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词条 Minor chord
释义

  1. Acoustic consonance of the minor chord

  2. Just intonation

  3. Minor chord table

  4. See also

  5. References

{{Infobox chord|

chord_name=minor triad|

first_interval=root|

second_interval=minor third|

third_interval=perfect fifth|

tuning=10:12:15[1]|

forte_number=3-11|

complement=9-11


}}

In music theory, a minor chord is a chord having a root, a minor third, and a perfect fifth.[2] When a chord has these three notes alone, it is called a minor triad. For example, the minor triad built on C, called a C minor triad, has pitches C–E{{music|flat}}–G:

{

\\override Score.TimeSignature #'stencil = ##f

\\relative c' {

   \\clef treble    \\time 4/4   \\key c \\major

1

} }

A minor triad can be represented by the integer notation {0, 3, 7}.

A minor triad can also be described by its intervals: it has as a minor third interval on the bottom and a major third on top or as a root note. 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).

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"[3] 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

{{unreferenced section|date=March 2017}}

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, E{{music|flat}}, 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 ({{Audio|Just minor triad on C.mid|play}}).[4] This is the first occurrence of a minor triad in the harmonic series (if on C: E–G–B).[5] This may be found on iii, vi, {{music|b}}vi, {{music|b}}iii, and vii.[6]

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 {{audio|19th harmonic on C.mid|Play}} (297.5 cents, the nineteenth harmonic) with only 2 cents error.[7]

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.[8]{{full citation needed|date=March 2017}}

In the 16th through 18th centuries, prior to 12-TET, the minor third in 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)[4] the false minor triad,[9] {{audio|Supertonic minor triad on C.mid|Play}}, 16:19:24[10] {{audio|19th harmonic minor triad on C.mid|Play}}, 12:14:18 (6:7:9)[11][12] {{audio|Septimal minor triad on C.mid|Play}} (septimal minor third), and the Pythagorean minor triad[10] (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, 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.[13] 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

ChordRootMinor thirdPerfect fifth
CmCb}}G
#m#}}E#}}
bmb}}b}} (E)b}}
DmDFA
#m#}}#}}#}}
bmb}}b}}b}}
EmEGB
FmFb}}C
#m#}}A#}}
bmb}}bb}} (A)b}}
GmGb}}D
#m#}}B#}}
bmb}}b}} (B)b}}
AmACE
#m#}}#}}#}} (F)
bmb}}b}}F
BmBD#}}

See also

  • Major and minor
  • Musical tuning
  • Major chord
  • Otonality and Utonality

References

1. ^{{cite book|last=Shirlaw|first=Matthew|title=The Theory of Harmony|page=81|ISBN=978-1-4510-1534-8|quote=20:24:30}}
2. ^{{cite book|last=Miller|first=Michael|url=https://books.google.com/books?id=sTMbuSQdqPMC|title=The Complete Idiot's Guide to Music Theory|edition=2nd|page=114|location=Indianapolis|publisher=Alpha|date=2005|ISBN=1-59257-437-8}}
3. ^{{cite book|authorlink=Roger Kamien|last=Kamien|first=Roger|date=2008|title=Music: An Appreciation|edition=6th brief|page=46|ISBN=978-0-07-340134-8}}
4. ^1 {{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)}}
5. ^{{cite book|last=Hauptmann|first=Moritz|date=1888|title=The Nature of Harmony and Metre|page=15|publisher=Swan Sonnenschein}}
6. ^{{cite book|last=Wright|first=David|date=2009|title=Mathematics and Music|page=140–141|ISBN=978-0-8218-4873-9}}
7. ^{{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}}
8. ^Ellis (1954), p.298.
9. ^{{cite book|last=Shirlaw|first=Matthew|title=The Theory of Harmony|page=375|ISBN=978-1-4510-1534-8|}}
10. ^1 {{cite book|last=Ruland|first=Heiner|date=1992|title=Expanding Tonal Awareness|page=39|ISBN=978-1-85584-170-3}}
11. ^{{cite book|first=Hermann|last=Helmholtz|date=1885|title=On the Sensations of Tone as a Physiological Basis for the Theory of Music|page=468|publisher=Longmans, Green}}
12. ^{{cite journal|first=William Smythe Babcock|last=Mathews|date=1805|journal=Music: A Monthly Magazine Devoted to the Art, Science, Technic and Literature of Music|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.}}
13. ^{{cite book|last=Lester|first=Joel|date=1994|title=Compositional Theory in the Eighteenth Century|page=194|ISBN=978-0-674-15523-7}}
{{Chords}}{{DEFAULTSORT:Minor Chord}}

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