text:
ERCO Ercoupe

The ERCO Ercoupe is an American low-wing monoplane aircraft that was first flown in 1937. It was originally manufactured by the Engineering and Research Corporation (ERCO) shortly before World War II; several other manufacturers continued its production after the war. The final model, the Mooney M-10, first flew in 1968 and the last model year was 1970. It was designed to be the safest fixed-wing aircraft that aerospace engineering could provide at the time, and the type continues to enjoy a faithful following.

Fred Weick

In 1931, aeronautical engineer Fred Weick was assistant chief of the aeronautics division of the National Advisory Committee for Aeronautics (NACA). In 1934 he asked permission to build an aircraft based on the 1931 Stout Skycar, using fabric instead of aluminum covering, and control modifications based on NACA research. Weick and a group of co-workers designed and assembled the experimental aircraft with a group of his colleagues who worked on the project in their spare time and paid for it themselves. The resulting aircraft, known as the W-1, featured tricycle landing gear, a parasol wing, and a pusher propeller configuration.

Fred Weick listed the W-1 design goals that were tested in later seminars:
 * Tricycle landing gear with castering nosewheel, steerable if desired
 * Suitable longitudinal and lateral stability with limited up-elevator deflection, to prevent loss of control due to stalling and spinning.
 * A glide-control flap
 * Two-control operation using controls for pitch and roll.

In 1934, the Bureau of Air Commerce approached Weick's team looking for standards for a competition for a safe and practical $700 aircraft. In 1936 the winner of the competition was the Stearman-Hammond Y-1, incorporating many of the safety features of the W-1. Two other winners were the Waterman Aeroplane and a roadable autogyro, the Autogiro Company of America AC-35. The W-1 was not intended for production to qualify as a competitor, but was purchased by the Bureau for continued experimental tests in spin-control safety. After the prototype W-1 underwent a forced landing, an updated W-1A was built by Fairchild, incorporating leading edge cuffs.

ERCO
Weick left NACA in 1936 and joined Engineering and Research Corporation's (ERCO) fledgling aircraft team as chief designer, primarily to continue improving his aircraft design. Focusing his efforts on a number of design issues, primarily simplicity and safety, Weick strove to create a reasonably priced aircraft that would not stall or spin. Retaining the tricycle gear for ease of maneuvering on the ground, and limited stall-spin features, Weick switched to a low-wing monoplane configuration in his new model, powered by an engine in tractor configuration.

The ERCO 310, which included a fully cowled engine, made its first flight in October 1937 at College Park Airport and was soon renamed the "Ercoupe". The easy-to-fly design included unique design features, including a large glazed canopy - with almost as much visibility as a bubble canopy - for improved visibility. The prototype 310 featured an ERCO-made inverted four-cylinder engine, the ERCO I-L 116, which was quickly dropped due to its high manufacturing cost compared to the new four-cylinder Continental A-65 air-cooled boxer engine. Lacking rudder pedals, the Ercoupe was flown using only the control wheel. A two-control system linked the rudder and aileron systems, which controlled yaw and roll, with the steerable nosewheel. The control wheel controlled the pitch and the steering of the aircraft, both on the ground and in the air, simplifying control and coordinated turning and eliminating the need for rudder pedals. A completely new category of pilot's license was created by the CAA for Ercoupe pilots who had never used a rudder pedal.

The Ercoupe was the first aircraft certified by the Civil Aeronautics Administration (CAA) as "characteristically incapable of spinning." The high-winged General Skyfarer obtained the second certification by licensing the ERCO technology. The first production Ercoupe, serial no. 1, NC15692 built in 1939 was donated to the National Air and Space Museum. In 1941 that aircraft, designated YO-55, was used in US Army Air Force testing.

The two-seat ERCO Ercoupe 415 went on sale in 1940. LIFE magazine described the aircraft as "nearly foolproof" and showed pictures of a pilot landing with his hands in the air. Only 112 aircraft were delivered before World War II intervened, halting all civil aircraft production. By mid-1941 aluminum supplies were being diverted to war-related production, so ERCO decided to manufacture Ercoupes for military use by using wood as the principal building material. The substitution of wood resulted in a heavier but quieter aircraft, because the wood absorbed vibrations from the engine and airflow. Ercoupes were flown during the war by the Civilian Pilot Training Program for flight instruction, and the Civil Air Patrol used them to patrol for German submarines.

Postwar sales

Although World War II had interrupted production of the Ercoupe, general aviation manufacturers were enthusiastic about the prospects of a postwar aviation boom. Thousands of men and women were trained as pilots by the government, and the hope was that they would want to include flying in their civilian life. Production of the model 415-C resumed in 1945, and in 1946 alone 4,311 aircraft were produced and sold at a cost of US$2,665. This was the same price as in 1941. At its peak, ERCO was turning out 34 Ercoupes per day, operating three shifts per day. The aircraft was aggressively marketed through unconventional outlets such as the men's department of the Macy's department store chain.

However, private aircraft sales slumped after the war and the bottom dropped out of the civil aircraft market in late 1946, ending prospects for a boom market for civil aircraft sales. A 30-day layoff at the factory in November resulted in rivets tossed around the factory and some aircraft sides and signs being painted. The year ended with an Ercoupe flown by a test pilot and mechanic breaking up in flight.

Other production
Aeronca obtained a licence to produce the Ercoupe 415 as the Aeronca 12AC Chum in 1946 and built two prototypes: NX39637, with the Ercoupe twin-tail, and NX83772 with a larger, single tail, metal wings and trailing-link struts in the main undercarriage. The Chum was powered by a Continental C-85J with a 108 mph cruise speed. No production ensued.
 * Aeronca

In 1947 ERCO sold its remaining Ercoupe inventory to Sanders Aviation, which continued to produce the aircraft in the same ERCO-owned factory. A total of 213 aircraft were sold by 1950. During this time, ERCO's chief engineer Fred Wieck moved on to Texas A&M, where he developed the agricultural Piper Pawnee aircraft and eventually the popular Piper Cherokee with John Thorp and Karl Bergey.
 * Sanders Aviation

Univair Aircraft Corporation of Aurora, Colorado purchased the Ercoupe design from the Engineering and Research Company in 1950. It provided spare parts and customer support to the existing aircraft.
 * Univair Aircraft Industries

 * Forney/Fornaire Aircoupe

In April 1955, Univair sold the Ercoupe type certificate to the Forney Aircraft Company of Fort Collins, Colorado, which later became the Fornaire Aircraft Company. The aircraft produced differed from the 415-G in its engine/propeller combination they were upgraded to a C-90 engine, revised engine cowling, larger baggage compartment, and aluminum-covered wing panels. The F-1A model had three axis controls and bucket seats. Production began in 1958 and ended in 1959.

 * 56 of the F-1 Forney Deluxe were produced in 1958 and sold for $6,995 each.
 * 59 of the F-1 Forney Explorer, Execta and Expediter were produced in 1959 and sold for $6,995.
 * 23 of the F-1A Forney Trainer were produced in 1959. It was sold for $7,450.

A total of 138 aircraft were produced.

Between August 1960 and March 1964, the rights to the Aircoupe aircraft were held by the AirCoupe division of Air Products Company of Carlsbad, New Mexico. The company was started by the city, with the hope of establishing aircraft manufacture as a local industry. It purchased the type certificate from Forney when a potential deal with Beechcraft fell through. Only a few airframes were produced before the type certificate was sold to Alon, Incorporated on March 16, 1964. 25 of the F-1A Forney Trainer were produced for US$7,450 each.
 * Air Products Company Aircoupe

Alon Inc. was founded by John Allen and Lee O. Higdon, two executives who had retired from aircraft manufacturer Beechcraft to found their own company. They had previously negotiated with Forney Aircraft to purchase production of the Aircoupe so that Beechcraft could use the design as an introductory trainer. The deal was canceled by Olive Ann Beech, who decided to concentrate resources on the Beechcraft Musketeer. This decision caused the executives to leave Beechcraft and establish Alon in McPherson, Kansas, which purchased the type certificate for the Aircoupe from the City of Carlsbad, New Mexico on March 16, 1964.
 * Alon Aircoupe

"A new company formed by former Beechcraft executives Allen and Higdon, who have purchased all assets, jigs, tools, and engineering of the program from the city of Carlsbad NM. They expect to deliver the first of 30-50 Aircoupes to be built next year for about $8,000."

The Alon A-2 and A-2A Aircoupes featured a sliding canopy, a Continental C90 90 hp engine, separate bucket seats and an improved instrument panel. The A-2 also differed from earlier two-control models in having limited-movement rudder pedals. This was done in order to make it a more acceptable training aircraft and to make it easier to counteract increased P-factor yaw during a climb from the more powerful engine. Nosewheel steering was no longer interlinked with the control yoke, and was changed to the more common practice of being interlinked with the rudder pedals (this was the same system that was installed in the Forney F-1A). The older two axes control system was offered as an option. The single control (non-differential) wheel brakes remained. The airplane had a higher rate of climb, a higher speed for best climb rate, and better engine cooling. Its non-spinning characteristics remained unchanged.

Alon produced 245 A-2s from 1964 to 1967, with peak production of 137 in 1966. The last 25 A-2s produced by Alon had spring-steel landing gear in place of the original main gear struts, light alloy castings and trailing links. The base price in 1967 was up to $7975. Production of the A-2 ceased in September 1967, and on October 9, 1967, Alon was purchased by, and became a division of, the Mooney Airplane Company of Kerrville, Texas.
 * Mooney A-2A and M10 Cadet

Mooney began producing the aircraft in 1968 as the Mooney A-2A. Next the company redesigned the fuselage from the cockpit back, with square windows behind the sliding canopy. Even as it produced the A-2A Cadet, Mooney was busy re-designing the aircraft. On February 23, 1968, the first Mooney M10 Cadet flew. The aircraft has a single fin, with a vertical leading edge, as most Mooneys do.

The type certificate was sold to Univair Aircraft Corporation of Aurora, Colorado in October, 1974 and remains with Univair. The company has not produced any new aircraft but continues to produce replacement parts and provide technical assistance to Ercoupe owners.
 * Univair

Military

Three model 415-C aircraft were procured by the United States Army Air Forces for use during World War II.

On 12 August 1941, the first USAAF rocket-assist takeoff was made by a Wright Field test pilot, Capt. Homer Boushey, using a small civilian-type Ercoupe aircraft. Subsequent refinements of this technique were made for assisting heavily loaded aircraft in taking off from limited space.

An additional Ercoupe was evaluated by the Royal Air Force in 1947. This aircraft was serial number 4784, carried Royal Air Force markings VX 147 and was polished metal all over with RAF roundels.

Light sport use
The Ercoupe is a type certified aircraft. However, some Univair Ercoupe 415-C and 415-CD models meet the FAA requirements to be flown by sport pilots as light-sport aircraft. The characteristics of the Ercoupe helped Jessica Cox (who was born without arms) to become a qualified pilot.

ERCO/Sanders

 * 310
 * 1937 prototype originally powered by a 37 hp Continental A40 engine and with tricycle landing gear, metal construction, fabric-covered wings, and a single tail fin. The engine was later swapped with a 65 hp ERCO IL-116.

 * 415
 * Initial production aircraft powered by 65 hp ERCO IL-116 engines. The -A and -B suffixes were never used; the company's official records use only the -C suffix, which stood for "Continental", once the IL-116 was no longer used. 10 aircraft were built from 1939 to 1940.

 * Wooden Ercoupe
 * Two aircraft were built using birch and plywood in 1941 to demonstrate use of non-strategic materials, but no further aircraft were built and the test articles were scrapped.

 * 415-C Ercoupe
 * First variant to enter large-scale production. Prewar 415-C Ercoupes were powered by 65 hp Continental A65-8 engines, while postwar Ercoupes were powered by 75 hp Continental C75-12 engines.  Maximum gross weight was 1260 lb.  4,520 total built; 112 pre-war and 4,408 post-war.

 * 415-D Ercoupe
 * As 415-C but with fuel capacity increased by 1 gal and a modified up-elevator limit. Gross weight was also increased to 1400 lb.  77 built.  One 415-D was modified under a Supplemental Type Certificate to fit a 108 hp Lycoming O-235-C2C powerplant.

 * 415-CD Ercoupe
 * As 415-D but with a revised elevator limit as well as a modified nose gear and ventilation system. Gross weight was reduced back to 1260 lb.  275 built.

 * 415-E Ercoupe
 * As 415-D but powered by an 85 hp Continental C85-12 or C85-12F engine, introduced the split elevator with 20° of up-elevator travel. Gross weight was once again increased to 1400 lb.  139 built.

 * 415-F Ercoupe
 * As 415-D but powered by a 90 hp Continental C90 engine.

 * 415-G Club-Air
 * As 415-E but with a rear Kiddy-Seat and a modified windscreen.

 * 415-H Club-Air
 * As 415-G but powered by a 75 hp Continental C75 engines. A total of 70 415-G and 415-H aircraft were built.

 * YO-55
 * A single Ercoupe was acquired for evaluation for the military observation role.

 * XPQ-13
 * Target drone variant of the Ercoupe.

 * Twin Ercoupe
 * In 1948 J. B. Collie of Southeast Air Service produced a Twin Ercoupe by joining two Ercoupe fuselages with a new centre section, similar to the North American P-82 Twin Mustang, for use in airshows by Thrasher Brothers Air Circus, Elberton GA. Flown by Grady Thrasher and his brother, who rolled, looped, and spun it.  The aircraft had a smoke system for each engine, and could be flown from either cockpit.

Forney/Air Products

 * F-1 Aircoupe
 * Forney/Fornaire-built development of the ERCO 415-G. Powered by a 90 hp Continental C90-12F engine, the F-1 differed from the 415-G in that it had a metal-clad outer wing, an improved canopy, a redesigned canopy, as well as a new instrument panel and seats.  115 built.

 * F-1A Aircoupe
 * As F-1 but with modified control runs as well as a bew rear spar and nosewheel leg. 50 built by Air Products Co.

Alon

 * A-2 Aircoupe
 * Alon-built derivative of the F-1A powered by a 90 hp Continental C90-16F. Other differences included a sliding canopy as well as improved fuel tanks and instruments.  244 built.

 * A-2A Aircoupe
 * As A-2 but with spring steel main landing gear. 64 built.

 * A-3 Argus 130
 * As A-2A but powered by a 130 hp Franklin engine and with a "two-plus-two" cabin. One prototype built.

 * XA-4
 * Four-seat development of the A-2 powered by a 150 hp Lycoming O-320-A engine. The XA-4 also featured a stretched fuselage, a redesigned cowling, modified wings, and a single swept tail fin.  One prototype built.

Derivatives

 * Mooney M10 Cadet
 * A single-tailed version of the Alon Aircoupe, powered by a 90 hp Continental C90-16F, aka Mooney-Coupe, with 59 aircraft built.

 * Bryan Autoplane
 * Leland D. Bryan built a series of roadable aircraft using an Ercoupe fuselage, calling this line the Bryan Autoplane. Significant modifications included a double-articulated folding wing mechanism and a pusher engine. It still retained Ercoupe features, such as the twin tail and the center section. The first flight was in 1953, and the model II flew 65 hours. The Model III with a single wing-fold mechanism crashed in 1974, killing Bryan.

 * Lasher Little Thumper
 * C. W. Lasher built and flew a single-seat open-cockpit taildragger aircraft called "Little Thumper", using an Ercoupe center section and wing assembly and an Aeronca Champ aft fuselage.

title: ERCO Ercoupe


text:
Associated bundle

In mathematics, the theory of fiber bundles with a structure group $$G$$ (a topological group) allows an operation of creating an associated bundle, in which the typical fiber of a bundle changes from $$F_1$$ to $$F_2$$, which are both topological spaces with a group action of $$G$$. For a fiber bundle F with structure group G, the transition functions of the fiber (i.e., the cocycle) in an overlap of two coordinate systems Uα and Uβ are given as a G-valued function gαβ on Uα∩Uβ. One may then construct a fiber bundle F′ as a new fiber bundle having the same transition functions, but possibly a different fiber.

An example
A simple case comes with the Möbius strip, for which $$G$$ is the cyclic group of order 2, $$\mathbb{Z}_2$$. We can take as $$F$$ any of: the real number line $$\mathbb{R}$$, the interval $$[-1,\ 1]$$, the real number line less the point 0, or the two-point set $$\{-1,\ 1\}$$. The action of $$G$$ on these (the non-identity element acting as $$x\ \rightarrow\ -x$$ in each case) is comparable, in an intuitive sense. We could say that more formally in terms of gluing two rectangles $$[-1,\ 1] \times I$$ and $$[-1,\ 1] \times J$$ together: what we really need is the data to identify $$[-1,\ 1]$$ to itself directly at one end, and with the twist over at the other end. This data can be written down as a patching function, with values in G. The associated bundle construction is just the observation that this data does just as well for $$\{-1,\ 1\}$$ as for $$[-1,\ 1]$$.

Construction
In general it is enough to explain the transition from a bundle with fiber $$F$$, on which $$G$$ acts, to the associated principal bundle (namely the bundle where the fiber is $$G$$, considered to act by translation on itself). For then we can go from $$F_1$$ to $$F_2$$, via the principal bundle. Details in terms of data for an open covering are given as a case of descent.

This section is organized as follows. We first introduce the general procedure for producing an associated bundle, with specified fibre, from a given fibre bundle. This then specializes to the case when the specified fibre is a principal homogeneous space for the left action of the group on itself, yielding the associated principal bundle. If, in addition, a right action is given on the fibre of the principal bundle, we describe how to construct any associated bundle by means of a fibre product construction.

Associated bundles in general
Let $\pi:E\to X$ be a fiber bundle over a topological space X with structure group G and typical fibre F. By definition, there is a left action of G (as a transformation group) on the fibre F. Suppose furthermore that this action is effective. There is a local trivialization of the bundle E consisting of an open cover Ui of X, and a collection of fibre maps$$\varphi_i : \pi^{-1}(U_i) \to U_i \times F$$such that the transition maps are given by elements of G. More precisely, there are continuous functions gij : (Ui ∩ Uj) → G such that$$\psi_{ij}(u,f) := \varphi_i \circ \varphi_j ^{-1}(u,f) = \big(u, g_{ij}(u) f \big),\quad \text{for each } (u,f)\in (U_i \cap U_j)\times F\, .$$

Now let F′ be a specified topological space, equipped with a continuous left action of G. Then the bundle associated with E with fibre F′ is a bundle E′ with a local trivialization subordinate to the cover Ui whose transition functions are given by$$\psi'_{ij}(u,f') = \big(u, g_{ij}(u) f' \big),\quad \text{for each } (u,f')\in (U_i \cap U_j)\times F'\,,$$where the G-valued functions gij(u) are the same as those obtained from the local trivialization of the original bundle E. This definition clearly respects the cocycle condition on the transition functions, since in each case they are given by the same system of G-valued functions. (Using another local trivialization, and passing to a common refinement if necessary, the gij transform via the same coboundary.) Hence, by the fiber bundle construction theorem, this produces a fibre bundle E′ with fibre F′ as claimed.

Principal bundle associated with a fibre bundle
As before, suppose that E is a fibre bundle with structure group G. In the special case when G has a free and transitive left action on F′, so that F′ is a principal homogeneous space for the left action of G on itself, then the associated bundle E′ is called the principal G-bundle associated with the fibre bundle E. If, moreover, the new fibre F′ is identified with G (so that F′ inherits a right action of G as well as a left action), then the right action of G on F′ induces a right action of G on E′. With this choice of identification, E′ becomes a principal bundle in the usual sense. Note that, although there is no canonical way to specify a right action on a principal homogeneous space for G, any two such actions will yield principal bundles which have the same underlying fibre bundle with structure group G (since this comes from the left action of G), and isomorphic as G-spaces in the sense that there is a G-equivariant isomorphism of bundles relating the two.

In this way, a principal G-bundle equipped with a right action is often thought of as part of the data specifying a fibre bundle with structure group G, since to a fibre bundle one may construct the principal bundle via the associated bundle construction. One may then, as in the next section, go the other way around and derive any fibre bundle by using a fibre product.

Fiber bundle associated with a principal bundle
Let π : P → X be a principal G-bundle and let ρ : G → Homeo(F) be a continuous left action of G on a space F (in the smooth category, we should have a smooth action on a smooth manifold). Without loss of generality, we can take this action to be effective.

Define a right action of G on P × F via
 * $$(p,f)\cdot g = (p\cdot g, \rho(g^{-1})f)\, .$$

We then identify by this action to obtain the space E = P ×ρ F = (P × F) /G. Denote the equivalence class of (p,f) by [p,f]. Note that
 * $$[p\cdot g,f] = [p,\rho(g)f] \mbox{ for all } g\in G.$$

Define a projection map πρ : E → X by πρ([p,f]) = π(p). Note that this is well-defined.

Then πρ : E → X is a fiber bundle with fiber F and structure group G. The transition functions are given by ρ(tij) where tij are the transition functions of the principal bundle P.

This construction can also be seen categorically. More precisely, there are two continuous maps $$P \times G \times F \to P \times F$$, given by acting with G on the right on P and on the left on F. The associated vector bundle $$P \times_\rho F$$ is then the coequalizer of these maps.

Reduction of the structure group
The companion concept to associated bundles is the reduction of the structure group of a $$G$$-bundle $$B$$. We ask whether there is an $$H$$-bundle $$C$$, such that the associated $$G$$-bundle is $$B$$, up to isomorphism. More concretely, this asks whether the transition data for $$B$$ can consistently be written with values in $$H$$. In other words, we ask to identify the image of the associated bundle mapping (which is actually a functor).

Examples of reduction
Examples for vector bundles include: the introduction of a metric resulting in reduction of the structure group from a general linear group GL(n) to an orthogonal group O(n); and the existence of complex structure on a real bundle resulting in reduction of the structure group from real general linear group GL(2n,R) to complex general linear group GL(n,C).

Another important case is finding a decomposition of a vector bundle V of rank n as a Whitney sum (direct sum) of sub-bundles of rank k and n-k, resulting in reduction of the structure group from GL(n,R) to GL(k,R) × GL(n-k,R).

One can also express the condition for a foliation to be defined as a reduction of the tangent bundle to a block matrix subgroup - but here the reduction is only a necessary condition, there being an integrability condition so that the Frobenius theorem applies.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Associated bundle


text:
Rincewind

Rincewind is a fictional character who appears in several of the Discworld novels by Terry Pratchett. He was a failed student at Unseen University for wizards in Ankh-Morpork, often described as "the magical equivalent to the number zero". He spent most of his time running away from people who wanted to kill him for various reasons. The reason that he was still alive and running was explained by noting that while he was born with a wizard's spirit, he had the body of a long-distance sprinter.

Rincewind was portrayed by David Jason in the film adaptation of The Colour of Magic. Pratchett said in an interview that he unwittingly took Rincewind's name from "Churm Rincewind", a fictitious person referred to in early "'Beachcomber" columns in the Daily Express.

In books
In The Colour of Magic, Rincewind acted as a guide for the tourist Twoflower, who hailed from the Agatean Empire in the Counterweight Continent, across the disc from the 'hub' continent where Ankh-Morpork is situated. He was recruited for this because only he can communicate with Twoflower (they use Be-Trobi as a lingua franca), Twoflower agreed to pay him in rhinu (large gold coins), and because the Patrician of Ankh-Morpork wished to prevent an Agatean attack on Ankh-Morpork sparked by Twoflower's death. He and Twoflower wandered around for quite a while, and were chased by everything from the personification of Death to a Lovecraftian creature named Bel-Shamharoth.

Rincewind and Twoflower parted ways at the end of The Light Fantastic and Twoflower gave Rincewind his sapient-pearwood Luggage. Rincewind's adventures continued, and he was chased across various regions of the Discworld in spite of, or often driven by, his desire to find somewhere he can relish boredom in peace and quiet.

During the events of The Last Hero, in which the Discworld risks being destroyed if Cohen the Barbarian and his Silver Horde succeed in their plan to "return fire to the Gods with interest", Rincewind said that he did not wish to volunteer for a dangerous mission. When asked to explain, he said he merely refused for appearances, because someone was bound to nominate him because of his knowledge of the geography of Cori Celesti or his friendship with Cohen, so even if he refused, somehow events would conspire against him and he would end up going on the mission anyway as he attempted to escape.

Raising Steam mentions Rincewind in footnotes, which refer to him as a professor at the university, studying the effects of different flowers on the nervous system.

In other media
Rincewind is the main character of the text adventure The Colour of Magic, based on the book of the same name.

Rincewind is also the player character of the 1995 Discworld video game. After a dragon is spotted in Ankh-Morpork, Unseen University's archchancellor sends Rincewind to find the source of the trouble. In the sequel, Discworld II: Missing Presumed...!?, Death disappears and the archchancellor puts Rincewind in charge of finding him and convincing him to get back to work. In both games, Rincewind is voiced by Eric Idle.

Character
Rincewind has the ability to pick up the essentials of foreign languages quickly and fluency only slightly less quickly, and appears to have the ability to blend in to any situation. During The Colour of Magic, when he was projected into a universe that may or may not have been our own, he assumed the role of a nuclear physicist. In keeping with his nature, the role was as a physicist who specialized in the 'breakaway oxidation phenomena' of certain reactors—or, to put another way, what happens when those reactors caught fire (Terry Pratchett served as the press officer for several nuclear power plants before he became a full-time writer). Rincewind speculated on the nature of science, expressing hope in The Colour of Magic that there was something "better than magic" in the world, and speculated on the possibility of harnessing lightning, for which he was mocked by "sensible" Discworld citizens. Rincewind is also fairly streetwise. He is often depicted as a harsh critic of the selected stupidities surrounding him, even though he can't help but comply with whatever absurdity that arises. For example, in the computer games starring him, he consistently spotted the ludicrous events around him and would then make jokes and puns to the unaware participants. He also seems to display, despite his apparent failure as a wizard, a fairly extensive magical knowledge, recognizing various spells, magical artefacts and concepts throughout his escapades.

Some of Rincewind's talents once stemmed from a semi-sentient and highly destructive spell that had lodged itself inside his mind and scared off all other spells (mentioned in The Colour of Magic and The Light Fantastic; though even without the spell's interference he was still an extremely incompetent wizard). The spell occasionally tried to make itself heard when Rincewind was going through a stressful time; as he was falling to his near-death, he said the first seven out of eight words of the spell.

In Sourcery and Unseen Academicals Rincewind claims that he never knew his mother as she ran away before he was born. <!-- Rincewind is most frequently seen wearing his hat with the word WIZZARD emblazoned across it in sequins.

Rincewind's age is indeterminate, although the first two books describe him as young. This is further complicated by cover paintings of the books which show him being young, others old, and comments made by Death about Rincewind's life-timer. Every living being on the Disc has an hourglass, usually kept in Death's home, that gradually records his life from birth to death. Rincewind's life-timer is described as resembling something created by a glassblower with the hiccups in a time machine, due to his being hit by so much magic and being forcefully shuttled through time and space so many times. Based on the amount of sand, Rincewind should have died long ago, but the shape of it is such that the sand often flows backwards or diagonally, with the result being that even Death has no idea when Rincewind will die. This represents something of a curiosity to Death, who keeps the hour-glass on his desk as a paperweight so that he can keep an eye on it. He is described as "middle aged" in The Science of Discworld IV. He is said to have been exposed to the Octavo when he was fifteen, and stayed at the Unseen University for sixteen more years after that, which means that in The Colour of Magic he is 31 years old.

Over the course of his adventures, he has turned cowardice into a fully fledged philosophy of life. He believes that, when running, "to" is never important, what matters is "from". When it was pointed out that running just lands him in more trouble, his response was "Yes, but you can run away from that too, that's the beauty of it." In The Last Continent, Death, while on the subject of Rincewind, contemplates that if there is an "eternal, ever-renewed hero, the champion with a thousand faces", natural balances may have created an eternal coward, the "hero with a thousand retreating backs". By The Last Hero Rincewind has started describing running away as a religion in the valid belief that no one will take it seriously; it might not give you eternal life, exactly, but it certainly gives you more life. Very few of his various travelling companions take him seriously. This is partially because Rincewind has an unusually pessimistic outlook on life, and partially because bad things seem to single him out for misfortune. Many of his companions have noticed, however, that Rincewind manages to survive everything that happens to him, and suspect that there's a deeper purpose behind this, although he himself insists it's just a coincidence. Rincewind apparently believes in karma, however. From his point of view, he has preemptive karma—if it even looks as if something good will happen to him in the future, his karma will ensure that something bad happens immediately, and continues happening so that the good things never come around. It hasn't helped that he's not as selfish as he makes himself out to be and has risked his life to help people such as Coin and Twoflower.

Rincewind has the dubious privilege of being the Chosen of The Lady, the Discworld's most mysterious goddess. It is for this reason that he is constantly finding himself embroiled in unpleasant situations and coming out more-or-less on top. However, if he ever realised this, much less acted as though nothing could seriously harm him, then she would instantly lose interest. Since he considers himself the most unlucky person ever, this means he will probably never work out that he is in the Lady's favour. As a result, he comes off as incredibly tenacious. In The Last Hero he willingly goes along with the mission to Dunmanifestin, knowing that he can't be too reliant on luck and instead playing into Fate's hands/

He has also developed an obsession with potatoes, which is implied to be a result of misplaced sexual feelings. Interesting Times states that later on in his life he will have to undergo therapy for this affliction, involving a pretty woman, a plate of potatoes and a large stick with a nail in it.

Finally, Rincewind considered himself a racist ("the hundred meters, the mile, the marathon, he's run them all"). However, when he finds out the real meaning of the word, he considers racism to be illogical, stating that he divides the human race into two categories, people who are trying to kill him and people who aren't, which doesn't leave room for fine details such as skin colour. He has also spawned a religion among trees. -->

Rincewind has received several titles during his stay at the Unseen University; some of them because nobody else wants them, others to keep him busy doing work unrelated to magic. These titles and their accompanying tenure include the condition that he cannot have any salary, influence, or opinions. They do, however, include meals, his laundry done, and (as a result of all the impressive-sounding but essentially meaningless titles that have been bestowed upon him) up to eight buckets of coal a day during the entire year.

Concept and creation
Pratchett said that Rincewind's job is "to meet more interesting people", saying that there is not much he can do with a character who's a coward and doesn't care who knows it. Pratchett noted that one of his major problems was that he has a "lack of an inner monologue".

The Luggage
The Luggage is a large chest that follows Rincewind literally wherever he goes—even onto Roundworld, which Rincewind initially only visited virtually. It is made of sapient pearwood, a magical, intelligent plant that is nearly extinct, impervious to magic, and only grows in a few places outside the Agatean Empire, generally on sites of very old magic. As such, whilst considered oddities on the Hubland continent, such chests were commonplace in the Agatean Empire. It can produce hundreds of little legs and move very fast if the need arises. It has been described as "half suitcase, half homicidal maniac". Interesting Times demonstrated that Luggages were capable of reproducing, which Twoflower suggested was chiefly the result of what the Luggage learnt in Ankh-Morpork.

Its function is to act as both a luggage carrier and bodyguard for its owner. The Luggage is fiercely defensive of its owner, and is generally homicidal in nature, killing or eating several people and monsters and destroying various ships, walls, doors, geographic features, and other obstacles throughout the series. Its mouth contains "lots of big square teeth, white as sycamore, and a pulsating tongue, red as mahogany". The inside area of The Luggage does not appear to be constrained by its external dimensions, and contains many conveniences: even after it has just devoured a monster, the next time it opens the owner will find his underwear, neatly pressed and smelling slightly of lavender. It is unknown exactly what happens to anyone it 'eats'.

One of the most notable features of The Luggage is its ability to follow its current owner anywhere, including places like inside its owner's mind, off the edge of the Disc, Death's Domain, inside the Octavo, the Dungeon Dimensions, and even (literally) to Hell and back. Like all luggage, it's constantly getting lost and having to track its owner down. It has only one way of overcoming obstacles, and that is to simply ignore them and smash a hole through them—including a wall to a magic shop that had since relocated to another city by magical means.

Reception and legacy
In her review of Night Watch, A. S. Byatt noted the lack of recent appearances of Rincewind and the grimmer presentation of the Witches and Ankh-Morpork as signs of Pratchett's imagination getting darker.

While the current release (version 3.0.0) of VLC media player is named Vetinari, a previous release (version 2.1.0) was named Rincewind. Other releases of VLC media player have been named "The Luggage" (version 1.1.0), and release 2.0.0 was named "Twoflower", the character that gave The Luggage to Rincewind (in The Light Fantastic).

Rincewind and Discworld witch Nanny Ogg appeared on first-class Royal Mail stamps in March 2011. The issue included wizards, witches and enchanters from British fiction, and also included characters from the Arthurian Legend, from J. K. Rowling's Harry Potter series, and from the Narnia series of C. S. Lewis.

Paul Whitelaw, writing for The Scotsman, felt that David Jason was "clearly several decades too old" to be Rincewind in the film adaptation of The Colour of Magic.

The Cretaceous gymnosperm species Phoenicopsis rincewindii is named after Rincewind.

title: Rincewind


text:
User:Sannse/Grammy to-do list

Award categories

 * Record of the Year*
 * Album of the Year*
 * Song of the Year*
 * Best New Artist*
 * Grammy Hall of Fame
 * Grammy Legend Award
 * Grammy Lifetime Achievement Award
 * Grammy Tech Award
 * Grammy Trustees Award

Alternative

 * Best Alternative Music Album*

Blues

 * Best Traditional Blues Album*
 * Best Contemporary Blues Album*

Children's

 * Best Album for Children*
 * <S>Best Musical Album for Children</S>*
 * <S>Best Spoken Word Album for Children</S>*

Classical

 * <S>Best Orchestral Performance</S>*
 * <S>Best Classical Vocal Performance</S>*
 * <S>Best Classical Performance, Operatic or Choral</S>*
 * Best Opera Recording
 * <S>Best Choral Performance</S>
 * <S>Best Classical Performance - Instrumental Soloist or Soloists (with or without orchestra)</S>
 * <S>Best Instrumental Soloist(s) Performance (with orchestra)</S>
 * <S>Best Instrumental Soloist Performance (without orchestra)</S>
 * <S>Best Small Ensemble Performance (with or without conductor)</S>
 * <S>Best Chamber Music Performance</S>
 * <S>Best Classical Contemporary Composition</S>
 * <S>Best Classical Album</S>
 * <S>Best Classical Crossover Album</S>
 * <S>Best New Classical Artist</S>

Comedy

 * <S>Best Comedy Album</S>
 * <S>Best Spoken Comedy Album</S>

Composing and arranging

 * <S>Best Instrumental Composition</S>
 * <S>Best Song Written for a Motion Picture, Television or Other Visual Media (now in the "Film/TV/Media" field)</S>
 * <S>Best Score Soundtrack Album for a Motion Picture, Television or Other Visual Media (now in the "film/TV/media" field)</S>
 * <S>Best Arrangement</S>
 * <S>Best Instrumental Arrangement</S>
 * <S>Best Instrumental Arrangement Accompanying Vocalist(s)</S>
 * <S>Best Vocal Arrangement for Two or More Voices</S>

Country

 * <S>Best Female Country Vocal Performance</S>
 * <S>Best Male Country Vocal Performance</S>
 * <S>Best Country Performance, Duo or Group - Vocal or Instrumental</S>
 * <S>Best Country Performance by a Duo or Group with Vocal</S>
 * <S>Best Country Collaboration with Vocals</S>
 * <S>Best Country Instrumental Performance</S>
 * <S>Best Country & Western Recording</S>
 * <S>Best Country & Western Single</S>
 * <S>Best Country Song</S>
 * <S>Best Country Album</S>
 * <S>Best Bluegrass Album</S>
 * <S>Best New Country & Western Artist</S>

Dance

 * <S>Best Dance Recording (previously in "Pop")</S>
 * <S>Best Electronic/Dance Album</S>

Disco

 * <S>Best Disco Recording</S>

Film/TV/Media

 * <S>Best Compilation Soundtrack Album for a Motion Picture, Television or Other Visual Media</S>
 * <S>Best Song Written for a Motion Picture, Television or Other Visual Media (previously in the "composing and arranging" field)</S>
 * <S>Best Score Soundtrack Album for a Motion Picture, Television or Other Visual Media (previously in the "composing and arranging" field)</S>

Folk

 * <S>Best Ethnic or Traditional Folk Recording</S>
 * <S>Best Traditional Folk Album</S>
 * <S>Best Contemporary Folk Album</S>
 * <S>Best Native American Music Album</S>
 * <S>Best Hawaiian Music Album</S>

Gospel

 * <S>Best Gospel Performance</S>
 * <S>Best Gospel Performance, Traditional</S>
 * <S>Best Gospel Performance, Contemporary</S>
 * <S>Best Gospel Vocal Performance, Female </S>
 * <S>Best Gospel Vocal Performance, Male </S>
 * <S>Best Gospel Vocal Performance by a Duo or Group, Choir or Chorus</S>
 * <S>Best Soul Gospel Performance</S>
 * <S>Best Soul Gospel Performance, Traditional</S>
 * <S>Best Soul Gospel Performance, Contemporary</S>
 * <S>Best Soul Gospel Performance, Female</S>
 * <S>Best Soul Gospel Performance, Male</S>
 * <S>Best Soul Gospel Performance, Male or Female</S>
 * <S>Best Soul Gospel Performance by a Duo or Group, Choir or Chorus</S>
 * <S>Best Inspirational Performance</S>
 * <S>Best Pop/Contemporary Gospel Album</S>
 * <S>Best Rock Gospel Album</S>
 * <S>Best Traditional Soul Gospel Album</S>
 * <S>Best Contemporary Soul Gospel Album</S>
 * <S>Best Southern, Country or Bluegrass Gospel Album</S>
 * <S>Best Gospel Choir or Chorus Album</S>

Historical

 * <S>Best Historical Album</S>

Jazz

 * <S>Best Jazz Vocal Performance, Female</S>
 * <S>Best Jazz Vocal Performance, Male</S>
 * <S>Best Jazz Vocal Performance, Duo or Group</S>
 * <S>Best Jazz Instrumental Solo</S>
 * <S>Best Jazz Instrumental Album, Individual or Group</S>
 * <S>Best Large Jazz Ensemble Album</S>
 * <S>Best Jazz Fusion Performance</S>
 * <S>Best Original Jazz Composition</S>
 * <S>Best Jazz Vocal Album</S>
 * <S>Best Contemporary Jazz Album</S>
 * <S>Best Latin Jazz Album</S>

Latin

 * <S>Best Latin Recording</S>
 * <S>Best Latin Pop Album</S>
 * <S>Best Traditional Tropical Latin Album</S>
 * <S>Best Mexican/Mexican-American Album</S>
 * <S>Best Latin Rock/Alternative Album</S>
 * <S>Best Tejano Album</S>
 * <S>Best Salsa Album</S>
 * <S>Best Merengue Album</S>
 * <S>Best Salsa/Merengue Album </S>

Musical Show

 * <S>Best Musical Show Album</S>
 * <S>Best Sound Track Album or Recording of Original Cast From a Motion Picture or Television</S>

Music Video

 * <S>Best Short Form Music Video</S>
 * <S>Best Long Form Music Video</S>
 * <S>Best Concept Music Video</S>
 * <S>Best Performance Music Video</S>
 * <S>Video of the Year</S>

New Age

 * <S>Best New Age Album</S>

Packaging and notes

 * <S>Best Album Cover</S>
 * <S>Best Album Cover - Classical</S>
 * <S>Best Album Cover - Other Than Classical</S>
 * <S>Best Album Cover, Graphic Arts</S>
 * <S>Best Album Cover, Photography</S>
 * <S>Best Recording Package</S>
 * <S>Best Boxed or Special Limited Edition Package</S>
 * <S>Best Album Notes</S>
 * <S>Best Album Notes - Classical </S>

Polka

 * <S>Best Polka Album</S>

Pop

 * <S>Best Vocal Performance, Female</S>
 * <S>Best Vocal Performance, Male</S>
 * <S>Best Performance by a Vocal Group</S>
 * <S>Best Performance by a Chorus</S>
 * <S>Best Performance by a Vocal Group or Chorus </S>
 * <S>Best Instrumental Performance</S>
 * <S>Best Female Pop Vocal Performance</S>
 * <S>Best Male Pop Vocal Performance</S>
 * <S>Best Contemporary (R&R) Solo Vocal Performance - Male or Female</S>
 * <S>Best Pop Performance by a Duo or Group with Vocal</S>
 * <S>Best Contemporary Performance by a Chorus </S>
 * <S>Best Pop Collaboration with Vocals</S>
 * <S>Best Performance by an Orchestra - for Dancing </S>
 * <S>Best Performance by an Orchestra or Instrumentalist with Orchestra - Primarily Not Jazz or for Dancing</S>
 * <S>Best Pop Instrumental Performance</S>
 * <S>Best Pop Instrumental Performance with Vocal Coloring</S>
 * <S>Best Contemporary Song</S>
 * <S>Best Pop Vocal Album</S>
 * <S>Best Pop Instrumental Album</S>

Production and engineering

 * <S>Best Engineered Album, Non-Classical</S>
 * <S>Best Engineered Album, Classical</S>
 * <S>Best Engineered Recording - Special or Novel Effects</S>
 * <S>Best Remixed Recording, Non-Classical</S>
 * <S>Producer of the Year, Non-Classical</S>
 * <S>Producer of the Year, Classical</S>
 * <S>Remixer of the Year, Non-Classical</S>

R&B

 * <S>Best Female R&B Vocal Performance</S>
 * <S>Best Male R&B Vocal Performance</S>
 * <S>Best R&B Solo Vocal Performance, Male or Female</S>
 * <S>Best R&B Performance by a Duo or Group with Vocals</S>
 * <S>Best Traditional R&B Vocal Performance</S>
 * <S>Best R&B Instrumental Performance</S>
 * <S>Best Urban/Alternative Performance</S>
 * <S>Best Rhythm & Blues Recording </S>
 * <S>Best R&B Song</S>
 * <S>Best R&B Album</S>
 * <S>Best Contemporary R&B Album</S>

Rap

 * <S>Best Rap Performance</S>
 * <S>Best Rap Solo Performance</S>
 * <S>Best Female Rap Solo Performance</S>
 * <S>Best Male Rap Solo Performance</S>
 * <S>Best Rap Performance by a Duo or Group</S>
 * <S>Best Rap/Sung Collaboration</S>
 * <S>Best Rap Song</S>
 * <S>Best Rap Album</S>

Reggae

 * <S>Best Reggae Album</S>

Rock

 * <S>Best Female Rock Vocal Performance </S>
 * <S>Best Male Rock Vocal Performance</S>
 * <S>Best Rock Vocal Performance, Solo</S>
 * <S>Best Rock Performance by a Duo or Group with Vocal</S>
 * <S>Best Rock Instrumental Performance</S>
 * <S>Best Hard Rock Performance</S>
 * <S>Best Metal Performance</S>
 * <S>Best Hard Rock/Metal Performance Vocal or Instrumental</S>
 * <S>Best Rock Song</S>
 * <S>Best Rock Album</S>

Surround Sound

 * <S>Best Surround Sound Album</S>

Spoken

 * <S>Best Spoken Word Album</S>
 * <S>Best Spoken Comedy Album</S>

Traditional Pop

 * <S>Best Traditional Pop Vocal Album</S>

World

 * <S>Best World Music Album</S>
 * <S>Best Traditional World Music Album</S>
 * <S>Best Contemporary World Music Album</S>

Awards by year
Years reflect the year in which the awards were presented, for music released in the previous year.

also to do:

 * video awards - check "video producer" vs "producer" etc.
 * look at consistency of ordering
 * delinking engineers, others?
 * 2004 - check full results on all page
 * Check stared (*) articles for redirects
 * Ricky Skaggs, The Judds and Alison Krauss awards - formatting

title: User:Sannse/Grammy to-do list


text:
Canon (music)

In music, a canon is a contrapuntal (counterpoint-based) compositional technique that employs a melody with one or more imitations of the melody played after a given duration (e.g., quarter rest, one measure, etc.). The initial melody is called the leader (or dux), while the imitative melody, which is played in a different voice, is called the follower (or comes). The follower must imitate the leader, either as an exact replication of its rhythms and intervals or some transformation thereof. Repeating canons in which all voices are musically identical are called rounds—familiar singalong versions of "Row, Row, Row Your Boat" and "Frère Jacques" that call for each successive group of voices to begin the same song a bar or two after the previous group began are popular examples.

An accompanied canon is a canon accompanied by one or more additional independent parts that do not imitate the melody.

Medieval and Renaissance
During the Middle Ages, Renaissance, and Baroque—that is, through the early 18th century—any kind of imitative musical counterpoints were called fugues, with the strict imitation now known as canon qualified as fuga ligata, meaning "fettered fugue". Only in the 16th century did the word "canon" begin to be used to describe the strict, imitative texture created by such a procedure. The word is derived from the Greek "κανών", Latinised as canon, which means "law" or "norm". In contrapuntal usage, the word refers to the "rule" explaining the number of parts, places of entry, transposition, and so on, according to which one or more additional parts may be derived from a single written melodic line. This rule was usually given verbally, but could also be supplemented by special signs in the score, sometimes themselves called canoni. The earliest known non-religious canons are English rounds, a form first given the name rondellus by Walter Odington at the beginning of the 14th century; the best known is "Sumer is icumen in" (composed around 1250), called a rota ("wheel") in the manuscript source. The term "round" only first came to be used in English sources in the 16th century.

Canons featured in the music of the Italian Trecento and the 14th-century ars nova in France. An Italian example is "Tosto che l'alba" by Gherardello da Firenze. In both France and Italy, canons were often featured in hunting songs. The medieval and modern Italian word for hunting is "caccia", while the medieval French word is spelled "chace" (modern spelling: "chasse"). A well-known French chace is the anonymous "Se je chant mains". Richard Taruskin describes "Se je chant mains" as evoking the atmosphere of a falcon hunt: "The middle section is truly a tour de force, but of a wholly new and off-beat type: a riot of hockets set to 'words' mixing French, bird-language, and hound-language in an onomatopoetical mélange." Guillaume de Machaut also used the 3-voice "chace" form in movements from his masterpiece Le Lai de la Fontaine (1361). Referring to the setting of the fourth stanza of this work, Taruskin says "a well-wrought chace can be far more than the sum of its parts; and this particular chace is possibly Machaut's greatest feat of subtilitas."

An example of late 14th century canon which featured some of the rhythmic complexity of the late 14th century ars subtilior school of composers is La harpe de melodie by Jacob de Senleches. According to Richard Hoppin, "This virelai has two canonic voices over a free and textless tenor."

In many pieces in three contrapuntal parts, only two of the voices are in canon, while the remaining voice is a free melodic line. In Dufay's song "Resvelons nous, amoureux", the lower two voices are in canon, but the upper part is what David Fallows describes as a "florid top line":

Baroque
Both J. S. Bach and Handel featured canons in their works. The final variation of Handel's keyboard Chaconne in G major (HWV 442) is a canon in which the player's right hand is imitated at the distance of one beat, creating rhythmic ambiguity within the prevailing triple time:

Classical
An example of a classical strict canon is the Minuet of Haydn's String Quartet in D Minor, Op. 76, No. 2. "Throughout its sinewy length, between upper and lower strings. Here is the superbly logical fulfilment of the two-part octave doubling of Haydn's earliest divertimento minuets":

Beethoven
Beethoven's works feature a number of passages in canon. The following comes from his Symphony No. 4:

Antony Hopkins describes the above as "a delightfully naïve canon". More sophisticated and varied in its treatment of intervals and harmonic implications is the canonic passage from the second movement of his Piano Sonata 28 in A major, Op. 101:

Beethoven's most spectacular and dramatically effective use of canon occurs in the first act of his opera Fidelio. Here, four of the characters sing a quartet in canon, "a sublime musical wonder", accompanied by orchestration of the utmost delicacy and refinement. "Each of the four participants delivers his or her quatrain", "The use of canon to embody the differing perspectives of the participants a first glance seems odd, but the rigid form allows for some character differentiation and does in fact make a dramatic point". "Everyone sings the same music to very different words, sinking their private thoughts into musical or at least linear anonymity". "The softly padding gait, the dove-tailed perfection of the counterpoint, induce a trance that, carrying the protagonists outside Time, hints that there are realms of truth beyond the masks they pathetically or comically present to the world."

Romantic era
In the Romantic era, the use of devices such as canon was even more often subtly hidden, as for example in Schumann's piano piece "Vogel als Prophet" (1851). According to Nicholas Cook, "the canon is, as it were, absorbed into the texture of the music—it is there, but one doesn't easily hear it." Peter Latham describes Brahms' Intermezzo in F minor, Op. 118, No. 4 as a piece "rich in canons". In the following passage, the left hand shadows the right at the time distance of one beat and at the pitch interval of an octave lower:

Michael Musgrave writes that as a result of the strict canon at the octave, the piece is "of an anxious, suppressed nature, ... in the central section this tension is temporarily eased through a very contained passage which employs the canon in chordal terms between the hands." According to Denis Matthews, "[what] looks on paper like another purely intellectual exercise... in practice it produces a warmly melodic effect."

20th century to present
Stravinsky composed canons, including a Canon on a Russian Popular Tune and the Double Canon. Conlon Nancarrow composed a number of canons for player piano. (See Mensuration and tempo canons below.) Anton Webern employed canonic textures in his work; his Op. 16 work is a collection of five canons for soprano, clarinet, and bass clarinet.

Types
Considering the many types of canon "in the tonal repertoire", it may be ironic that "canon—the strictest type of imitation—has such a wide variety of possibilities". The most rigid and ingenious forms of canon are not strictly concerned with pattern but also with content. Canons are classified by various traits including the number of voices, the interval at which each successive voice is transposed in relation to the preceding voice, whether voices are inverse, retrograde, or retrograde-inverse; the temporal distance between each voice, whether the intervals of the second voice are exactly those of the original or if they are adjusted to fit the diatonic scale, and the tempo of successive voices. However, canons may use more than one of the above methods.

Contour Canon

A Contour Canon can be recognized in the traditional sense, similar to a strict canon or to a canon by inversion, where an original theme or design is presented, and is then followed by a response of the same theme, as well as in an untraditional fashion, where Subcontouric Cells are positioned in such a way that they assemble a canon. In this untraditional fashion, a contour’s cells are presented and altered in a rotational motion, until the entire image or contour can be seen in its Prime form. Each cell in a pairing of Subcontouric Cells cycles through their rotational variations, until they have established themselves in their intended contour position, or Prime Form, such as (1-1)(1-2), referred to as a contour’s Cell Cycle.

Terminology
Although, for clarity, this article uses leader and follower(s) to denote the leading voice in a canon and those that imitate it, musicological literature also uses the traditional Latin terms dux and comes for "leader" and "follower", respectively.

Number of voices
A canon of two voices may be called a canon in two, similarly a canon of x voices would be called a canon in x. This terminology may be used in combination with a similar terminology for the interval between each voice, different from the terminology in the following paragraph.

Another standard designation is "Canon: Two in One", which means two voices in one canon. "Canon: Four in Two" means four voices with two simultaneous canons. While "Canon: Six in Three" means six voices with three simultaneous canons, and so on.

Simple
A simple canon (also known as a round) imitates the leader perfectly at the octave or unison. Well-known canons of this type include the famous children's songs Row, Row, Row Your Boat and Frère Jacques.

Interval
If the follower imitates the precise interval quality of the leader, then it is called a strict canon; if the follower imitates the interval number (but not the quality—e.g., a major third may become a minor third), it is called a free canon.

Contrapuntal derivations
The follower is by definition a contrapuntal derivation of the leader.

Canon by inversion
An inversion canon (also called an al rovescio canon) has the follower moving in contrary motion to the leader. Where the leader would go down by a particular interval, the follower goes up by that same interval.

Retrograde or crab canon
In a retrograde canon, also known as a canon cancrizans (Latin for crab canon, derived from the Latin cancer = crab), the follower accompanies the leader backward (in retrograde). Alternative names for this type are canon per recte et retro or canon per rectus et inversus.

Mensuration and tempo canons
In a mensuration canon (also known as a prolation canon, or a proportional canon), the follower imitates the leader by some rhythmic proportion. The follower may double the rhythmic values of the leader (augmentation or sloth canon) or it may cut the rhythmic proportions in half (diminution canon). Phasing involves the application of modulating rhythmic proportions according to a sliding scale. The cancrizans, and often the mensuration canon, take exception to the rule that the follower must start later than the leader; that is, in a typical canon, a follower cannot come before the leader (for then the labels 'leader' and 'follower' should be reversed) or at the same time as the leader (for then two lines together would constantly be in unison, or parallel thirds, etc., and there would be no counterpoint), whereas in a crab canon or mensuration canon the two lines can start at the same time and still respect good counterpoint.

Many such canons were composed during the Renaissance, particularly in the late fifteenth and early sixteenth centuries; Johannes Ockeghem wrote an entire mass (the Missa prolationum) in which each section is a mensuration canon, and all at different speeds and entry intervals. In the 20th century, Conlon Nancarrow composed complex tempo or mensural canons, mostly for the player piano as they are extremely difficult to play. Larry Polansky has an album of mensuration canons, Four-Voice Canons. Arvo Pärt has written several mensuration canons, including Cantus in Memoriam Benjamin Britten, Arbos and Festina Lente. Per Nørgård's infinity series has a sloth canon structure. This self-similarity of sloth canons makes it "fractal like".

Other types
The most familiar of the canons is the perpetual/infinite canon (in Latin: canon perpetuus) or round. As each voice of the canon arrives at its end it can begin again, in a perpetuum mobile fashion; e.g., "Three Blind Mice". Such a canon is also called a round or, in medieval Latin terminology, a rota. Sumer is icumen in is one example of a piece designated rota.

Additional types include the spiral canon, accompanied canon, and double or triple canon. A double canon is a canon with two simultaneous themes; a triple canon has three.

Double canon
A double canon is a composition that unfolds two different canons simultaneously. A duet aria, "Herr, du siehst statt guter Werke" from J. S. Bach's Cantata BWV 9, Es ist das Heil uns kommen her features a double canon "between flute and oboe on the one hand and the soprano and alto voices on the other. But what is most interesting in this movement is that the very attractive melodic surface of the canon belies its dogmatic message by offering a moving simplicity of tone to indicate the comfort that particular doctrine provides for the believer. Canonic devices often bear the association of strictness and the law in Bach's work."

Mirror canon
In a mirror canon (or canon by contrary motion), the subsequent voice imitates the initial voice in inversion. They are not very common, though examples of mirror canons can be found in the works of Bach, Mozart (e.g., the trio from Serenade for Wind Octet in C minor, K. 388/384a), Anton Webern, and other composers.

Table canon
A table canon is a retrograde and inverse canon meant to be placed on a table in between two musicians, who both read the same line of music in opposite directions. As both parts are included in each single line, a second line is not needed. Bach wrote a few table canons.

Rhythmic canon
Olivier Messiaen employed a technique which he called "rhythmic canon", a polyphony of independent strands in which the pitch material differs. An example is found in the piano part of the first of the Trois petites liturgies de la présence divine, where the left hand (doubled by strings and maracas), and the right hand (doubled by vibraphone) play the same rhythmic sequence in a 3:2 ratio, but the right hand adapts a sequence of 13 chords in the sixth mode (B–C–D–E–F–F–G–A–B) onto the 18 duration values, while the left hand twice states nine chords in the third mode. Peter Maxwell Davies was another post-tonal composer who favoured rhythmic canons, where the pitch materials are not obliged to correspond.

The notion of rhythmic canon transfers Messiaen's idea of mode of limited transposition from the domain of pitch to the domain of time: "Messiaen considered a set of disjoint pitch classes with the same interval content which covers the twelve-tone tempered scale. For instance, four pitch classes {C, E♭, F#, A} and two transpositions, by one and by two semitones, cover the twelve-tone scale and, consequently, meet this requirement. This is similar to what is called in mathematics tiling, that is, covering an area, e.g., a square, by disjoint equal figures.

...By analogy with covering the scale by a few pitch classes and their transpositions, the pulse train was covered by a certain rhythmic pattern with different delays. The disjointedness of pitch classes implied no common beats in different instances of the rhythmic pattern.

...A rhythmic canon is one whose tone onsets result in a regular pulse train with no simultaneous tone onsets at a time. In that sense, a rhythmic canon tiles time, covering a regular pulse train by disjoint equal rhythms from different voices. Note that the established term "rhythmic canon" is somewhat misleading, and "disjoint rhythm canon" might be more exact.

...It turned out, however, that solutions to the time-tiling problem are mainly trivial and musically not interesting. A typical solution is a metronome rhythm entering with equal delays, e.g., a sequence of every fourth beat, entering at the first, at the second, and at the third beat, which is a rhythm analogy of the transpositions of pitch class classes {C, E♭, F♯, A}. Non-trivial solutions have been found by Dan Tudor Vuza for a circular time with periods 72, 108, 120,..."

- Andranik Tangian

Computational methods for finding rhythmic canons, both infinite and finite, with arbitrary generative rhythmic patterns were developed in the 2000s with further generalization to so-called "rhythmic fugues" with a few generative rhythmic patterns.

Puzzle canon

A puzzle canon, riddle canon, or enigma canon is a canon in which only one voice is notated and the rules for determining the remaining parts and the time intervals of their entrances must be guessed. "The enigmatical character of a [puzzle] canon does not consist of any special way of composing it, but only of the method of writing it down, of which a solution is required." Clues hinting at the solution may be provided by the composer, in which case the term "riddle canon" can be used. J. S. Bach presented many of his canons in this form, for example in The Musical Offering. Mozart, after solving Father Martini's puzzles, composed his own riddles, K. 73r, using Latin epigrams such as Sit trium series una and Ter ternis canite vocibus ("Let there be one series of three parts" and "sing three times with three voices").

Other notable contributors to the genre include Ciconia, Ockeghem, Byrd, Beethoven, Brumel, Busnois, Haydn, Josquin des Prez, Mendelssohn, Pierre de la Rue, Brahms, Schoenberg, Nono and Maxwell Davies. According to Oliver B. Ellsworth, the earliest known enigma canon appears to be an anonymous ballade, "En la maison Dedalus", found at the end of a collection of five theory treatises from the third quarter of the fourteenth century collected in the Berkeley Manuscript.

Thomas Morley complained that sometimes a solution, "which being founde (it might bee) was scant worth the hearing", J. G. Albrechtsberger admits that, "when we have traced the secret, we have gained but little; as the proverb says, 'Parturiunt montes, etc.'" but adds that, "these speculative passages ... serve to sharpen acumen".

Elaborate use of canon technique

 * Josquin des Prez, Missa L'homme armé super voces musicales, Agnus Dei 2: One voice with the words 'ex una voce tres' (three voice parts out of one), a mensuration canon in three voices.
 * Josquin des Prez, Missa L'homme armé sexti toni, Agnus Dei 2: two simultaneous canons in the four upper voices, and at the same time a crab canon in the two lower voices.
 * Johann Sebastian Bach's Goldberg Variations contains nine canons of increasing interval size, ranging from unison to ninth. Each canon additionally obeys the overall structure and harmonic sequence common to all variations in the composition.

Contemporary canons
In his early work, such as Piano Phase (1967) and Clapping Music (1972), Steve Reich used a process he calls phasing which is a "continually adjusting" canon with variable distance between the voices, in which melodic and harmonic elements are not important, but rely simply on the time intervals of imitation.

title: Canon (music)


text:
Lebesgue covering dimension

In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in a topologically invariant way.

Informal discussion
For ordinary Euclidean spaces, the Lebesgue covering dimension is just the ordinary Euclidean dimension: zero for points, one for lines, two for planes, and so on. However, not all topological spaces have this kind of "obvious" dimension, and so a precise definition is needed in such cases. The definition proceeds by examining what happens when the space is covered by open sets.

In general, a topological space X can be covered by open sets, in that one can find a collection of open sets such that X lies inside of their union. The covering dimension is the smallest number n such that for every cover, there is a refinement in which every point in X lies in the intersection of no more than n + 1 covering sets. This is the gist of the formal definition below. The goal of the definition is to provide a number (an integer) that describes the space, and does not change as the space is continuously deformed; that is, a number that is invariant under homeomorphisms.

The general idea is illustrated in the diagrams below, which show a cover and refinements of a circle and a square.

Formal definition
The first formal definition of covering dimension was given by Eduard Čech, based on an earlier result of Henri Lebesgue.

A modern definition is as follows. An open cover of a topological space $X$ is a family of open sets $U$$α$ such that their union is the whole space, $$\cup_\alpha$$ $U$$α$ = $X$. The order or ply of an open cover $$\mathfrak A$$ = {$U$$α$} is the smallest number $m$ (if it exists) for which each point of the space belongs to at most $m$ open sets in the cover: in other words $U$$α$ 1 ∩ ⋅⋅⋅ ∩ $U$$α$ $m$+1 = $$\emptyset$$ for $α$1, ..., $α$$m$+1 distinct. A refinement of an open cover $$\mathfrak A$$ = {$U$$α$} is another open cover $$\mathfrak B$$ = {$V$$β$}, such that each $V$$β$ is contained in some $U$$α$. The covering dimension of a topological space $X$ is defined to be the minimum value of $n$ such that every finite open cover $$\mathfrak A$$ of X has an open refinement $$\mathfrak B$$ with order $n$ + 1. The refinement $$\mathfrak B$$ can always be chosen to be finite. Thus, if $n$ is finite, $V$$β$ 1 ∩ ⋅⋅⋅ ∩ $V$$β$ $n$+2 = $$\emptyset$$ for $β$1, ..., $β$$n$+2 distinct. If no such minimal $n$ exists, the space is said to have infinite covering dimension.

As a special case, a non-empty topological space is zero-dimensional with respect to the covering dimension if every open cover of the space has a refinement consisting of disjoint open sets, meaning any point in the space is contained in exactly one open set of this refinement.

Examples
The empty set has covering dimension -1: for any open cover of the empty set, each point of the empty set is not contained in any element of the cover, so the order of any open cover is 0.

Any given open cover of the unit circle will have a refinement consisting of a collection of open arcs. The circle has dimension one, by this definition, because any such cover can be further refined to the stage where a given point x of the circle is contained in at most two open arcs. That is, whatever collection of arcs we begin with, some can be discarded or shrunk, such that the remainder still covers the circle but with simple overlaps.

Similarly, any open cover of the unit disk in the two-dimensional plane can be refined so that any point of the disk is contained in no more than three open sets, while two are in general not sufficient. The covering dimension of the disk is thus two.

More generally, the n-dimensional Euclidean space $$\mathbb{E}^n$$ has covering dimension n.

Properties

 * Homeomorphic spaces have the same covering dimension. That is, the covering dimension is a topological invariant.
 * The covering dimension of a normal space X is $$\le n$$ if and only if for any closed subset A of X, if $$ f:A\rightarrow S^n $$ is continuous, then there is an extension of $$ f $$ to $$ g:X\rightarrow S^n $$. Here, $$ S^n $$ is the n-dimensional sphere.
 * Ostrand's theorem on colored dimension. If $X$ is a normal topological space and $$\mathfrak A$$ = {$U$$α$} is a locally finite cover of $X$ of order ≤ $n$ + 1, then, for each 1 ≤ $i$ ≤ $n$ + 1, there exists a family of pairwise disjoint open sets $$\mathfrak B$$$i$ = {$V$$i$,$α$} shrinking $$\mathfrak A$$, i.e. $V$$i$,$α$ ⊆ $U$$α$, and together covering $X$.

Relationships to other notions of dimension

 * For a paracompact space $X$, the covering dimension can be equivalently defined as the minimum value of $n$, such that every open cover $$\mathfrak A$$ of $X$ (of any size) has an open refinement $$\mathfrak B$$ with order $n$ + 1. In particular, this holds for all metric spaces.
 * Lebesgue covering theorem. The Lebesgue covering dimension coincides with the affine dimension of a finite simplicial complex.
 * The covering dimension of a normal space is less than or equal to the large inductive dimension.
 * The covering dimension of a paracompact Hausdorff space $$X$$ is greater or equal to its cohomological dimension (in the sense of sheaves), that is, one has $$H^i(X,A) = 0$$ for every sheaf $$A$$ of abelian groups on $$X$$ and every $$i$$ larger than the covering dimension of $$X$$.
 * In a metric space, one can strengthen the notion of the multiplicity of a cover: a cover has $r$-multiplicity $n + 1$ if every $r$-ball intersects with at most $n + 1$ sets in the cover. This idea leads to the definitions of the asymptotic dimension and Assouad–Nagata dimension of a space: a space with asymptotic dimension $n$ is $n$-dimensional "at large scales", and a space with Assouad–Nagata dimension $n$ is $n$-dimensional "at every scale".

Historical

 * Karl Menger, General Spaces and Cartesian Spaces, (1926) Communications to the Amsterdam Academy of Sciences. English translation reprinted in Classics on Fractals, Gerald A.Edgar, editor, Addison-Wesley (1993) ISBN 0-201-58701-7
 * Karl Menger, Dimensionstheorie, (1928) B.G Teubner Publishers, Leipzig.

Modern

 * V. V. Fedorchuk, The Fundamentals of Dimension Theory, appearing in Encyclopaedia of Mathematical Sciences, Volume 17, General Topology I, (1993) A. V. Arkhangel'skii and L. S. Pontryagin (Eds.), Springer-Verlag, Berlin ISBN 3-540-18178-4.
 * V. V. Fedorchuk, The Fundamentals of Dimension Theory, appearing in Encyclopaedia of Mathematical Sciences, Volume 17, General Topology I, (1993) A. V. Arkhangel'skii and L. S. Pontryagin (Eds.), Springer-Verlag, Berlin ISBN 3-540-18178-4.

title: Lebesgue covering dimension


text:
Friedrich Wilhelm von Seydlitz

Friedrich Wilhelm Freiherr von Seydlitz (3 February 1721 – 8 November 1773 ) was a Prussian officer, lieutenant general, and among the greatest of the Prussian cavalry generals. He commanded one of the first Hussar squadrons of Frederick the Great's army and is credited with the development of the Prussian cavalry to its efficient level of performance in the Seven Years' War. His cavalryman father retired and then died while Seydlitz was still young. Subsequently, he was mentored by Margrave Frederick William of Brandenburg-Schwedt. Seydlitz's superb horsemanship and his recklessness combined to make him a stand-out subaltern, and he emerged as a redoubtable Rittmeister (cavalry captain) in the War of Austrian Succession (1740–1748) during the First and Second Silesian wars.

Seydlitz became legendary throughout the Prussian Army both for his leadership and for his reckless courage. During the Seven Years' War, he came into his own as a cavalry general, known for his coup d'œil, his ability to assess at a glance the entire battlefield situation and to understand intuitively what needed to be done: he excelled at converting the King's directives into flexible tactics. At the Battle of Rossbach, his cavalry was instrumental in routing the French and Imperial armies. His cavalry subsequently played an important role in crushing the Habsburg and Imperial left flank at the Battle of Leuthen. Seydlitz was wounded in battle several times. After the Battle of Kunersdorf in August 1759, he semi-retired to recover from his wounds, charged with the protection of the city of Berlin. He was not healthy enough to campaign again until 1761.

Frederick rewarded him with Order of the Black Eagle on the field after the Battle of Rossbach; he had already received the Pour le Mérite for his action at the Battle of Kolin. Although estranged from Frederick for several years, the two were reconciled during Seydlitz's final illness. Seydlitz died in 1773, and Frederick's heirs included his name on the equestrian statue of Frederick the Great in Berlin, in a place of honor.

Early life
Seydlitz was born on 3 February 1721, in Kalkar in the Duchy of Cleves, where his father, Daniel Florian von Seydlitz, was a major of Prussian cavalry with the Cuirassier Regiment Markgraf Friedrich Wilhelm of Brandenburg-Schwedt No. 5. In 1726, his father left military service and moved the family to Schwedt, where he became a forestry master in East Prussia; the senior Seydlitz died in 1728, leaving a widow and children in restricted financial circumstances. Limited schooling was available to young Seydlitz; sources differ whether he knew how to speak and write in French, the lingua franca of Frederick the Great's Court. One biographer, Bernhard von Poten, maintained that his German was good, and if he knew French, he preferred German and wrote it with a "fine, firm hand, unusually correct, in well-formed sentences and with apt expression," and he knew enough Latin to express himself well. His future sovereign, Frederick, always addressed him in German.

By Seydlitz's seventh year, he could ride a horse well, raced with older boys, and he was, by most accounts, a wild and high-spirited child. At the age of fourteen he went as a page to the court of the Margrave Frederick Wilhelm of Brandenburg-Schwedt, who had been his father's colonel. The Margrave was a grandson of the Great Elector, and a nephew to both Frederick I of Prussia and Leopold of Anhalt Dessau. Himself a reckless man, the "Mad" Margrave inspired in young Seydlitz a passion for feats of daredevil horsemanship. Seydlitz did not limit this passion to horses: the Margrave once dared him to ride a wild stag, which he did. Seydlitz became a skilled horseman, and many stories tell of his feats, the best known of which involved riding between the sails of a windmill in full swing. Seydlitz remained in his position as a page to the Margrave until King Frederick William appointed him as cornet in the Margrave's Cuirassier Regiment No. 5 (his father's old regiment) on 13 February 1740.

Military career
Seydlitz's first months as a cornet were made difficult by the regimental colonel, who considered him a spy for the Margrave, and abused him by sending him on useless errands and generally making it clear that the cornet was no match for the colonel. Within a year of Seydlitz's commission, the old King Frederick William died and his son, Frederick II of Prussia, ascended to the throne. Frederick claimed Silesia from the Habsburg's Maria Theresa, and made a broad appeal to arms. The Margrave's regiment played an important role in the ensuing war, during which Seydlitz came to the notice of the King several times. Once, when Frederick asked the caliber of the artillery shelling the Prussian line, opinions were divided and vague. Seydlitz rode in front of the battery, halting in their line of fire. When he saw a ball hit the ground, he picked it up, wrapped it in his handkerchief and presented it to the King.

In May 1742, while stationed with his regiment in Kranowitz during the First Silesian War, the regimental colonel ordered him to take 30 men and hold a village post until infantry came to his assistance; despite heavy fire, the grudging colonel did not send reinforcements. Realizing what had happened, the brigade's general took three squadrons of heavy cavalry to relieve Seydlitz, but these were turned back by fire from the Austrian line. Subsequently, Seydlitz was forced to surrender his small unit. He entered into Austrian captivity with several of his closest comrades, including Charles de Warnery.

Frederick exchanged an Austrian captain for Cornet Seydlitz. Upon his return from captivity, Seydlitz had a choice to wait for the first lieutenancy that became available in a cuirassier regiment, or take the immediate command of a troop of hussars, as a captain. Hussars were the newest form of service in the Prussian army, and not as prestigious an assignment as cuirassiers, but Seydlitz chose the immediate promotion to a lesser unit. In 1743, the King made him a Rittmeister (captain) in the 4th Hussars. He entirely skipped the rank of lieutenant. With the 4th Hussars, he was stationed in the city of Trebnitz and he brought his squadron to a state of conspicuous efficiency.

In August 1744, the King entered Bohemia, took Prague, and then moved south. Lieutenant General Count Nassau led the vanguard, and Seydlitz participated with the Natzmer Hussars, commanded by Major Hans Heinrich Adam Schütz, a violent man of whose conduct of warfare Seydlitz disapproved. Seydlitz served through the Second Silesian War. On 22 May, Hans Karl von Winterfeldt, trusted by the King as a good judge of character, reported to Frederick: "Certainly, at Hohenfriedberg, on the 4 June, [Seydlitz] captured the Saxon general [Georg Sigismund] von Schlichting personally, after he had cut the reins from him." Based largely on his conduct at Hohenfriedberg and Winterfeldt's recommendation, Frederick promoted Seydlitz to major on 28 July at the unusually young age of twenty-four.

Seydlitz led his squadron at the Battle of Soor on 30 September, scouting the enemy's position before the battle, and then participating in the action. He was also present in the engagement at Katholisch-Hennersdorf on 23 November, which proved convincingly to Frederick the benefit of close support during a cavalry charge. At the successful action on 27 November, Seydlitz led 15 squadrons in an attack on the Austrian rear guard. The Austrians were dispersed and nearly destroyed.

Development of cavalry tactics
After Frederick concluded the peace on 25 December 1748, Seydlitz returned with his squadron to Trebnitz. In the subsequent years of peace, Seydlitz developed flexible cavalry tactics. He assembled a plan on tactical form and training for the Prussian cavalry and presented it to the King. Frederick approved the procedures and Seydlitz established a rigorous training program. He would leave his own estate by jumping the gate; he required similar horsemanship from all his men, regardless of whether they were cuirassiers, hussars or dragoons. They had to be capable of galloping across broken fields, wheeling in formation, and riding in close action. Furthermore, they had to be prepared to support any movement of infantry, or to react to any action from the enemy. Under Seydlitz's direction, possibly influenced by the ideas of Frederik Sirtema van Grovestins, Prussian cavalry learned to use only their swords, as pistols or carbines could not be fired with accuracy and had to be reloaded. Frederick set up straw dummies for his troopers to shoot; their shots were woefully inaccurate, but Seydlitz's tactics demonstrated that the troopers could hit their target with a sword every time. Generally, cavalry horses were the sturdy warm-blood Trakehners, from Frederick's stud farm in Trakenhen, East Prussia.

On 21 September 1752, after a successful review in which the different cavalry forms demonstrated their competencies, the King promoted Seydlitz to lieutenant colonel and the commander-in-chief of cavalry and, on 13 October of the same year, to the commander of the Dragoon Regiment Württemberg No. 12, whose staff was at Treptow. Frederick was not satisfied with the regiment's performance, and instructed Seydlitz to "put it back into order". In 1753 Frederick appointed Seydlitz to the command of the 8th Cuirassiers. In Seydlitz's hands, this regiment soon became a model for the rest of the Prussian Army's mounted force. In 1755 Frederick promoted him to colonel.

By the start of the Seven Years' War, Seydlitz's transformed cavalry had become Frederick's pride and joy: it had unrivaled training and an esprit de corps bolstered by Frederick's confidence in its members, and by their confidence in Seydlitz. The King had issued orders that no Prussian cavalryman would allow himself to be attacked without a commensurate response, under penalty of being cashiered; consequently, Prussian cavalrymen were active, impetuous and aggressive. For the King, Seydlitz's cavalry became the dynamic factor in the army of the state, and would be the tool by which Frederick could challenge empires. In 1756, Seydlitz's cavalry became Frederick's weapon of choice.

Seven Years' War
In May 1757, in defiance of the custom of holding the heavy cavalry in reserve, Seydlitz brought his regiment forward to join the advance guard at the Battle of Prague. Here he nearly lost his life attempting to ride through a marshy pool; his horse became stuck in quicksand and his troopers pulled him away. At the Prussian loss at Kolin in June 1757, he and a cavalry brigade checked the Austrian pursuit by a brilliant charge. Two days later, the King promoted him to major general and awarded him the Pour le Mérite. Seydlitz felt he had deserved the promotion for a long time, for he responded to Hans Joachim von Zieten's congratulations by saying, "It was high time, Excellency, if they wanted more work out of me. I am already thirty-six."

Another example of his leadership and his coup d'œil, the ability to see at a glance what needed to be done, occurred after the Battle of Kolin. The loss at Kolin forced the King to lift the siege at Prague. The King's brother, Augustus William, took command of the army and ordered the retreat from Prague. Seydlitz was attached to the advanced corps of Karl Christoph von Schmettau in a brigade of ten squadrons. As Seydlitz's wing entered Lusatia, near the town of Zittau, the Austrians were present in force, and Seydlitz with his squadrons were trapped in the town. Tricking the Austrians into thinking his troop was a foraging party, his cavalry burst on the Austrian cavalry before they could climb into their saddles. Seydlitz led his cavalry in an escape, in close column, and was quickly out of sight.

Battle of Rossbach
On the morning of the Battle of Rossbach, Frederick passed over two senior generals and placed Seydlitz in command of the whole of the cavalry, much to those men's annoyance and to Seydlitz's satisfaction. At Rossbach, Seydlitz's coup d'œil and his understanding of the King's objectives led to battlefield success. After positioning the cavalry in two ranked lines, he watched the French army move for several minutes, while puffing on his pipe; his troopers never took their eyes off him. When he threw his pipe away, this was the signal they had waited for: the first line of massed squadrons surged forward, smashing the unprepared French in the flank. Typically, cavalry action in the mid-eighteenth century meant a single cavalry charge; the cavalry would spend the rest of the action pursuing fleeing troops. At Rossbach, though, not content with this single attack, Seydlitz called his second formation of squadrons in another charge; he then withdrew all 38 squadrons into a copse, where they regrouped under cover of the trees. Without waiting for new orders from the King, Seydlitz deployed the Prussian cavalry a third time; this proved a critical factor in the battle. As trained, Seydlitz's squadrons charged headlong into the French columns: a massive wall of horses galloping flank to flank, their riders flashing swords and maneuvering at full speed. By the end of the battle, only seven infantry battalions of Frederick's army had fired a shot; the rest of the victory had been the work of Seydlitz's 38 squadrons and Karl Friedrich von Moller's artillery.

That day, the Prussians took as trophies 72 cannons (62 percent of the French/Imperial artillery), seven flags, and 21 standards. With some 3,500 horsemen and 20 cannons, plus a portion of Prince Henry's regiment of infantry, the Prussian army had defeated the combined armies of two European powers, France and the Holy Roman Empire. The tactics at Rossbach became a landmark in the history of military art. The same night, on the field, the King awarded Seydlitz the Order of the Black Eagle, and promoted him to lieutenant general. Seydlitz had been wounded during the melée and he remained out of action for four months, nursed by a lady in Leipzig.

Campaign 1758–59
Seydlitz rejoined the King in 1758 and on 25 August, at the Battle of Zorndorf, Seydlitz's cavalry again secured the victory. He led thirty-six squadrons into a mass of Russian cavalry mingled with infantry. This charge broke the Russian right wing and sent them running for the woods. At the Prussian debacle at Hochkirch, on 14 October 1758, he covered the Prussian retreat with 108 squadrons, and in the disaster of Kunersdorf, on 12 August 1759, he received another severe wound in a hopeless attempt to storm a hill held by the Russians; his 8th Cuirassiers was one of the few intact regiments at the end of the battle. While recuperating in Berlin, he helped organize a defense of the city during the Austro-Russian raid (October 1760). Although he was unable to prevent the Russians from briefly occupying the city, Frederick later praised Seydlitz for his conduct.

Seydlitz's health frequently kept him off the battlefield, and he did not reappear at the front until 1761. Then, he received command of a wing of Prince Henry's army, composed of troops of all arms, and many of his fellow officers expressed doubts as to his fitness for this command, as his service had been with the cavalry exclusively. Subsequently, though, at Freiberg on 29 October 1762, his direction of both his infantry and his cavalry in turn decided the outcome of the battle.

Later life

After the Seven Years' War concluded with the Treaty of Hubertusburg (1763), Seydlitz became inspector general of the cavalry in Silesia, where eleven regiments were permanently stationed and where Frederick sent all his most promising officers to be trained. In 1767, Frederick promoted Seydlitz to general of cavalry.

Seydlitz's later years were marred by domestic unhappiness. During his convalescence in Berlin, on 18 April 1761, he had married Susannah Johanna Albertine Hacke, daughter of Hans Christoph Friedrich Graf von Hacke, and she was eventually unfaithful to him, reportedly due to the syphilis from which he had suffered for decades. He had at least one daughter, according to an early biographer, Anton König, and two according to another biographer, Robert Lawley. The oldest daughter married first to an official from Breslau, and was divorced. She married second to a Polish count, and divorced soon after. She eventually converted to Catholicism, but died in a madhouse in Brieg. The youngest lived to old age and died in poverty near Lausitz.

By the end of the decade, some misunderstanding brought an end to his formerly close friendship with the King. Seydlitz's health had been declining for years and he suffered from recurrent bouts of syphilis; in 1772, after an attack of apoplexy, he completed a couple of stays at the spa at Carlsbad to take the mineral waters. While these helped somewhat, his other activities continued without moderation, and to his detriment. A subordinate brought him two healthy Circassian beauties, whose company he enjoyed but who undoubtedly stressed his tenuous health. In August 1773, in his last illness, Frederick and Seydlitz met again at Seydlitz's home at Minkovsky near Ohlau (now Oława, Poland). The King sat beside his sickbed, horrified at Seydlitz's condition, and even persuaded him to take some of his medications, but Seydlitz would not look at him; the illness had already deformed his face. Eventually paralyzed, whether from another stroke or the underlying tertiary syphilis, Seydlitz died at Ohlau in Silesia in November 1773.

Character
Seydlitz was generally admired for the superb coup d'œil that allowed him to utilize the cavalry to its full potential. His 19th-century biographer, K. A. Varnhagen von Ense, related that Seydlitz lived above all for the service, and promoted the training of his hussars before all else. According to Anton Balthasar König, who wrote in 1780–1790, Seydlitz performed best at taverns and excelled in practical jokes: one would gather that Seydlitz was a drunkard, a rake, and a savage, but another of his biographers, Bernhard von Poten, cited conflicting descriptions offered by Seydlitz's contemporaries, particularly Warnery, as more accurate. Nevertheless, there is some evidence to support König's assertion, at least of Seydlitz's excesses: Seydlitz was no doubt dependent upon his tobacco and had been since his teenage years, although he smoked a pipe rather than using snuff, as many officers did; he was indeed reckless, as his career testified; he enjoyed the company of women; and Seydlitz indeed suffered from recurring illness.

Memorials
In 1851, Frederick William IV, Frederick's great-great nephew, included Seydlitz's name on the Equestrian statue of Frederick the Great in Berlin, honoring those who had helped to build the Prussian state. Seydlitz holds a position of honor as one of the four full-sized mounted figures, sharing the first tier of the plinth with the King's brother, his cousin, and Hans Joachim von Zieten. A bronze sculpture installed at Wilhelmplatz, in Berlin, was created by Anton Lulvès, a copper worker from Hamburg. SMS Seydlitz, representing the first generation of battlecruisers, was ordered in 1910 and commissioned in May 1913, the fourth such vessel built for the Imperial German Navy's High Seas Fleet. The heavy cruiser GERMAN CRUISER Seydlitz, of the Admiral Hipper-class cruiser, was launched in 1939, but never completed.

title: Friedrich Wilhelm von Seydlitz