middle interval is used in the trichord. Pythagorean pentatonic uses 32/27 as the middle interval.

			A trichord is structurally equivalent to a fourth-bounded chthonic triad, and so a trichordal scale may be conceptualized as a chthonic generator chain, especially since the whole tone separating the trichords is itself a form of chthonic. Interestingly, this implies that trichordal scales place no notes in between the notes of their chords, having the three notes of a chthonic chord fall on consecutive scale steps.

			===== Pentachord =====
			A pentachord consists of five notes spanning a perfect fourth. A pentachord may be constructed by dividing the steps of a trichord; therefore, a trichord or a chthonic triad consists of alternating notes of a pentachord. Because of this, it is also structurally useful to insert the perfect tritone (or augmented fourth/diminished fifth) between the fourth and the fifth to maintain a relatively even spacing of intervals.

			Pentachords appear in pajara temperament, where sssLsssssL is a "pentachordal" scale based on the pentachord sssL.

			Pentachordal extensions may be used to improve melodic cohesion in trichordal scales.

Vector at 19:21, 16 May 2026

2026-05-16T19:21:21Z

← Older revision		Revision as of 19:21, 16 May 2026
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	[[File:The swry.png\|thumb\|376x376px\|A map of tetrachord tunings]]		[[File:The swry.png\|thumb\|376x376px\|A map of tetrachord tunings]]
	A '''tetrachord''' is some division of the [[perfect fourth]] into three parts, creating four distinct notes (hence tetra-). A '''tetrachordal scale''' is a scale constructed by joining two tetrachords with an interval of 9/8 (because 4/3 * 9/8 * 4/3 is an octave), and is resultantly a heptatonic scale (because the unison and octave are equivalent). Often, the additional assumption is made that the two tetrachords are identical. The [[Diatonic\|diatonic scale]] is a tetrachordal scale, because its step pattern LLsLLLs can be broken into two tetrachords of LLs separated by a large step representing 9/8. The simplest otonal tetrachord is 9:10:11:12.		A '''tetrachord''' is some division of the [[perfect fourth]] into three parts, creating four distinct notes (hence tetra-). A '''tetrachordal scale''' is a scale constructed by joining two tetrachords with an interval of 9/8 (because 4/3 * 9/8 * 4/3 is an octave), and is resultantly a heptatonic scale (because the unison and octave are equivalent). Often, the additional assumption is made that the two tetrachords are identical. The [[Diatonic\|diatonic scale]] is a tetrachordal scale, because its step pattern LLsLLLs can be broken into two tetrachords of LLs separated by a large step representing 9/8. The simplest otonal tetrachord is 9:10:11:12. When singing a scale, heptatonic or pentatonic forms are naturally common due to the fact that 4/3 and especially 3/2 can be easily sung without a reference, and tetrachords formalize this natural occurrence into scale-building. Tetrachords may be classified based on the size of their largest interval

	== Ancient Greek theory ==		== Ancient Greek-inspired theory ==
	''In Ancient Greek, the notes we consider "lower" were considered "higher"; for the sake of consistency, the English-language meanings of "low" and "high" will be used throughout this section.''		''In Ancient Greek, the notes we consider "lower" were considered "higher"; for the sake of consistency, the English-language meanings of "low" and "high" will be used throughout this section.''

	The notes of a tetrachord are named in Ancient Greek music theory. They are, from lowest to highest in pitch, ''hypate'', ''parhypate'', ''lichanos'', and ''mese''. The hypate and mese are always a perfect fourth apart, and the parhypate and lichanos are considered "movable", and vary between tunings.		The notes of a tetrachord are named in Ancient Greek music theory. They are, from lowest to highest in pitch, ''hypate'', ''parhypate'', ''lichanos'', and ''mese''. The hypate and mese are always a perfect fourth apart, and the parhypate and lichanos are considered "movable", and vary between tunings.

	~~In Ancient Greek theory, the~~ largest interval of a tetrachord is never between the hypate and parhypate, and is in fact usually between the lichanos and mese (that is, the version of the diatonic scale constructed from tetrachords would be in what we today call the Phrygian mode, sLLLsLL); in fact, the interval between the hypate and parhypate is usually the smallest of the three intervals of the tetrachord. Ideally, both of these always hold true, but in practice it was variable especially in certain types of scales.		The largest interval of a tetrachord is never between the hypate and parhypate, and is in fact usually between the lichanos and mese (that is, the version of the diatonic scale constructed from tetrachords would be in what we today call the Phrygian mode, sLLLsLL); in fact, the interval between the hypate and parhypate is usually the smallest of the three intervals of the tetrachord. Ideally, both of these always hold true, but in practice it was variable especially in certain types of scales.

	=== Genera ===		=== Genera ===
	The ~~Ancient Greek~~ tetrachords are divided into three genera, based on the size of the largest interval (the "characteristic interval").		The tetrachords are divided into three genera, based on the size of the largest interval (the "characteristic interval").

	* In the '''[[diatonic]] genus''', the characteristic interval is less than half of the span of the tetrachord (less than about 249 cents). The characteristic interval may be the middle interval of the tetrachord rather than the highest interval. The MOS diatonic scale and the utonal counterpart of 9:10:11:12 fall into this category, and so does the Zarlino diatonic if its largest interval is interpreted as 9/8. A diatonic tetrachord may be seen as '''[[Semitone]] - [[Whole Tone]] - Whole Tone'''.		* In the '''[[diatonic]] genus''', the characteristic interval is less than half of the span of the tetrachord (less than about 249 cents). The characteristic interval may be the middle interval of the tetrachord rather than the highest interval. The MOS diatonic scale and the utonal counterpart of 9:10:11:12 fall into this category, and so does the Zarlino diatonic if its largest interval is interpreted as 9/8. A diatonic tetrachord may be seen as '''[[Semitone]] - [[Whole Tone]] - Whole Tone'''.

Vector: Created page with "A map of tetrachord tunings A '''tetrachord''' is some division of the perfect fourth into three parts, creating four distinct notes (hence tetra-). A '''tetrachordal scale''' is a scale constructed by joining two tetrachords with an interval of 9/8 (because 4/3 * 9/8 * 4/3 is an octave), and is resultantly a heptatonic scale (because the unison and octave are equivalent). Often, the additional assumption is made that the two tet..."

2026-03-27T00:48:20Z

Created page with "thumb|376x376px|A map of tetrachord tunings A '''tetrachord''' is some division of the perfect fourth into three parts, creating four distinct notes (hence tetra-). A '''tetrachordal scale''' is a scale constructed by joining two tetrachords with an interval of 9/8 (because 4/3 * 9/8 * 4/3 is an octave), and is resultantly a heptatonic scale (because the unison and octave are equivalent). Often, the additional assumption is made that the two tet..."

New page

[[File:The swry.png|thumb|376x376px|A map of tetrachord tunings]]
A '''tetrachord''' is some division of the [[perfect fourth]] into three parts, creating four distinct notes (hence tetra-). A '''tetrachordal scale''' is a scale constructed by joining two tetrachords with an interval of 9/8 (because 4/3 * 9/8 * 4/3 is an octave), and is resultantly a heptatonic scale (because the unison and octave are equivalent). Often, the additional assumption is made that the two tetrachords are identical. The [[Diatonic|diatonic scale]] is a tetrachordal scale, because its step pattern LLsLLLs can be broken into two tetrachords of LLs separated by a large step representing 9/8. The simplest otonal tetrachord is 9:10:11:12.

== Ancient Greek theory ==
''In Ancient Greek, the notes we consider "lower" were considered "higher"; for the sake of consistency, the English-language meanings of "low" and "high" will be used throughout this section.''

The notes of a tetrachord are named in Ancient Greek music theory. They are, from lowest to highest in pitch, ''hypate'', ''parhypate'', ''lichanos'', and ''mese''. The hypate and mese are always a perfect fourth apart, and the parhypate and lichanos are considered "movable", and vary between tunings.

In Ancient Greek theory, the largest interval of a tetrachord is never between the hypate and parhypate, and is in fact usually between the lichanos and mese (that is, the version of the diatonic scale constructed from tetrachords would be in what we today call the Phrygian mode, sLLLsLL); in fact, the interval between the hypate and parhypate is usually the smallest of the three intervals of the tetrachord. Ideally, both of these always hold true, but in practice it was variable especially in certain types of scales.

=== Genera ===
The Ancient Greek tetrachords are divided into three genera, based on the size of the largest interval (the "characteristic interval").

* In the '''[[diatonic]] genus''', the characteristic interval is less than half of the span of the tetrachord (less than about 249 cents). The characteristic interval may be the middle interval of the tetrachord rather than the highest interval. The MOS diatonic scale and the utonal counterpart of 9:10:11:12 fall into this category, and so does the Zarlino diatonic if its largest interval is interpreted as 9/8. A diatonic tetrachord may be seen as '''[[Semitone]] - [[Whole Tone]] - Whole Tone'''.
* In the '''chromatic genus''', the characteristic interval is larger than half of the span of the tetrachord. It is also always the step between the lichanos and mese. The upper bound of the chromatic genus is vague, but chromatic tetrachords generally have a characteristic interval of a minor third. In this case, the middle interval may be the smaller of the two remaining intervals, but is usually still the larger of the two. A chromatic tetrachord may be seen as '''Semitone - Semitone - [[Third#Minor thirds|Minor 3rd]]'''.
* In the '''enharmonic genus''', the characteristic interval is larger than that of the chromatic genus, generally a major third. Similarly to the chromatic genus, the middle interval (between the parhypate and lichanos) may be the smaller of the two remaining intervals. An enharmonic tetrachord may be seen as '''Quartertone - Quartertone - [[Third#Major thirds|Major 3rd]].'''

=== Modes ===
A tetrachordal scale has seven modes like any other heptatonic scale. The systems described by different Ancient Greek theorists varied, but in the original system, three of these modes were used; if the notes of a tetrachordal scale in its basic arrangement described in the page's header are labeled EFGABCDE (like the modern Phrygian mode) such that A-B is the 9/8 interval separating the two tetrachords, then that arrangement is called ''Dorian'' in ancient Greek theory; the rotation DEFGABCD is ''Phrygian'', and CDEFGABC is ''Lydian''.

By extension (and by Aristoxenos' theory), BCDEFGAB may be called ''Mixolydian'', ABCDEFGA may be called ''Hypodorian'' or ''Locrian'', GABCDEFG may be called ''Hypophrygian,'' and FGABCDEF may be called ''Hypolydian''. Note that the order of these mode names is loosely opposite their order in modern theory.

== Modern xenharmonic interpretation ==
''Complete section''