Major and minor

Last updated April 08, 2024

In Western music, the adjectives major and minor may describe an interval, chord, scale, or key. A composition, movement, section, or 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 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 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). 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".^[1]

Scales and chords

Parallel major and (natural) minor scales on C

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 scale degree (the mediant) is a major third above the 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. 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 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 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]."^[1] 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,"^[1] at least to contemporary Western ears.

Minor keys are sometimes said to have a more interesting, possibly darker sound than plain major scales.^[2] Harry Partch considers minor as, "the immutable faculty of ratios, which in turn represent an immutable faculty of the human ear."^[3] 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".^[3]

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. Transposition is done by moving all intervals up or down a certain constant interval, and does change the key but not the mode, which requires the alteration of intervals. The use of triads only available in the minor mode, such as the use of A♭-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 ratio and a fifth is the relatively simple 3:2 ratio. The table below gives frequency ratios that are mathematically exact for just intonation, which meantone temperaments seek to approximate.

Note name	C	D	E	F	G	A	B	C′
frequency ratio (just int.)	1 / 1	9 / 8	5 / 4	4 / 3	3 / 2	5 / 3	15 / 8	2 / 1
Interval name (from C)	perf 1^st	^Maj2^nd	^Maj3^rd	perf 4^th	perf 5^th	^Maj6^th	^Maj7^th	perf 8^th
Interval size (in cents)	0000¢0	0203.9¢	0386.3¢	0498.0¢	0702.0¢	0884.4¢	1088.3¢	12000¢

In just intonation, a minor chord is often (but not exclusively) tuned in the frequency ratio 10:12:15 ( play ^ⓘ). In 12 tone equal temperament (12 TET, at present 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.

In 12 TET, the perfect fifth (700 cents) is only about two cents narrower than the justly tuned perfect fifth (3:2, or 702.0 cents), but the minor third (300 cents) is noticeably (about 16 cents) narrower than the just minor third (6:5, or 315.6 cents). Moreover, the minor third (300 cents) more closely approximates the 19-limit (Limit) minor third (19:16 Play ^ⓘ or, 297.5 cents, the nineteenth harmonic) with only about a 2 cent error.^[4]

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 12 TET major third is about 14 cents sharp from the just major third (5:4, or 386.3 cents), but only about 4 cents narrower than the 19 limit major third (24:19, or 404.4 cents); while the 12 TET minor third closely approximates the 19:16 minor third which many find pleasing.^[4]^(p298)^{[lower-alpha 1]}

Advanced theory

In the Neo-Riemannian theory, the minor mode is considered the inverse of the major mode, an upside down major scale based on (theoretical) undertones rather than (actual) overtones (harmonics) (See also: Utonality).

The 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 is A♭ (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, subdominant, or dominant function, with, for instance, in C, A minor being considered the tonic parallel (US relative), Tp, the use of minor mode root chord progressions in major such as A♭-major–B♭-major–C-major is analyzed as sP–dP–T, the minor subdominant parallel (see: parallel chord), the minor dominant parallel, and the major tonic.^[5]

Notes

↑ In the 16th through 18th centuries, prior to 12 TET, the minor third in meantone temperament was 310 cents Play and much rougher than the 300 cent 12 TET minor third. [4] (p298)

Related Research Articles

In music theory, a diatonic scale is any heptatonic scale that includes five whole steps and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps, depending on their position in the scale. This pattern ensures that, in a diatonic scale spanning more than one octave, all the half steps are maximally separated from each other.

The major scale is one of the most commonly used musical scales, especially in Western music. It is one of the diatonic scales. Like many musical scales, it is made up of seven notes: the eighth duplicates the first at double its frequency so that it is called a higher octave of the same note.

In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.

In music theory, the tritone is defined as a musical interval spanning three adjacent whole tones. For instance, the interval from F up to the B above it is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B.

In music theory, the key of a piece is the group of pitches, or scale, that forms the basis of a musical composition in Western classical music, art music, and pop music.

Tonality or key: Music which uses the notes of a particular scale is said to be "in the key of" that scale or in the tonality of that scale.

In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.

In music theory, the wolf fifth is a particularly dissonant musical interval spanning seven semitones. Strictly, the term refers to an interval produced by a specific tuning system, widely used in the sixteenth and seventeenth centuries: the quarter-comma meantone temperament. More broadly, it is also used to refer to similar intervals produced by other tuning systems, including Pythagorean and most meantone temperaments.

A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent notes in a 12-tone scale, visually seen on a keyboard as the distance between two keys that are adjacent to each other. For example, C is adjacent to C♯; the interval between them is a semitone.

In classical music, a third is a musical interval encompassing three staff positions, and the major third is a third spanning four half steps or two whole steps. Along with the minor third, the major third is one of two commonly occurring thirds. It is qualified as major because it is the larger interval of the two: the major third spans four semitones; the minor third, three. For example, the interval from C to E is a major third, as the note E lies four semitones above C, and there are three staff positions from C to E. Diminished and augmented thirds span the same number of staff positions, but consist of a different number of semitones.

The intervals from the tonic (keynote) in an upward direction to the second, to the third, to the sixth, and to the seventh scale degrees of a major scale are called major.

In music theory, a minor third is a musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions. The minor third is one of two commonly occurring thirds. It is called minor because it is the smaller of the two: the major third spans an additional semitone. For example, the interval from A to C is a minor third, as the note C lies three semitones above A. Coincidentally, there are three staff positions from A to C. Diminished and augmented thirds span the same number of staff positions, but consist of a different number of semitones. The minor third is a skip melodically.

In music from Western culture, a sixth is a musical interval encompassing six note letter names or staff positions, and the major sixth is one of two commonly occurring sixths. It is qualified as major because it is the larger of the two. The major sixth spans nine semitones. Its smaller counterpart, the minor sixth, spans eight semitones. For example, the interval from C up to the nearest A is a major sixth. It is a sixth because it encompasses six note letter names and six staff positions. It is a major sixth, not a minor sixth, because the note A lies nine semitones above C. Diminished and augmented sixths span the same number of note letter names and staff positions, but consist of a different number of semitones.

The intervals from the tonic (keynote) in an upward direction to the second, to the third, to the sixth, and to the seventh scale degrees (of a major scale are called major.

In music theory, a major chord is a chord that has a root, a major third, and a perfect fifth. When a chord comprises only these three notes, it is called a major triad. For example, the major triad built on C, called a C major triad, has pitches C–E–G:

In music theory, a minor chord is a chord that has a root, a minor third, and a perfect fifth. 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:

In Western classical music, an augmented fifth is an interval produced by widening a perfect fifth by a chromatic semitone. For instance, the interval from C to G is a perfect fifth, seven semitones wide, and both the intervals from C♭ to G, and from C to G♯ are augmented fifths, spanning eight semitones. Being augmented, it is considered a dissonant interval.

In music theory, a comma is a very small interval, the difference resulting from tuning one note two different ways. Strictly speaking, there are only two kinds of comma, the syntonic comma, "the difference between a just major 3rd and four just perfect 5ths less two octaves", and the Pythagorean comma, "the difference between twelve 5ths and seven octaves". The word comma used without qualification refers to the syntonic comma, which can be defined, for instance, as the difference between an F♯ tuned using the D-based Pythagorean tuning system, and another F♯ tuned using the D-based quarter-comma meantone tuning system. Intervals separated by the ratio 81:80 are considered the same note because the 12-note Western chromatic scale does not distinguish Pythagorean intervals from 5-limit intervals in its notation. Other intervals are considered commas because of the enharmonic equivalences of a tuning system. For example, in 53TET, B♭ and A♯ are both approximated by the same interval although they are a septimal kleisma apart.

Quarter-comma meantone, or  1 / 4 -comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. In this system the perfect fifth is flattened by one quarter of a syntonic comma ( 81 : 80 ), with respect to its just intonation used in Pythagorean tuning ; the result is $3 / 2 \times [80 / 81] 1 / 4 = 4 \sqrt 5 \approx 1.49535$ , or a fifth of 696.578 cents. This fifth is then iterated to generate the diatonic scale and other notes of the temperament. The purpose is to obtain justly intoned major thirds. It was described by Pietro Aron in his Toscanello de la Musica of 1523, by saying the major thirds should be tuned to be "sonorous and just, as united as possible." Later theorists Gioseffo Zarlino and Francisco de Salinas described the tuning with mathematical exactitude.

In music, 53 equal temperament, called 53 TET, 53 EDO, or 53 ET, is the tempered scale derived by dividing the octave into 53 equal steps. Each step represents a frequency ratio of 2^1⁄53, or 22.6415 cents, an interval sometimes called the Holdrian comma.

In music, the septimal major third, also called the supermajor third, septimal supermajor third, and sometimes Bohlen–Pierce third is the musical interval exactly or approximately equal to a just 9:7 ratio of frequencies, or alternately 14:11. It is equal to 435 cents, sharper than a just major third (5:4) by the septimal quarter tone (36:35). In 24-TET the septimal major third is approximated by 9 quarter tones, or 450 cents. Both 24 and 19 equal temperament map the septimal major third and the septimal narrow fourth (21:16) to the same interval.

The harmonic seventh interval, also known as the septimal minor seventh, or subminor seventh, is one with an exact 7:4 ratio (about 969 cents). This is somewhat narrower than and is, "particularly sweet", "sweeter in quality" than an "ordinary" just minor seventh, which has an intonation ratio of 9:5 (about 1018 cents).

Five-limit tuning, 5-limit tuning, or 5-prime-limit tuning (not to be confused with 5-odd-limit tuning), is any system for tuning a musical instrument that obtains the frequency of each note by multiplying the frequency of a given reference note (the base note) by products of integer powers of 2, 3, or 5 (prime numbers limited to 5 or lower), such as 2⁻³·3¹·5¹ = 15/8.

References

1 2 3 Kamien, Roger (2008). Music: An Appreciation, 6th Brief Edition, p. 46. ISBN 978-0-07-340134-8.
↑ Craig Wright (September 18, 2008)."Listening to Music: Lecture 5 Transcript" Archived 2010-08-04 at the Wayback Machine , Open Yale Courses.
1 2 Partch, Harry (2009). Genesis of a Music: An Account of a Creative Work, Its Roots, and Its Fulfillments, pp. 89–90. ISBN 9780786751006.
1 2 3 A.J. Ellis, writing in von Helmholtz, H.L.; Ellis, A.J. (1954). On the Sensations of Tone as a Physiological Basis for the Theory of Music. Translated by Ellis, A.J. (reprint ed.). New York, NY: Dover Publications. p. 455.
↑ Gjerdingen, Robert (1990). Studies on the Origin of Harmonic Tonality. Princeton: Princeton University Press. ISBN 978-0-691-09135-8. JSTOR j.ctt7ztxzh. English translation of Carl Dahlhaus's Untersuchungen über die Entstehung der harmonischen Tonalität (1968).

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[5] In the 16th through 18th centuries, prior to 12 TET, the minor third in meantone temperament was 310 cents Play ^ⓘ and much rougher than the 300 cent 12 TET minor third.^[4]^(p298)

[Kamien-1] 1 2 3 Kamien, Roger (2008). Music: An Appreciation, 6th Brief Edition, p. 46. ISBN 978-0-07-340134-8.

[2] Craig Wright (September 18, 2008)."Listening to Music: Lecture 5 Transcript" Archived 2010-08-04 at the Wayback Machine , Open Yale Courses.

[Genesis-3] 1 2 Partch, Harry (2009). Genesis of a Music: An Account of a Creative Work, Its Roots, and Its Fulfillments, pp. 89–90. ISBN 9780786751006.

[Ellis-Helmhz-1954-4] 1 2 3 A.J. Ellis, writing in von Helmholtz, H.L.; Ellis, A.J. (1954). On the Sensations of Tone as a Physiological Basis for the Theory of Music. Translated by Ellis, A.J. (reprint ed.). New York, NY: Dover Publications. p. 455.

[6] Gjerdingen, Robert (1990). Studies on the Origin of Harmonic Tonality. Princeton: Princeton University Press. ISBN 978-0-691-09135-8. JSTOR j.ctt7ztxzh. English translation of Carl Dahlhaus's Untersuchungen über die Entstehung der harmonischen Tonalität (1968).

[1]

[2]

[3]

[4]

[lower-alpha 1]

[5]