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56-486: 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. A major interval is one semitone larger than a minor interval. The words perfect , diminished , and augmented are also used to describe

112-481: A commonly used version of 5 limit tuning have four different sizes, and can be classified as follows: The most frequently occurring semitones are the just ones ( S 3 , 16:15, and S 1 , 25:24): S 3 occurs at 6 short intervals out of 12, S 1 3 times, S 2 twice, and S 4 at only one interval (if diatonic D ♭ replaces chromatic D ♭ and sharp notes are not used). The smaller chromatic and diatonic semitones differ from

168-456: A diatonic and chromatic semitone in the tuning. Well temperament was constructed so that enharmonic equivalence could be assumed between all of these semitones, and whether they were written as a minor second or augmented unison did not effect a different sound. Instead, in these systems, each key had a slightly different sonic color or character, beyond the limitations of conventional notation. Like meantone temperament, Pythagorean tuning

224-546: A diminished seventh chord , or an augmented sixth chord . Its use is also often the consequence of a melody proceeding in semitones, regardless of harmonic underpinning, e.g. D , D ♯ , E , F , F ♯ . (Restricting the notation to only minor seconds is impractical, as the same example would have a rapidly increasing number of accidentals, written enharmonically as D , E ♭ , F ♭ , G [REDACTED] , A [REDACTED] ). Harmonically , augmented unisons are quite rare in tonal repertoire. In

280-411: 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. 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

336-448: A major third or a minor third , respectively. 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

392-519: A whole tone or major second is 2 semitones wide, a major third 4 semitones, and a perfect fifth 7 semitones). In music theory , a distinction is made between a diatonic semitone , or minor second (an interval encompassing two different staff positions , e.g. from C to D ♭ ) and a chromatic semitone or augmented unison (an interval between two notes at the same staff position, e.g. from C to C ♯ ). These are enharmonically equivalent if and only if twelve-tone equal temperament

448-465: A caustic dissonance, having no resolution. Some composers would even use large collections of harmonic semitones ( tone clusters ) as a source of cacophony in their music (e.g. the early piano works of Henry Cowell ). By now, enharmonic equivalence was a commonplace property of equal temperament , and instrumental use of the semitone was not at all problematic for the performer. The composer was free to write semitones wherever he wished. The exact size of

504-493: A family of intervals that may vary both in size and name. In Pythagorean tuning , seven semitones out of twelve are diatonic, with ratio 256:243 or 90.2 cents ( Pythagorean limma ), and the other five are chromatic, with ratio 2187:2048 or 113.7 cents ( Pythagorean apotome ); they differ by the Pythagorean comma of ratio 531441:524288 or 23.5 cents. In quarter-comma meantone , seven of them are diatonic, and 117.1 cents wide, while

560-519: A fundamental part of the musical language, even to the point where the usual accidental accompanying the minor second in a cadence was often omitted from the written score (a practice known as musica ficta ). By the 16th century, the semitone had become a more versatile interval, sometimes even appearing as an augmented unison in very chromatic passages. Semantically , in the 16th century the repeated melodic semitone became associated with weeping, see: passus duriusculus , lament bass , and pianto . By

616-450: A melodic half step, no "tendency was perceived of the lower tone toward the upper, or of the upper toward the lower. The second tone was not taken to be the 'goal' of the first. Instead, the half step was avoided in clausulae because it lacked clarity as an interval." However, beginning in the 13th century cadences begin to require motion in one voice by half step and the other a whole step in contrary motion. These cadences would become

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672-427: A more interesting, possibly darker sound than plain major scales. Harry Partch considers minor as, "the immutable faculty of ratios, which in turn represent an immutable faculty of the human ear." 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". Changes of mode, which involve

728-440: A pitch ratio of 16:15 ( play ) or 1.0666... (approximately 111.7  cents ), called the just diatonic semitone . This is a practical just semitone, since it is the interval that occurs twice within the diatonic scale between a: The 16:15 just minor second arises in the C major scale between B & C and E & F, and is, "the sharpest dissonance found in the scale". An "augmented unison" (sharp) in just intonation

784-477: A semitone depends on the tuning system used. Meantone temperaments have two distinct types of semitones, but in the exceptional case of equal temperament , there is only one. The unevenly distributed well temperaments contain many different semitones. Pythagorean tuning , similar to meantone tuning, has two, but in other systems of just intonation there are many more possibilities. In meantone systems, there are two different semitones. This results because of

840-419: Is a broken circle of fifths . This creates two distinct semitones, but because Pythagorean tuning is also a form of 3-limit just intonation , these semitones are rational. Also, unlike most meantone temperaments, the chromatic semitone is larger than the diatonic. The Pythagorean diatonic semitone has a ratio of 256/243 ( play ), and is often called the Pythagorean limma . It is also sometimes called

896-401: Is a different, smaller semitone, with frequency ratio 25:24 ( play ) or 1.0416... (approximately 70.7 cents). It is the interval between a major third (5:4) and a minor third (6:5). In fact, it is the spacing between the minor and major thirds, sixths, and sevenths (but not necessarily the major and minor second). Composer Ben Johnston used a sharp ( ♯ ) to indicate a note

952-455: Is called hemitonia; that of having no semitones is anhemitonia . A musical scale or chord containing semitones is called hemitonic; one without semitones is anhemitonic. The minor second occurs in the major scale , between the third and fourth degree, ( mi (E) and fa (F) in C major), and between the seventh and eighth degree ( ti (B) and do (C) in C major). It is also called the diatonic semitone because it occurs between steps in

1008-482: Is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent notes in a 12-tone scale (or half of a whole step ), 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 a 12-note approximately equally divided scale, any interval can be defined in terms of an appropriate number of semitones (e.g.

1064-449: Is raised 70.7 cents, or a flat ( ♭ ) to indicate a note is lowered 70.7 cents. (This is the standard practice for just intonation, but not for all other microtunings.) Two other kinds of semitones are produced by 5 limit tuning. A chromatic scale defines 12 semitones as the 12 intervals between the 13 adjacent notes, spanning a full octave (e.g. from C 4 to C 5 ). The 12 semitones produced by

1120-492: 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 ]." 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," at least to contemporary Western ears. Minor keys are sometimes said to have

1176-421: Is the diminished octave ( d8 , or dim 8 ). The augmented unison is also the inversion of the augmented octave , because the interval of the diminished unison does not exist. This is because a unison is always made larger when one note of the interval is changed with an accidental. Melodically , an augmented unison very frequently occurs when proceeding to a chromatic chord, such as a secondary dominant ,

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1232-429: Is the septimal diatonic semitone of 15:14 ( play ) available in between the 5 limit major seventh (15:8) and the 7 limit minor seventh / harmonic seventh (7:4). There is also a smaller septimal chromatic semitone of 21:20 ( play ) between a septimal minor seventh and a fifth (21:8) and an octave and a major third (5:2). Both are more rarely used than their 5 limit neighbours, although

1288-467: Is used; for example, they are not the same thing in meantone temperament , where the diatonic semitone is distinguished from and larger than the chromatic semitone (augmented unison), or in Pythagorean tuning , where the diatonic semitone is smaller instead. See Interval (music) § Number for more details about this terminology. In twelve-tone equal temperament all semitones are equal in size (100 cents). In other tuning systems, "semitone" refers to

1344-531: The Baroque era (1600 to 1750), the tonal harmonic framework was fully formed, and the various musical functions of the semitone were rigorously understood. Later in this period the adoption of well temperaments for instrumental tuning and the more frequent use of enharmonic equivalences increased the ease with which a semitone could be applied. Its function remained similar through the Classical period, and though it

1400-467: The Pythagorean minor semitone . It is about 90.2 cents. It can be thought of as the difference between three octaves and five just fifths , and functions as a diatonic semitone in a Pythagorean tuning . The Pythagorean chromatic semitone has a ratio of 2187/2048 ( play ). It is about 113.7 cents . It may also be called the Pythagorean apotome or the Pythagorean major semitone . ( See Pythagorean interval .) It can be thought of as

1456-419: The diatonic scale . The minor second is abbreviated m2 (or −2 ). Its inversion is the major seventh ( M7 or Ma7 ). Listen to a minor second in equal temperament . Here, middle C is followed by D ♭ , which is a tone 100 cents sharper than C, and then by both tones together. Melodically , this interval is very frequently used, and is of particular importance in cadences . In

1512-482: The functional harmony . It may also appear in inversions of a major seventh chord , and in many added tone chords . In unusual situations, the minor second can add a great deal of character to the music. For instance, Frédéric Chopin 's Étude Op. 25, No. 5 opens with a melody accompanied by a line that plays fleeting minor seconds. These are used to humorous and whimsical effect, which contrasts with its more lyrical middle section. This eccentric dissonance has earned

1568-412: The perfect and deceptive cadences it appears as a resolution of the leading-tone to the tonic . In the plagal cadence , it appears as the falling of the subdominant to the mediant . It also occurs in many forms of the imperfect cadence , wherever the tonic falls to the leading-tone. Harmonically , the interval usually occurs as some form of dissonance or a nonchord tone that is not part of

1624-459: 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 ". Major and minor may also refer to scales and chords that contain

1680-471: 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. 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

1736-489: 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,

Major and minor - Misplaced Pages Continue

1792-407: The [major] scale ." Play B & C The augmented unison , the interval produced by the augmentation , or widening by one half step, of the perfect unison, does not occur between diatonic scale steps, but instead between a scale step and a chromatic alteration of the same step. It is also called a chromatic semitone . The augmented unison is abbreviated A1 , or aug 1 . Its inversion

1848-450: 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

1904-532: The break in the circle of fifths that occurs in the tuning system: diatonic semitones derive from a chain of five fifths that does not cross the break, and chromatic semitones come from one that does. The chromatic semitone is usually smaller than the diatonic. In the common quarter-comma meantone , tuned as a cycle of tempered fifths from E ♭ to G ♯ , the chromatic and diatonic semitones are 76.0 and 117.1 cents wide respectively. Extended meantone temperaments with more than 12 notes still retain

1960-442: The difference between four perfect octaves and seven just fifths , and functions as a chromatic semitone in a Pythagorean tuning . The Pythagorean limma and Pythagorean apotome are enharmonic equivalents (chromatic semitones) and only a Pythagorean comma apart, in contrast to diatonic and chromatic semitones in meantone temperament and 5-limit just intonation . A minor second in just intonation typically corresponds to

2016-405: The equal-tempered semitone. To cite a few: For more examples, see Pythagorean and Just systems of tuning below. There are many forms of well temperament , but the characteristic they all share is that their semitones are of an uneven size. Every semitone in a well temperament has its own interval (usually close to the equal-tempered version of 100 cents), and there is no clear distinction between

2072-539: The example to the right, Liszt had written an E ♭ against an E ♮ in the bass. Here E ♭ was preferred to a D ♯ to make the tone's function clear as part of an F dominant seventh chord, and the augmented unison is the result of superimposing this harmony upon an E pedal point . In addition to this kind of usage, harmonic augmented unisons are frequently written in modern works involving tone clusters , such as Iannis Xenakis ' Evryali for piano solo. The semitone appeared in

2128-407: The former was often implemented by theorist Cowell , while Partch used the latter as part of his 43 tone scale . Under 11 limit tuning, there is a fairly common undecimal neutral second (12:11) ( play ), but it lies on the boundary between the minor and major second (150.6 cents). In just intonation there are infinitely many possibilities for intervals that fall within

2184-454: The irrational [ sic ] remainder between the perfect fourth and the ditone ( 4 3 / ( 9 8 ) 2 = 256 243 ) {\displaystyle \left({\begin{matrix}{\frac {4}{3}}\end{matrix}}/{{\begin{matrix}({\frac {9}{8}})\end{matrix}}^{2}}={\begin{matrix}{\frac {256}{243}}\end{matrix}}\right)} ." In

2240-407: The larger by the syntonic comma (81:80 or 21.5 cents). The smaller and larger chromatic semitones differ from the respective diatonic semitones by the same 128:125 diesis as the above meantone semitones. Finally, while the inner semitones differ by the diaschisma (2048:2025 or 19.6 cents), the outer differ by the greater diesis (648:625 or 62.6 cents). In 7 limit tuning there

2296-399: 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

Major and minor - Misplaced Pages Continue

2352-438: The minor diatonic semitone is 17:16 or 105.0 cents, and septendecimal limma is 18:17 or 98.95 cents. Though the names diatonic and chromatic are often used for these intervals, their musical function is not the same as the meantone semitones. For instance, 15:14 would usually be written as an augmented unison, functioning as the chromatic counterpart to a diatonic 16:15. These distinctions are highly dependent on

2408-414: 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. 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

2464-399: 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. 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

2520-482: 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

2576-405: The music theory of Greek antiquity as part of a diatonic or chromatic tetrachord , and it has always had a place in the diatonic scales of Western music since. The various modal scales of medieval music theory were all based upon this diatonic pattern of tones and semitones. Though it would later become an integral part of the musical cadence , in the early polyphony of the 11th century this

2632-489: The musical context, and just intonation is not particularly well suited to chromatic use (diatonic semitone function is more prevalent). 19-tone equal temperament distinguishes between the chromatic and diatonic semitones; in this tuning, the chromatic semitone is one step of the scale ( play 63.2 cents ), and the diatonic semitone is two ( play 126.3 cents ). 31-tone equal temperament also distinguishes between these two intervals, which become 2 and 3 steps of

2688-491: The other five are chromatic, and 76.0 cents wide; they differ by the lesser diesis of ratio 128:125 or 41.1 cents. 12-tone scales tuned in just intonation typically define three or four kinds of semitones. For instance, Asymmetric five-limit tuning yields chromatic semitones with ratios 25:24 (70.7 cents) and 135:128 (92.2 cents), and diatonic semitones with ratios 16:15 (111.7 cents) and 27:25 (133.2 cents). For further details, see below . The condition of having semitones

2744-542: The piece its nickname: the "wrong note" étude. This kind of usage of the minor second appears in many other works of the Romantic period, such as Modest Mussorgsky 's Ballet of the Unhatched Chicks . More recently, the music to the movie Jaws exemplifies the minor second. In just intonation a 16:15 minor second arises in the C major scale between B & C and E & F, and is "the sharpest dissonance found in

2800-467: The range of the semitone (e.g. the Pythagorean semitones mentioned above), but most of them are impractical. In 13 limit tuning, there is a tridecimal ⁠ 2 / 3 ⁠ tone (13:12 or 138.57 cents) and tridecimal ⁠ 1 / 3 ⁠ tone (27:26 or 65.34 cents). In 17 limit just intonation, the major diatonic semitone is 15:14 or 119.4 cents ( Play ), and

2856-412: The same two semitone sizes, but there is more flexibility for the musician about whether to use an augmented unison or minor second. 31-tone equal temperament is the most flexible of these, which makes an unbroken circle of 31 fifths, allowing the choice of semitone to be made for any pitch. 12-tone equal temperament is a form of meantone tuning in which the diatonic and chromatic semitones are exactly

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2912-472: The same, because its circle of fifths has no break. Each semitone is equal to one twelfth of an octave. This is a ratio of 2 (approximately 1.05946), or 100 cents, and is 11.7 cents narrower than the 16:15 ratio (its most common form in just intonation , discussed below ). All diatonic intervals can be expressed as an equivalent number of semitones. For instance a major sixth equals nine semitones. There are many approximations, rational or otherwise, to

2968-512: The scale, respectively. 53-ET has an even closer match to the two semitones with 3 and 5 steps of its scale while 72-ET uses 4 ( play 66.7 cents ) and 7 ( play 116.7 cents ) steps of its scale. In general, because the smaller semitone can be viewed as the difference between a minor third and a major third, and the larger as the difference between a major third and a perfect fourth, tuning systems that closely match those just intervals (6/5, 5/4, and 4/3) will also distinguish between

3024-504: 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. Semitone A semitone , also called a minor second , half step , or a half tone , is the smallest musical interval commonly used in Western tonal music, and it

3080-401: Was not the case. Guido of Arezzo suggested instead in his Micrologus other alternatives: either proceeding by whole tone from a major second to a unison, or an occursus having two notes at a major third move by contrary motion toward a unison, each having moved a whole tone. "As late as the 13th century the half step was experienced as a problematic interval not easily understood, as

3136-401: Was used more frequently as the language of tonality became more chromatic in the Romantic period, the musical function of the semitone did not change. In the 20th century, however, composers such as Arnold Schoenberg , Béla Bartók , and Igor Stravinsky sought alternatives or extensions of tonal harmony, and found other uses for the semitone. Often the semitone was exploited harmonically as

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