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Kirnberger Temperament
The Kirnberger temperaments are three irregular Musical temperament, temperaments developed in the second half of the 18th century by Johann Kirnberger. Kirnberger was a student of Johann Sebastian Bach who greatly admired his teacher; he was one of Bach's principal proponents. Kirnberger's tuning systems, or ''well temperaments'' are a way to artificially splice together two arcs on the "natural" spiral of fifths to turn it into an "unnatural" circle. In Kirnberger's and his teacher Johann Sebastian Bach, Bach's time, keyboard musicians were experimenting with different unobtrusive ways to alter the spacing of notes around the spiral of fifths to close it into a circle, so that every note needed for every key signature, key was at hand, even if some rarely used key signatures might be very dissonant, but tolerable. The first Kirnberger temperament, Kirnberger I, had similarities to Pythagorean tuning, which stressed the importance of perfect fifths all throughout the ci ...
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Musical Temperament
In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system. Tempering is the process of altering the size of an interval by making it narrower or wider than pure. "Any plan that describes the adjustments to the sizes of some or all of the twelve fifth intervals in the circle of fifths so that they accommodate pure octaves and produce certain sizes of major thirds is called a ''temperament''." Temperament is especially important for keyboard instruments, which typically allow a player to play only the pitches assigned to the various keys, and lack any way to alter pitch of a note in performance. Historically, the use of just intonation, Pythagorean tuning and meantone temperament meant that such instruments could sound "in tune" in one key, or some keys, but would then have more dissonance in other keys. In the w ...
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Pythagorean Wolf Fifth
In music theory, the wolf fifth (sometimes also called Procrustean fifth, or imperfect fifth) is a particularly dissonant musical interval spanning seven semitones. Strictly, the term refers to an interval produced by a specific tuning system, widely used in the sixteenth and seventeenth centuries: the quarter-comma meantone temperament. More broadly, it is also used to refer to similar intervals (of close, but variable magnitudes) produced by other tuning systems, including Pythagorean and most meantone temperaments. When the twelve notes within the octave of a chromatic scale are tuned using the quarter-comma meantone systems of temperament, one of the twelve intervals apparently spanning seven semitones is actually a diminished sixth, which turns out to be much wider than the in-tune genuine fifths, In mean-tone systems, this interval is usually from C to A or from G to E but can be moved in either direction to favor certain groups of keys. The eleven perfect fifths so ...
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Harp
The harp is a stringed musical instrument that has individual strings running at an angle to its soundboard; the strings are plucked with the fingers. Harps can be made and played in various ways, standing or sitting, and in orchestras or concerts. Its most common form is triangular in shape and made of wood. Some have multiple rows of strings and pedal attachments. Ancient depictions of harps were recorded in Mesopotamia (now Iraq), Persia (now Iran) and Egypt, and later in India and China. By medieval times harps had spread across Europe. Harps were found across the Americas where it was a popular folk tradition in some areas. Distinct designs also emerged from the African continent. Harps have symbolic political traditions and are often used in logos, including in Ireland. Historically, strings were made of sinew (animal tendons). Other materials have included gut (animal intestines), plant fiber, braided hemp, cotton cord, silk, nylon, and wire. In pedal harp scor ...
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Guitar
The guitar is a stringed musical instrument that is usually fretted (with Fretless guitar, some exceptions) and typically has six or Twelve-string guitar, twelve strings. It is usually held flat against the player's body and played by strumming or Plucked string instrument, plucking the strings with the dominant hand, while simultaneously pressing selected strings against frets with the fingers of the opposite hand. A guitar pick may also be used to strike the strings. The sound of the guitar is projected either Acoustics, acoustically, by means of a resonant hollow chamber on the guitar, or Amplified music, amplified by an electronic Pickup (music technology), pickup and an guitar amplifier, amplifier. The guitar is classified as a chordophone, meaning the sound is produced by a vibrating string stretched between two fixed points. Historically, a guitar was constructed from wood, with its strings made of catgut. Steel guitar strings were introduced near the end of the nineteen ...
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Viols
The viola da gamba (), or viol, or informally gamba, is a bowed and fretted string instrument that is played (i.e. "on the leg"). It is distinct from the later violin, or ; and it is any one of the earlier viol family of bowed, fretted, and stringed instruments with hollow wooden bodies and pegboxes where the tension on the strings can be increased or decreased to adjust the pitch of each of the strings. Although treble, tenor and bass were most commonly used, viols came in different sizes, including (high treble, developed in 18th century), treble, alto, small tenor, tenor, bass and contrabass (called ). These members of the viol family are distinguished from later bowed string instruments, such as the violin family, by both appearance and orientation when played—as typically the neck is oriented upwards and the rounded bottom downwards to settle on the lap or between the knees. The viola da gamba uses the alto clef. Seven and occasionally eight frets made of "stretche ...
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Lutes
A lute ( or ) is any plucked string instrument with a neck and a deep round back enclosing a hollow cavity, usually with a sound hole or opening in the body. It may be either fretted or unfretted. More specifically, the term "lute" commonly refers to an instrument from the family of European lutes which were themselves influenced by Indian short-necked lutes in Gandhara which became the predecessor of the Islamic, the Sino-Japanese and the European lute families. The term also refers generally to any necked string instrument having the strings running in a plane parallel to the sound table (in the Hornbostel–Sachs system). The strings are attached to pegs or posts at the end of the neck, which have some type of turning mechanism to enable the player to tighten the tension on the string or loosen the tension before playing (which respectively raise or lower the pitch of a string), so that each string is tuned to a specific pitch (or note). The lute is plucked or strummed ...
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Musical Temperament
In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system. Tempering is the process of altering the size of an interval by making it narrower or wider than pure. "Any plan that describes the adjustments to the sizes of some or all of the twelve fifth intervals in the circle of fifths so that they accommodate pure octaves and produce certain sizes of major thirds is called a ''temperament''." Temperament is especially important for keyboard instruments, which typically allow a player to play only the pitches assigned to the various keys, and lack any way to alter pitch of a note in performance. Historically, the use of just intonation, Pythagorean tuning and meantone temperament meant that such instruments could sound "in tune" in one key, or some keys, but would then have more dissonance in other keys. In the w ...
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Quarter Comma Meantone
Quarter-comma meantone, or -comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. In this system the perfect fifth is flattened by one quarter of a syntonic comma with respect to its just intonation used in Pythagorean tuning (frequency ratio the result is \tfrac \times \left(\tfrac\right)^ = \sqrt \approx 1.49535, or a fifth of 696.578  cents. (The 12th power of that value is 125, whereas 7 octaves is 128, and so falls 41.059 cents short.) This fifth is then iterated to generate the diatonic scale and other notes of the temperament. The purpose is to obtain justly intoned major thirds (with a frequency ratio equal to It was described by Pietro Aron in his ''Toscanello de la Musica'' of 1523, by saying the major thirds should be tuned to be "sonorous and just, as united as possible". Later theorists Gioseffo Zarlino and Francisco de Salinas described the tuning with mathematical exa ...
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Meantone
Meantone temperaments are musical temperaments; that is, a variety of tuning systems constructed, similarly to Pythagorean tuning, as a sequence of equal fifths, both rising and descending, scaled to remain within the same octave. But rather than using perfect fifths, consisting of frequency ratios of value 3:2, these are ''tempered'' by a suitable factor that narrows them to ratios that are slightly less than 3:2, in order to bring the major or minor thirds closer to the just intonation ratio of 5:4 or 6:5 , respectively. Among temperaments constructed as a sequence of fifths, a regular temperament is one in which all the fifths are chosen to be of the same size. Twelve-tone equal temperament () is obtained by making all semitones the same size, with each equal to one-twelfth of an octave; i.e. with ratios . Relative to Pythagorean tuning, it narrows the perfect fifths by about 2  cents or of a Pythagorean comma to give a frequency ratio of 2^:1. This produces ma ...
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Wolf Interval
In music theory, the wolf fifth (sometimes also called Procrustean fifth, or imperfect fifth) is a particularly dissonant musical interval spanning seven semitones. Strictly, the term refers to an interval produced by a specific tuning system, widely used in the sixteenth and seventeenth centuries: the quarter-comma meantone temperament. More broadly, it is also used to refer to similar intervals (of close, but variable magnitudes) produced by other tuning systems, including Pythagorean and most meantone temperaments. When the twelve notes within the octave of a chromatic scale are tuned using the quarter-comma meantone systems of temperament, one of the twelve intervals apparently spanning seven semitones is actually a diminished sixth, which turns out to be much wider than the in-tune genuine fifths, In mean-tone systems, this interval is usually from C to A or from G to E but can be moved in either direction to favor certain groups of keys. The eleven perfect fifths ...
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Syntonic Comma
In music theory Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first is the "Elements of music, ..., the syntonic comma, also known as the chromatic diesis, the Didymean comma, the Ptolemy, Ptolemaic comma, or the diatonic comma is a small Comma (music), comma type interval (music), interval between two musical notes, equal to the frequency ratio (= 1.0125) (around 21.51 cent (music), cents). Two notes that differ by this interval would sound different from each other even to untrained ears, but would be close enough that they would be more likely interpreted as out-of-tune versions of the same note than as different notes. The comma is also referred to as a ''Didymean comma'' because it is the amount by which Didymus the Musician, Didymus corrected the Pythagorean interval, Pythagorean major thir ...
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