A semitone, or half-step is a musical interval. In Music theory, the term interval describes the relationship between the pitches of two Notes Intervals may be described as vertical It is the smallest interval commonly used in Western European Tonal music, and is considered the most dissonant. The most commonly written form of this interval is the minor second, notated using two adjacent letter names (e. g. C and D♭), but the augmented unison is also used, both notes having the same letter-name, with one of the notes being inflected by an accidental (e. g. C and C♯).

In twelve-tone equal temperament all semitones are equal in size. Equal temperament is a Musical temperament, or a system of tuning in which every pair of adjacent notes has an identical Frequency ratio. Any equal-tempered interval can be defined in terms of an appropriate number of semitones (e. g. an octave is 12 semitones wide). In Music, an octave ( is the the use of which is "common in most musical systems In other tuning systems the term "semitone" refers to a family of intervals which may vary both in size and name. Often a distinction is made between a diatonic semitone (notated as a minor second), and a chromatic semitone (as an augmented unison). These are enharmonically equivalent in equal temperament. In modern Music and notation, an enharmonic equivalent is a Note ( enharmonic tone) interval ( enharmonic interval) or

Minor second

The melodic minor second is an integral part of most cadences of the Common practice period. The common practice period, in the history of European Art music (broadly called Classical music) spanning the Baroque, Classical, and

The minor second occurs in the major scale, between the third and fourth degree, (mi and fa), and between the seventh and eighth degree (si and do). In Music theory, the major scale or Ionian scale is one of the diatonic scales It is made up of seven distinct Notes plus an eighth It is also called the diatonic semitone because it occurs between steps in the diatonic scale. In Music theory, a diatonic scale (from the Greek διατονικος, meaning " through tones" also known as the heptatonia prima and The minor second is abbreviated m2. Its inversion is the major seventh (M7). A major seventh ( is the larger of two commonly occurring Musical intervals that span seven Diatonic scale degrees

Melodically, this interval is very frequently used, and is of particular importance in cadences. In Music, a melody (from Greek μελῳδία - melōidía, "singing chanting" also tune, voice, or In Western Musical theory, a harmonic cadence (Latin cadentia, "a falling" is a formula of two chords that conclude In the perfect and deceptive cadences it appears as a resolution of the leading-tone to the tonic. In Music theory, the term interval describes the relationship between the pitches of two Notes Intervals may be described as vertical Deception (also called beguilement or subterfuge) is the act of convincing another to believe Information that is not true or not the whole truth as in In Western Musical theory, a harmonic cadence (Latin cadentia, "a falling" is a formula of two chords that conclude In Music theory, a leading-tone (called the leading- note outside the US is a note or pitch which resolves or "leads" In the plagal cadence, it appears as the falling of the subdominant to the mediant. In Western Musical theory, a harmonic cadence (Latin cadentia, "a falling" is a formula of two chords that conclude In Music, the subdominant is the technical name for the fourth tonal degree of the Diatonic scale. In Music, the mediant is the third degree of the Diatonic scale, being the "middle" note of the tonic It also occurs in many forms of the imperfect cadence, wherever the tonic falls to the leading-tone. In Western Musical theory, a harmonic cadence (Latin cadentia, "a falling" is a formula of two chords that conclude

Harmonically, the interval usually occurs as some form of dissonance or a nonchord tone that is not part of the functional harmony. In Western music, harmony is the use of different pitches simultaneously and chords actual or implied in Music. A nonchord tone, nonharmonic tone, or non-harmony note is a note in a piece of Music which is not a part of the chord that is formed A diatonic function, in tonal Music theory, is the specific recognized Roles of Notes or chords in relation to the key. It may also appear in inversions of a major seventh chord, and in many added tone chords. In Music, a major seventh chord is any Seventh chord where the "third" note is a Major third above the root An added tone chord is a triadic chord with an extra "added" note such as the added Sixth.

Minor Second (equal temperament)

The file plays middle C, followed by C# (a tone 100 cents sharper than C), followed by both tones together. C or Do is the first Note of the fixed-Do Solfege. In Western Music, the expression " Middle C " refers to the note

Problems listening to the file? See media help.

A harmonic minor second in J.S. Bach's Prelude in C major from the WTC book 1, mm. WikipediaWikiProject Composers#Lead section.2 This article is written in British English including maximised use of "-ise" The Well-Tempered Clavier ( Das Wohltemperirte Clavier in the original old German spelling BWV 846–893 is a collection of solo keyboard music composed by 7-9. The minor second may be viewed as a suspension of the B resolving into the following A minor seventh chord. A nonchord tone, nonharmonic tone, or non-harmony note is a note in a piece of Music which is not a part of the chord that is formed

The opening measures of Frédéric Chopin's "wrong note" Étude. The Études of Frédéric Chopin are 27 solo Piano pieces They comprise two separate collections of twelve numbered Opus 10 and 25 plus a set

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. Étude Op 25 No 5 in E minor is an étude composed by Frédéric Chopin in 1837 These are used to humorous and whimsical effect, which contrasts with its more lyrical middle section. This eccentric dissonance has earned 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. Romantic Music is a Musicological term referring to a particular period theory compositional practice and canon in European music history from about 1815 to 1910 Modest Petrovich Mussorgsky (Моде́ст Петро́вич Му́соргский Modest Petrovič Musorgskij) ( March 21 March 9 1839 &ndash March Pictures at an Exhibition (Картинки с выставки &ndash Воспоминание о Викторе Гартмане Kartinki s vystavki &ndash Vospominaniye

Augmented unison

Augmented unisons often appear as a consequence of secondary dominants, such as those in the soprano voice of this sequence from Felix Mendelssohn's Song Without Words Op. Secondary dominant (also applied dominant) is a type of chord used in musical Harmony. A sequence in music occurs when a given melodic or harmonic passage is immediately repeated at a different pitch level Jakob Ludwig Felix Mendelssohn Bartholdy, born and generally known as Felix Mendelssohn (February 3 1809 &ndash November 4 1847 was a German Composer Lieder ohne Worte (Songs without Words is a series of eight books each consisting of six "songs" written for the solo Piano by Romantic composer 102 No. 3, mm. 47-49.

The augmented 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 aug 1. Its inversion is the diminished octave (dim 8). In Music, a diminished octave ( is an interval that spans eight Diatonic scale degrees

Melodically, an augmented unison very frequently occurs when proceeding to a chromatic chord, such as a secondary dominant, a diminished seventh chord, or an augmented sixth chord. In Music, a melody (from Greek μελῳδία - melōidía, "singing chanting" also tune, voice, or Secondary dominant (also applied dominant) is a type of chord used in musical Harmony. In Music theory, a diminished seventh ( is an interval encompassing nine Semitones or a particular chord containing this interval An augmented sixth chord contains the interval of an Augmented sixth above its "root 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♭♭, A♭♭♭).

Franz Liszt's second Transcendental Etude, measure 63. The Transcendental Etudes (Études d'exécution transcendante S

Harmonically, augmented unisons are quite rare in tonal repertoire. In Western music, harmony is the use of different pitches simultaneously and chords actual or implied in Music. In 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. A seventh chord is a chord consisting of a triad plus a note forming an interval of a Seventh above the chord's root. In tonal music, a pedal point (also pedal tone pedal note organ point or pedal is a Sustained tone typically in the bass, during which at least one

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. A tone cluster is a musical chord comprising at least three consecutive tones in a scale. Iannis Xenakis (Ιάννης Ξενάκης (May 29 1922 - February 4 2001 was a Greek modernist composer musical theoretician and architect . .

History

The semitone appeared in the music theory of Greek antiquity as part of a diatonic tetrachord, and it has always had a place in the diatonic scales of Western music since. Traditionally a tetrachord is a series of four tones filling in the interval of a perfect fourth a 43 frequency proportion The various modal scales of medieval music theory were all based upon this diatonic pattern of tones and semitones. In Music, a scale is an ordered series of Musical intervals which along with the key or tonic, define the pitches However mode The term medieval music encompasses European music written during the Middle Ages. A major second () also called a whole step or a whole tone, is a Musical interval that occurs between the first and second degrees of a

Though it would later become an integral part of the musical cadence, in the early polyphony of the 11th century this was not the case. In Western Musical theory, a harmonic cadence (Latin cadentia, "a falling" is a formula of two chords that conclude 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. Guido of Arezzo or Guido Aretinus or Guido da Arezzo or Guido Monaco or Guido D'Arezzo (991/992&ndashafter 1033 was a music theorist The Micrologus is a treatise on Medieval music written by Guido of Arezzo, dating to approximately 1026. A major second () also called a whole step or a whole tone, is a Musical interval that occurs between the first and second degrees of a A major third ( is one of two commonly occurring Musical intervals that span three Diatonic scale degrees the other being the Minor third.

“As late as the 13th century the half step was experienced as a problematic interval not easily understood, as the irrational [sic] remainder between the perfect fourth and the ditone ( ). See also Whole-tone scale List of meantone intervals List of intervals in 5-limit just intonation ” In 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. A clausula (plural clausulae) is a Polyphonic composition performed as a musical alternative to the original Plainchant passage that it is intended to replace ” (Dahlhaus, 1990)

A dramatic chromatic scale in the opening measures of Luca Marenzio's Solo e pensoso, ca. Carl Dahlhaus ( June 10 1928 – March 13, 1989) a Musicologist from Berlin, has been one of the major contributors to the Luca Marenzio (also Marentio) ( October 18 ? 1553? &ndash August 22, 1599) was an Italian composer of the late Renaissance 1580. ( Listen )

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 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). In European music prior to about 1600, musica ficta (from Latin 'false' or 'feigned' music referred to chromatically altered pitches not notated in the By the 16th century, the semitone had become a more versatile interval, sometimes even appearing as an augmented unison in very chromatic passages.

By the Baroque era, the tonal harmonic framework was fully formed, and the various musical functions of the semitone were rigorously understood. Baroque music describes an era and a set of styles of European classical music which were in widespread use between approximately 1600 and 1750. Tonality is a system of Music in which specific hierarchical pitch relationships are based on a key "center" or tonic. 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. Well temperament (also circular or circulating temperament is a type of tempered tuning described in twentieth-century Music theory In modern Music and notation, an enharmonic equivalent is a Note ( enharmonic tone) interval ( enharmonic interval) or Its function remained similar through the Classical period, and though it 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. Classical music is a broad term that usually refers to mainstream music produced in or rooted in the traditions of Western liturgical and Secular music Romantic Music is a Musicological term referring to a particular period theory compositional practice and canon in European music history from about 1815 to 1910

In the 20th century, however, composers such as Arnold Schoenberg, Bela Bartok, and Igor Stravinsky sought alternatives or extensions of tonal harmony, and found other uses for the semitone. Arnold Schoenberg ( pronounced ˈʃøːnbɛrk (13 September 1874 &ndash 13 July 1951 was an Austrian and later American Composer, associated with Béla Viktor János Bartók (March 25 1881&ndashSeptember 26 1945 was a Hungarian Composer and Pianist, considered to be one of the greatest Igor Fyodorovich Stravinsky (Игорь Фёдорович Стравинский) ( &ndash 6 April 1971 was a Russian born Composer, considered by many to Often the semitone was exploited harmonically as 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. A tone cluster is a musical chord comprising at least three consecutive tones in a scale. g. the early piano works of Henry Cowell). Henry Cowell ( March 11, 1897 – December 10, 1965) was an American Composer, musical theorist, Pianist 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. Equal temperament is a Musical temperament, or a system of tuning in which every pair of adjacent notes has an identical Frequency ratio. The composer was free to write semitones wherever he wished.

This excerpt from the first of Arnold Schoenberg's Three Piano Pieces, Op. Arnold Schoenberg ( pronounced ˈʃøːnbɛrk (13 September 1874 &ndash 13 July 1951 was an Austrian and later American Composer, associated with 11 (m. 40) demonstrates completely unrestrained use of the semitone and related intervals. ( Listen )

Semitones in different tunings

The exact size of a semitone depends on the tuning system used. In Music, there are two common meanings for tuning: Tuning practice, the act of tuning an instrument or voice Meantone temperaments have two distinct types of semitones, but in the exceptional case of Equal temperament, there is only one. Meantone temperament is a Musical temperament, which is a system of Musical tuning. Equal temperament is a Musical temperament, or a system of tuning in which every pair of adjacent notes has an identical Frequency ratio. The unevenly distributed well temperaments contain many different semitones. Well temperament (also circular or circulating temperament is a type of tempered tuning described in twentieth-century Music theory Pythagorean tuning, similar to meantone tuning, has two, but in other systems of just intonation there are many more possibilities. Pythagorean tuning is a system of Musical tuning in which the Frequency relationships of all intervals are based on the ratio 32.

Meantone temperament

In meantone systems, there are two different semitones. Meantone temperament is a Musical temperament, which is a system of Musical tuning. This results because of 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. In Music theory, the circle of fifths (or '''circle of fourths''') shows the relationships among the twelve tones of the Chromatic scale, their corresponding

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. Quarter-comma meantone was the most common meantone temperament in the sixteenth and seventeenth centuries and was sometimes used later In Musical tuning, a temperament is a system of tuning which slightly compromises the pure intervals of Just intonation in order to meet other requirements of the The perfect fifth ( is the Musical interval between a note and the note seven Semitones above it on the musical scale 0490 and 117. 108 cents wide respectively.

Extended meantone temperaments with more than 12 notes still retain 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. In music 31 equal temperament, which can be abbreviated 31-tET 31- EDO, 31-ET is the tempered scale derived by dividing the Octave into 31 equal-sized

Equal temperament

12-tone equal temperament is actually a form of meantone tuning in which the diatonic and chromatic semitones are exactly the same, because its circle of fifths has no break. Equal temperament is a Musical temperament, or a system of tuning in which every pair of adjacent notes has an identical Frequency ratio. Each semitone is equal to one twelfth of an octave. This is a ratio of 2^1/12 (approximately 1. The twelfth root of two or \sqrt{2} is an algebraic Irrational number, representing the Frequency Ratio between any two consecutive 059463094), or 100 cents, and is 11. 7313 cents narrower than the 16:15 ratio (its most common form in just intonation). In music just intonation is any Musical tuning in which the frequencies of Notes are related by Ratios of Whole numbers Any interval

All diatonic intervals can be expressed as an equivalent number of semitones. For instance a whole tone equals two semitones. A major second () also called a whole step or a whole tone, is a Musical interval that occurs between the first and second degrees of a

There are many approximations, rational or otherwise, to the equal tempered semitone. To cite a few:

• 18 / 17 (98. 9545922 cents) was suggested by Vincenzo Galilei and used by luthiers of the Renaissance. Vincenzo Galilei (c 1520 &ndash July 2, 1591) was an Italian lutenist, Composer, and music theorist, and the father of Renaissance music is European music written during the Renaissance, approximately 1400 - 1600
• (100. 4404523 cents) was suggested by Marin Mersenne as a constructible and more accurate alternative. Marin Mersenne, Marin Mersennus or le Père Mersenne ( September 8, 1588 &ndash September 1, 1648) was A point in the Euclidean plane is a constructible point if given a fixed Coordinate system (or a fixed Line segment of unit Length
• ( 139 / 138 )⁸ (99. 9995131 cents) was used by Julián Carrillo as part of a sixteenth-tone system. Julián Carrillo Trujillo ( January 28, 1875 &ndash September 9, 1965) was a Mexican

• See also Pythagorean and Just systems of tuning below for more examples.

Well temperament

There are many forms of well temperament, but the characteristic they all share is that their semitones are of an uneven size. Well temperament (also circular or circulating temperament is a type of tempered tuning described in twentieth-century Music theory 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 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. In modern Music and notation, an enharmonic equivalent is a Note ( enharmonic tone) interval ( enharmonic interval) or Instead, in these systems, each key had a slightly different sonic color or character, beyond the limitations of conventional notation. In Music theory, the term key is used in many different and sometimes contradictory ways

Pythagorean tuning

Like meantone temperament, Pythagorean tuning is a broken circle of fifths. Pythagorean tuning is a system of Musical tuning in which the Frequency relationships of all intervals are based on the ratio 32. In Music theory, the circle of fifths (or '''circle of fourths''') shows the relationships among the twelve tones of the Chromatic scale, their corresponding This creates two distinct semitones, but because Pythagorean tuning is also a form of 3-limit just intonation, these semitones are rational. In music just intonation is any Musical tuning in which the frequencies of Notes are related by Ratios of Whole numbers Any interval Also, unlike most meantone temperaments, the chromatic semitone is larger than the diatonic.

The Pythagorean diatonic semitone has a ratio of 256/243, and is often called the Pythagorean limma. See also Whole-tone scale List of meantone intervals List of intervals in 5-limit just intonation It is also sometimes called the Pythagorean minor semitone.

The Pythagorean chromatic semitone has a ratio of 2187/2048. It may also be called the Pythagorean apotome or the Pythagorean major semitone. (See Pythagorean interval. See also Whole-tone scale List of meantone intervals List of intervals in 5-limit just intonation )

Just intonation

A minor second in just intonation most often corresponds to a pitch ratio of 16/15 or 1. In music just intonation is any Musical tuning in which the frequencies of Notes are related by Ratios of Whole numbers Any interval A ratio is an expression which compares quantities relative to each other 0666. . . (approximately 111. 731 cents), called the just diatonic semitone. The cent is a logarithmic unit of measure used for musical intervals. This is the most practical just semitone, as it is the difference between a perfect fourth and major third ( ). The perfect fourth () is a Musical interval which spans four scale degrees A major third ( is one of two commonly occurring Musical intervals that span three Diatonic scale degrees the other being the Minor third. In 5-limit just intonation, there is another semitone of 25/24 available between two major thirds (25/16) and a perfect fifth (3/2), sometimes called a just chromatic semitone because of its smaller size, but it is less common. The perfect fifth ( is the Musical interval between a note and the note seven Semitones above it on the musical scale

There are various other ratios which may function as a minor second. In 7-limit there is the septimal diatonic semitone of 15/14 available between the 5-limit major seventh (15/8) and the 7-limit minor seventh (7/4). A major seventh ( is the larger of two commonly occurring Musical intervals that span seven Diatonic scale degrees A minor seventh ( is the smaller of two commonly occurring Musical intervals that span seven Diatonic scale degrees There is also a smaller septimal chromatic semitone of 21/20 between a 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 the former was oft implemented by theorist Henry Cowell, whilst Harry Partch used the latter as part of his infamous 43-tone scale. Henry Cowell ( March 11, 1897 – December 10, 1965) was an American Composer, musical theorist, Pianist Harry Partch ( June 24, 1901 &ndash September 3, 1974) was an American Composer and instrument creator The 43-tone scale is a Just intonation scale with 43 pitches in each Octave, invented and used by Harry Partch.

Under 11-limit tuning, there is a fairly common undecimal neutral second (12/11), but it lies on the boundary between the minor and major second. A neutral second or medium second is a Musical interval between a Minor second and a Major second. A major second () also called a whole step or a whole tone, is a Musical interval that occurs between the first and second degrees of a In just intonation there are infinitely many possibilities for intervals that fall within the range of the semitone (e. g. the Pythagorean semitones mentioned above), but most of them are impractical.

Though the names diatonic and chromatic are often used for these intervals, their musical function is not the same as the two 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 the musical context, and just intonation is not particularly well suited to chromatic usage (diatonic semitone function is more prevalent).

Other equal temperaments

19-tone equal temperament distinguishes between the chromatic and diatonic semitones; in this tuning, the chromatic semitone is one step of the scale, and the diatonic semitone is two. In music 19 equal temperament, called 19-TET 19- EDO, or 19-ET is the tempered scale derived by dividing the octave into 19 equally large steps 31-tone equal temperament also distinguishes between these two intervals, which become 2 and 3 steps of the scale, respectively. In music 31 equal temperament, which can be abbreviated 31-tET 31- EDO, 31-ET is the tempered scale derived by dividing the Octave into 31 equal-sized 53-ET has an even closer match to the two semitones as 3 and 5 steps of its scale. In music 53 equal temperament, called 53-TET 53- EDO, or 53-ET is the tempered scale derived by dividing the octave into fifty-three equally large steps In general, because the two semitones can be viewed as the difference between major and minor thirds, and the difference between major thirds and perfect fourths, tuning systems that match these just intervals closely will also distinguish between the two types of semitones and match their just intervals closely.

See also

• List of meantone intervals
• List of musical intervals
• Major second
• Neutral second
• Pythagorean interval
• Regular temperament
• Template:Semitones

References

• Dahlhaus, Carl, trans. The following is a list of intervals of Meantone temperament. Background List See also List of meantone intervals A major second () also called a whole step or a whole tone, is a Musical interval that occurs between the first and second degrees of a A neutral second or medium second is a Musical interval between a Minor second and a Major second. See also Whole-tone scale List of meantone intervals List of intervals in 5-limit just intonation Regular temperament is any tempered system of Musical tuning such that each frequency ratio is obtainable as a product of powers of a finite number of generators Gjerdingen, Robert O. Studies in the Origin of Harmonic Tonality. Princeton University Press: Princeton, 1990. ISBN 0-691-09135-8.
• Hoppin, Richard. Medieval Music. W. W. Norton: New York, 1978. ISBN 0-393-09090-6
• Groud, Donald, and Claude Palisca. A History of Western Music. 6th ed. . W. W. Norton: New York, 2001. ISBN 0-393-97527-4