View source for Trichord

{{For|the piano stringing configuration (three unison strings per note)|Unison (piano)#Trichord}}

{{redirect|3-11|major earthquake in Japan|2011 Tohoku earthquake and tsunami}}
[[File:Trichords in C major.png|thumb|upright=1.4|The seven contiguous trichords in C major. See also: [[Cardinality equals variety]].]]


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</score>|width=350|caption=[[Anton Webern|Webern]]'s [[Concerto for Nine Instruments (Webern)|Concerto]], Op. 24, tone row,{{sfn|Whittall|2008|loc=97}} composed of four trichords: P RI R I.}}

In [[music theory]], a '''trichord''' ({{IPA-cen|t|r|aɪ|k|ɔːr|d}}) is a group of three different [[pitch class]]es found within a larger group.{{sfn|Friedmann|1990|loc=42}}<ref>{{Cite web |title=Trichord |url=https://ultimatelexicon.com/definitions/t/trichord/ |access-date=2025-09-17 |website=UltimateLexicon.com |language=en}}</ref> A trichord is a [[wikt:contiguity|contiguous]] three-note [[set (music)|set]] from a [[musical scale]]{{sfn|Houlahan and Tacka|2008|loc=54}} or a twelve-[[tone row]].

In [[musical set theory]] there are twelve trichords given [[inversional equivalency]], and, without inversional equivalency, nineteen trichords. These are numbered 1–12, with symmetrical trichords being unlettered and with uninverted and inverted nonsymmetrical trichords lettered A or B, respectively. They are often listed in prime form, but may exist in different [[voicing (music)|voicings]]; different [[chord inversion|inversions]] at different [[transposition (music)|transpositions]]. For example, the [[major chord]], 3-11B (prime form: [0,4,7]), is an inversion of the [[minor chord]], 3-11A (prime form: [0,3,7]). 3-5A and B are the [[Viennese trichord]] (prime forms: [0,1,6] and [0,5,6]).

==Historical Russian definition==

{{See also|Genus (music)}}

In late-19th to early 20th-century Russian musicology, the term trichord (трихорд ({{IPA|/trixоrd/}})) meant something more specific: a set of three pitches, each at least a tone apart but all within the range of a fourth or fifth.
The possible trichords on C would then be:
{| class="wikitable"
|-
! colspan="3"| Note
! colspan="3"| Number
! Intervals
|-
| C
| D
| F
| 0
| 2
| 5
| 2, 3 (M2, m3)
|-
| C
| D
| G
| 0
| 2
| 7
| 2, 5 (M2, P4)
|-
| C
| D{{music|#}}/E{{music|b}}
| F
| 0
| 3
| 5
| 3, 2 (m3, M2)
|-
| C
| E{{music|b}}
| G
| 0
| 3
| 7
| 3, 4 (m3, M3)
|-
| C
| E
| F{{music|#}}/G{{music|b}}
| 0
| 4
| 6
| 4, 2 (M3, M2)
|-
| C
| E
| G
| 0
| 4
| 7
| 4, 3 (M3, m3)
|-
| C
| F
| G
| 0
| 5
| 7
| 5, 2 (P4, M2)
|}
Several of these pitch sets interlocking could form a larger set such as a [[pentatonic scale]] (such as '''C'''–D–'''F'''–G–B{{music|b}}–'''C''''). It was first coined by theorist {{ill|Pyotr Sokalsky|ru|Сокальский, Пётр Петрович}} in his 1888 book ''Русская народная музыка'' ("Russian Folk Music") to explain the observed traits of the rural Russian folk music (especially from southern regions) that was just beginning to be recorded and published at this time. The term gained wide acceptance and usage, but as time went on it became less relevant to contemporary [[ethnomusicological]] findings; ethnomusicologist [[Kliment Kvitka]] opined in his 1928 article on Sokalsky's theories that it should also properly be used for pitch sets of three notes in the interval of a third, which had been found to be just as characteristic of Russian folk traditions (but which was unknown in Sokalsky's time). By mid-century, a group of Moscow-based ethnomusicologists (K. V. Kvitka, Ye. V. Gippius, A. V. Rudnyova, N. M. Bachinskaya, L. S. Mukharinskaya, among others) boycotted the use of the term altogether, yet it could still be seen in the mid-20th century due to its heavy use in the works of earlier theorists.{{sfn|Kastal'skii|1961|loc=9}}

==Etymology==

The term is derived by analogy from the 20th-century use of the word "[[tetrachord]]". Unlike the tetrachord and [[hexachord]], there is no traditional standard scale arrangement of three notes, nor is the trichord necessarily thought of as a [[harmony|harmonic]] entity.{{sfn|Rushton|2001}}

[[Milton Babbitt]]'s serial theory of combinatoriality makes much of the properties of three-note, four-note, and six-note segments of a twelve-tone row, which he calls, respectively, ''trichords'', ''tetrachords'', and ''hexachords'', extending the traditional sense of the terms and retaining their implication of contiguity. He usually reserves the term "source set" for their unordered counterparts (especially hexachords), but does occasionally employ terms such as "source tetrachords" and "combinatorial trichords, tetrachords, and hexachords" instead.{{sfn|Babbitt|1955|loc=57–58, 60}}{{sfn|Babbitt|1961|loc=76}}{{sfn|Babbitt|2003|loc=59}}

[[Allen Forte]] occasionally makes informal use of the term ''trichord''{{sfn|Forte|1973|loc=124, 126}} to mean what he usually calls "sets of three elements",{{sfn|Forte|1973|loc=3, 23, 27, 47}} and other theorists (notably including [[Howard Hanson|Howard]],{{sfn|Hanson|1960|loc=5}} and [[Carlton Gamer|Carlton]]{{sfn|Gamer|1967|loc=37, 46, 50–52}}) mean by the term ''[[Triad (music)|triad]]'' a three-note pitch collection which is not necessarily a contiguous segment of a scale or a tone row and not necessarily (in twentieth-century music) tertian or diatonic either.

==Number of unique trichords==
{{Unreferenced section|date=May 2020}}
Typically, there are [[12TET|12 tones]] in the western scale. Computing the number of unique trichords is a mathematical problem. A computer program can quickly iterate all the triads and remove the ones that are merely transpositions of others, leaving (as noted above) nineteen or, to within inversional equivalence, twelve. As an example, the following list contains all trichords that can be made including the note C, but includes 36 that are merely transpositions or transposed inversions of others:<br>

# C D♭ D [0,1,2] – this combination has no name (half step cluster, with doubly diminished third and quintuply diminished fifth, spelled enharmonically)
# C D♭ E♭ [0,1,3] – Phyrigian Trichord
# C D♭ E [0,1,4] – E[[Augmented triad|aug]] with [[Suspended chord|sus6]]
# C D♭ F [0,1,5] – D{{music|flat}}[[Major seventh chord|maj seventh]] (omit 5th)
# C D♭ G♭ [0,1,6] – D{{music|flat}}[[Suspended chord|sus/maj7,Rite chord.2, Tritone-fourth.1]]
# C D♭ G [0,5,6] (= inv. of [0,1,6])
# C D♭ A♭ [0,4,5] (= inv. of [0,1,5])
# C D♭ A [0,3,4] (= inv. of [0,1,4]) – D{{music|flat}}aug with sus7
# C D♭ B♭ [0,2,3] (= inv. of [0,1,3])
# C D♭ B [0,1,2] – this combination has no name (half step cluster, with doubly diminished third and quintuply diminished fifth, spelled enharmonically)
# C D E♭ [0,2,3] (= inv. of [0.1.3]) – this combination has no name
# C D E [0,2,4] – E[[Augmented triad|aug]] with [[Suspended chord|sus#6]]
# C D F [0,2,5] – F[[Suspended chord|sus6]]
# C D G♭ [0,2,6] – D[[Dominant seventh chord|dom seventh]] (enharmonic spelling, omit 5th)
# C D G [0,2,7] – C[[Suspended chord|sus2]]
# C D A♭ [0,4,6] (= inv. of [0,2,6]) – Ddim sus7
# C D A [0,3,5] (= inv. of [0,2,5]) – Dsus7
# C D B♭ [0,2,4] – D[[Augmented triad|aug]] with [[Suspended chord|sus#6]]
# C D B [0,1,3]
# C E♭ E [0,3,4] (= inv. of [0,1,4]) – E[[Augmented triad|aug]] with [[Suspended chord|sus7]]
# C E♭ F [0,3,5] (= inv. of [0,2,5]) – F[[Suspended chord|sus#6]]
# C E♭ G♭ [0,3,6] – C[[Diminished triad|dim]]
# C E♭ G [0,3,7] – C[[Minor chord|minor]]
# C E♭ A♭ [0,4,7] (= inv. of [0,3,7]) – A{{music|flat}}[[Major chord|major]]
# C E♭ A [0,3,6] – A{{music|flat}}[[diminished triad|dim]]
# C E♭ B♭ [0,2,5]
# C E♭ B [0,1,4]
# C E F [0,4,5] (= inv. of [0,2,5]) – F[[Suspended chord|sus7]]
# C E G♭ [0,4,6] (= inv. of [0,2,6]) – E[[Augmented triad|aug]] with [[Suspended chord|sus2]]
# C E G [0,4,7] (= inv. of 0,3,7]) – C[[Major chord|major]]
# C E A♭ [0,4,8] – C/E/A{{music|flat}}[[Augmented triad|aug]]
# C E A [0,3,7] – A[[minor chord|minor]]
# C E B♭ [0,2,6] – C[[Dominant seventh chord|dom seventh]] (omit 5th)
# C E B [0,1,5] – C[[Major seventh chord|maj seventh]] (omit 5th)
# C F G♭ [0,5,6] (= inv. of [0,1,6]) – F[[Suspended chord|sus#1]]
# C F G [0,2,7]
# C F A♭ [0,3,7] – F[[minor chord|minor]]
# C F A [0,4,7] – F[[major chord|major]]
# C F B♭ [0,2,7]
# C F B [0,1,6]
# C G♭ G [0,1,6]
# C G♭ A♭ [0,2,6] – A{{music|flat}}[[Dominant seventh chord|dom seventh]] (omit 5th)
# C G♭ A [0,3,6] – F{{music|sharp}} dim
# C G♭ B♭ [0,4,6] (= inv. of [0,2,6])
# C G♭ B [0,5,6] (= inv. of [0,1,6])
# C G A♭ [0,1,5] – A{{Music|flat}}[[Major seventh chord|maj seventh]] (omit 5th)
# C G A [0,2,5]
# C G B♭ [0,3,5]
# C G B [0,4,5] (= inv. of [0,1,5])
# C A♭ A [0,1,4]
# C A♭ B♭ [0,2,4] – C[[Augmented triad|aug]] with [[Suspended chord|sus#6]]
# C A♭ B [0,1,4]
# C A B♭ [0,1,2]
# C A B [0,2,3] – this combination has no name
# C B♭ B [0,1,2] – this combination has no name (half step cluster, with doubly diminished third and quintuply diminished fifth, spelled enharmonically)


While some of these chords are recognizable and ubiquitous, many others are unusual or rarely used. Although this list enumerates only trichords containing the note C, the number of ''all'' possible trichords inside a single octave is 220 (the [[binomial coefficient]] of picking three keys out of twelve).

==See also==

* [[Triad (music)|Triad]]
* [[Hexachord|All-trichord hexachord]]

==References==
{{reflist|18em}}
'''Sources'''
* {{wikicite|ref={{harvid|Babbitt|1955}}|reference=[[Milton Babbitt|Babbitt, Milton]] (1955). "Some Aspects of Twelve-Tone Composition". ''The Score and I. M. A. Magazine'', no. 12 (June): 53–61.}}
* {{wikicite|ref={{harvid|Babbitt|1961}}|reference=Babbitt, Milton (1961). "Set Structure as a Compositional Determinant". ''[[Journal of Music Theory]]'' 5, no. 1 (Spring): 72–94.}}
* {{wikicite|ref={{harvid|Babbitt|2003}}|reference=Babbitt, Milton (2003). "Twelve-Tone Invariants as Compositional Determinants (1960)". In ''The Collected Essays of Milton Babbitt'', edited by Stephen Peles, Stephen Dembski, Andrew Mead, and Joseph Straus, 55–69. Princeton: Princeton University Press.}}
* {{cite book|last=Forte|first=Allen|author-link=Allen Forte|year=1973|title=The Structure of Atonal Music|place=New Haven and London|publisher=Yale University Press}} {{ISBN|0-300-01610-7}} (cloth) {{ISBN|0-300-02120-8}} (pbk).
* {{cite book|last=Friedmann|first=Michael L.|year=1990|title=Ear Training for Twentieth-Century Music|isbn=978-0-300-04537-6}}{{Full|date=September 2014|reason=Place and publisher needed}}
* {{wikicite|ref={{harvid|Gamer|1967}}|reference=Gamer, Carleton (1967). "Some Combinational Resources of Equal-Tempered Systems". ''[[Journal of Music Theory]]'' 11, no. 1 (Spring): 32–59.}}
* {{cite book|last=Hanson|first=Howard|author-link=Howard Hanson|year=1960|title=Harmonic Materials of Modern Music: Resources of the Tempered Scale|url=https://archive.org/details/harmonicmaterial00hans|place=New York|publisher=Appleton-Century-Crofts}}
* {{wikicite|ref={{harvid|Houlahan and Tacka|2008}}|reference=Houlahan, Mícheál, and Philip Tacka (2008). ''Kodály Today: A Cognitive Approach to Elementary Music Education''. Oxford and New York: Oxford University Press. {{ISBN|978-0-19-531409-0}}.}}
* {{wikicite|ref={{harvid|Kastal'skii|1961}}|reference=Kastal'skii, Aleksandr Dmitrievich (1961). Особенности народно-русской музыкальной системы [Properties of the Russian Folk Music System], edited by T. V. Popova. Moscow: Gosudarstvennoe muzykal'noe izdatel'stvo. (Reprint of a 1923 original.)}}
* {{wikicite|ref={{harvid|Rushton|2001}}|reference=[[Rushton, Julian]] (2001). "Trichord". ''[[The New Grove Dictionary of Music and Musicians]]'', second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (musicologist)|John Tyrrell]]. London: Macmillan.}}
* {{wikicite|ref={{harvid|Whittall|2008}}|reference=[[Arnold Whittall|Whittall, Arnold]] (2008). ''The Cambridge Introduction to Serialism''. New York: Cambridge University Press. {{ISBN|978-0-521-68200-8}} (pbk).}}

==Further reading==
* Gilbert, Steven E. (1970). "The Trichord: An Analytic Outlook for Twentieth-Century Music". Ph.D. diss. New Haven: Yale University.

{{Pitch segments}}

[[Category:Simultaneities (music)]]
[[Category:Chords]]