Minor chord: Difference between revisions
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second_interval=[[minor third]]| | second_interval=[[minor third]]| | ||
third_interval=[[perfect fifth]]| | third_interval=[[perfect fifth]]| | ||
tuning=[[just intonation|10:12:15]]<ref>{{cite book|last=Shirlaw|first=Matthew|title=The Theory of Harmony| date=16 June 2015 |page=81|isbn=978-1-4510-1534-8|quote=20:24:30}}</ref>| | tuning=[[just intonation|10:12:15]]<ref>{{cite book|last=Shirlaw|first=Matthew|title=The Theory of Harmony| date=16 June 2015 |page=81|publisher=Fb&c Limited |isbn=978-1-4510-1534-8|quote=20:24:30}}</ref>| | ||
forte_number=3-11| | forte_number=3-11| | ||
complement=9-11 | complement=9-11 | ||
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A minor triad can also be described by its [[Interval (music)|intervals]]: the interval between the bottom and middle notes is a minor third, and the interval between the middle and top notes is a [[major third]]. By contrast, a [[major triad]] has a major third on the bottom and minor third on top. They both contain fifths, because a minor third (three semitones) plus a major third (four semitones) equals a [[perfect fifth]] (seven semitones). Chords that are constructed of consecutive (or "stacked") thirds are called ''[[tertian]].'' | A minor triad can also be described by its [[Interval (music)|intervals]]: the interval between the bottom and middle notes is a minor third, and the interval between the middle and top notes is a [[major third]]. By contrast, a [[major triad]] has a major third on the bottom and minor third on top. They both contain fifths, because a minor third (three semitones) plus a major third (four semitones) equals a [[perfect fifth]] (seven semitones). Chords that are constructed of consecutive (or "stacked") thirds are called ''[[tertian]].'' | ||
In Western [[classical music]] from 1600 to 1820 and in Western [[Popular music|pop]], [[Folk music|folk]] and [[rock music]], a major chord is usually played as a triad. Along with the major triad, the minor triad is one of the basic building blocks of [[tonality|tonal]] music and the [[common practice period]]. In Western music, a minor chord, in comparison, "sounds darker than a major chord"<ref name="Kamien">{{cite book|author-link=Roger Kamien|last=Kamien|first=Roger|date=2008|title=Music: An Appreciation|edition=6th brief|page=[https://archive.org/details/music00roge/page/46 46]|isbn=978-0-07-340134-8|url=https://archive.org/details/music00roge/page/46}}</ref> but is still considered highly [[consonance and dissonance|consonant]], stable, or as not requiring [[resolution (music)|resolution]]. | In Western [[classical music]] from 1600 to 1820 and in Western [[Popular music|pop]], [[Folk music|folk]] and [[rock music]], a major chord is usually played as a triad. Along with the major triad, the minor triad is one of the basic building blocks of [[tonality|tonal]] music and the [[common practice period]]. In Western music, a minor chord, in comparison, "sounds darker than a major chord"<ref name="Kamien">{{cite book|author-link=Roger Kamien|last=Kamien|first=Roger|date=2008|title=Music: An Appreciation|edition=6th brief|page=[https://archive.org/details/music00roge/page/46 46]|publisher=McGraw-Hill Education |isbn=978-0-07-340134-8|url=https://archive.org/details/music00roge/page/46}}</ref> but is still considered highly [[consonance and dissonance|consonant]], stable, or as not requiring [[resolution (music)|resolution]]. | ||
Some minor chords with additional notes, such as the [[minor seventh chord]], may also be called minor chords. | Some minor chords with additional notes, such as the [[minor seventh chord]], may also be called minor chords. | ||
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[[Image:Harmonic Series.png|thumb|480x480px|An illustration of the harmonic series as musical notation. The numbers above the harmonic indicate the number of [[Cent (music)|cents]] it deviates from [[equal temperament]]. Red notes are sharp. Blue notes are flat.|alt=]] | [[Image:Harmonic Series.png|thumb|480x480px|An illustration of the harmonic series as musical notation. The numbers above the harmonic indicate the number of [[Cent (music)|cents]] it deviates from [[equal temperament]]. Red notes are sharp. Blue notes are flat.|alt=]] | ||
In [[just intonation]], a minor chord is often (but not exclusively) tuned in the frequency ratio 10:12:15 ({{Audio|Just minor triad on C.mid|play}}).<ref name="J&G">{{cite book|last1=Johnston|first1=Ben|last2=Gilmore|first2=Bob|date=2006|chapter=A Notation System for Extended Just Intonation|orig-year=2003|title="Maximum Clarity" and Other Writings on Music|page=78|isbn=978-0-252-03098-7|quote=D−, F, A (10/9–4/3–5/3)}}</ref> This is the first occurrence of a minor triad in the [[harmonic series (music)|harmonic series]] (if on C: E–G–B).<ref>{{cite book|last=Hauptmann|first=Moritz|date=1888|title=The Nature of Harmony and Metre|url=https://archive.org/details/natureharmonyan00haupgoog|page=[https://archive.org/details/natureharmonyan00haupgoog/page/n64 15]|publisher=Swan Sonnenschein}}</ref> This may be found on iii, vi, {{music|b}}vi, {{music|b}}iii, and vii.<ref>{{cite book|last=Wright|first=David|date=2009|title=Mathematics and Music|pages=140–141|isbn=978-0-8218-4873-9}}</ref> | In [[just intonation]], a minor chord is often (but not exclusively) tuned in the frequency ratio 10:12:15 ({{Audio|Just minor triad on C.mid|play}}).<ref name="J&G">{{cite book|last1=Johnston|first1=Ben|last2=Gilmore|first2=Bob|date=2006|chapter=A Notation System for Extended Just Intonation|orig-year=2003|title="Maximum Clarity" and Other Writings on Music|page=78|publisher=University of Illinois Press |isbn=978-0-252-03098-7|quote=D−, F, A (10/9–4/3–5/3)}}</ref> This is the first occurrence of a minor triad in the [[harmonic series (music)|harmonic series]] (if on C: E–G–B).<ref>{{cite book|last=Hauptmann|first=Moritz|date=1888|title=The Nature of Harmony and Metre|url=https://archive.org/details/natureharmonyan00haupgoog|page=[https://archive.org/details/natureharmonyan00haupgoog/page/n64 15]|publisher=Swan Sonnenschein}}</ref> This may be found on iii, vi, {{music|b}}vi, {{music|b}}iii, and vii.<ref>{{cite book|last=Wright|first=David|date=2009|title=Mathematics and Music|pages=140–141|publisher=American Mathematical Soc. |isbn=978-0-8218-4873-9}}</ref> | ||
In 12-TET, or twelve-tone [[equal temperament]] (now the most common tuning system in the [[West]]), a minor chord has 3 [[semitone]]s between the root and third, 4 between the third and fifth, and 7 between the root and fifth. It is represented by the [[pitch class|integer notation]] 0,3,7. The 12-TET fifth (700 [[cent (music)|cents]]) is only two cents narrower than the just perfect fifth (3:2, 701.9 cents), but the 12-TET minor third (300 cents) is noticeably (about 16 cents) narrower than the just minor third (6:5, 315.6 cents). The 12-TET minor third (300 cents) more closely approximates the [[19-limit]] ([[Limit (music)]]) minor third 16:19 {{audio|19th harmonic on C.mid|Play}} (297.5 cents, the nineteenth [[harmonic]]) with only 2 cents error.<ref>{{cite book|translator-first=Alexander J.|translator-last=Ellis|first=Hermann|last=Helmholtz|title=On the Sensations of Tone as a Physiological Basis for the Theory of Music|page=455|publisher=Dover Publications|location=New York|date=1954}}</ref> | In 12-TET, or twelve-tone [[equal temperament]] (now the most common tuning system in the [[West]]), a minor chord has 3 [[semitone]]s between the root and third, 4 between the third and fifth, and 7 between the root and fifth. It is represented by the [[pitch class|integer notation]] 0,3,7. The 12-TET fifth (700 [[cent (music)|cents]]) is only two cents narrower than the just perfect fifth (3:2, 701.9 cents), but the 12-TET minor third (300 cents) is noticeably (about 16 cents) narrower than the just minor third (6:5, 315.6 cents). The 12-TET minor third (300 cents) more closely approximates the [[19-limit]] ([[Limit (music)]]) minor third 16:19 {{audio|19th harmonic on C.mid|Play}} (297.5 cents, the nineteenth [[harmonic]]) with only 2 cents error.<ref>{{cite book|translator-first=Alexander J.|translator-last=Ellis|first=Hermann|last=Helmholtz|title=On the Sensations of Tone as a Physiological Basis for the Theory of Music|page=455|publisher=Dover Publications|location=New York|date=1954}}</ref> | ||
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Ellis proposes that the conflict between mathematicians and physicists on one hand and practicing musicians on the other regarding the supposed inferiority of the minor chord and scale to the major may be explained due to physicists' comparison of just minor and major triads, in which case minor comes out the loser, versus the musicians' comparison of the equal tempered triads, in which case minor comes out the winner since the ET major third is 14 cents sharp from the just major third while the ET minor third closely approximates the consonant 19:16 minor third, which many find pleasing.<ref>Ellis (1954), p.298.</ref>{{full citation needed|date=March 2017}} | Ellis proposes that the conflict between mathematicians and physicists on one hand and practicing musicians on the other regarding the supposed inferiority of the minor chord and scale to the major may be explained due to physicists' comparison of just minor and major triads, in which case minor comes out the loser, versus the musicians' comparison of the equal tempered triads, in which case minor comes out the winner since the ET major third is 14 cents sharp from the just major third while the ET minor third closely approximates the consonant 19:16 minor third, which many find pleasing.<ref>Ellis (1954), p.298.</ref>{{full citation needed|date=March 2017}} | ||
In the 16th through 18th centuries, prior to 12-TET, the minor third in [[Quarter-comma meantone#Construction of the chromatic scale|meantone temperament]] was 310 cents {{audio|Quarter-comma meantone minor third on C.mid|Play}} and much rougher than the 300 cent ET minor third. Other just minor chord tunings include the supertonic triad in just intonation (27:32:40)<ref name="J&G"/> the '''false minor triad''',<ref>{{cite book|last=Shirlaw|first=Matthew|title=The Theory of Harmony| date=16 June 2015 |page=375|isbn=978-1-4510-1534-8}}</ref> {{audio|Supertonic minor triad on C.mid|Play}}, 16:19:24<ref name="Ruland">{{cite book|last=Ruland|first=Heiner|date=1992|title=Expanding Tonal Awareness|page=39|isbn=978-1-85584-170-3}}</ref> {{audio|19th harmonic minor triad on C.mid|Play}}, 12:14:18 (6:7:9)<ref>{{cite book|first=Hermann|last=Helmholtz|date=1885|title=On the Sensations of Tone as a Physiological Basis for the Theory of Music|url=https://archive.org/details/onsensationston00unkngoog|page=[https://archive.org/details/onsensationston00unkngoog/page/n493 468]|publisher=Longmans, Green}}</ref><ref>{{cite journal|first=William Smythe Babcock|last=Mathews|date=1805|journal=Music: A Monthly Magazine | In the 16th through 18th centuries, prior to 12-TET, the minor third in [[Quarter-comma meantone#Construction of the chromatic scale|meantone temperament]] was 310 cents {{audio|Quarter-comma meantone minor third on C.mid|Play}} and much rougher than the 300 cent ET minor third. Other just minor chord tunings include the supertonic triad in just intonation (27:32:40)<ref name="J&G"/> the '''false minor triad''',<ref>{{cite book|last=Shirlaw|first=Matthew|title=The Theory of Harmony| date=16 June 2015 |page=375|publisher=Fb&c Limited |isbn=978-1-4510-1534-8}}</ref> {{audio|Supertonic minor triad on C.mid|Play}}, 16:19:24<ref name="Ruland">{{cite book|last=Ruland|first=Heiner|date=1992|title=Expanding Tonal Awareness|page=39|publisher=Rudolf Steiner Press |isbn=978-1-85584-170-3}}</ref> {{audio|19th harmonic minor triad on C.mid|Play}}, 12:14:18 (6:7:9)<ref>{{cite book|first=Hermann|last=Helmholtz|date=1885|title=On the Sensations of Tone as a Physiological Basis for the Theory of Music|url=https://archive.org/details/onsensationston00unkngoog|page=[https://archive.org/details/onsensationston00unkngoog/page/n493 468]|publisher=Longmans, Green}}</ref><ref>{{cite journal|first=William Smythe Babcock|last=Mathews|date=1805|journal=Music: A Monthly Magazine |volume=7|page=608|quote=The tones re, fa, and la, as given on the accordion, are vibrationally 6:7:9. This is ''not'' a minor triad, nor anything very near it although its fifth is just the same as in the minor and the major, and the ratio 6:9 being simply 2:3.}}</ref> {{audio|Septimal minor triad on C.mid|Play}} ([[septimal minor third]]), and the Pythagorean minor triad<ref name="Ruland"/> (54:64:81) {{audio|Pythagorean minor triad on C.mid|Play}}. More tunings of the minor chord are also available in various equal temperaments other than 12-TET. | ||
Rather than directly from the [[harmonic series (music)|harmonic series]], [[Georg Andreas Sorge|Sorge]] derived the minor chord from joining two major triads; for example the A minor triad being the confluence of the F and C major triads.<ref name="Lester">{{cite book|last=Lester|first=Joel|date=1994|title=Compositional Theory in the Eighteenth Century|page=194|isbn=978-0-674-15523-7}}</ref> A–C–E = ''F''–A–C–E–''G''. Given justly tuned major triads this produces a justly tuned minor triad: 10:12:15 on 8:5. | Rather than directly from the [[harmonic series (music)|harmonic series]], [[Georg Andreas Sorge|Sorge]] derived the minor chord from joining two major triads; for example the A minor triad being the confluence of the F and C major triads.<ref name="Lester">{{cite book|last=Lester|first=Joel|date=1994|title=Compositional Theory in the Eighteenth Century|page=194|isbn=978-0-674-15523-7}}</ref> A–C–E = ''F''–A–C–E–''G''. Given justly tuned major triads this produces a justly tuned minor triad: 10:12:15 on 8:5. | ||
Latest revision as of 23:33, 29 June 2025
Template:Short description Script error: No such module "Infobox".Template:Template other
In music theory, a minor chord is a chord that has a root, a minor third, and a perfect fifth.[1] When a chord comprises only these three notes, it is called a minor triad. For example, the minor triad built on A, called an A minor triad, has pitches A–C–E: <score sound="1"> { \omit Score.TimeSignature \relative c' { <a c e>1 } } </score>
In harmonic analysis and on lead sheets, a C minor chord can be notated as Cm, C−, Cmin, or simply the lowercase "c". A minor triad is represented by the integer notation {0, 3, 7}.
A minor triad can also be described by its intervals: the interval between the bottom and middle notes is a minor third, and the interval between the middle and top notes is a major third. By contrast, a major triad has a major third on the bottom and minor third on top. They both contain fifths, because a minor third (three semitones) plus a major third (four semitones) equals a perfect fifth (seven semitones). Chords that are constructed of consecutive (or "stacked") thirds are called tertian.
In Western classical music from 1600 to 1820 and in Western pop, folk and rock music, a major chord is usually played as a triad. Along with the major triad, the minor triad is one of the basic building blocks of tonal music and the common practice period. In Western music, a minor chord, in comparison, "sounds darker than a major chord"[2] but is still considered highly consonant, stable, or as not requiring resolution.
Some minor chords with additional notes, such as the minor seventh chord, may also be called minor chords.
Acoustic consonance of the minor chord
Script error: No such module "Unsubst". A unique particularity of the minor chord is that this is the only chord of three notes in which the three notes have one harmonic – hearable and with a not too high row – in common (more or less exactly, depending on the tuning system used). This harmonic, common to the three notes, is situated 2 octaves above the high note of the chord. This is the sixth harmonic of the root of the chord, the fifth of the middle note, and the fourth of the high note:
- In the example C, ETemplate:Music, G, the common harmonic is a G 2 octaves above.
Demonstration:
- Minor third = 6:5 = 12:10
- Major third = 5:4 = 15:12
- So the ratios of minor chord are 10:12:15
- And the explication of the unique harmonic in common, between the three notes, is verified by : 10 × 6 = 12 × 5 = 15 × 4
Just intonation
In just intonation, a minor chord is often (but not exclusively) tuned in the frequency ratio 10:12:15 ({{errorTemplate:Main other|Audio file "Just minor triad on C.mid" not found}}Template:Category handler).[3] This is the first occurrence of a minor triad in the harmonic series (if on C: E–G–B).[4] This may be found on iii, vi, Template:Musicvi, Template:Musiciii, and vii.[5]
In 12-TET, or twelve-tone equal temperament (now the most common tuning system in the West), a minor chord has 3 semitones between the root and third, 4 between the third and fifth, and 7 between the root and fifth. It is represented by the integer notation 0,3,7. The 12-TET fifth (700 cents) is only two cents narrower than the just perfect fifth (3:2, 701.9 cents), but the 12-TET minor third (300 cents) is noticeably (about 16 cents) narrower than the just minor third (6:5, 315.6 cents). The 12-TET minor third (300 cents) more closely approximates the 19-limit (Limit (music)) minor third 16:19 {{errorTemplate:Main other|Audio file "19th harmonic on C.mid" not found}}Template:Category handler (297.5 cents, the nineteenth harmonic) with only 2 cents error.[6]
Ellis proposes that the conflict between mathematicians and physicists on one hand and practicing musicians on the other regarding the supposed inferiority of the minor chord and scale to the major may be explained due to physicists' comparison of just minor and major triads, in which case minor comes out the loser, versus the musicians' comparison of the equal tempered triads, in which case minor comes out the winner since the ET major third is 14 cents sharp from the just major third while the ET minor third closely approximates the consonant 19:16 minor third, which many find pleasing.[7]Template:Full citation needed
In the 16th through 18th centuries, prior to 12-TET, the minor third in meantone temperament was 310 cents {{errorTemplate:Main other|Audio file "Quarter-comma meantone minor third on C.mid" not found}}Template:Category handler and much rougher than the 300 cent ET minor third. Other just minor chord tunings include the supertonic triad in just intonation (27:32:40)[3] the false minor triad,[8] {{errorTemplate:Main other|Audio file "Supertonic minor triad on C.mid" not found}}Template:Category handler, 16:19:24[9] {{errorTemplate:Main other|Audio file "19th harmonic minor triad on C.mid" not found}}Template:Category handler, 12:14:18 (6:7:9)[10][11] {{errorTemplate:Main other|Audio file "Septimal minor triad on C.mid" not found}}Template:Category handler (septimal minor third), and the Pythagorean minor triad[9] (54:64:81) {{errorTemplate:Main other|Audio file "Pythagorean minor triad on C.mid" not found}}Template:Category handler. More tunings of the minor chord are also available in various equal temperaments other than 12-TET.
Rather than directly from the harmonic series, Sorge derived the minor chord from joining two major triads; for example the A minor triad being the confluence of the F and C major triads.[12] A–C–E = F–A–C–E–G. Given justly tuned major triads this produces a justly tuned minor triad: 10:12:15 on 8:5.
Minor chord table
Chord Root Minor third Perfect fifth Cm C ETemplate:Music G CTemplate:Musicm CTemplate:Music E GTemplate:Music DTemplate:Musicm DTemplate:Music FTemplate:Music (E) ATemplate:Music Dm D F A DTemplate:Musicm DTemplate:Music FTemplate:Music ATemplate:Music ETemplate:Musicm ETemplate:Music GTemplate:Music BTemplate:Music Em E G B Fm F ATemplate:Music C FTemplate:Musicm FTemplate:Music A CTemplate:Music GTemplate:Musicm GTemplate:Music BTemplate:Music (A) DTemplate:Music Gm G BTemplate:Music D GTemplate:Musicm GTemplate:Music B DTemplate:Music ATemplate:Musicm ATemplate:Music CTemplate:Music (B) ETemplate:Music Am A C E ATemplate:Musicm ATemplate:Music CTemplate:Music ETemplate:Music (F) BTemplate:Musicm BTemplate:Music DTemplate:Music F Bm B D FTemplate:Music
See also
References
External links
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- ↑ Ellis (1954), p.298.
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