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The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each. Typically, cents are used to express small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is too small to be perceived between successive notes. Cents, as described by Alexander John Ellis, follow a tradition of measuring intervals by logarithms that began with Juan Caramuel y Lobkowitz in the 17th century. Ellis chose to base his measures on the hundredth part of a semitone, , at Robert Holford Macdowell Bosanquet's suggestion. He made extensive measurements of musical instruments from around the world, using cents extensively to report and compare the scales employed, and further described and employed the system in his 1875 edition of Hermann von Helmholtz's ''On the Sensations of Tone''. It has become the standard method of representing an ...
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Iring
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each. Typically, cents are used to express small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is too small to be perceived between successive notes. Cents, as described by Alexander John Ellis, follow a tradition of measuring intervals by logarithms that began with Juan Caramuel y Lobkowitz in the 17th century. Ellis chose to base his measures on the hundredth part of a semitone, , at Robert Holford Macdowell Bosanquet's suggestion. He made extensive measurements of musical instruments from around the world, using cents extensively to report and compare the scales employed, and further described and employed the system in his 1875 edition of Hermann von Helmholtz's ''On the Sensations of Tone''. It has become the standard method of representing an ...
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Centitone
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each. Typically, cents are used to express small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is too small to be perceived between successive notes. Cents, as described by Alexander John Ellis, follow a tradition of measuring intervals by logarithms that began with Juan Caramuel y Lobkowitz in the 17th century. Ellis chose to base his measures on the hundredth part of a semitone, , at Robert Holford Macdowell Bosanquet's suggestion. He made extensive measurements of musical instruments from around the world, using cents extensively to report and compare the scales employed, and further described and employed the system in his 1875 edition of Hermann von Helmholtz's ''On the Sensations of Tone''. It has become the standard method of representing ...
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Equally Tempered
An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, which gives an equal perceived step size as pitch is perceived roughly as the logarithm of frequency. In classical music and Western music in general, the most common tuning system since the 18th century has been twelve-tone equal temperament (also known as 12 equal temperament, 12-TET or 12-ET; informally abbreviated to twelve equal), which divides the octave into 12 parts, all of which are equal on a logarithmic scale, with a ratio equal to the 12th root of 2 ( ≈ 1.05946). That resulting smallest interval, the width of an octave, is called a semitone or half step. In Western countries the term ''equal temperament'', without qualification, generally means 12-TET. In modern times, 12-TET is usually tuned relative to a standard pitch ...
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Gaspard De Prony
Baron Gaspard Clair François Marie Riche de Prony (22 July 1755 – 29 July 1839) was a French mathematician and engineer, who worked on hydraulics. He was born at Chamelet, Beaujolais, France and died in Asnières-sur-Seine, France. Education and early works He was Engineer-in-Chief of the École Nationale des Ponts et Chaussées. The trigonometric and logarithmic tables of the cadastre In 1791, de Prony embarked on the task of producing logarithmic and trigonometric tables for the French Cadastre. The effort was sanctioned by the French National Assembly, which, after the French Revolution wanted to bring uniformity to the multiple measurements and standards used throughout the nation. In particular, his tables were intended for precise land surveys, as part of a greater cadastre effort. The tables were vast, calculating logarithms from 1 to 200,000, with values calculated to between fourteen and twenty-nine decimal places, (which de Prony recognized was excessively pre ...
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Joseph Sauveur
Joseph Sauveur (24 March 1653 – 9 July 1716) was a French mathematician and physicist. He was a professor of mathematics and in 1696 became a member of the French Academy of Sciences. Life Joseph Sauveur was born in La Flèche, the son of a provincial notary. Despite a hearing and speech impairment that kept him totally mute until he was seven, Joseph benefited from a fine education at the Jesuit College of La Flèche. At seventeen, his uncle agreed to finance his studies in philosophy and theology at Paris. Joseph, however, discovered Euclid and turned to anatomy and botany. He soon met Cordemoy, reader to the son of Louis XIV; and Cordemoy soon sang his praises to Bossuet, preceptor to the Dauphin. Despite his handicap, Joseph promptly began teaching mathematics to the Dauphine's pages and also to a number of princes, among them Eugene of Savoy. By 1680, he was something of a pet at court, where he gave anatomy courses to courtiers and calculated for them the odds in the ...
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Amusia
Amusia is a musical disorder that appears mainly as a defect in processing pitch but also encompasses musical memory and recognition. Two main classifications of amusia exist: acquired amusia, which occurs as a result of brain damage, and congenital amusia, which results from a music-processing anomaly present since birth. Studies have shown that congenital amusia is a deficit in fine-grained pitch discrimination and that 4% of the population has this disorder. Acquired amusia may take several forms. Patients with brain damage may experience the loss of ability to produce musical sounds while sparing speech, much like aphasics lose speech selectively but can sometimes still sing. Other forms of amusia may affect specific sub-processes of music processing. Current research has demonstrated dissociations between rhythm melody and emotional processing of music. Amusia may include impairment of any combination of these skill sets. Signs and symptoms Symptoms of amusia are gene ...
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Verdi
Giuseppe Fortunino Francesco Verdi (; 9 or 10 October 1813 – 27 January 1901) was an Italian composer best known for his operas. He was born near Busseto to a provincial family of moderate means, receiving a musical education with the help of a local patron. Verdi came to dominate the Italian opera scene after the era of Gioachino Rossini, Gaetano Donizetti, and Vincenzo Bellini, whose works significantly influenced him. In his early operas, Verdi demonstrated a sympathy with the Risorgimento movement which sought the unification of Italy. He also participated briefly as an elected politician. The chorus "Va, pensiero" from his early opera ''Nabucco'' (1842), and similar choruses in later operas, were much in the spirit of the unification movement, and the composer himself became esteemed as a representative of these ideals. An intensely private person, Verdi did not seek to ingratiate himself with popular movements. As he became professionally successful, he was able ...
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Ellens Dritter Gesang
"" ("", D. 839, Op. 52, No. 6, 1825), in English: "Ellen's Third Song", was composed by Franz Schubert in 1825 as part of his Op. 52, a setting of seven songs from Walter Scott's 1810 popular narrative poem ''The Lady of the Lake'', loosely translated into German. It is one of Schubert's most popular works. Beyond the song as originally composed by Schubert, it is often performed and recorded by many singers under the title "Ave Maria" (the Latin name of the prayer Hail Mary, and also the opening words and refrain of Ellen's song, a song which is itself a prayer to the Virgin Mary), in musically simplified arrangements and with various lyrics that commonly differ from the original context of the poem. It was arranged in three versions for piano by Franz Liszt. ''The Lady of the Lake'' and the "Ave Maria" The piece was composed as a setting of a song (verse XXIX from Canto Three) from Walter Scott's popular narrative poem ''The Lady of the Lake'', in a German translation by ( ...
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Vibrato
Vibrato (Italian language, Italian, from past participle of "wikt:vibrare, vibrare", to vibrate) is a musical effect consisting of a regular, pulsating change of pitch (music), pitch. It is used to add expression to vocal and instrumental music. Vibrato is typically characterised in terms of two factors: the amount of pitch variation ("extent of vibrato") and the speed with which the pitch is varied ("rate of vibrato"). In singing it can occur spontaneously through variations in the larynx. The vibrato of a string instrument and wind instrument is an imitation of that vocal function. Vibrato and tremolo The terms vibrato and tremolo are sometimes incorrectly used interchangeably, although (in the classical world) they are properly defined as separate effects with vibrato defined as a periodic variation in the pitch (frequency) of a musical note, and tremolo as a fast repetition of the same note (usually a semiquaver) in order to produce the audible effect of a longer note, es ...
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Timbre
In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or musical tone, tone. Timbre distinguishes different types of sound production, such as choir voices and musical instruments. It also enables listeners to distinguish different instruments in the same category (e.g., an oboe and a clarinet, both Woodwind instrument, woodwind instruments). In simple terms, timbre is what makes a particular musical instrument or human voice have a different sound from another, even when they play or sing the same note. For instance, it is the difference in sound between a guitar and a piano playing the same note at the same volume. Both instruments can sound equally tuned in relation to each other as they play the same note, and while playing at the same amplitude level each instrument will still sound distinctively with its own unique tone color. Experienced musicians are able to distinguish between diff ...
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Just Noticeable Difference
In the branch of experimental psychology focused on sense, sensation, and perception, which is called psychophysics, a just-noticeable difference or JND is the amount something must be changed in order for a difference to be noticeable, detectable at least half the time. This limen is also known as the difference limen, difference threshold, or least perceptible difference. Quantification For many sensory modalities, over a wide range of stimulus magnitudes sufficiently far from the upper and lower limits of perception, the 'JND' is a fixed proportion of the reference sensory level, and so the ratio of the JND/reference is roughly constant (that is the JND is a constant proportion/percentage of the reference level). Measured in physical units, we have: \frac = k, where I\! is the original intensity of the particular stimulation, \Delta I\! is the addition to it required for the change to be perceived (the JND), and ''k'' is a constant. This rule was first discovered by Ernst H ...
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Unison Versus Cent Waveform
In music, unison is two or more musical parts that sound either the same pitch or pitches separated by intervals of one or more octaves, usually at the same time. ''Rhythmic unison'' is another term for homorhythm. Definition Unison or perfect unison (also called a prime, or perfect prime)Benward & Saker (2003), p. 53. may refer to the (pseudo-) interval formed by a tone and its duplication (in German, ''Unisono'', ''Einklang'', or ''Prime''), for example C–C, as differentiated from the second, C–D, etc. In the unison the two pitches have the ratio of 1:1 or 0 half steps and zero cents. Although two tones in unison are considered to be the same pitch, they are still perceivable as coming from separate sources, whether played on instruments of a different type: ; or of the same type: . This is because a pair of tones in unison come from different locations or can have different "colors" (timbres), i.e. come from different musical instruments or human voices. Voices w ...
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