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Encyclopedia > Augmented unison
semitone
Inverse major seventh; diminished octave
Name
Other names minor second
or diatonic semitone;
augmented unison
or chromatic semitone
Abbreviation m2; aug1
Size
Semitones 1
Interval class 1
Just interval 16:15; 25:24 (and others)
Cents
Equal temperament 100
Just intonation 112; 71 (and others)

A semitone, or half-step is a musical interval. It is the smallest interval commonly used in Western 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♯). It has been suggested that this article be split into multiple articles accessible from a disambiguation page. ... The musical interval of a Major seventh the first note (the root or tonic) and the seventh, the leading tone, in a major scale. ... In music, specifically, musical set theory an interval class, or unordered pitch-class interval, is an interval measured by the distance between its two pitch classes ordered so they are as close as possible. ... In music, just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by whole number ratios; that is, by positive rational numbers. ... The cent is a logarithmic unit of measure used for musical intervals. ... An equal temperament is a musical temperament, or system of tuning, in which an interval, usually the octave, is divided into a series of equal steps (equal frequency ratios). ... In music, just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by whole number ratios; that is, by positive rational numbers. ... Left: halftone spots. ... In poetry, dissonance is the deliberate avoidance of patterns of repeated vowel sounds (see assonance). ...


In twelve-tone equal temperament all semitones are equal in size. Any equal-tempered interval can be defined in terms of an appropriate number of semitones (e.g. an octave is 12 semitones wide). 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 music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. ... In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ...

Contents

Minor second

The melodic minor second is an integral part of most cadences of the Common practice period.
The melodic minor second is an integral part of most cadences of the Common practice period.

The minor second occurs in the major scale, between the third and fourth degree, (mi and fa), and between the seventh and eighth degree (ti and do). It is also called the diatonic semitone because it occurs between steps in the diatonic scale. The minor second is abbreviated m2. Its inversion is the major seventh (M7). In music the common practice period is a long period in western musical history spanning from before the classical era proper to today, dated, on the outside, as 1600-1900. ... In music theory, the major scale (or major mode) is one of the diatonic scales. ... In music theory, a diatonic scale (from the Greek diatonikos, to stretch out; also known as the heptatonia prima; set form 7-35) is a seven-note musical scale comprising five whole-tone and two half-tone steps, in which the half tones are maximally separated. ... The musical interval of a Major seventh the first note (the root or tonic) and the seventh, the leading tone, in a major scale. ...


Melodically, this interval is very frequently used, and is of particular importance in cadences. In 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. Look up melody in Wiktionary, the free dictionary. ... In Western musical theory a cadence (Latin cadentia, a falling) is a particular series of intervals or chords that ends a phrase, section, or piece of music. ... Look up Perfect in Wiktionary, the free dictionary. ... Deception is providing intentionally misleading information to others. ... In Western musical theory a cadence (Latin cadentia, a falling) is a particular series of intervals or chords that ends a phrase, section, or piece of music. ... In music theory, a leading-tone (called the leading-note outside the US) is a note or pitch which is resolves or leads to a note one semitone higher or lower, being an lower and upper leading-tone, respectively. ... Tonic may mean: A concept from musical harmony and musical theory: see Tonic (music); A carbonated beverage flavoured with quinine, used in cocktails: see Tonic water. ... In Western musical theory a cadence (Latin cadentia, a falling) is a particular series of intervals (a caesura) or chords that ends a phrase, section, or piece of music. ... In music, the subdominant is the technical name for the fourth tonal degree of the diatonic scale. ... For mediant in mathematics, see Mediant (mathematics) In music, the mediant is the third degree of the diatonic scale. ...


Harmonically, the interval usually occurs as some form of dissonance or a nonchord tone that is not part of the functional harmony. It may also appear in inversions of a major seventh chord, and in many added tone chords. Harmony is the result of polyphony (more than one note being played simultaneously). ... In music, a consonance (Latin consonare, sounding together) is a harmony, chord, or interval considered stable, as opposed to a dissonance, which is considered unstable. ... A nonchord tone, nonharmonic tone, or non-harmony note is a note in a piece of common practice music which is not in the chord that is formed by the other notes; for example, if a piece of music is currently on a C Major chord, the notes CEG are... A diatonic function, in tonal music theory, is the specific, recognized roles of notes or chords in relation to the key. ... A seventh chord is a chord consisting of a triad plus a note forming an interval of a seventh above the chords root. ... An added tone chord is a triadic chord with an extra added note, such as the added sixth. ...

A harmonic minor second in J.S. Bach's Prelude in C major from the WTC book 1, mm. 7-9. The minor second may be viewed as a suspension of the B resolving into the following A minor seventh chord.
A harmonic minor second in J.S. Bach's Prelude in C major from the WTC book 1, mm. 7-9. The minor second may be viewed as a suspension of the B resolving into the following A minor seventh chord.
The opening measures of Frédéric Chopin's "wrong note" Étude.
The opening measures of Frédéric Chopin's "wrong note" Étude.

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 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. Johann Sebastian Bach (pronounced ) (21 March 1685 O.S. – 28 July 1750 N.S.) was a prolific German composer and organist whose sacred and secular works for choir, orchestra and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity. ... Title-page of Das wohltemperirte Clavier A flat major (As-dur) fugue from the second part of Das wohltemperirte Clavier (manuscript) The Well-Tempered Clavier (in the original German: Das wohltemperierte Clavier[1]) is a collection of solo keyboard music composed by Johann Sebastian Bach. ... In music theory, a suspension is a nonchord tone that occurs when the harmony shifts from one chord to another, but one or more notes of the first chord are held over, suspended, into the second but then resolved to a chord tone. ... Fryderyk Franciszek Chopin (in French, Frédéric François Chopin) (English: IPA: or ; French: ), (March 1, 1810[1] â€“ October 17, 1849) was a Polish pianist and composer of the Romantic era. ... The Études of Frédéric Chopin are a set of technical studies for piano. ... Fryderyk Franciszek Chopin (in French, Frédéric François Chopin) (English: IPA: or ; French: ), (March 1, 1810[1] â€“ October 17, 1849) was a Polish pianist and composer of the Romantic era. ... The Études of Frédéric Chopin are a set of technical studies for piano. ... The era of Romantic music is defined as the period of European classical music that runs roughly from the early 1800s to the first decade of the 20th century, as well as music written according to the norms and styles of that period. ... Modest Petrovich Mussorgsky (Russian: , Modest Petrovič Musorgskij, French: ) (March 9/21, 1839 – March 16/28, 1881), one of the Russian composers known as the Five, was an innovator of Russian music. ... Mussorgsky in 1874 Pictures at an Exhibition (Russian: , Kartínki s výstavki – Vospominániye o Víktore Gártmane, Pictures from an Exhibition – a Remembrance of Viktor Hartmann) is a famous suite of ten piano pieces composed by Modest Mussorgsky in 1874. ...


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. 102 No. 3, mm. 47-49.
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. 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). Secondary dominants are a kind of chord used in musical harmony. ... A sequence in music occurs when a given melodic or harmonic passage is successively repeated at different pitches (transposed). ... Felix Mendelssohn at the age of 30 Jakob Ludwig Felix Mendelssohn Bartholdy, born and known generally as Felix Mendelssohn (February 3, 1809 – November 4, 1847) was a German composer and conductor of the early Romantic period. ... Lieder ohne Worte (Songs without Words) are a series of eight musical volumes consisting of six songs each (a total of 48) written for the solo piano by Romantic composer Felix Mendelssohn. ... In music, chromatic indicates the inclusion of notes not in the prevailing scale and is also used for those notes themselves (Shir-Cliff et al 1965, p. ...


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. 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♭♭♭). Look up melody in Wiktionary, the free dictionary. ... Secondary dominants are a kind of chord used in musical harmony. ... A seventh chord is a chord or triad which has a note the seventh above the tonic in it. ... An augmented sixth chord is a chord which has the interval of an augmented sixth between its highest and lowest notes and also a major third above the lowest note. ...

Franz Liszt's second Transcendental Etude, measure 63.
Franz Liszt's second Transcendental Etude, measure 63.

Harmonically, augmented unisons are quite rare in tonal repertoire. 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. Franz Liszt (Hungarian: Liszt Ferenc) (October 22, 1811 – July 31, 1886) was a Hungarian virtuoso pianist and composer of the Romantic period. ... The Transcendental Etudes (sometimes Études dexécution transcendante or Transcendental Studies) is a series of twelve compositions written for solo piano by Hungarian composer Franz Liszt, begun in 1826 and finalized in 1851. ... Harmony is the result of polyphony (more than one note being played simultaneously). ... Franz Liszt (Hungarian: Liszt Ferenc) (October 22, 1811 – July 31, 1886) was a Hungarian virtuoso pianist and composer of the Romantic period. ... A seventh chord is a chord or triad which has a note the seventh above the tonic in it. ... In tonal music, a pedal point (also pedal tone, organ point, or just pedal) is a sustained tone, typically in the bass, during which at least one foreign, i. ...


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, in music and in Western tuning, is a chord or simultaneity comprised of consecutive tones separated chromatically. ... Iannis Xenakis Iannis Xenakis (Ιάννης Ξενάκης) (May 29, 1922 Brăila – February 4, 2001 Paris) was a Greek composer and architect who spent much of his life in Paris. ...


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. The various modal scales of medieval music theory were all based upon this diatonic pattern of tones and semitones. The tetrachord is a concept of music theory borrowed from ancient Greece. ... In music, a mode is an ordered series of musical intervals, which, along with the key or tonic, define the pitches. ... A musician plays the vielle in a 14th century medieval manuscript. ... The musical interval of a major second — also called a whole-tone — is the relationship between the first note (the root or tonic) and the second note in a major scale (and also a minor scale). ...


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. 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. In Western musical theory a cadence (Latin cadentia, a falling) is a particular series of intervals or chords that ends a phrase, section, or piece of music. ... Statue of Guido in Arezzo Guido of Arezzo or Guido Aretinus or Guido da Arezzo or Guido Monaco or Guido DArezzo (991/992 – after 1033) was a music theorist of the Medieval era. ... A major second is one of three commonly occuring musical intervals that span two diatonic scale degrees; the others being the minor second, which is one semitone smaller, and the augmented second, which is one semitone larger. ... A major third is the larger of two commonly occuring musical intervals that span three diatonic scale degrees. ...


"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 ( )." 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." (Dahlhaus, 1990) The musical interval of a ditone is literally two tones, whole tones or major seconds, often called a major third. ... In Western musical theory a cadence (Latin cadentia, a falling) is a particular series of intervals (a caesura) or chords that ends a phrase, section, or piece of music. ... Carl Dahlhaus (June 10, 1928- May 1989), a musicologist from Berlin, has been one of the major contributors to the development of musicology as a scholarly discipline during the post-war era. ...

A dramatic chromatic scale in the opening measures of Luca Marenzio's Solo e pensoso, ca. 1580. ( Listen )
A dramatic chromatic scale in the opening measures of Luca Marenzio's Solo e pensoso, ca. 1580. ( Image:Loudspeaker.png 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). By the 16th century, the semitone had become a more versatile interval, sometimes even appearing as an augmented unison in very chromatic passages. Luca Marenzio (1553? - August 22, 1599) was an Italian composer of the late Renaissance. ... Image File history File links Loudspeaker. ... In European music prior to about 1600, musica ficta (from Latin, false or feigned music) referred to chromatically altered pitches, not notated in the music, which were to be supplied by singers. ... In music, chromatic indicates the inclusion of notes not in the prevailing scale and is also used for those notes themselves (Shir-Cliff et al 1965, p. ...


By the Baroque era, 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 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. Baroque music describes an era and a set of styles of European classical music which were in widespread use between approximately 1600 to 1750 (see Dates of classical music eras for a discussion of the problems inherent in defining the beginning and end points). ... Tonality is a system of writing music according to certain hierarchical pitch relationships around a key center or tonic. ... Well temperament (also circular or circulating temperament) is a type of tempered tuning described in twentieth-century music theory. ... In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ... Classical music is a term with three distinct meanings: The European tradition of music which is associated with high culture, as distinct from popular or folk forms (including works in this tradition in non-European countries). ... The era of Romantic music is defined as the period of European classical music that runs roughly from the early 1800s to the first decade of the 20th century, as well as music written according to the norms and styles of that period. ...


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. 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 cacaphony 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. Schoenberg redirects here. ... B la Bart k (March 25, 1881 – September 26, 1945) was a composer, pianist and collector of East European folk music. ... Igor Fyodorovich Stravinsky (Russian: Игорь Фёдорович Стравинский, Igor Fëdorovič Stravinskij) (June 17, 1882 – April 6, 1971) was a Russian composer who first achieved international fame with three ballets commissioned by the impresario Serge Diaghilev and performed by Diaghilevs Ballets Russes (Russian Ballet): LOiseau de feu (The Firebird) (1910), Petrushka (1911... A tone cluster, in music and in Western tuning, is a chord or simultaneity comprised of consecutive tones separated chromatically. ... Henry Cowell (March 11, 1897 - December 10, 1965) was an American composer, musical theorist, pianist, teacher, publisher, and impresario. ... An equal temperament is a musical temperament, or system of tuning, in which an interval, usually the octave, is divided into a series of equal steps (equal frequency ratios). ...

This excerpt from the first of Arnold Schoenberg's Three Piano Pieces, Op. 11 (m. 40) demonstrates completely unrestrained use of the semitone and related intervals. ( Listen )
This excerpt from the first of Arnold Schoenberg's Three Piano Pieces, Op. 11 (m. 40) demonstrates completely unrestrained use of the semitone and related intervals. ( Image:Loudspeaker.png Listen )

Schoenberg redirects here. ... Image File history File links Loudspeaker. ...

Semitones in different tunings

The exact size of 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 music, there are two common meanings for tuning: Tuning practice The act of tuning an instrument or voice. ... Meantone temperament is a system of musical tuning. ... An equal temperament is a musical temperament, or system of tuning, in which an interval, usually the octave, is divided into a series of equal steps (equal frequency ratios). ... Well temperament (also circular or circulating temperament) is a type of tempered tuning described in twentieth-century music theory. ... Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. ...


Meantone temperament

In meantone systems, there are two different semitones. 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. Meantone temperament is a system of musical tuning. ... In music theory, the circle of fifths (or cycle of fifths) is a geometrical space that depicts relationships among the 12 equal-tempered pitch classes comprising the familiar chromatic scale. ...


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 76.0490 and 117.108 cents wide respectively. 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 system. ... The perfect fifth or diapente is one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one semitone smaller, and the augmented fifth, which is one semitone larger. ...

Chromatic semitone 76.05 76.05 76.05 76.05 76.05
Pitch C C♯ D E♭ E F F♯ G G♯ A B♭ B C
Cents 0.000 76.05 193.2 310.3 386.3 503.4 579.5 696.6 772.6 889.7 1007 1083 1200
Diatonic semitone 117.1 117.1 117.1 117.1 117.1 117.1 117.1

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.


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. Each semitone is equal to one twelfth of an octave. This is a ratio of 21/12 (approximately 1.059463094), or 100 cents, and is 11.7313 cents narrower than the 16:15 ratio (its most common form in just intonation). An equal temperament is a musical temperament, or system of tuning, in which an interval, usually the octave, is divided into a series of equal steps (equal frequency ratios). ... The Twelfth root of two is a quantity representing the frequency ratio between any two consecutive notes of a modern chromatic scale in equal temperament. ... In music, just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by whole number ratios; that is, by positive rational numbers. ...


All diatonic intervals can be expressed as an equivalent number of semitones. For instance a whole tone equals two semitones. A major second is one of three commonly occuring musical intervals that span two diatonic scale degrees; the others being the minor second, which is one semitone smaller, and the augmented second, which is one semitone larger. ...


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.
  • (100.4404523 cents) was suggested by Marin Mersenne as a constructible and more accurate alternative.
  • ( 139 / 138 )8 (99.9995131 cents) was used by Julián Carrillo as part of a sixteenth-tone system.
  • See also Pythagorean and Just systems of tuning below for more examples.

Vincenzo Galilei (1520 – July 2, 1591) was an Italian lutenist, composer, and music theorist, and the father of the famous astronomer Galileo Galilei. ... An engravers impression of Antonio Stradivari examining an instrument. ... Renaissance music is European classical music written during the Renaissance, approximately 1400 to 1600. ... Marin Mersenne, Marin Mersennus or le Père Mersenne (September 8, 1588 – September 1, 1648) was a French theologian, philosopher, mathematician and music theorist. ... A point in the Euclidean plane is a constructible point if, given a fixed coordinate system (or a fixed line segment of unit length), one can construct the point with unruled straightedge and compass. ... Julián Carrillo, 1945. ...

Well temperament

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 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 sytems, each key had a slightly different sonic color or character, beyond the limitations of conventional notation. Well temperament (also circular or circulating temperament) is a type of tempered tuning described in twentieth-century music theory. ... In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ... In music theory, the key identifies the tonic triad, the chord, major or minor, which represents the final point of rest for a piece, or the focal point of a section. ...


Pythagorean tuning

Like meantone temperament, Pythagorean tuning 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. Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. ... In music theory, the circle of fifths (or cycle of fifths) is a geometrical space that depicts relationships among the 12 equal-tempered pitch classes comprising the familiar chromatic scale. ... In music, just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by whole number ratios; that is, by positive rational numbers. ...


The Pythagorean diatonic semitone has a ratio of 256/243, and is often called the Pythagorean limma. 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.) The intervals of Pythagorean tuning are just intervals involving only powers of two and three. ...

Just intonation

A minor second in just intonation most often corresponds to a pitch ratio of 16/15 or 1.0666... (approximately 111.731 cents), called the just diatonic semitone. This is the most practical just semitone, as it is the difference between a perfect fourth and major 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. In music, just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by whole number ratios; that is, by positive rational numbers. ... A ratio is a dimensionless, or unitless, quantity denoting an amount or magnitude of one quantity relative to another. ... The cent is a logarithmic unit of measure used for musical intervals. ... The perfect fourth or diatessaron, abbreviated P4, is one of two musical intervals that span four diatonic scale degrees; the other being the augmented fourth, which is one semitone larger. ... A major third is the larger of two commonly occuring musical intervals that span three diatonic scale degrees. ... The perfect fifth or diapente is one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one semitone smaller, and the augmented fifth, which is one semitone larger. ...


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). 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), but this is rarely used. The musical interval of a Major seventh the first note (the root or tonic) and the seventh, the leading tone, in a major scale. ... The musical interval of a minor seventh the first note (the root or tonic) and the seventh in a minor scale. ...


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. 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. A neutral second is a musical interval half-way between a minor second and a major second. ... A major second is one of three commonly occuring musical intervals that span two diatonic scale degrees; the others being the minor second, which is one semitone smaller, and the augmented second, which is one semitone larger. ...


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).


See also

Diatonic intervals edit
Perfect : unison (0) | fourth (5) | fifth (7) | octave (12)
Major : second (2) | third (4) | sixth (9) | seventh (11)
Minor : second (1) | third (3)| sixth (8) | seventh (10)
Augmented : unison (1) | second (3) | third (5) | fourth (6) | fifth (8) | sixth (10) | seventh (12)
Diminished : second (0) | third (2) | fourth (4) | fifth (6) | sixth (7) | seventh (9) | octave (11)
semitones of equal temperament are given in brackets

The following is a list of intervals of meantone temperament. ... Equal-tempered refers to 12-tone equal temperament. ... A major second is one of three commonly occuring musical intervals that span two diatonic scale degrees; the others being the minor second, which is one semitone smaller, and the augmented second, which is one semitone larger. ... A neutral second is a musical interval half-way between a minor second and a major second. ... In music theory, an interval is the relationship between two notes or pitches, the lower and higher members of the interval. ... For other uses, see Unison (disambiguation). ... The perfect fourth or diatessaron, abbreviated P4, is one of two musical intervals that span four diatonic scale degrees; the other being the augmented fourth, which is one semitone larger. ... The perfect fifth or diapente is one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one semitone smaller, and the augmented fifth, which is one semitone larger. ... In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. ... A major second is one of three commonly occuring musical intervals that span two diatonic scale degrees; the others being the minor second, which is one semitone smaller, and the augmented second, which is one semitone larger. ... A major third is the larger of two commonly occuring musical intervals that span three diatonic scale degrees. ... The musical interval of a major sixth is the relationship between the first note (the root or tonic) and the sixth note in a Major scale. ... The musical interval of a Major seventh the first note (the root or tonic) and the seventh, the leading tone, in a major scale. ... A minor second is the smallest of three commonly occuring musical intervals that span two diatonic scale degrees; the others being the major second and the augmented second, which are larger by one and two semitones respectively. ... A minor third is the smaller of two commonly occurring musical intervals that span three diatonic scale degrees. ... A minor sixth is the smaller of two commonly occuring musical intervals that span six diatonic scale degrees. ... The musical interval of a minor seventh the first note (the root or tonic) and the seventh in a minor scale. ... The musical interval of a minor third is the relationship between the first note (the root or tonic) and the third note in a minor scale. ... This article is about the musical interval. ... An augmented fifth is one of three musical intervals that span five diatonic scale degrees. ... An augmented sixth is one of three musical intervals that span six diatonic scale degrees. ... In music, a diminished third is the interval produced by flattening a minor third by a chromatic semitone. ... This article is about the musical interval. ... A seventh chord is a chord or triad which has a note the seventh above the tonic in it. ...

References

  • Dahlhaus, Carl, trans. 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

External links

  • Tonalsoft Encyclopedia of Microtonal Music Theoryen:semitone

 
 

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