AcharyaChanakya/simple-wikipedia huggingface dataset:
The spiral has the property that the angle ɸ between the tangent and radial line at the point ("r",θ) is constant. This property can be expressed in differential geometric terms as
The derivative r'(θ) is proportional to the parameter "b". In other words, it controls how "tightly" and in which direction the spiral spirals. In the extreme case that "b" = 0 ("ɸ" = π/2) the spiral becomes a circle of radius "a". Conversely, in the limit that "b" approaches infinity ("ɸ" → 0) the spiral tends toward a straight line. The complement of ɸ is called the "pitch".
Spira mirabilis, Latin for "miraculous spiral", is another name for the logarithmic spiral. While this curve had already been named by other mathematicians, the name "miraculous" or "marvelous" spiral was given to this curve by Jakob Bernoulli, because he was fascinated by one of its unique mathematical properties: the size of the spiral increases, but the shape stays the same with each added curve. Maybe because of this property, the spira mirabilis has evolved in nature, seen in some living beings, such as nautilus shells and sunflower heads. Jakob Bernoulli wanted the shape on his headstone, but, by error, an Archimedean spiral was placed there instead.
The logarithmic spiral can be distinguished from the Archimedean spiral by the fact that the distances between the turnings of a logarithmic spiral increase in geometric progression, while in an Archimedean spiral these distances are constant.
Logarithmic spirals are self-similar in that they are self-congruent under all similarity transformations (scaling them gives the same result as rotating them). Scaling by a factor formula_6 gives the same as the original, without rotation. They are also congruent to their own involutes, evolutes, and the pedal curves based on their centers.
Starting at a point "P" and moving inwards along the spiral, one has to circle the origin infinitely often before reaching it; yet, the total distance covered on this path is finite. This was first realized by Evangelista Torricelli even before calculus had been invented. The total distance covered is "r"/cos(α), where "r" is the straight-line distance from "P" to the origin.
One can construct approximate logarithmic spirals with pitch about 17.03239 degrees using Fibonacci numbers or the golden ratio as is explained in those articles. Similarly, the exponential function exactly maps all lines not parallel with the real or imaginary axis in the complex plane, to all logarithmic spirals in the complex plane with centre at 0. (Up to adding integer multiples of 2π"i" to the lines, the mapping of all lines to all logarithmic spirals is onto.) The pitch angle of the logarithmic spiral is the angle between the line and the imaginary axis.
In several natural phenomena one may find curves that are close to being logarithmic spirals. Here follows some examples and reasons:
Small white
The small white ("Pieris rapae") is a small to mid-sized butterfly of the 'yellows' & 'whites' Pieridae family. It is also commonly known as the small cabbage white or just the cabbage white.
It is common across Europe, North Africa and Asia and has also been accidentally introduced to North America, Australia and New Zealand where they have become pests on cultivated cabbages and other mustard family crops.
It looks like a smaller version of the Large White. The upperside is creamy white with black tips to the forewings. Females also have two black spots in the center of the forewings. Its underwings are yellowish with black .
Like its close relative the large white this is a strong flyer and the British population is increased by continental immigrants in most years. Like other 'white' butterflies it hibernates as a pupa. Like the large white, it is sometimes known as the cabbage white' or cabbage butterfly.
It has two flight periods, April–May and July–August.
Its caterpillars can be a pest on cultivated cabbages. . It also lays eggs on wild members of the cabbage family such as the charlock "Sinapis arvensis" and hedge mustard "Sisybrium officinale". The eggs are laid singly on foodplant leaves.
Known in the United States as "imported cabbage worms", the caterpillars are green and well camouflaged. Unlike the large white they do not store the mustard oils from their foodplants and so are not distastful to predators like birds.
Argonauta
Argonauta, the argonauts, is the only living genus in the Argonautidae family. They are a group of pelagic octopods.
They are also called paper nautiluses, because of the paper-thin eggcase that females make. This structure does not have the gas-filled chambers of nautilus shells, and is not a true cephalopod shell. It is an evolutionary innovation unique to the genus "Argonauta".
Argonauts are found in tropical and subtropical waters worldwide: they live in open ocean. Like most octopods, they have a rounded body, eight arms and no fins. However, unlike octopuses, argonauts live close to the sea surface rather than on the seabed. "Argonauta" species have very large eyes and small distal webs. They have a mantle-funnel locking apparatus, which is a way to identify the genus. It consists of knob-like cartilages in the mantle and corresponding depressions in the funnel. Unlike the closely related genera "Ocythoe" and "Tremoctopus", "Argonauta" species lack water pores.
In Argonauts, males and females are quite different in size and lifespan. Females grow up to 10 cm and make shells up to 30 cm, while males rarely grow larger than 2 cm. The males only mate once in their short lifetime, but the females can get pregnant repeatedly. The females have been known since ancient times while the males were only described in the late 19th Century. The males use a modified arm, the hectocotylus, to transfer sperm to the female. For fertilization, the arm is inserted into the female's pallial cavity, then is detached from the male.
The hectocotylus was originally described as a parasitic worm. The hectocotyl arm and its correct function were described by Aristotle. His account was disbelieved for over 2000 years, but was rediscovered in the early 19th century.
Female argonauts make a laterally compressed, calcareous eggcase in which they live. The eggcase curiously resembles the shells of extinct ammonites. It is secreted by the tips of the female's two greatly expanded dorsal tentacles (third left arms) before egg laying. After she deposits her eggs in the floating eggcase, the female herself takes shelter in it, often along with the male's detached hectocotylus. She is usually found with her head and tentacles protruding from the opening, but she retreats deeper inside if disturbed.
These ornate, curved white eggcases are occasionally found floating on the sea surface, sometimes with the female argonaut still clinging to it. It is made of calcite, with a 3-layered structure The argonauts may have evolved to use ammonite shells for their egg laying, eventually becoming able to mend the shells and perhaps even make their own.
The egg case also contains a bubble of gas used for buoyancy similar to shelled cephalopods, although it does not have chambers as seen in other shelled cephalopods.
"Argonauta argo" is the largest species in the genus and also produces the largest eggcase, which may reach a length of 300 mm. The smallest species is "Argonauta bottgeri", with a maximum recorded size of 67 mm.
The beaks of "Argonauta" species are distinctive. They are characterised by a very small rostrum and a fold that runs to the lower edge or near the free corner. The rostrum is 'pinched in' at the sides. This makes it much narrower than in other octopuses, with the exception of the closely allied monotypic genera "Ocythoe" and "Vitreledonella". Argonaut beaks are most similar to those of "Ocythoe tuberculata" and "Vitreledonella richardi". They differ in 'leaning back' to a greater degree than the former and because they have a more curved jaw angle than the latter.
Feeding mostly occurs during the day. Argonauts use tentacles to grab prey and drag it toward the mouth. It then bites the prey to inject it with poison from the salivary gland. They feed on small crustaceans, molluscs, but also jellyfish and salps. If the prey is shelled, the argonaut uses its radula to drill into the organism, then inject the poison.
Argonauts are capable of changing their color. They can blend in with their surroundings to avoid predators. They also produce ink, which is ejected when the animal is being attacked. This ink paralyzes the olfaction of the attacker, providing time for the argonaut to escape. The female is also able to pull back the web covering of her shell, making a silvery flash, which may deter a predator from attacking.
Argonauts are preyed upon by tunas, billfishes, and dolphins. Shells and remains of argonauts have been recorded from the stomachs of "Alepisaurus ferox" and "Coryphaena hippurus".
Male argonauts have been seen living inside salps, which are planktonic tunicates. Little is known about this relationship.
The genus "Argonauta" contains up to seven existing species. Several extinct species are also known.
The extinct species "Obinautilus awaensis" was originally assigned to "Argonauta", but has since been transferred to the genus "Obinautilus".
Minor can mean:
Camouflage is a visual disguise. Without it, an animal would be recognised easily. If the natural colour of an animal makes it look like its surroundings, that is camouflage. A tiger's stripes in the long grass, and the battledress of a modern soldier are examples.
Camouflage is a form of deception. The word camouflage comes from the French word "camoufler," which means "to disguise".
In nature, most animals blend into their environment or conceal their shape. They are very hard to see. This way they survive, and if they survive, then they can reproduce. There are exceptions: animals which are dangerous to eat (e.g. wasps) advertise with warning colouration.
Prey animals hide from predators. Predators must search for prey without being seen. Natural camouflage is one way to do this: an animal can blend in with its surroundings. Another way is for the animal to disguise itself as something harmless.
Some camouflaged animals also copy movements in nature, e.g., of a leaf blowing in the wind. Other animals attach natural materials to their body for concealment. A few animals change color in changing environments. Seasonally: (many Arctic animals, such as the arctic fox, or arctic hare). Or quickly, like the chameleon and the cuttlefish. Some herd animals, like zebra, have a pattern which makes it difficult for the predator when they are running.
Mimicry is a special kind of camouflage, where an animal or plant looks like another, usually one which is unpleasant to eat or dangerous.
Most animals are dark on top and light underneath. With light coming from the sky, this "countershading" makes them less visible. That this is the correct explanation is proved by cases where the animal lives upside down. A famous example is the Nile catfish, which swims belly uppermost. In this case, the belly is dark, and the back is light in colour.
Transparent or partly transparent animals are common in the pelagic layer of the sea. These are the layers into which light penetrates. The effect of transparency or silvering works is better under water than above it. This is because the amount of light which penetrates is less and less as the depth increases. Also, the proportion of the light reflected is much less under water (0.001–0.6%) than in air (2–5%).
In biology, an extant group is one which has survived to the present day, and so it is a living group. This distinguishes it from an extinct group.
The term 'extant' can also be used to describe species or higher groups (such as genera or families) which are still in existence (living).
Example: in the group of molluscs known as the cephalopods, there are about 600 extant species and 7500 extinct species.
Echinoderm
Echinoderms are a successful phylum of marine animals. They include sea stars, brittle stars, sea urchins, sea cucumbers and their relatives.
Echinoderms have these features:
Echinoderms live in all parts of the ocean, but mostly on the sea floor. Some are filter feeders, and others (starfish) are important predators of molluscs and other shell-fish. They are extremely common near the shore, and on reefs.
They have a long and abundant fossil record. This phylum appeared in the early Cambrian period; it contains about 7,000 living and 13,000 extinct species. The four or five main groups are called sub-phyla by some authorities, and classes by others.
Echinodermata is the largest animal phylum which is entirely marine: no animals in this group live on land or in fresh or brackish water.
For many purposes it is better to use the following classification. It is easier to learn and understand, and is based more on the living forms.
Only with the crinoids is it necessary to deal with the fossil forms, because the stalked crinoids were so important on the Palaeozoic sea floors.
All echinoderms have fivefold radial symmetry in their body at some stage of life. The holothurians have bilateral symmetry as adults, and do not have so much of a skeleton as other groups.
Echinoderms have a hydraulic water vascular system. This network of fluid-filled canals moves and feeds the animal, and allows gas exchange. There is also a complete digestive tube. They have a simple radial nervous system that consists of a modified nerve net. There are nerve rings with radiating nerves around the mouth extending into each arm. The branches of these nerves coordinate the movements of the animal. Echinoderms have no brain, although some do have ganglia. They usually move with their tube feet, but brittle stars use their arms to pull against rocks. Some feather stars and sea cucumbers can swim.
The sexes are usually separate. Sexual reproduction typically consists of releasing eggs and sperm into the water, with fertilization taking place externally. Their larvae are planktonic.
Many echinoderms have remarkable powers of regeneration. A starfish arm cut off will regenerate. A section as small as a single arm, with some central disk and neural tissue, can regenerate the whole organism.
Most of the adults have radial symmetry. If they are not sessile or attached, they are at least benthic (bottom-dwellers). In contrast, echinoderm larvae are planktonic, and have bilateral symmetry. Echinoderm larvae are ciliated free-swimming organisms that have a bilaterally symmetry rather like embryonic chordates. The first stage in all groups except the crinoids is the dipleurula, which has a row of cilia winding round its body. All the groups have second and third stage larvae. The larvae grow, and are carried away from their parents.
Later, the adult body grows into a radial form, with the body arranged in five parts around a central axis. This means they often have a star-shaped pattern.
There is no geological evidence about the origin of echinoderms. The first undoubted fossils in the Lower Cambrian are already well developed, and fall into five or six different groups. "Arkarua", from the Ediacaran, is thought to be an echinoderm. "Tribrachidium" is another possible, from the same period. On general biological grounds, it seems that echinoderms, and some related phyla, may have been derived from worm-like ancestors.
Of all invertebrate phyla, the echinoderms are the closest relatives to the chordata, that is, animals who have spinal cord, such as vertebrates. With the chordates and hemichordates, echinoderms are deuterostomes, one of the two major divisions of the animal kingdom.
Argonaut
The word Argonaut might refer to:
Das Rheingold ("The Rhinegold") is an opera by Richard Wagner. It is the first of the four operas that together tell a story called "Der Ring des Nibelungen" ("The Ring of the Nibelung").
"Das Rheingold" is an opera in one act, divided into four scenes. It is a very long act, lasting 2 ½ hours, but it is normally played without an interval as the music is continuous, even between the scenes.
The characters in the opera are Gods, Giants, Nibelungs and the Rhinedaughters. The Nibelungs are a race of dwarfs. They are cunning and evil and live underneath the surface of the earth.
The first scene takes place in the river Rhine where the three Rhinemaidens: Woglinde, Wellgunde and Flosshilde, are guarding the precious Rhine gold. Alberich, an evil Nibelung, arrives and tries to catch the Rhinemaidens. From what they say Alberich learns that the gold they are guarding has magic powers. Alberich wants the gold, but the Rhinemaidens say that anyone who wants to have it has to renounce (give up) love. They think that Alberich will not do that because he is very fond of girls, but Alberich does renounce love and so he gets the gold.
The second scene takes place in Valhalla, which is where the gods live. Wotan, the chief god, is there with his wife Fricka. Two giants have been building an enormous castle for the gods. Wotan has promised them that he would pay them for their work by giving them Freia, the Goddess of Youth and Beauty. Fricka is worried about the promise that Wotan has made, but Wotan tells his wife that he is not going to keep his promise. He thinks he can find a way of tricking the giants. Freia enters. She is frightened because the giants are coming for her.
The giants, Fasolt and Fafner, enter. They want to have Freia in payment for having built the castle. The problem for the gods is that Freia has a garden in which she grows golden apples. If the gods no longer have these golden apples they will grow old and die. Wotan does not know what to do.
Loge, the god of fire, enters. Wotan is cross with Loge for not having found something else to pay the giants with. Loge says he has been all over the world looking for something. He tells everyone that the gold from the Rhine has magic power, and how Alberich renounced love so that he could steal it from the Rhinemaidens. He tells them that a ring can be made from the gold, and that whoever has the ring will have power over all the world. The giants hear what Loge is saying and decide that they want the gold instead of Freia. They take Freia as hostage, saying that they will be back later to collect the gold. If they do not get it then they will keep Freia forever.
Wotan asks Loge how they are going to get the gold. Loge tells them that they should steal it from Alberich. After all, Alberich stole it from the Rhinemaidens, so it does not belong to him. Wotan and Loge go down below the earth to the Nibelungs.
Underneath the earth Alberich is forcing the Nibelungs to work for him. They are hammering at the anvil. Mime, who is Alberich’s brother, has used some of the gold to make a helmet. This helmet is called the Tarn helmet. Anyone who wears it can change their shape or become invisible. Alberich treats his brother very cruelly.
Wotan and Loge tell Alberich that they have heard how clever he is. They ask him to show them what he can do with the Tarn helmet. Alberich puts on the helmet and changes himself into a huge dragon. Wotan and Loge pretend to be impressed. They ask him whether he can change himself into something small. Alberich show off again, changing himself into a frog. Wotan immediately puts his foot on him and catches him. Wotan and Loge take all the gold and go back to Valhalla.
Wotan and Loge tease Alberich. Alberich asks them what they want so that he can be free. Wotan demands the gold. The Nibelungs pile the gold up. Alberich is not too worried, because he still has the ring which gives him magic power. He thinks he can use this power later to get the gold back. Wotan sees the ring on Alberich’s finger. He tells him to give him the ring. Alberich is terrified, but Wotan tears it from his finger. Before Alberich goes he puts a curse on the ring. Whoever has had the ring will die. This is very important to the whole story of the four operas.
The two giants appear with Freia. The gods have become very weak, but once Freia returns they start to become stronger again. Wotan tells the giants they can have their gold. The giants say that they must pile up the gold in front of Freia until they cannot see her. They do this, but the giants say there is still a tiny hole through which they can see Freia’s eye. They see the ring on Wotan’s finger and tell him to put it in the hole. Wotan says they can have anything they want but not the ring.
Erda appears. Erda is the Earth Goddess. She is very wise. She reminds Wotan that there is a curse on the ring and that he should quickly give the ring to the giants. Wotan has no choice. He puts the ring in the hole. Now the giants are happy.
Immediately, however, the giants start to argue with one another and Fafner kills Fasolt. The curse on the ring is working. Loge tells Wotan he was wise to give up the ring. However, Fricka is still worried because Wotan did have the ring.
Donner, the god of Thunder, enters and swings his hammer. There is a flash of lightning and a crash of thunder. The clouds vanish, a rainbow makes a bridge to Valhalla and the gods enter Valhalla. The Rhinemaidens are heard crying out to Wotan to give the gold back, but Wotan takes no notice. The gods are now at the height of their glory. We shall see, at the end of the fourth opera, that the curse will catch up with them and that they, too, will die.
The music of "Das Rheingold" is beautifully written to fit every person and every situation. The famous opening starts with a low chord of E flat which describes the bottom of the river Rhine. At first the notes of the chords are held on, then gradually a ripple of broken chords and arpeggios suggest the ripples of the water. The harps make a sound like the waves. The harmony just consists of the same E flat chord for the first 136 bars until the Rhine Maidens start to sing.
Each character in the opera has his own musical leitmotif which can change and combine to show their changing moods and situations. There are big, heavy chords for the giants, creepy chromatic winding music for Loge, the god of fire, who is supposed to be very crafty, dignified music for the Earth Goddess Erda etc. There is a special leitmotif for the curse, which is heard at various times in all four operas.
Wagner actually called "Das Rheingold" a "prologue" to the other three operas, which he saw as the main operas of the cycle.
Die Walküre
Die Walküre ("The Valkyrie") is an opera by Richard Wagner. It is the second of the four operas that together tell a story called "Der Ring des Nibelungen" ("The Ring of the Nibelung"). The story continues from the first opera which was called "Das Rheingold". It is a very beautiful piece.
"Die Walküre" was first performed on 26 June 1870 in Munich. The first performance that was part of the whole Ring cycle took place on 14 August 1876.
The opera starts with a storm. The young man Siegmund is out in the storm and comes to a house. The house belongs to Hunding who lives there with his wife Sieglinde. An ash tree is growing in the middle of the house. Siegmund and Sieglinde are twins who were separated as children, so neither of them knows who the other one is. Their father is Wotan, the chief god, but they don’t know this either. Their mother was a mortal (an ordinary person, not a goddess) or perhaps a she-wolf, which is how the goddess Fricka refers to her.
Sieglinde lets Siegmund into the house and gives him a drink of mead. They start to fall in love. Hunding arrives and asks Siegmund who he is. Siegmund says that his name ought to be Woeful because he has had an unhappy life. When he was small he came home once and found his house burned down, his mother murdered and his twin sister had been abducted (taken away). He then remembers that some years later he went to help a young lady who had been forced to marry a cruel man. He had killed some of the man’s friends. Hunding realizes that he himself was this man, so that he is Siegmund’s enemy. He says to Siegmund that he can sleep in his house tonight because this is a law of hospitality, but in the morning he will have to fight him.
Sieglinde goes to prepare a drink for her husband. She puts a drug in it which will make Hunding sleep deeply. Siegmund meanwhile is thinking about something his father had promised him. He had told him that he would thrust a magic sword called “Nothung” into a tree. No one would get that sword until, one day, when Siegmund found himself in great difficulty, he would be able to pull it from the tree and use it.
Sieglinde enters and tells Siegmund a story about how, on the day she was forced to marry Hunding, an old man had come into the house and thrust a sword into the ash tree in the middle of the room. They start to realize that they are brother and sister, but it does not stop them from falling in love and they sing passionately about their love for one another. Siegmund pulls the sword from the tree and the two lovers embrace.
Wotan is the chief god, whom we heard in "Das Rheingold". He is trying to get rid of the curse of the Rheingold, and has built a grand plan around Siegmund. Wotan tells his daughter Brünnhilde that she must make sure that Siegmund wins the fight with Hunding. Brünnhilde (the out-of-wedlock daughter of Wotan and Erda, the Earth-Mother goddess) has the power to do this. She is one of eight daughters of Wotan who are Valkyries (German: Walküren). Their job is to collect the dead bodies of brave heroes who have died in battle and take them back to Valhalla, the house of the gods.
Wotan’s wife Fricka arrives in a chariot pulled by a ram. Brünnhilde disappears, and there follows a big argument between husband and wife. Fricka says to Wotan that Siegmund and Sieglinde must be punished for breaking Hunding's marriage, and for loving one another because brothers and sisters are not allowed to be lovers (this is called “incest”). She says that she herself is the goddess of marriage and must make sure that marriage laws are obeyed. Fricka says that the gods will all be disgraced. Wotan says that he went to the world to have children with mortal women because the gods needed a race of heroes who would protect them. But Fricka says to Wotan that he is wrong: Siegmund cannot be a free hero if he is being protected by Wotan. Giving in, Wotan now tells Brünnhilde that she must leave Siegmund to his fate.
Sieglinde tells Siegmund that she feels guilty and that he ought to leave her, but they are desperately in love. When she hears Hunding’s horn she imagines that Siegmund will be torn apart by the dogs and she faints. Brünnhilde pities Siegmund. She tells Siegmund that he must follow her to Valhalla. When Siegmund asks whether he can take Sieglinde with her Brünnhilde says that he cannot do this. Siegmund refuses to go. Brünnhilde tells him that he cannot escape his fate. Siegmund continues to plead with Brünnhilde, and in the end she is so moved that she changes her mind. She breaks Wotan's order, and says that she will protect Siegmund in battle. Hunding appears and the two men fight. Brünnhilde protects Siegmund with her shield. Siegmund is nearly winning when suddenly Wotan appears and smashes Siegmund’s sword into pieces. Hunding kills Siegmund.
The other Valkyries are wondering where Brünnhilde is. They see her coming on her horse, but instead of a hero she is carrying a woman (it is Sieglinde). The Valkyries are angry with Brünnhilde because she disobeyed Wotan. Sieglinde wants to die, but when she is told that she has a baby in her womb she asks Brünnhilde to save her. She escapes into the forest with bits of Siegmund’s sword. One day the baby she is now bearing will grow up, become a hero, and use the bits to make another sword.
Wotan goes to the Valkyries. He is furious with Brünnhilde because she disobeyed him. He punishes her. He tells her that she is no longer a Valkyrie. She will fall asleep on a rock and any man who finds her can have her. Brünnhilde pleads with Wotan. She asks him whether he could, at least, put a fire round her so that the only man who could get her would be a hero. In the end Wotan agrees. Loge, the god of fire, arrives and lights the fire. At the end of the opera Brünnhilde is asleep on the rock, surrounded by the fire. There she will stay until, one day, a hero comes to rescue her.
The music contains many wonderful moments. The most famous bit is the beginning of Act Three where the Valkyries are riding on their horses. This music is known as "The Ride of the Valkyries". It is very dramatic music. The very beginning of Act One is also very dramatic. The music describes a storm. The orchestra is a very large one, including special tubas which are known as “Wagner tubas”. There are no separate arias in these operas: all the sections flows into one another. Sometimes a character has a section when they are telling a story. There are beautiful sections like the one in Act One where Siegmund is remembering about his father and the sword, or the love music between Siegmund and Sieglinde. By using leitmotifs (music which goes with certain ideas or characters) he gets many subtle effects. When Siegmund looks at the ash tree we hear the sword motive because the sword is in the tree, although at that moment he does not know about it. We also hear Wotan’s theme when Siegmund talks about his father. We (the listener) know who his father is, but Siegmund does not. The music tells us lots of things that the characters in the story may not understand. This makes the music very powerful and exciting.
Siegfried (opera)
Siegfried is an opera by Richard Wagner. It is the third of the four operas that together tell a story called "Der Ring des Nibelungen" ("The Ring of the Nibelung"). The story continues from the end of the second opera which was called "Die Walküre".
The first performance of "Siegfried" took place when the whole Ring cycle (all four operas) were performed in the Festspielhaus in Bayreuth on 16 August 1876.
The first part of the opera takes place in a forest where the giant Fafner lives. He has used the magic tarn helmet to change himself into a dragon so that he can guard the treasure of the gold and the ring (we saw how he got the treasure in the first opera, "Das Rheingold"). Siegfried, who was not yet born at the end of the second opera, "Die Walküre", is now a young lad. He has been brought up by the dwarf Mime, Alberich's brother. Mime is just as horrible as his brother.
Mime is hammering away at the anvil, trying to repair the sword that was smashed to pieces by Wotan in Act Two of "Die Walküre". He wants to make the bits into a strong sword, but every time he thinks he has managed it Siegfried picks up the sword and breaks it with his strength. The reason that Mime wants to make the sword is so that he can give it to Siegfried (who is obviously the hero who is meant to have the sword in the end) and tell him to fight the dragon. Then Mime will be able to get the ring from him so that he can have power over all the world. When Siegfried enters he brings a bear from the forest. The bear chases Mime and Siegfried laughs. Then he lets the bear go free.
Mime says to Siegfried that he should be thankful to him for looking after him as a child and bringing him up. He has never told Siegfried who his parents were (they were Siegmund and Sieglinde, both now dead). Siegfried does not understand anything about how babies are born. He has never seen a woman before. He only knows Mime who is pretending to be his father. Siegfried has noticed that young birds look like their parents and he asks Mime why he does not look like him. In the end Mime is forced to tell Siegfried about his parents and about the sword that was smashed by Wotan. Siegfried tells Mime to forge (make) the sword so that he can kill the dragon. Siegfried goes off.
Wotan, the chief god, appears. He is disguised as a wanderer. Mime says he wants to ask him three questions, and if he cannot answer them he can chop off his head. Wotan agrees. First Mime asks him the name of the race of people who live below the earth. Wotan says they are the Nibelungs. Then Mime asks who are the people who live on the earth’s surface. Wotan says they are the giants. Then he asks him who lives in the sky. Wotan says they are the gods. He has answered all three questions correctly. He now tells Mime it is his turn to ask Mime three questions which he must answer if he wants to keep his head. Mime is terrified, but has to agree.
First Wotan asks him who are the people whom Wotan loves a lot although he has to be harsh with them. Mime answers: the Wälsung race. Then Wotan asks him the name of the sword that Wotan left for Siegfried. Mime answers: Nothung. Finally Wotan asks him who can put the pieces of the sword together. Mime is now terrified because he does not know the answer. Wotan tells him the answer: it is the person who does not know fear. He says to Mime that he can keep his head for the moment. He will leave it to the fearless person to chop it off later.
When Mime and Siegfried are together again, Mime tries to frighten Siegfried so that he knows what fear is. He tells him all about the huge dragon in the cave. "Does that not frighten you?" he asks him. "Not a bit" answers Siegfried, who likes the thought of fighting a dragon. Siegfried works at the anvil and starts to make the sword. Mime is thinking of how he will trick Siegfried after the dragon has been killed, so that he can get the sword and kill Siegfried. At last Siegfried manages to make the mighty sword. He calls out its name: "Nothung"! Then he crashes the sword down on the anvil which splits into two pieces.
Outside the dragon’s cave Wotan, still disguised as a wanderer, meets Alberich (Mime’s brother who has not been in the story since the first opera). Alberich hates Wotan for having snatched the ring from him. Wotan does not care, and even wakes the dragon up, but the dragon does not want to fight them.
Mime and Siegfried appear. Siegfried is not frightened at all. He just wants to know where the dragon’s heart is so that he can kill it. Mime leaves him alone. Siegfried sits down in the forest and thinks. He is glad to know now that the ugly Mime is not his father. He hears a bird singing and he tries to imitate the bird’s song with a pipe he has made from a reed. He blows his horn and the dragon appears. Siegfried plunges the sword into the dragon’s heart. Siegfried instinctively puts his hand in the dragon’s mouth and tastes its blood. Suddenly he can understand what the bird is saying. The bird (originally sung by a boy but normally now by a woman) tells him to take the ring and the tarn helmet (which allows the wearer to change shape or make himself invisible). He takes them.
Mime and Alberich appear. They are arguing about who shall have the ring and the tarn helmet. Siegfried appears with both. Mime offers Siegfried a drink which is drugged. The bird warns Siegfried not to drink it. Siegfried kills Mime by chopping his head off with the sword. The bird then tells Siegfried about his beautiful bride Brünnhilde who is lying on a rock, protected by fire, waiting to be rescued by him.
Erda, the wise Earth Goddess, tells Wotan about the Norns who are weaving the rope of destiny. She is surprised to hear how Wotan has punished Brünnhilde. Wotan says he now looks forward to the end of the gods, and wants Siegfried to take his place.
Siegfried arrives. He tells Wotan (who is a stranger to him) about his heroic deed with the dragon. He finds Wotan annoying and smashes Wotan’s sword. He goes to the rock where Brünnhilde is lying.
Siegfried bursts through the flames and finds the sleeping Brünnhilde. He gently takes off her helmet, then her breastplate. Suddenly he sees that she is a woman. He has never seen a woman before. For the first time in his life he is frightened, yet he very much wants to wake her up. He kisses her lips and she opens her eyes and sits up. She tells him that she has always loved him, even long before he was born. Siegfried feels his passion growing and tries to put his arms round her, but now it is Brünnhilde who is frightened. She tells him not to spoil the purity of their love. Finally they embrace.
It took Wagner more than 15 years to write this opera which is one reason why the music of Act Three is slightly different in style. Some ideas from the love music of Siegfried and Brünnhilde were later re-used by Wagner in a separate orchestral piece, called the "Siegfried Idyll". Many of the leitmotifs (musical ideas that belong to particular characters or ideas) are ones that were heard in the "Das Rheingold" or "Die Walküre". One unusual instrument in the orchestra is the anvil. It is played when Mime, and later Siegfried, are hammering on the anvil trying to forge the pieces of the sword together. The rhythm of this music is the same rhythm heard earlier in the Nibelung scene in "Das Rheingold".
When Wagner started working on the opera he called it "Der junge Siegfried" ("The young Siegfried") but by 1856 he had changed the title to "Siegfried".
The German word “Sieg” means “victory” and “Fried” or “Friede” means “peace”. It is a good name for a hero. The role of Siegfried is sung by a tenor. The singer needs a very strong voice, often called a “Heldentenor” in German (a “heroic tenor”). He is on stage for most of the opera which lasts about four hours.
Götterdämmerung
Götterdämmerung is an opera by Richard Wagner. It is the fourth and last of the cycle of operas that together tell a story called "Der Ring des Nibelungen" ("The Ring of the Nibelung"). The story continues from the end of the third opera which was called "Siegfried". "Götterdämmerung" is the German name for "Ragnarök".
"Götterdämmerung" is the longest of the four operas. It takes about five hours to perform. It consists of a prologue and three acts. Wagner finished composing the opera in the autumn of 1874. It was first performed on 17 August 1876 as part of the complete Ring cycle.
The three Norns, daughters of Erda the Earth Goddess, are spinning the rope of destiny. This rope is a symbol of what has to happen in the end. They take it in turns to tell the story of the past, spinning as they sing and passing on the rope to the next one. The first Norn tells how Wotan went to drink from the Well of Wisdom for which he lost an eye. He then cut a spear from a tree which then died. The second Norn tells how a young hero broke Wotan’s spear and how the gods were sent from Valhalla to chop down the World Ash. The third Norn tells how the logs from the ash tree have been piled round Valhalla ready for a fire that will burn everything. The Norns have visions of the future. The rope breaks. The Norns disappear into the earth.
Brünnhilde and Siegfried come out of a cave by the rock where they were left at the end of the third opera. Siegfried has to go off to do heroic deeds. He gives Brünnhilde the ring as a token of his love for her. She gives him her horse which is called Grane (pronounce: GRAH-ne). Siegfried travels down the river Rhine.
Act One takes place in the Hall of the Gibichung palace. Gunther is the chief of the Gibichungs. His half-brother Hagen tells him he would look more important if he got married. He also says that Gunther’s sister Gutrune ought to get married. He tells him about Brünnhilde who, he thinks, is still asleep on the rock surrounded by fire that no one except Siegfried would be able to get through. He says that if they manage to get Siegfried to marry Gutrune, then she could persuade him to go and catch Brünnhilde for Gunther. He says that they could give Siegfried a potion (a special drink) which would make him forget that he loved Brünnhilde.
They hear Siegfried’s horn outside and the great hero arrives. Siegfried asks Hagen whether he knows him. Of course, Hagen does. Siegfried is carrying the magic tarn helmet which allows a person to change their shape or become invisible. Siegfried, however, does not know what the tarn helmet can do, and Hagen has to explain it to him. Gutrune appears and offers Siegfried a drink. It is the potion which is going to make him forget any other woman. He drinks to the health of Brünnhilde. As soon as he has drunk it he looks at Gutrune and is in love with her. He agrees to marry her, and he agrees to get a wife for Gunther. Hagen tells him about Brünnhilde on the rock. Siegfried has forgotten about her. He agrees to put on the tarn helmet and disguise himself as Gunther and to go and get Brünnhilde. He goes off, leaving Hagen guarding the palace.
The next scene takes place on the top of the Valkyrie rock. Her sister Waltraute arrives on a flying horse. She says that Wotan (their father, the chief God) returned to Valhalla with his spear broken. She says he told the gods to pile up the logs from the World Ash for a fire which will burn everything. Wotan desperately wants the ring to be given back to the Rhine Maidens (who were guardians of the gold, from which the ring was forged, in the first opera). Brünnhilde refuses to give her the ring that Siegfried had given her as a token of their love. Waltraute disappears.
After the weather calms the flames flicker again. Siegfried arrives, disguised as Gunther. Brünnhilde is horrified to see a person she thinks is a stranger. Siegfried says she is his bride, forces the ring from her finger and drags her into a cave for the night, although placing the sword between them.
Back at the palace Alberich tries to persuade his son Hagen to get the ring. Hagen wants to get the ring, but only for himself. Siegfried arrives. He no longer wears the tarn helmet so he looks like himself. Hagen blows his horn to call his vassals (soldiers) for a celebration. Gunther is to marry Brünnhilde and Siegfried is to marry Gutrune. Brünnhilde cannot understand why Siegfried is doing this. She sees the ring on his finger and asks him how he got it, as she thinks Gunther snatched it from her. Siegfried says that he won it by killing a dragon. He tells people how he tricked Brünnhilde and swears that a sword lay between them during the night, although Brünnhilde tries to make people think otherwise.
Brünnhilde is left alone with Gunther and Hagen. She tells them that, although Siegfried is so strong and impossible to kill in battle, he has one weak spot on his back. Gunther does not like the idea of having Siegfried killed, but Hagen promises him that he can then have the ring. They decide to kill Siegfried and to tell Gutrune that he was killed by a wild boar.
The last act takes place in a wild forest. Siegfried’s hunting horn is heard, and then the hunting horn of the Gibichungs. By the river Siegfried happens to meet the Rhine Maidens and teases them by showing them the ring, but does not let them have it. They tell him about the curse on the ring but Siegfried does not believe them. He meets Hagen. They drink together. Siegfried tells the men all about his life, how he was brought up by Mime, about the sword, the dragon and the bird singing. Then he cannot remember any more. Hagen gives him another drugged drink which makes him start to remember what actually happened. He remembers Brünnhilde and how he found her surrounded by fire. He gradually realizes how he has been tricked and feels unbearable sadness. Two ravens fly overhead and Hagen plunges his spear into Siegfried’s back. He dies while speaking the name of Brünnhilde. His body is carried off to a funeral march.
Back at the palace his body is brought in. Gutrune accuses Gunther of murdering him, but Gunther says Hagen did it. Hagen says he did it because Siegfried, when disguised as Gunther, had slept with Brünnhilde. He tries to snatch the ring from the dead Siegfried’s finger, Gunther tries to stop him but is murdered by Hagen. He tries again to snatch the ring but to everybody’s horror the arm of the dead hero rises in the air.
Brünnhilde enters and tells everyone how she promised Siegfried her love. Gutrune curses Hagen and falls onto her brother’s dead body. Brünnhilde orders a funeral pyre (a fire) to be prepared. She sings to Wotan that Siegfried is now at peace in death and that she understands more now. She takes the ring and promises to return it to the Rhine Maidens. She lights the fire which flares up and she rides on her horse Grane into the flames. The whole building catches fire, the Rhine overflows. Hagen jumps into the water trying to get the ring from the Rhine Maidens who drown him. The flood dies down and Valhalla (the gods’ palace) is lit up by the fire. The gods and the heroes die in the flames. The Twilight of the Gods has now happened.
The music of this long opera is extremely cleverly linked so that musical ideas flow into one another and combine to comment on the drama. Many of the themes have been heard in the other three operas. It is a very exhausting opera to sing, especially for Brünnhilde. There are usually two long intervals during a performance. The orchestra is very large and includes eight harps.
Der Ring des Nibelungen ("The Ring of the Nibelung" (Alberich)) is a cycle of four operas by Richard Wagner.
The story of each opera can be found in the separate articles.
Sometimes it is known as a “tetralogy” meaning: four works that belong together.
Wagner took the story of the operas from a book called the "Nibelungenlied" (the "Nibelung Song") which was written in the 12th century by a German poet. We do not know the name of the poet. The story is about the ancient gods from German mythology.
Wagner made a lot of changes to the story in order to make it suitable for his four operas. Wagner’s story tells of a hoard of gold which is being guarded by the Rhinemaidens. The dwarf Alberich steals the gold and uses some of it to make a ring which makes the owner powerful over all the world. When Wotan, the chief god, steals it from him, Alberich puts a curse on the ring. The ring will bring death to whoever has it. The ring goes through the hands of several characters, all of whom die in the end.
Alberich belongs to a race of dwarfs called the “Nibelungs”. The word “Nibelungen” in the title of the cycle: "Der Ring des Nibelungen" (“The Ring of the Nibelung”), refers to Alberich (it is singular, not plural).
The story of Wagner’s Ring cycle sounds quite fantastic and strange, like a fairy tale. Although the characters seems very different from real people, the story tells us all about basic human emotions. It is a story about greed, love, lust, intrigue etc. This is what makes it so powerful.
Wagner’s music matches each character and situation beautifully. It develops continuously: there are no breaks in the music during the acts. Wagner used what he called leitmotifs (leading motives). These are tunes or chords or little musical phrases which are linked to particular people in the opera. In this way he can hint at things very cleverly in the music. For example: there is a leitmotiv for the curse. Whenever we hear this curse motive we know that the curse of the ring is working.
Wagner spent about twenty years writing the Ring cycle. He started in the 1850s when he was living in Switzerland. He wrote all the libretto (the words) himself, as he always did for his operas. By 1857 he had finished the first two operas and two thirds of "Siegfried". It was many years later that he finally finished "Siegfried" and wrote the final opera as well.
Wagner wanted to have the Ring cycle performed in a special opera house which would be built in the way he wanted. He needed a lot of money for his ideas, and he was very lucky to find someone who adored his music and was happy to give him a lot of money. This was King Ludwig II of Bavaria (sometimes called the “mad king of Bavaria” because he did become insane). Wagner told the King that the Ring cycle would be performed in Munich which was the capital city of Bavaria. Later, when it seemed impossible to build a new opera house there, Wagner broke his promise and built his opera house in Bayreuth instead. The King did not seem to mind and still gave him lots of money for the project as well as a nice house to live in. "Das Rheingold" was first performed in Munich in 1869 and "Die Walküre" in 1870. The whole Ring cycle was first performed in 1876 in the new opera house called the "Festspielhaus" in Bayreuth.
Väki