Editing Major and minor

{{Short description|Musical concepts}}
{{About|the musical concept|the academic disciplines|Academic major|and|Academic minor}}
In [[Western culture#Music|Western music]], the adjectives '''major''' and '''minor''' may describe an [[Interval (music)|interval]], [[chord (music)|chord]], [[scale (music)|scale]], or [[key (music)|key]]. A [[musical composition|composition]], [[movement (music)|movement]], [[section (music)|section]], or [[Phrase (music)|phrase]] may also be referred to by its key, including whether that key is major or minor.

The words derive from Latin words meaning "large" and "small," and were originally applied to the intervals between notes, which may be larger or smaller depending on how many [[Semitone|semitones]] (half-steps) they contain. Chords and scales are described as major or minor when they contain the corresponding intervals, usually major or minor thirds.

==Intervals==
A major interval is one [[semitone]] larger than a minor interval. The words ''perfect'', ''diminished'' and ''augmented'' are also used to describe the [[Interval quality|quality of an interval]]. Only the intervals of a second, third, sixth, and seventh (and the [[compound intervals]] based on them) may be major or minor (or, rarely, diminished or augmented). [[Unison (music)|Unisons]], fourths, fifths, and octaves and their compound interval must be perfect (or, rarely, diminished or augmented). In Western music, a [[minor chord]] "sounds darker than a [[major chord]]".<ref name="Kamien">[[Roger Kamien|Kamien, Roger]] (2008). ''Music: An Appreciation'', 6th Brief Edition, p.&nbsp;46. {{ISBN|978-0-07-340134-8}}.</ref>

== Scales and chords ==
{{main|Major scale|Minor scale|Major chord|Minor chord}}
{{Image frame|content=<score sound="1">
{
\override Score.TimeSignature #'stencil = ##f
\relative c' {
  \clef treble
  \time 9/4
  c4 d e f g a b c2 \bar "||"
} }
</score>

<score sound="1">
{
\override Score.TimeSignature #'stencil = ##f
\relative c' {
  \clef treble
  \time 9/4
  c4 d es f g aes bes c2 \bar "||"
} }
</score>|width=300|caption=[[Parallel key|Parallel]] major and (natural) minor scales on&nbsp;C}}
[[File:Major and minor thirds.png|thumb|right|Major and minor third in a major chord: major third 'M' on bottom, minor third 'm' on top[[File:Major and minor thirds.mid]]]]
''Major'' and ''minor'' may also refer to scales and chords that contain a [[major third]] or a [[minor third]], respectively.

* A [[major scale]] is a scale in which the third [[degree (music)|scale degree]] (the [[mediant]]) is a major third above the [[Tonic (music)|tonic]] note. In a [[minor scale]], the third degree is a minor third above the tonic.
* Similarly, in a [[major triad]] or [[major seventh chord]], the third is a major third above the chord's [[root (chord)|root]]. In a [[minor triad]] or [[minor seventh chord]], the third is a minor third above the root.

==Keys==
The hallmark that distinguishes major keys from minor is whether the third [[scale degree]] is major or minor. Major and minor keys are based on the corresponding scales, and the [[Tonic (music)|tonic triad]] of those keys consist of the corresponding chords; however, a major key can encompass minor chords based on other roots, and vice versa.

As [[Musicology|musicologist]] [[Roger Kamien]] explains, "the crucial difference is that in the minor scale there is only a [[half step]] between '2nd and 3rd note' and between '5th and 6th note' as compared to the major scales where the difference between '3rd and 4th note' and between '7th and 8th note' is [a [[half step]]]."<ref name="Kamien" /> This alteration in the third degree "greatly changes" the mood of the music, and "music based on minor scales tends to" be considered to "sound serious or melancholic,"<ref name="Kamien" /> at least to contemporary Western ears.

Minor keys are sometimes said to have a more interesting, possibly darker sound than plain major scales.<ref>Craig Wright (September 18, 2008).[http://oyc.yale.edu/music/listening-to-music/content/transcripts/transcript-5-melody-notes-scales-nuts-and-bolts "Listening to Music: Lecture 5 Transcript"] {{webarchive|url=https://web.archive.org/web/20100804193937/http://oyc.yale.edu/music/listening-to-music/content/transcripts/transcript-5-melody-notes-scales-nuts-and-bolts |date=2010-08-04 }}, ''Open Yale Courses''.</ref> [[Harry Partch]] considers minor as, "the immutable faculty of ratios, which in turn represent an immutable faculty of the human ear."<ref name="Genesis">[[Harry Partch|Partch, Harry]] (2009). ''[[Genesis of a Music]]: An Account of a Creative Work, Its Roots, and Its Fulfillments'', pp. 89–90. {{ISBN|9780786751006}}.</ref> The minor key and scale are also considered less justifiable than the major, with [[Paul Hindemith]] calling it a "clouding" of major, and [[Moritz Hauptmann]] calling it a "falsehood of the major".<ref name="Genesis" />

Changes of mode, which involve the alteration of the third, and [[mode mixture]] are often analyzed as minor changes unless structurally supported because the root and overall key and tonality remain unchanged. This is in contrast with, for instance, [[transposition (music)|transposition]]. Transposition is done by moving all intervals up or down a certain constant interval, and ''does'' change the [[key (music)|key]] but not the [[Musical mode|mode]], which requires the alteration of intervals. The use of [[triad (music)|triad]]s only available in the minor mode, such as the use of A{{music|flat}}-major in C major, is relatively decorative [[chromaticism]], considered to add color and weaken the sense of key without entirely destroying or losing it.

==Intonation and tuning==
Musical tuning of intervals is expressed by the ratio between the pitches' frequencies. Simple fractions can sound more harmonious than complex fractions; for instance, an [[octave]] is a simple 2:1&nbsp;ratio and a [[Perfect fifth|fifth]] is the relatively simple 3:2&nbsp;ratio. The table below gives frequency ratios that are mathematically exact for [[just intonation]], which [[meantone temperament]]s seek to approximate.
:{| class="wikitable"  style="text-align:center;vertical-align:center;"
|-
| '''Note name'''
| '''C''' || '''D''' || '''E''' || '''F''' || '''G''' || '''A''' || '''B''' || '''C'''′  
|-
| '''frequency ratio'''<br/>([[just intonation|just int.]])
| {{big|{{sfrac| 1 | 1 }} }} || {{big|{{sfrac| 9 | 8 }} }} || {{big|{{sfrac| 5 | 4 }} }} || {{big|{{sfrac| 4 | 3 }} }} || {{big|{{sfrac| 3 | 2 }} }} || {{big|{{sfrac| 5 | 3 }} }} || {{big|{{sfrac| 15 | 8 }} }} || {{big|{{sfrac| 2 | 1 }} }}
|-
| '''Interval name'''<br/>(from '''C''')
| {{small|perf&thinsp;}}{{big|1}}{{sup|&thinsp;st}} || {{sup|Maj&thinsp;}}{{big|2}}{{sup|&thinsp;nd}} || {{sup|Maj&thinsp;}}{{big|3}}{{sup|&thinsp;rd}} || {{small|perf&thinsp;}}{{big|4}}{{sup|&thinsp;th}} || {{small|perf&thinsp;}}{{big|5}}{{sup|&thinsp;th}} || {{sup|Maj&thinsp;}}{{big|6}}{{sup|&thinsp;th}} || {{sup|Maj&thinsp;}}{{big|7}}{{sup|&thinsp;th}} || {{small|perf&thinsp;}}{{big|8}}{{sup|&thinsp;th}}
|-
| '''Interval size'''<br/>(in [[musical cents|cents]])
| &nbsp; {{0}}{{0}}0{{0}}¢{{0}} &nbsp; || &nbsp; {{0}}203.9¢ &nbsp; || &nbsp; {{0}}386.3¢ &nbsp; || &nbsp; {{0}}498.0¢ &nbsp; || &nbsp; {{0}}702.0¢ &nbsp; || &nbsp; {{0}}884.4¢ &nbsp; || &nbsp; 1088.3¢ &nbsp; || &nbsp; 1200{{0}}¢ &nbsp; 
|}

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}}). In [[12 tone equal temperament|12&nbsp;tone equal temperament]] {{nobr|(12 {{sc|TET}},}} at present the most common tuning system in the West) a minor chord has 3&nbsp;[[semitone]]s between the root and third, 4&nbsp;between the third and fifth, and 7&nbsp;between the root and fifth.

In {{nobr|12 {{sc|TET}},}} the perfect fifth (700&nbsp;[[cent (music)|cents]]) is only about two cents narrower than the justly tuned perfect fifth (3:2, or 702.0&nbsp;cents), but the minor third (300 cents) is noticeably (about 16&nbsp;cents) narrower than the just minor third (6:5, or 315.6&nbsp;cents). Moreover, the minor third (300&nbsp;cents) more closely approximates the [[19-limit]] ([[Limit (music)|Limit]]) minor third (19:16 {{audio|19th harmonic on C.mid|Play}} or, 297.5&nbsp;cents, the nineteenth [[harmonic]]) with only about a 2&nbsp;cent error.<ref name=Ellis-Helmhz-1954>A.J. Ellis, writing in {{cite book |author2-link=Alexander John Ellis |first2=A.J. |last2=Ellis |translator=[[Alexander John Ellis|Ellis, A.J.]] |author1-link=Hermann von Helmholtz |first1=H.L. |last1=von&nbsp;Helmholtz |title-link=Sensations of Tone |title=On the Sensations of Tone as a Physiological Basis for the Theory of Music |page=455 |publisher=Dover Publications |place=New York, NY |year=1954 |edition=reprint}}</ref>

[[Alexander John Ellis|A.J. Ellis]] proposed 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 just 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 {{nobr|12 {{sc|TET}} }} major third is about 14&nbsp;cents sharp from the just major third (5:4, or 386.3&nbsp;cents), but only about 4&nbsp;cents narrower than the 19&nbsp;limit major third (24:19, or 404.4&nbsp;cents); while the {{nobr|12 {{sc|TET}} }} minor third closely approximates the 19:16&nbsp;minor third which many find pleasing.<ref name=Ellis-Helmhz-1954/>{{rp|style=ama|p=298}}{{efn|In the 16th through 18th&nbsp;centuries, prior to 12&nbsp;TET, the minor third in [[Quarter-comma meantone#Construction of the chromatic scale|meantone temperament]] was 310&nbsp;cents {{audio|Quarter-comma meantone minor third on C.mid|Play}} and much rougher than the 300&nbsp;cent {{nobr|12 {{sc|TET}} }} minor third.<ref name=Ellis-Helmhz-1954/>{{rp|style=ama|p=298}} }}

==Advanced theory==
[[File:Minor as upside down major.png|thumb|right|300px|Minor as upside down major]]In the [[Neo-Riemannian theory]], the minor mode is considered the [[Melodic inversion|inverse]] of the major mode, an upside down major scale based on (theoretical) [[Undertone series|undertones]] rather than (actual) [[Overtone|overtones]] ([[harmonic]]s) (See also: [[Utonality]]).

The [[Root (chord)|root]] of the minor triad is thus considered the top of the fifth, which, in the United States, is called the fifth. So in C minor, the tonic is actually G and the [[Leading-tone|leading tone]] is A{{music|b}} (a half step), rather than, in major, the root being C and the leading tone B (a half step). Also, since all chords are analyzed as having a [[Tonic (music)|tonic]], [[subdominant]], or [[Dominant (music)|dominant]] [[Function (music)|function]], with, for instance, in C, A minor being considered the tonic parallel (tP) (US relative), the use of minor mode root chord progressions in major such as A{{music|b}}-major–B{{music|b}}-major–C-major is analyzed as sP–dP–T, the minor subdominant parallel (see: [[parallel and counter parallel|parallel chord]]), the minor dominant parallel, and the major tonic.<ref>{{Cite book|last=Gjerdingen|first=Robert|author-link=Robert Gjerdingen|title=Studies on the Origin of Harmonic Tonality|location=Princeton|publisher=Princeton University Press|year=1990|isbn=978-0-691-09135-8|jstor=j.ctt7ztxzh}} English translation of [[Carl Dahlhaus]]'s ''Untersuchungen über die Entstehung der harmonischen Tonalität'' (1968).</ref>

==See also==
* [[Gypsy scale]]
* [[List of major/minor compositions]]
* [[Music written in all major or minor keys]]
* [[Otonality and utonality]]

==Notes==
{{notelist}}

==References==
{{reflist}}

{{Key (music)}}
{{Tonality}}
{{Authority control}}
{{DEFAULTSORT:Major And Minor}}
[[Category:Intervals (music)]]
[[Category:Harmony]]
[[Category:Musical scales]]