Ausmultiplikation is a German term used by the composer Karlheinz Stockhausen to describe a technique in which a long note is replaced by shorter "melodic configurations, internally animated around central tones", resembling the ornamental technique of divisions in Renaissance music. Stockhausen first described this technique in connection with his "opus 1", Kontra-Punkte, composed in 1952–53, but in his formula composition there is a related method of substituting a complete or partial formula for a single long tone in a much slower, "more background" projection of the formula; when this is done at more than one level, the result is reminiscent of a fractal. Hartwell, Robin. 2012. "Threats and Promises: Lucifer and Stockhausen's Sunday from Light". Perspectives of New Music 50, nos. 1 & 2: 393–424. Kohl, Jerome. 1990. "Into the Middleground: Formula Syntax in Stockhausen's Licht". Perspectives of New Music 28, no. 2: 262–91. Stockhausen, Karlheinz. 1989. "Wille zur Form und Wille zum Abenteuer". In his Texte zur Musik 6, edited by Christoph von Blumröder, 320–46.
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A chord, in music, is any harmonic set of pitches consisting of multiple notes that are heard as if sounding simultaneously. For many practical and theoretical purposes and broken chords, or sequences of chord tones, may be considered as chords. Chords and sequences of chords are used in modern West African and Oceanic music, Western classical music, Western popular music. In tonal Western classical music, the most encountered chords are triads, so called because they consist of three distinct notes: the root note, intervals of a third and a fifth above the root note. Chords with more than three notes include added tone chords, extended chords and tone clusters, which are used in contemporary classical music and other genres. A series of chords is called a chord progression. One example of a used chord progression in Western traditional music and blues is the 12 bar blues progression. Although any chord may in principle be followed by any other chord, certain patterns of chords are more common in Western music, some patterns have been accepted as establishing the key in common-practice harmony—notably the resolution of a dominant chord to a tonic chord.
To describe this, Western music theory has developed the practice of numbering chords using Roman numerals to represent the number of diatonic steps up from the tonic note of the scale. Common ways of notating or representing chords in Western music include Roman numerals, the Nashville number system, figured bass, macro symbols, chord charts; the English word chord derives from Middle English cord, a shortening of accord in the original sense of agreement and harmonious sound. A sequence of chords is known as a chord harmonic progression; these are used in Western music. A chord progression "aims for a definite goal" of establishing a tonality founded on a key, root or tonic chord; the study of harmony involves chords and chord progressions and the principles of connection that govern them. Ottó Károlyi writes that, "Two or more notes sounded are known as a chord," though, since instances of any given note in different octaves may be taken as the same note, it is more precise for the purposes of analysis to speak of distinct pitch classes.
Furthermore, as three notes are needed to define any common chord, three is taken as the minimum number of notes that form a definite chord. Hence, Andrew Surmani, for example, states, "When three or more notes are sounded together, the combination is called a chord." George T. Jones agrees: "Two tones sounding together are termed an interval, while three or more tones are called a chord." According to Monath. However, sonorities of two pitches, or single-note melodies, are heard as implying chords. A simple example of two notes being interpreted as a chord is when the root and third are played but the fifth is omitted. In the key of C major, if the music comes to rest on the two notes G and B, most listeners will hear this as a G major chord. Since a chord may be understood as such when all its notes are not audible, there has been some academic discussion regarding the point at which a group of notes may be called a chord. Jean-Jacques Nattiez explains that, "We can encounter'pure chords' in a musical work," such as in the Promenade of Modest Mussorgsky's Pictures at an Exhibition but, "Often, we must go from a textual given to a more abstract representation of the chords being used," as in Claude Debussy's Première arabesque.
In the medieval era, early Christian hymns featured organum, with chord progressions and harmony an incidental result of the emphasis on melodic lines during the medieval and Renaissance. The Baroque period, the 17th and 18th centuries, began to feature the major and minor scale based tonal system and harmony, including chord progressions and circle progressions, it was in the Baroque period that the accompaniment of melodies with chords was developed, as in figured bass, the familiar cadences. In the Renaissance, certain dissonant sonorities that suggest the dominant seventh occurred with frequency. In the Baroque period, the dominant seventh proper was introduced and was in constant use in the Classical and Romantic periods; the leading-tone seventh remains in use. Composers began to use nondominant seventh chords in the Baroque period, they became frequent in the Classical period, gave way to altered dominants in the Romantic period, underwent a resurgence in the Post-Romantic and Impressionistic period.
The Romantic period, the 19th century, featured increased chromaticism. Composers began to use secondary dominants in the Baroque, they became common in the Romantic period. Many contemporary popular Western genres continue to rely on simple diatonic harmony, though far from universally: notable exceptions include the music of film scores, which use chromatic, atonal or post-tonal harmony, modern jazz, in which chords may include up to seven notes; when referring to chords that do not function as harmony, such as in atonal music, the term "sonority" is used to avoid any tonal implications of the word "chord". Chords can be represent
In music, a fugue is a contrapuntal compositional technique in two or more voices, built on a subject, introduced at the beginning in imitation and which recurs in the course of the composition. It is not to be confused with a fuguing tune, a style of song popularized by and limited to early American music and West Gallery music. A fugue has three main sections: an exposition, a development and a final entry that contains the return of the subject in the fugue's tonic key; some fugues have a recapitulation. In the Middle Ages, the term was used to denote any works in canonic style. Since the 17th century, the term fugue has described what is regarded as the most developed procedure of imitative counterpoint. Most fugues open with a short main theme, the subject, which sounds successively in each voice; this is followed by a connecting passage, or episode, developed from heard material. Episodes and entries are alternated until the "final entry" of the subject, by which point the music has returned to the opening key, or tonic, followed by closing material, the coda.
In this sense, a fugue is a style of composition, rather than a fixed structure. The form evolved during the 18th century from several earlier types of contrapuntal compositions, such as imitative ricercars, capriccios and fantasias; the famous fugue composer Johann Sebastian Bach shaped his own works after those of Johann Jakob Froberger, Johann Pachelbel, Girolamo Frescobaldi, Dieterich Buxtehude and others. With the decline of sophisticated styles at the end of the baroque period, the fugue's central role waned giving way as sonata form and the symphony orchestra rose to a dominant position. Composers continued to write and study fugues for various purposes; the English term fugue originated in the 16th century and is derived from the French word fugue or the Italian fuga. This in turn comes from Latin fuga, itself related to both fugere and fugare; the adjectival form is fugal. Variants include fugato. A fugue is written according to certain predefined rules. Further entries of the subject will occur throughout the fugue, repeating the accompanying material at the same time.
The various entries may not be separated by episodes. What follows is a chart displaying a typical fugal outline, an explanation of the processes involved in creating this structure. S = subject. After the statement of the subject, a second voice enters and states the subject with the subject transposed to another key, known as the answer. To make the music run smoothly, it may have to be altered slightly; when the answer is an exact copy of the subject to the new key, with identical intervals to the first statement, it is classified as a real answer. A tonal answer is called for when the subject begins with a prominent dominant note, or where there is a prominent dominant note close to the beginning of the subject. To prevent an undermining of the music's sense of key, this note is transposed up a fourth to the tonic rather than up a fifth to the supertonic. Answers in the subdominant are employed for the same reason. While the answer is being stated, the voice in which the subject was heard continues with new material.
If this new material is reused in statements of the subject, it is called a countersubject. The countersubject is written in invertible counterpoint at the fifteenth; the distinction is made between the use of free counterpoint and regular countersubjects accompanying the fugue subject/answer, because in order for a countersubject to be heard accompanying the subject in more than one instance, it must be capable of sounding above or below the subject, must be conceived, therefore, in invertible counterpoint. In tonal music, invertible contrapuntal lines must be written according to certain rules because several intervallic combinations, while acceptable in one particular orientation, are no longer permissible when inverted. For example, when the note "G" sounds in one voice above the note "C" in lower voice, the interval of a fifth is formed, considered consonant and acceptable; when this interval is inverted, it forms a fourth, considered a dissonance in tonal contrapuntal practice, requires special treatment, or preparation and resolution, if it is to be used.
The countersubject, if sounding at the same time as the ans
Debate is a process that involves formal discussion on a particular topic. In a debate, opposing arguments are put forward to argue for opposing viewpoints. Debate occurs in public meetings, academic institutions, legislative assemblies, it is a formal type of discussion with a moderator and an audience, in addition to the debate participants. Logical consistency, factual accuracy and some degree of emotional appeal to the audience are elements in debating, where one side prevails over the other party by presenting a superior "context" or framework of the issue. In a formal debating contest, there are rules for participants to discuss and decide on differences, within a framework defining how they will do it. Debating is carried out in debating chambers and assemblies of various types to discuss matters and to make resolutions about action to be taken by voting. Deliberative bodies such as parliaments, legislative assemblies, meetings of all sorts engage in debates. In particular, in parliamentary democracies a legislature decides on new laws.
Formal debates between candidates for elected office, such as the leaders debates, are sometimes held in democracies. Debating is carried out for educational and recreational purposes associated with educational establishments and debating societies. Informal and forum debate is common, shown by TV shows such as the Australian talk show, Q&A; the outcome of a contest may be decided by audience vote, by judges, or by some combination of the two. Although debating in various forms has a long history and can be traced back to the philosophical and political debates of Ancient Greece, such as Athenian democracy, Shastrartha in Ancient India, modern forms of debating and the establishment of debating societies occurred during the Age of Enlightenment in the 18th century. Debating societies emerged in London in the early eighteenth century, soon became a prominent fixture of national life; the origins of these societies are not certain in many cases, although by the mid-18th century, London fostered an active debating society culture.
Debating topics covered a broad spectrum of topics while the debating societies allowed participants from both genders and all social backgrounds, making them an excellent example of the enlarged public sphere of the Age of Enlightenment. Debating societies were a phenomenon associated with the simultaneous rise of the public sphere, a sphere of discussion separate from traditional authorities and accessible to all people that acted as a platform for criticism and the development of new ideas and philosophy. John Henley, a clergyman, founded an Oratory in 1726 with the principal purpose of "reforming the manner in which such public presentations should be performed." He made extensive use of the print industry to advertise the events of his Oratory, making it an omnipresent part of the London public sphere. Henley was instrumental in constructing the space of the debating club: he added two platforms to his room in the Newport district of London to allow for the staging of debates, structured the entrances to allow for the collection of admission.
These changes were further implemented. The public was now willing to pay to be entertained, Henley exploited this increasing commercialization of British society. By the 1770s, debating societies were established in London society; the year 1785 was pivotal: The Morning Chronicle announced on March 27: The Rage for publick debate now shews itself in all quarters of the metropolis. Exclusive of the oratorical assemblies at Carlisle House, Free-mason's Hall, the Forum, Spring Gardens, the Cassino, the Mitre Tavern and other polite places of debating rendezvous, we hear that new Schools of Eloquence are preparing to be opened in St. Giles, Clare-Market, Hockley in the Hole, Rag-Fair, Duke's Place and the Back of the Borough. In 1780, 35 differently named societies advertised and hosted debates for anywhere between 650 and 1200 people; the question for debate was introduced by a president or moderator who proceeded to regulate the discussion. Speakers were given set amounts of time to argue their point of view, and, at the end of the debate, a vote was taken to determine a decision or adjourn the question for further debate.
Speakers were not permitted to slander or insult other speakers, or diverge from the topic at hand, again illustrating the value placed on politeness by late 18th century debaters. Princeton University in the future United States was home to a number of short-lived student debating societies throughout the mid-1700s, its influential American Whig Society was co-founded in 1769 by future revolutionary James Madison; the first of the post-revolutionary debating societies, the Dialectic and Philanthropic Societies, were formed at the University of North Carolina at Chapel Hill in 1795 and are still active. The first student debating society in Great Britain was the St Andrews Debating Society, formed in 1794 as the Literary Society; the Cambridge Union Society was founded in 1815, claims to be the oldest continually operating debating society in the World. This claim is arguably valid because Princeton's societies had been shut down during the American Revolutionary War, while the UNC societies' operations were suspended during the American Civil War.
Over the next few decades, similar societies emerged at several other prominent universities. Examples include the Yale Political Union and the Conférence Olivaint. Submitted by IIIT NUZVID In parliaments and other legislatures, members debate proposals regarding legislation, before voting on resolutions which become laws. Debates are conducted by proposing a law, or changes to a l
In music, counterpoint is the relationship between voices that are harmonically interdependent yet independent in rhythm and contour. It has been most identified in the European classical tradition developing during the Renaissance and in much of the common practice period in the Baroque; the term originates from the Latin punctus contra punctum meaning "point against point". Counterpoint has been used to designate a voice or an entire composition. Counterpoint focuses on melodic interaction—only secondarily on the harmonies produced by that interaction. In the words of John Rahn: It is hard to write a beautiful song, it is harder to write several individually beautiful songs that, when sung sound as a more beautiful polyphonic whole. The internal structures that create each of the voices separately must contribute to the emergent structure of the polyphony, which in turn must reinforce and comment on the structures of the individual voices; the way, accomplished in detail is...'counterpoint'.
Counterpoint theory has been given a mathematical foundation in the work initiated by Guerino Mazzola. In particular, his model gives a structural foundation of forbidden parallels of fifths and the dissonant fourth; the model has been extended to microtonal contexts by Octavio Agustin. Some examples of related compositional techniques include: the round, the canon, the most complex contrapuntal convention: the fugue. All of these are examples of imitative counterpoint. In 1725 Johann Joseph Fux published Gradus ad Parnassum, in which he described five species: Note against note. A succession of theorists quite imitated Fux's seminal work with some small and idiosyncratic modifications in the rules. Many of Fux's rules concerning the purely linear construction of melodies have their origin in solfeggi. Concerning the common practice era, alterations to the melodic rules were introduced to enable the function of certain harmonic forms; the combination of these melodies produced the figured bass.
The following rules apply to melodic writing in each species, for each part: The final must be approached by step. If the final is approached from below the leading tone must be raised in a minor key, but not in Phrygian or Hypophrygian mode. Thus, in the Dorian mode on D, a C♯ is necessary at the cadence. Permitted melodic intervals are the perfect fourth and octave, as well as the major and minor second and minor third, ascending minor sixth; the ascending minor sixth must be followed by motion downwards. If writing two skips in the same direction—something that must be only done—the second must be smaller than the first, the interval between the first and the third note may not be dissonant; the three notes should be from the same triad. In general, do not write more than two skips in the same direction. If writing a skip in one direction, it is best to proceed after the skip with motion in the other direction; the interval of a tritone in three notes should be avoided as is the interval of a seventh in three notes.
There must be a climax or high point in the line countering the cantus firmus. This occurs somewhere in the middle of exercise and must occur on a strong beat. An outlining of a seventh is avoided within a single line moving in the same direction. And, in all species, the following rules govern the combination of the parts: The counterpoint must begin and end on a perfect consonance. Contrary motion should predominate. Perfect consonances must be approached by contrary motion. Imperfect consonances may be approached by any type of motion; the interval of a tenth should not be exceeded between two adjacent parts. Build from the bass, upward. In first species counterpoint, each note in every added part sounds against one note in the cantus firmus. Notes in all parts are sounded and move against each other simultaneously. Since all notes in First species counterpoint are whole notes, rhythmic independence is not available. In the present context, a "step" is a melodic interval of whole step. A "skip" is an interval of a fourth.
An interval of a fifth or larger is referred to as a "leap". A few further rules given by Fux, by study of the Palestrina style, given in the works of counterpoint pedagogues, are as follows. Begin and end on either the unison, octave, or fifth, unless the added part is underneath, in which case begin and end only on unison or octave. Use no unisons except at the beginning or end. Avoid parallel fifths or octaves between any two parts. Avoid moving in parallel fourths. Avoid moving in parallel thirds or sixths for long. Attempt to keep any two adjacent parts within a tenth of each other, unless an exceptionally pleasing line can be written by moving outside that range. Avoid having any two parts move in the same direction by skip Attempt to have as much contrary motion as possible. Avoid dissonant inter
In music, changing tones consists of two consecutive non-chord tones. The first moves in one direction by a step from a chord tone skips by a third in the opposite direction to another non-chord tone, finally resolves back to the original chord tone. Changing tones appear to resemble two consecutive neighbor tones; the changing tone functions as a way to decorate, or embellish, a chord tone and are used to provide rhythmic interest between common tones. In rare instances, changing tones can be heard as musical cryptograms, such as the cruciform melody
In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones. For instance, the interval from F up to the B above it is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, A–B. According to this definition, within a diatonic scale there is only one tritone for each octave. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the C major scale. A tritone is commonly defined as an interval spanning six semitones. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B and B–F. In twelve-equal temperament, the tritone divides the octave in half. In classical music, the tritone is a harmonic and melodic dissonance and is important in the study of musical harmony; the tritone can be used to avoid traditional tonality: "Any tendency for a tonality to emerge may be avoided by introducing a note three whole tones distant from the key note of that tonality."
Contrarily, the tritone found in the dominant seventh chord helps establish the tonality of a composition. These contrasting uses exhibit the flexibility and distinctness of the tritone in music; the condition of having tritones is called tritonia. A musical scale or chord containing tritones is called tritonic. Since a chromatic scale is formed by 12 pitches, it contains 12 distinct tritones, each starting from a different pitch and spanning six semitones. According to a complex but used naming convention, six of them are classified as augmented fourths, the other six as diminished fifths. Under that convention, a fourth is an interval encompassing four staff positions, while a fifth encompasses five staff positions; the augmented fourth and diminished fifth are defined as the intervals produced by widening the perfect fourth and narrowing the perfect fifth by one chromatic semitone. They both span six semitones, they are the inverse of each other, meaning that their sum is equal to one perfect octave.
In twelve-tone equal temperament, the most used tuning system, the A4 is equivalent to a d5, as both have the size of half an octave. In most other tuning systems, they are not equivalent, neither is equal to half an octave. Any augmented fourth can be decomposed into three whole tones. For instance, the interval F–B is an augmented fourth and can be decomposed into the three adjacent whole tones F–G, G–A, A–B, it is not possible to decompose a diminished fifth into three adjacent whole tones. The reason is that a whole tone is a major second, according to a rule explained elsewhere, the composition of three seconds is always a fourth. To obtain a fifth, it is necessary to add another second. For instance, using the notes of the C major scale, the diminished fifth B–F can be decomposed into the four adjacent intervals B–C, C–D, D–E, E–F. Using the notes of a chromatic scale, B–F may be decomposed into the four adjacent intervals B–C♯, C♯–D♯, D♯–E♯, E♯–F♮. Notice that the latter diminished second is formed by two enharmonically equivalent notes.
On a piano keyboard, these notes are produced by the same key. However, in the above-mentioned naming convention, they are considered different notes, as they are written on different staff positions and have different diatonic functions within music theory. A tritone is traditionally defined as a musical interval composed of three whole tones; as the symbol for whole tone is T, this definition may be written as follows: TT = T+T+TOnly if the three tones are of the same size can this formula be simplified to: TT = 3TThis definition, has two different interpretations. In a chromatic scale, the interval between any note and the previous or next is a semitone. Using the notes of a chromatic scale, each tone can be divided into two semitones: T = S+SFor instance, the tone from C to D can be decomposed into the two semitones C–C♯ and C♯–D by using the note C♯, which in a chromatic scale lies between C and D; this means that, when a chromatic scale is used, a tritone can be defined as any musical interval spanning six semitones: TT = T+T+T = S+S+S+S+S+S.
According to this definition, with the twelve notes of a chromatic scale it is possible to define twelve different tritones, each starting from a different note and ending six notes above it. Although all of them span six semitones, six of them are classified as augmented fourths, the other six as diminished fifths. Within a diatonic scale, whole tones are always formed by adjacent notes and therefore they are regarded as incomposite intervals. In other words, they cannot be divided into smaller intervals. In this context the above-mentioned "decomposition" of the tritone into six semitones is not allowed. If a diatonic scale is used, with its 7 notes it is possible to form only one sequence of three adjacent whole tones; this interval is an A4. For instance, in the C major diatonic scale, the only tritone is from F to B, it is a tritone because F–G, G–A, A–B are three adjacent whole tones. It is a fourth because the notes from F to B are four (F