A theorbo (, when played by Victor Coelho, also tuorbe; , ) is a plucked string instrument. As a name, theorbo signifies a number of long-necked lutes with second pegboxes, such as the liuto attiorbato, the French théorbe des pièces, the English theorbo, the archlute, the German baroque lute, the angélique or angelica. The etymology of the name tiorba has not yet been explained. It is hypothesized that its origin might have been in the Slavic or Turkish "torba", meaning "bag" or "turban".

Origin and development

Similar adaptations to smaller lutes (c.55+ cm string length) produced the liuto attiorbato and the archlute, also similar-looking but differently tuned instruments.

In the performance of basso continuo, theorboes were often paired with a small pipe organ. The most prominent players and composers of the chitarrone in Italy were Giovanni Girolamo Kapsberger and Alessandro Piccinini. Little solo music for the theorbo survives from England, but William Lawes and others used it in their chamber music, and it also appeared in opera orchestras. In France, theorboes were appreciated and used in orchestral music just as well as in chamber music, until the second half of the 18th century (Nicolas Hotman, Robert de Visée). Court orchestras at Vienna, Bayreuth and Berlin employed theorbo players still after 1750 (Ernst Gottlieb Baron, Francesco Conti).

Solo music for the theorbo is notated in tablature.

Theorbo tuning

This is theorbo tuning in A. Modern theorbo players usually play 14-course instruments, though (lowest course is G). A number of theorbo players will use an alternative tuning in G, a whole step lower, to facilitate playing in flat keys, which are unwieldy on instruments tuned in A, better suited for sharp keys.

While usually players will have the top two courses down an octave in reëntrant tuning, this does create problems for voice leading and the playing of harmonies above the bass when accompanying and playing Basso Continuo. A solution is to have only the top course down an octave (English theorbo).

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On November 22 of that year, Christgau launched a blog on MSN, "Expert Witness", which would only feature reviews of albums that he had graded B+ or higher, since those albums "are the gut and backbone of my musical pleasure;" the writing of reviews for which are "so rewarding psychologically that I'm happy to do it at blogger's rates."

Pazz & Jop

Style and tastes

Christgau readily admits to disliking the musical genres heavy metal, but in rare instances has recommended albums in most of these genres.

In December 1980, Christgau provoked angry responses from Voice readers when his column approvingly quoted his wife Carola Dibbell's reaction to the murder of John Lennon: "Why is it always Bobby Kennedy or John Lennon? Why isn't it Richard Nixon or Paul McCartney?"

Slate music critic Jody Rosen describes Christgau's writing as "often maddening, always thought-provoking... With Pauline Kael, Christgau is arguably one of the two most important American mass-culture critics of the second half of the 20th century. … All rock critics working today, at least the ones who want to do more than rewrite PR copy, are in some sense Christgauians."

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Category:1942 births Category:American atheists Category:American essayists Category:American music journalists Category:American music critics Category:Dartmouth College alumni Category:Living people

Saccheri entered the Jesuit order in 1685, and was ordained as a priest in 1694. He taught philosophy at Turin from 1694 to 1697, and philosophy, theology, and mathematics at Pavia from 1697 until his death. He was a protege of the mathematician Tommaso Ceva and published several works including Quaesita geometrica (1693), Logica demonstrativa (1697), and Neo-statica (1708).

He is primarily known today for his last publication, in 1733 shortly before his death. Now considered the second work in non-Euclidean geometry, Euclides ab omni naevo vindicatus (Euclid Freed of Every Flaw) languished in obscurity until it was rediscovered by Eugenio Beltrami in the mid-19th Century.

Many of Saccheri's ideas have precedent in the 11th Century Persian polymath Omar Khayyam's Discussion of Difficulties in Euclid (Risâla fî sharh mâ ashkala min musâdarât Kitâb 'Uglîdis), a fact ignored in most Western sources until recently.

It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. The Saccheri quadrilateral is now sometimes referred to as the Khayyam-Saccheri quadrilateral.

The intent of Saccheri's work was ostensibly to establish the validity of Euclid by means of a reductio ad absurdum proof of any alternative to Euclid's parallel postulate. To do this he assumed that the parallel postulate was false, and attempted to derive a contradiction. Since Euclid's postulate is equivalent to the statement that the sum of the internal angles of a triangle is 180°, he considered both the hypothesis that the angles add up to more or less than 180°.

The first led to the conclusion that straight lines are finite, contradicting Euclid's second postulate. So Saccheri correctly rejected it. However, today this principle is accepted as the basis of elliptic geometry, where both the second and fifth postulates are rejected.

The second possibility turned out to be harder to refute. In fact he was unable to derive a logical contradiction and instead derived many non-intuitive results; for example that triangles have a maximum finite area and that there is an absolute unit of length. He finally concluded that: "the hypothesis of the acute angle is absolutely false; because it is repugnant to the nature of straight lines". Today, his results are theorems of hyperbolic geometry.

There is some minor argument on whether Saccheri really meant this, as he published his work in the final year of his life, came extremely close to discovering non-Eucliean geometry and was a logician. Some believe Saccheri only concluded in such way in an intent to avoid criticism that might come from seemingly illogical aspects of hyperbolic geometry.

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Category:1667 births Category:1733 deaths Category:People from Sanremo Category:17th-century Italian people Category:18th-century Italian people Category:Italian mathematicians Category:17th-century mathematicians Category:18th-century mathematicians Category:Geometers Category:Italian Roman Catholics Category:Italian Jesuits Category:Roman Catholic cleric–scientists