In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, a scale ordered by decreasing pitch is a descending scale; some scales contain different pitches when ascending than when descending, for example, the melodic minor scale. In the context of the common practice period, most or all of the melody and harmony of a musical work is built using the notes of a single scale, which can be conveniently represented on a staff with a standard key signature. Due to the principle of octave equivalence, scales are considered to span a single octave, with higher or lower octaves repeating the pattern. A musical scale represents a division of the octave space into a certain number of scale steps, a scale step being the recognizable distance between two successive notes of the scale. However, there is no need for scale steps to be equal within any scale and as demonstrated by microtonal music, there is no limit to how many notes can be injected within any given musical interval.
A measure of the width of each scale step provides a method to classify scales. For instance, in a chromatic scale each scale step represents a semitone interval, while a major scale is defined by the interval pattern T–T–S–T–T–T–S, where T stands for whole tone, S stands for semitone. Based on their interval patterns, scales are put into categories including diatonic, major and others. A specific scale is defined by its characteristic interval pattern and by a special note, known as its first degree; the tonic of a scale is the note selected as the beginning of the octave, therefore as the beginning of the adopted interval pattern. The name of the scale specifies both its tonic and its interval pattern. For example, C major indicates a major scale with a C tonic. Scales are listed from low to high pitch. Most scales are octave-repeating. An octave-repeating scale can be represented as a circular arrangement of pitch classes, ordered by increasing pitch class. For instance, the increasing C major scale is C–D–E–F–G–A–B–, with the bracket indicating that the last note is an octave higher than the first note, the decreasing C major scale is C–B–A–G–F–E–D–, with the bracket indicating an octave lower than the first note in the scale.
The distance between two successive notes in a scale is called a scale step. The notes of a scale are numbered by their steps from the root of the scale. For example, in a C major scale the first note is the second D, the third E and so on. Two notes can be numbered in relation to each other: C and E create an interval of a third. A single scale can be manifested at many different pitch levels. For example, a C major scale can be started at C4 and ascending an octave to C5; as long as all the notes can be played, the octave they take on can be altered. Scales may be described according to the number of different pitch classes they contain: Chromatic, or dodecatonic Octatonic: used in jazz and modern classical music Heptatonic: the most common modern Western scale Hexatonic: common in Western folk music Pentatonic: the anhemitonic form is common in folk music in Asian music. Many music theorists concur that the constituent intervals of a scale have a large role in the cognitive perception of its sonority, or tonal character.
"The number of the notes that make up a scale as well as the quality of the intervals between successive notes of the scale help to give the music of a culture area its peculiar sound quality." "The pitch distances or intervals among the notes of a scale tell us more about the sound of the music than does the mere number of tones."Scales may be described by their symmetry, such as being palindromic, chiral, or having rotational symmetry as in Messiaen's modes of limited transposition. Scales can be described by their distribution patterns and possibilities for notation. For example, a heliotonic scale is one that can be notated with one note head on each line and space, using only single and double alterations, thus all heliotonic scales are heptatonic. Since heliotonia is a metric of a scale's tone distribution pattern, is related to evenness, spectra variation, the Myhill Property; the notes of a scale form intervals with each of the other notes of the chord in combination. A 5-note scale has 10 of these harmonic intervals, a 6-note scale has 15, a 7-note scale has 21, an 8-note scale has 28.
Though the scale is not a chord, might never be heard more than one note at a time, still the absence and placement of certain key intervals plays a large part in the sound of the scale, the natural movement of melody within the scale, the selection of chords taken from the scale. A musical scale that contains tritones is called tritonic (though the expression is used for any sca
In Western musical notation, the staff or stave is a set of five horizontal lines and four spaces that each represent a different musical pitch or in the case of a percussion staff, different percussion instruments. Appropriate music symbols, depending on the intended effect, are placed on the staff according to their corresponding pitch or function. Musical notes are placed by pitch, percussion notes are placed by instrument, rests and other symbols are placed by convention; the absolute pitch of each line of a non-percussive staff is indicated by the placement of a clef symbol at the appropriate vertical position on the left-hand side of the staff. For example, the treble clef known as the G clef, is placed on the second line, fixing that line as the pitch first G above "middle C"; the lines and spaces are numbered from bottom to top. The musical staff is analogous to a mathematical graph of pitch with respect to time. Pitches of notes are given by their vertical position on the staff and notes are played from left to right.
Unlike a graph, the number of semitones represented by a vertical step from a line to an adjacent space depends on the key, the exact timing of the beginning of each note is not directly proportional to its horizontal position. A time signature to the right of the clef indicates the relationship between timing counts and note symbols, while bar lines group notes on the staff into measures. Staff is more common in American English; the plural is staves in either case. The vertical position of the notehead on the staff indicates which note to play: higher-pitched notes are marked higher on the staff; the notehead can be placed with its center intersecting a line or in between the lines touching the lines above and below. Notes outside the range of the staff are placed on or between ledger lines—lines the width of the note they need to hold—added above or below the staff. Which staff positions represent which notes is determined by a clef placed at the beginning of the staff; the clef identifies a particular line as a specific note, all other notes are determined relative to that line.
For example, the treble clef puts the G above middle C on the second line. The interval between adjacent staff positions is one step in the diatonic scale. Once fixed by a clef, the notes represented by the positions on the staff can be modified by the key signature or accidentals on individual notes. A clefless staff may be used to represent a set of percussion sounds. A vertical line drawn to the left of multiple staves creates a system, indicating that the music on all the staves is to be played simultaneously. A bracket is an additional vertical line joining staves to show groupings of instruments that function as a unit, such as the string section of an orchestra. A brace is used to join multiple staves that represent an instrument, such as a piano, harp, or marimba. Sometimes a second bracket is used to show instruments grouped in pairs, such as the first and second oboes or first and second violins in an orchestra. In some cases, a brace is used for this purpose; when more than one system appears on a page two parallel diagonal strokes are placed on the left side of the score to separate them.
Four-part SATB vocal settings in hymnals, use a divisi notation on a two-staff system with soprano and alto voices sharing the upper staff and tenor and bass voices on the lower staff. Confusingly, the German System may refer to a single staff as well as to the Akkolade or system in the English sense; when music on two staves is joined by a brace, or is intended to be played at once by a single performer, a grand staff or great stave is created. The upper staff uses a treble clef and the lower staff has a bass clef. In this instance, middle C is centered between the two staves, it can be written on the first ledger line below the upper staff or the first ledger line above the lower staff. A centered line with a small alto clef is written, used to indicate that B, C, or D on the line can be played with either hand; when playing the piano or harp, the upper staff is played with the right hand and the lower staff with the left hand. In music intended for organ with pedalboard, a grand staff comprises three staves, one for each hand on the manuals and one for the feet on the pedalboard.
Early Western medieval notation was written with neumes, which did not specify exact pitches but only the shape of the melodies, i.e. indicating when the musical line went up or down. During the 9th through 11th centuries a number of systems were developed to specify pitch more including diastematic neumes whose height on the page corresponded with their absolute pitch level. Digraphic notation, using letter names similar to modern note names in conjunction with the neumes, made a brief appearance in a few manuscripts, but a number of manuscripts used one or more horizontal lines to indicate particular pitches; the treatise Musica
Free jazz is an approach to jazz that developed in the 1960s when musicians attempted to change or break down jazz conventions, such as regular tempos and chord changes. Musicians during this period believed that the bebop, hard bop, modal jazz, played before them was too limiting, they became preoccupied with creating something new. Free jazz has been combined with or substituted for the term "avant-garde jazz". Europeans tend to favor the term "free improvisation". Others have used "modern jazz", "creative music", "art music"; the ambiguity of free jazz presents problems of definition. Although it is played by small groups or individuals, free jazz big bands have existed. Although musicians and critics claim it is innovative and forward looking, it draws on early styles of jazz and has been described as an attempt to return to primitive religious, roots. Although jazz is an American invention, free jazz musicians drew from world music and ethnic music traditions from around the world. Sometimes they invented their own.
They emphasized emotional sound for its own sake. Some jazz musicians resist any attempt at classification. One difficulty is. Many musicians draw on free jazz concepts and idioms, free jazz was never distinct from other genres, but free jazz does have its own characteristics. Pharoah Sanders and John Coltrane used harsh overblowing or other extended techniques to elicit unconventional sounds from their instruments. Like other forms of jazz it places an aesthetic premium on expressing the "voice" or "sound" of the musician, as opposed to the classical tradition in which the performer is seen more as expressing the thoughts of the composer. Earlier jazz styles were built on a framework of song forms, such as twelve-bar blues or the 32-bar AABA popular song form with chord changes. In free jazz, the dependence on a fixed and pre-established form is eliminated, the role of improvisation is correspondingly increased. Other forms of jazz use regular meters and pulsed rhythms in 4/4 or 3/4. Free jazz retains pulsation and sometimes swings but without regular meter.
Frequent Accelerando and ritardando give an impression of rhythm. Previous jazz forms used harmonic structures cycles of diatonic chords; when improvisation occurred, it was founded on the notes in the chords. Free jazz by definition is free of such structures, but by definition it retains much of the language of earlier jazz playing, it is therefore common to hear diatonic, altered dominant and blues phrases in this music. Guitarist Marc Ribot commented that Ornette Coleman and Albert Ayler "although they were freeing up certain strictures of bebop, were in fact each developing new structures of composition." Some forms use composed melodies as the basis for group improvisation. Free jazz practitioners sometimes use such material. Other compositional structures are employed, some detailed and complex; the breakdown of form and rhythmic structure has been seen by some critics to coincide with jazz musicians' exposure to and use of elements from non-Western music African and Indian. The atonality of free jazz is credited by historians and jazz performers to a return to non-tonal music of the nineteenth century, including field hollers, street cries, jubilees.
This suggests that the movement away from tonality was not a conscious effort to devise a formal atonal system, but rather a reflection of the concepts surrounding free jazz. Jazz became "free" by removing dependence on chord progressions and instead using polytempic and polyrhythmic structures. Rejection of the bop aesthetic was combined with a fascination with earlier styles of jazz, such as dixieland with its collective improvisation, as well as African music. Interest in ethnic music resulted in the use of instruments from around the world, such as Ed Blackwell's West African talking drum, Leon Thomas's interpretation of pygmy yodeling. Ideas and inspiration were found in the music of John Cage, Musica Elettronica Viva, the Fluxus movement. Many critics at the music's inception, suspected that abandonment of familiar elements of jazz pointed to a lack of technique on the part of the musicians. Today such views are more marginal, the music has built a body of critical writing. Many critics have drawn connections between the term "free jazz" and the American social setting during the late 1950s and 1960s the emerging social tensions of racial integration and the civil rights movement.
Many argue those recent phenomena such as the landmark Brown v. Board of Education decision in 1954, the emergence of the "Freedom Riders" in 1961, the 1963 Freedom Summer of activist-supported black voter registration, the free alternative black Freedom Schools demonstrate the political implications of the word "free" in context of free jazz, thus many consider free jazz to be not only a rejection of certain musical credos and ideas, but a musical reaction to the oppression and experience of black Americans. Although free jazz is considered to begin in the late 1950s, there are compositions that precede this era that have notable connections to the free jazz aesthetic; some of the works of Lennie Tristano in the late 1940s "Intuition", "Digression", "Descent into the Maelstrom" exhibit the use of techniques associated with free jazz, such as atonal collective improvisation and lack of discrete chord changes. Other notable examples of proto-free jazz include City of Glass written in 1948 by Bob
In the history of Europe, the Middle Ages lasted from the 5th to the 15th century. It began with the fall of the Western Roman Empire and merged into the Renaissance and the Age of Discovery; the Middle Ages is the middle period of the three traditional divisions of Western history: classical antiquity, the medieval period, the modern period. The medieval period is itself subdivided into the Early and Late Middle Ages. Population decline, counterurbanisation, collapse of centralized authority and mass migrations of tribes, which had begun in Late Antiquity, continued in the Early Middle Ages; the large-scale movements of the Migration Period, including various Germanic peoples, formed new kingdoms in what remained of the Western Roman Empire. In the 7th century, North Africa and the Middle East—once part of the Byzantine Empire—came under the rule of the Umayyad Caliphate, an Islamic empire, after conquest by Muhammad's successors. Although there were substantial changes in society and political structures, the break with classical antiquity was not complete.
The still-sizeable Byzantine Empire, Rome's direct continuation, survived in the Eastern Mediterranean and remained a major power. The empire's law code, the Corpus Juris Civilis or "Code of Justinian", was rediscovered in Northern Italy in 1070 and became admired in the Middle Ages. In the West, most kingdoms incorporated the few extant Roman institutions. Monasteries were founded; the Franks, under the Carolingian dynasty established the Carolingian Empire during the 8th and early 9th century. It covered much of Western Europe but succumbed to the pressures of internal civil wars combined with external invasions: Vikings from the north, Magyars from the east, Saracens from the south. During the High Middle Ages, which began after 1000, the population of Europe increased as technological and agricultural innovations allowed trade to flourish and the Medieval Warm Period climate change allowed crop yields to increase. Manorialism, the organisation of peasants into villages that owed rent and labour services to the nobles, feudalism, the political structure whereby knights and lower-status nobles owed military service to their overlords in return for the right to rent from lands and manors, were two of the ways society was organised in the High Middle Ages.
The Crusades, first preached in 1095, were military attempts by Western European Christians to regain control of the Holy Land from Muslims. Kings became the heads of centralised nation-states, reducing crime and violence but making the ideal of a unified Christendom more distant. Intellectual life was marked by scholasticism, a philosophy that emphasised joining faith to reason, by the founding of universities; the theology of Thomas Aquinas, the paintings of Giotto, the poetry of Dante and Chaucer, the travels of Marco Polo, the Gothic architecture of cathedrals such as Chartres are among the outstanding achievements toward the end of this period and into the Late Middle Ages. The Late Middle Ages was marked by difficulties and calamities including famine and war, which diminished the population of Europe. Controversy and the Western Schism within the Catholic Church paralleled the interstate conflict, civil strife, peasant revolts that occurred in the kingdoms. Cultural and technological developments transformed European society, concluding the Late Middle Ages and beginning the early modern period.
The Middle Ages is one of the three major periods in the most enduring scheme for analysing European history: classical civilisation, or Antiquity. The "Middle Ages" first appears in Latin in 1469 as media tempestas or "middle season". In early usage, there were many variants, including medium aevum, or "middle age", first recorded in 1604, media saecula, or "middle ages", first recorded in 1625; the alternative term "medieval" derives from medium aevum. Medieval writers divided history into periods such as the "Six Ages" or the "Four Empires", considered their time to be the last before the end of the world; when referring to their own times, they spoke of them as being "modern". In the 1330s, the humanist and poet Petrarch referred to pre-Christian times as antiqua and to the Christian period as nova. Leonardo Bruni was the first historian to use tripartite periodisation in his History of the Florentine People, with a middle period "between the fall of the Roman Empire and the revival of city life sometime in late eleventh and twelfth centuries".
Tripartite periodisation became standard after the 17th-century German historian Christoph Cellarius divided history into three periods: ancient and modern. The most given starting point for the Middle Ages is around 500, with the date of 476 first used by Bruni. Starting dates are sometimes used in the outer parts of Europe. For Europe as a whole, 1500 is considered to be the end of the Middle Ages, but there is no universally agreed upon end date. Depending on the context, events such as the conquest of Constantinople by the Turks in 1453, Christopher Columbus's first voyage to the Americas in 1492, or the Protestant Reformation in 1517 are sometimes used. English historians use the Battle of Bosworth Field in 1485 to mark the end of the period. For Spain, dates used are the death of King Ferdinand II in 1516, the death of Queen Isabella I of Castile in 1504, or the conquest of Granada in 1492. Historians from Romance-speaking countries tend to divide the Middle Ages into two parts: an earlier "High" and late
Arthur von Oettingen
Arthur Joachim von Oettingen was a Baltic German physicist and music theorist, born at the Luua Manor, Tartu County, Livonia. He was the brother of ophthalmologist Georg von Oettingen, he studied astronomy and physics at the University of Dorpat, furthered his education of physics in Paris in the laboratories of Antoine César Becquerel and Henri Victor Régnault, afterwards at Berlin in the laboratories of Heinrich Gustav Magnus, Johann Christian Poggendorff and Heinrich Wilhelm Dove. In 1868 he became a professor at Dorpat. In 1893 he moved to the University of Leipzig, where he remained until 1919 as a teacher and honorary professor. In 1898 and 1904 he published the third and fourth volumes of Poggendorff's Biographisch-Literarisches Handwörterbuch der exakten Naturwissenschaften. Oettingen was a primary advocate of a theory of acoustical relationships known as "harmonic dualism"; this concept was expanded and elaborated on by musicologist Hugo Riemann. Oettingen is credited for introducing a measurement of musical interval known as the millioctave.
Harmoniesystem in dualer Entwicklung, Dorpat 1866. Meteorologische Beobachtungen angestellt in Dorpat im Jahre... Dorpat 1868-1877. Über den mathematischen Unterricht in der Schule, Dorpat 1873. Elemente des geometrisch-perspektivischen Zeichnens, Leipzig 1901. List of Baltic German scientists This article is based on a translation of an equivalent article at the German Wikipedia. Alexander Rehding. Hugo Riemann and the Birth of Modern Musical Thought. Cambridge University Press. ISBN 0-521-82073-1. Chemistry Tree: Arthur Joachim von Oettingen Details Stamps, Tartu University Meteorology Observatory 150 / 614-02.12.15, On 2 December 1865 Arthur von Oettingen launched meteorological observations at the Tartu University Physics Cabinet. 02.12.2015 – Tartu University Meteorology Observatory 150, On 2 December 1865 Arthur von Oettingen launched meteorological observations at the Tartu University Physics Cabinet
Gregorian chant is the central tradition of Western plainchant, a form of monophonic, unaccompanied sacred song of the Roman Catholic Church. Gregorian chant developed in western and central Europe during the 9th and 10th centuries, with additions and redactions. Although popular legend credits Pope Gregory I with inventing Gregorian chant, scholars believe that it arose from a Carolingian synthesis of Roman chant and Gallican chant. Gregorian chants were organized into four eight, 12 modes. Typical melodic features include a characteristic ambitus, characteristic intervallic patterns relative to a referential mode final and cadences, the use of reciting tones at a particular distance from the final, around which the other notes of the melody revolve, a vocabulary of musical motifs woven together through a process called centonization to create families of related chants; the scale patterns are organized against a background pattern formed of conjunct and disjunct tetrachords, producing a larger pitch system called the gamut.
The chants can be sung by using six-note patterns called hexachords. Gregorian melodies are traditionally written using neumes, an early form of musical notation from which the modern four-line and five-line staff developed. Multi-voice elaborations of Gregorian chant, known as organum, were an early stage in the development of Western polyphony. Gregorian chant was traditionally sung by choirs of men and boys in churches, or by men and women of religious orders in their chapels, it is the music of the Roman Rite, performed in the monastic Office. Although Gregorian chant supplanted or marginalized the other indigenous plainchant traditions of the Christian West to become the official music of the Christian liturgy, Ambrosian chant still continues in use in Milan, there are musicologists exploring both that and the Mozarabic chant of Christian Spain. Although Gregorian chant is no longer obligatory, the Roman Catholic Church still considers it the music most suitable for worship. During the 20th century, Gregorian chant underwent a popular resurgence.
Singing has been part of the Christian liturgy since the earliest days of the Church. Until the mid-1990s, it was accepted that the psalmody of ancient Jewish worship influenced and contributed to early Christian ritual and chant; this view is no longer accepted by scholars, due to analysis that shows that most early Christian hymns did not have Psalms for texts, that the Psalms were not sung in synagogues for centuries after the Destruction of the Second Temple in AD 70. However, early Christian rites did incorporate elements of Jewish worship that survived in chant tradition. Canonical hours have their roots in Jewish prayer hours. "Amen" and "alleluia" come from Hebrew, the threefold "sanctus" derives from the threefold "kadosh" of the Kedushah. The New Testament mentions singing hymns during the Last Supper: "When they had sung the hymn, they went out to the Mount of Olives" Matthew 26.30. Other ancient witnesses such as Pope Clement I, Tertullian, St. Athanasius, Egeria confirm the practice, although in poetic or obscure ways that shed little light on how music sounded during this period.
The 3rd-century Greek "Oxyrhynchus hymn" survived with musical notation, but the connection between this hymn and the plainchant tradition is uncertain. Musical elements that would be used in the Roman Rite began to appear in the 3rd century; the Apostolic Tradition, attributed to the theologian Hippolytus, attests the singing of Hallel psalms with Alleluia as the refrain in early Christian agape feasts. Chants of the Office, sung during the canonical hours, have their roots in the early 4th century, when desert monks following St. Anthony introduced the practice of continuous psalmody, singing the complete cycle of 150 psalms each week. Around 375, antiphonal psalmody became popular in the Christian East. In the fifth century, a singing school, the Schola Cantorum, was founded at Rome to provide training in church musicianship. Scholars are still debating how plainchant developed during the 5th through the 9th centuries, as information from this period is scarce. Around 410, St. Augustine described the responsorial singing of a Gradual psalm at Mass.
At c. 520, Benedict of Nursia established what is called the rule of St. Benedict, in which the protocol of the Divine Office for monastic use was laid down. Around 678, Roman chant was taught at York. Distinctive regional traditions of Western plainchant arose during this period, notably in the British Isles, Spain and Italy; these traditions may have evolved from a hypothetical year-round repertory of 5th-century plainchant after the western Roman Empire collapsed. John the Deacon, biographer of Pope Gregory I, modestly claimed that the saint "compiled a patchwork antiphonary", given his considerable work with liturgical development, he reorganized the Schola Cantorum and established a more uniform standard in church services, gathering chants from among the regional traditions as as he could manage. Of those, he retained what he could, revised where necessary, assigned particular chants to the various services. According to Donald Jay Grout, his goal was to organize the bodies of chants from diverse traditions into a uniform and orderly whole for use by the entire western region of the Church.
His renowned love for music was recorded only 34 years after his death. While legends magnified his real achievements
In music, an accidental is a note of a pitch, not a member of the scale or mode indicated by the most applied key signature. In musical notation, the sharp and natural symbols, among others, mark such notes—and those symbols are called accidentals. In the measure where it appears, an accidental sign raises or lowers the following note from its normal pitch, overriding sharps or flats in the key signature. A note is raised or lowered by a semitone, although microtonal music may use "fractional" accidental signs. There are occasionally double sharps or flats, which raise or lower the indicated note by a whole tone. Accidentals apply within the measure and octave in which they appear, unless canceled by another accidental sign, or tied into the following measure. If a note has an accidental and the note is repeated in a different octave within the same measure, the accidental does not apply to the same note of the different octave; the modern accidental signs derive from the two forms of the lower-case letter b used in Gregorian chant manuscripts to signify the two pitches of B, the only note that could be altered.
The "round" b became the flat sign, while the "square" b diverged into the natural signs. Sometimes the black keys on a musical keyboard are called accidentals, the white keys are called naturals. In most cases, a sharp raises the pitch of a note one semitone. A natural is used to cancel the effect of a sharp; this system of accidentals operates in conjunction with the key signature, whose effect continues throughout an entire piece, unless canceled by another key signature. An accidental can be used to cancel a previous accidental or reinstate the flats or sharps of the key signature Accidentals apply to subsequent notes on the same staff position for the remainder of the measure where they occur, unless explicitly changed by another accidental. Once a barline is passed, the effect of the accidental ends, except when a note affected by an accidental is tied to the same note across a barline. Subsequent notes at the same staff position in the second or bars are not affected by the accidental carried through with the tied note.
Under this system, the notes in the example above are: m. 1: G♮, G♯, G♯ m. 2: G♮, G♭, G♭ m. 3: G♭, G♯, G♮ Though this convention is still in use in tonal music, it may be cumbersome in music that features frequent accidentals, as is the case in atonal music. As a result, an alternative system of note-for-note accidentals has been adopted, with the aim of reducing the number of accidentals required to notate a bar; the system is as follows: An accidental carries through the bar affecting both the note it precedes and any following notes on the same line or space in the measure. Accidentals are not repeated on tied notes unless the tie goes from line to page to page. Accidentals are not repeated for repeated notes. If a sharp or flat pitch is followed directly by its natural form, a natural is used. Courtesy accidentals or naturals may be used to clarify ambiguities but are kept to a minimumBecause seven of the twelve notes of the chromatic equal-tempered scale are naturals this system can reduce the number of naturals required in a notated passage.
An accidental may change the note by more than a semitone: for example, if a G♯ is followed in the same measure by a G♭, the flat sign on the latter note means it is two semitones lower than if no accidental were present. Thus, the effect of the accidental must be understood in relation to the "natural" meaning of the note's staff position. In some atonal scores, an accidental is notated on every note, including natural notes and repeated pitches; this system was adopted for "the specific intellectual reason that a note with an accidental was not an inflected version of a natural note but a pitch of equal status." Double accidentals raise or lower the pitch of a note by two semitones, an innovation developed as early as 1615. This applies to the written note, ignoring key signature. An F with a double sharp applied raises it a whole step so it is enharmonically equivalent to a G. Usage varies on how to notate the situation in which a note with a double sharp is followed in the same measure by a note with a single sharp.
Some publications use the single accidental for the latter note, whereas others use a combination of a natural and a sharp, with the natural being understood to apply to only the second sharp. The double accidental with respect to a specific key signature raises or lowers the notes containing a sharp or flat by a semitone. For example, when in the key of C♯ minor or E major, F, C, G, D contain a sharp. Adding a double accidental to F in this case only raises F♯ by one further semitone, creating G natural. Conversely, adding a double sharp to any other note not sharped or flatted in the key signature raises the note by two semitones with respect to the chromatic scale. For example, in the aforementioned key signature, any note, not F, C, G, D is raised by two semitones instead of one, so an A double sharp raises the note A natural to the enharmonic equivalent of B natural. In modern scores, a barline cancels an accidental —but publishers use a courtesy accident