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User:Magefile

Collaboration?

Hi Magefile

I have a similar project and I looking for help to finish it off - see http://www.nongnu.org/fhsst. My name is Mark Horner and we'd like to put all our content on the web in the end but we are looking for help to finish it off. The licence is also the GFDL so all of the content can be imported into Wikibooks - in fact that would make it easier for us to put it on the web.

Please let me know if you could be convinced to help out - all my details are on the website.

--

Mark: thank you for your invitation. Unfortunately, I won't be able to help out with your project; I don't have the time to commit to anything more than a few minutes on the weekend (which is what Wikibooks is for me). I do not have any formal qualifications, and have not yet finished university, so I do not know how much I could contribute anyway - again, Wikibooks is great because it's a weekend hobby for everyone. Finally, what drew me to wikibooks is the anonymity - I hate giving out my identity, having my email available on the web, etc.

However, as you pointed out, your project is FDL, so you can take what you need from Wikibooks. I encourage you to take anything of mine as well, as long as it stays under that license. (You don't need the permission, as it's already FDL. But if you wish to get consent from the author(s) first anyway, consider my consent given)

I am very pleased to see a serious effort being made to provide a Free textbook that will be used in a high school (wikibooks is wonderful, but no schools are planning to use it any time soon). I do wonder, though - is English the dominant language in South Africa, or are you writing it in English in order to allow international work on, and use of, the project? Or perhaps both?

Thanks again.

-

---

I will probably be contributing mostly to the math/science areas (specifically, trig, algebra, geometry and physics).

If you wish to respond to something I've written elsewhere, post it on this page. --magefile 02:23, 13 May 2004 (UTC)

title: User:Magefile


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File:Multilayerceramic png1.PNG

multilayered ceramic capacitor, drawn by me, mspaint

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

title: File:Multilayerceramic png1.PNG


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Music Theory/Modes

Modes
Modes are alternative tonalities (scales) that can be derived from the familiar major scale by starting on a different scale tone. Music that uses the traditional major scale can be said to be in the Ionian mode. For example, in the key of C, the Ionian scale would be C D E F G A B.

The other familiar mode is Aeolian. It can be derived by starting the Ionian (major) scale on the sixth scale tone. For example, A Aeolian would be A B C D E F G. This is the A natural minor scale.

The other modes can be derived similarly, by starting the major scale on the other tones. If we stick with only the white notes on the piano, we can derive seven different modes. These are:

As you can see, each mode denotes a unique set of intervals above the root tone. The result of this is that music written in each mode has a very distinct sound. Progressions that sound familiar in one mode may sound otherworldly in another mode.

The tonic chord alone sounds different in many modes. In Ionian, Lydian and Mixolydian, the tonic triad is major. In Dorian, Phrygian and Aeolian, the tonic is minor. In Locrian, the tonic is diminished. Because the diminished triad sounds so unstable, Locrian is the most rarely employed mode.

However, since the modes all contain the same set of notes, any or all of them can be used within a single piece without accidentals. A certain mode can be achieved simply by creating a section which resolves to or is based on the tonic of that mode. Again using the white keys of the piano to illustrate, a section resolving to A would be in the A Aeolian mode, while one resolving to C would be in the C Ionian mode.

The modes can also be written by noting their differences from the Ionian, i.e. what sharpened or flattened notes they contain. This approach yields the following (in order of increasing number of flats):

Thus the E Phrygian is an E Ionian (major) scale with flattened second, third, sixth, and seventh degrees. It can be observed that, for a constant tonic, each mode contains the same notes as the previous except for one note being lowered, and that the lowered notes appear in the following order: IV (natural, lowered from IV♯), ♭VII, ♭III, ♭VI, ♭II, ♭V. This is known as the "order of flats", and can be used as an aid for memorizing the modes.

title: Music Theory/Modes


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Music Theory/Finding the Key and Mode of a Piece

Identifying keys
Finding the proper key is a matter of finding the I note, then finding what mode the notes seem to follow. This can be easy or difficult, depending on the piece of music. Some music does not really follow a mode at all, but non-modal key signatures are frowned upon.

The first place to start would be the chord structure. The most important chord is the I chord. This is the chord formed by the first, third, and fifth notes in a mode. This is why a C major chord is called C major, because the C major scale starts with C D E F G. Every mode naturally contains three major chords, three minor chords, and one diminished triad. By "naturally", it is meant that all of the notes in the chord are in the mode's scale. D major is not natural in the key of C because a D major consists of D, F#, and A, and F# does not occur in the C major scale. One major chord can be extended to a dominant seventh chord (in the key of C major, this would be G7), and all of the minor chords can be extended to a minor seventh chord.

Suppose we have a song and have determined it to have these chords: C, F, and G. This is a classic example of a three-chord song, of which the twelve-bar blues is a good example (but there are many other possible three-chord structures). Suppose the C chord occurs often and it is also the first and last chord in the song — it is probably the I chord, because the tendency is to begin on the I chord, move around a bit, and come back ("resolve") to the I chord. C, F, and G happen to be the three major chords that occur naturally in the C major scale. Therefore the chord progression is in C major and it is quite likely that any melody accompanying it is also in C major.

But what if a chord progression contains six major chords? Not all of those can occur naturally in a given mode, since each mode has only three. Does the mode change during the progression? Well, yes and no. Certainly, the key signature won't change with each chord change; it will only change when the piece as a whole is changed to another key, generally when a new chord becomes the I chord.

By the way, in case you forgot, harmonic minor and melodic minor scales use the same key signatures as the natural minor scale.

Another way
There is another way to figure out the key signature, which does not depend on matching the scale exactly. You still have to find the 1 note and write the notes of the scale. Let's say your song uses only five notes: 1 2 4 5 b7. (This is a Japanese scale.) It has a flatted seventh; everything else is the same as in the major scale. What modes have a flattened seventh? Everything except lydian and ionian. The one with the fewest sharps/flats of these is mixolydian. Therefore, this scale fits well into the mixolydian mode, and a piece written in this scale would have the appropriate key signature for the mixolydian mode.

Now let's try a different Japanese scale: 1 2 b3 5 b6. This one is even easier: what modes have a flatted third and a flatted sixth? Aeolian and locrian. But locrian does not have a 5 note, it has a b5 note instead. Therefore this piece uses the key signature for the natural minor scale.

Now a really puzzling one: 1 b3 4 b5 5 b7. What mode has a flatted third, fifth, and seventh? Locrian. But again this scale has the 5 note, which locrian does not! This scale doesn't fit into anything. There are two possibilities: the song is indeed in locrian and the 5 is outside the scale. Notes outside of a scale in a song are rare and usually stand out (sometimes to good effect and sometimes to bad effect, depending somewhat on your musical tastes); if a note is used often it is part of the scale. If you find the 5 note is not part of the scale, then the song is in locrian. However, it turns out this "modified locrian" with the 5 note is very common and it is called the blues scale. (If confronted with this apparent scale, this is the much more likely possibility. Another way to look at this is as the minor pentatonic with a b5. The minor pentatonic is 1 b3 4 5 b7.) The normal way to handle this particular oddball scale is to just interpret it as a major scale. That is, the "F blues" is F major.

More often than not, the bass instrument (typically a cello or electric bass) will play the tonic as the first note of the first measure (excluding pick-ups).

Atonal music
Some music is "atonal", meaning there is no tonal center and therefore no I note. Atonal music has a fairly distinct flavor, and generally does not occur in popular music — even rap music is tonal when it has any musical notes at all. The most well-known atonalists were probably Arnold Schönberg (who, incidentally, abhorred the word "atonal") and, after Schönberg's death, Igor Stravinsky (before Schönberg's death, Stravinsky made many tonal pieces). Atonal music is perhaps the musical equivalent of abstract art, that is, free from the confines of the usual way of things — at the possible cost of an inability to be understood by others because the work does not inspire the same thoughts in them.

What key signature do you use for atonal music? None at all. The very idea of a key implies the presence of a tonal center, which atonal music, by definition, lacks. But be sure that the piece really is atonal before arriving at this conclusion. The twelve-tone technique, which Schoenberg usually used (and Stravinsky used it as well), is almost a dead giveaway that a piece is atonal (but there are some tonal songs that use it).


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General Chemistry/Types of chemical reactions

The general form of a synthesis reaction is A + B → AB. Synthesis reactions "put things together".

Because of the very high reactivities of sodium metal and chlorine gas, this reaction releases a tremendous amount of heat and light energy. Recall that atoms release energy as they become stable, and consider the octet rule when determining why this reaction has such favorable features.

Decomposition Reactions
These are the same number of synthesis reactions, with the format AB → A + B. Decomposition reactions "take things apart". Just as synthesis reactions can only form one product, decomposition reactions can only start with one reactant. Compounds that are unstable decompose quickly without outside assistance. Also they help other atoms to decompose better.

Single Displacement Reactions
Single displacement reaction, also called single replacement, is a reaction in which 2 elements are substituted for another element in a compound. The starting materials are always pure elements, such as a pure zinc metal or hydrogen gas plus an aqueous compound. When a displacement reaction occurs, a new aqueous compound and a different pure element are generated as products. Its format is AB + C → AC + B. Single Diplacement Adding hydrochloric acid to zinc will cause a gas to bubble out:

$$\hbox{Zn}_{(s)} + 2\hbox{HCl}_{(aq)} \to \hbox{ZnCl}_{2(aq)} + \hbox{H}_{2(g)}$$

Double Displacement Reactions
In these reactions, two compounds swap components, in the format AB + CD → AD + CB

This is also called an "exchange". Here are the examples below:

1.) HCl + NaOH > NaCl + H 2 O

Precipitation
A precipitation reaction occurs when an ionic substance comes out of solution and forms an insoluble (or slightly soluble) solid. The solid which comes out of solution is called a precipitate. This can occur when two soluble salts (ionic compounds) are mixed and form an insoluble one—the precipitate.

In the solution, there exists both lead and iodide ions. Because lead iodide is insoluble, they spontaneously crystallise and form the precipitate.

Acid-Base Neutralization
In simple terms, an acid is a substance which can lose a H+ ion (i.e. a proton) and a base is a substance which can accept a proton. When equal amounts of an acid and base react, they neutralize each other, forming species which aren't as acidic or basic.

Acid base reactions often happen in aqueous solution, but they can also occur in the gaseous state. Acids and bases will be discussed in much greater detail in the acids and bases section.

Combustion
Combustion, better known as burning, is the combination of a substance with oxygen. The products are carbon dioxide, water, and possible other waste products. Combustion reactions release large amounts of heat. C3H8, better known as propane, undergoes combustion. The balanced equation is:

$$\hbox{C}_3\hbox{H}_8 + 5\hbox{O}_2 \to 3\hbox{CO}_2 + 4\hbox{H}_2\hbox{O}$$

Combustion is similar to a decomposition reaction, except that oxygen and heat are required for it to occur. If there is not enough oxygen, the reaction may not occur. Sometimes, with limited oxygen, the reaction will occur, but it produces carbon monoxide (CO) or even soot. In that case, it is called incomplete combustion. If the substances being burned contain atoms other than hydrogen and oxygen, then waste products will also form. Coal is burned for heating and energy purposes, and it contains sulfur. As a result, sulfur dioxide is released, which is a pollutant. Coal with lower sulfur content is more desirable, but more expensive, because it will release less of the sulfur-based pollutants.

Organic Reactions
Organic reactions occur between organic molecules (molecules containing carbon and hydrogen). Since there is a virtually unlimited number of organic molecules, the scope of organic reactions is very large. However, many of the characteristics of organic molecules are determined by functional groups—small groups of atoms that react in predictable ways.

Another key concept in organic reactions is Lewis basicity. Parts of organic molecules can be electrophillic (electron-loving) or nucleophillic (nucleus, or positive loving). Nucleophillic regions have an excess of electrons—they act as Lewis bases—whereas electrophillic areas are electron deficient and act as Lewis acids. The nucleophillic and electrophillic regions attract and react with each other. Organic reactions are beyond the scope of this book, and are covered in more detail in Organic Chemistry. However, most organic substances can undergo replacement reactions and combustion reactions, as you have already learned.

Redox
Redox is an abbreviation of reduction/oxidation reactions. This is exactly what happens in a redox reaction, one species is reduced and another is oxidized. Reduction involves a gain of electrons and oxidation involves a loss, so a redox reaction is one in which electrons are transferred between species. Reactions where something is "burnt" (burning means being oxidised) are examples of redox reactions, however, oxidation reactions also occur in solution, which is very useful and forms the basis of electrochemistry.

Redox reactions are often written as two half-reactions showing the reduction and oxidation processes separately. These half-reactions are balanced (by multiplying each by a coefficient) and added together to form the full equation. When magnesium is burnt in oxygen, it loses electrons (it is oxidised). Conversely, the oxygen gains electrons from the magnesium (it is reduced).

$$\begin{matrix} \hbox{Mg} &\to& \hbox{Mg}^{2+} + 2e^- & \times 2 \\ \hbox{O}_2 + 4e^- &\to& 2\hbox{O}^{2-} & \times 1 \\ 2\hbox{Mg} + \hbox{O}_2 + 4e^- &\to& 2\hbox{MgO} + 4e^- & \ \\ \end{matrix}$$

Redox reactions will be discussed in greater detail in the redox section.


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Cookbook:New England Cuisine

| North America | United States

New England cuisine is a type of American cuisine found in the north east United States. It is characterized by extensive use of seafood and dairy products and often involves either baking or slow cooking vegetables with a thickened broth.

Traditional New England dinners sometimes include side dishes of cottage cheese, boiled/or blanched green beans as well as soup or salad.

 * Recipes

 * Boston Baked Beans
 * Chowder
 * Lobster Thermidor
 * Tomato Pizza
 * Succotash

title: Cookbook:New England Cuisine


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Cookbook talk:New England Cuisine

This module uses text adapted from the Wikipedia article New England cuisine. The page history at the time the text was copied is included below.

* (cur) (last). . 15:32, 29 Apr 2004. . Maximus Rex (bold title) * (cur) (last). . 14:11, 10 Jan 2004. . WhisperToMe * (cur) (last). . 20:50, 14 Dec 2003. . Bcorr (rm Springfield Meatloaf ; add stub note) * (cur) (last). . 08:50, 3 Aug 2003. . 24.62.131.43   * (cur) (last). . 10:53, 9 Mar 2003. . Fwappler (Meatloaf -- Bart Simpson's most hated of all Loafs.) * (cur) (last). . 04:37, 4 Jun 2002. . 163.195.240.14   * (cur) (last). . m 08:51, 25 Feb 2002. . Conversion script (Automated conversion) * (cur) (last). . m 16:47, 24 Dec 2001. . Damian Yerrick (spell check) * (cur) (last). . 15:21, 24 Dec 2001. . 24.93.53.xxx

title: Cookbook talk:New England Cuisine


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Cookbook:Chowder

| US Cuisine | New England cuisine | Southern Cuisine | Soup

Chowder is any of a variety of soups, most of them thick and made with potatoes. To some Americans, it means clam chowder, made with cream or milk as New England Clam Chowder, or with tomato as Manhattan Clam Chowder. Corn Chowder is a thick soup filled with whole corn (maize) kernels. Chowder is often commonly associated with the New England region of the United States.

title: Cookbook:Chowder


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Cookbook talk:Chowder

This module uses text adapted from the Wikipedia article Chowder. The page history at the time the text was first adapted is included below.

* (cur) (last). . 16:17, 18 Dec 2003. . Fwappler (Bart Simpson's most to_loath:[[Participle|hated]] kind of Loafs) * (cur) (last). . m 13:46, 7 Sep 2003. . Heron (wikified) * (cur) (last). . m 13:43, 7 Sep 2003. . Heron (refers to -> is) * (cur) (last). . 08:51, 3 Aug 2003. . 24.62.131.43   * (cur) (last). . 22:20, 27 Mar 2002. . Vicki Rosenzweig (added some actual text before yet another Household Cyclopedia upload; *sigh*) * (cur) (last). . m 21:18, 27 Mar 2002. . 62.98.249.56

title: Cookbook talk:Chowder


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Cookbook:Cuisine of California

| North America | United States

The Cuisine of California covers a wide range of styles and recipes. A distinct subdivision, known as California Cuisine, is a gourmet food movement which, while originating in California, is now influential worldwide. This cookbook is primarily focused on the broader subject. Recipes associated with California Cuisine are indicated with CC.

Recipes

 * Au Jus Sandwich (early California restaurant creation)
 * Brown Rice with Ground Turkey (California health food tradition)
 * Burrito (Mission variety created in San Francisco)
 * Caesar Salad (early California restaurant creation)
 * California Fusion Peach Salsa (CC)
 * California Curry Chicken (modeled after the dish in California Indian restaurants, which may be different from the native Indian dish)
 * Cioppino (early California restaurant creation)
 * Fred Steak Marinade (recreation of a marinated steak from a California butcher)
 * French Dressing, also known as Catalina Dressing, from Los Angeles
 * Garlic Pork Chops with Black Mushrooms (CC)
 * Louis Dressing (early California restaurant creation)
 * Rosemary Grilled Salmon Steaks (CC)
 * San Francisco style Scallop Ceviche (CC)
 * Tempura Baked Halibut with Cilantro Aioli (CC)
 * Teriyaki Grilled Salmon Steaks (CC)
 * Thousand Island Dressing
 * Tetrazzini (a creation from San Francisco during the early 20th century in honor of the opera singer Luisa Tetrazzini) (CC)

title: Cookbook:Cuisine of California


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Cookbook talk:Cuisine of California

This module uses test adapted from the Wikipedia article Cuisine of California. The page history at the time the text was first adapted is included below.

* (cur) (last). . m 00:57, 28 Apr 2004. . Sfdan (em dashes, sp) * (cur) (last). . 17:15, 27 Apr 2004. . Gentgeen (+ Puck) * (cur) (last). . 04:12, 26 Feb 2004. . Sfdan * (cur) (last). . 20:20, 25 Jan 2004. . Cody666 * (cur) (last). . 14:09, 10 Jan 2004. . WhisperToMe * (cur) (last). . m 20:04, 20 Nov 2003. . Jengod * (cur) (last). . 00:45, 19 Nov 2003. . Seglea (note on Alice Waters and Chez Panisse) * (cur) (last). . m 02:25, 9 Nov 2003. . Jengod (link fusion) * (cur) (last). . 14:12, 16 Oct 2003. . 12.46.6.70 (intial article)

title: Cookbook talk:Cuisine of California


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General Chemistry/Covalent bonds

Covalent bonds create molecules, which can be represented by a molecular formula. For chemicals such as a basic sugar (C6H12O6), the ratios of atoms have a common multiple, and thus the empirical formula is CH2O. Note that a molecule with a certain empirical formula is not necessarily the same as one with the same molecular formula.

Formation of Covalent Bonds
Covalent bonds form between two atoms which have incomplete octets — that is, their outermost shells have fewer than eight electrons. They can share their electrons in a covalent bond. The simplest example is water (H2O). Oxygen has six valence electrons (and needs eight) and the hydrogens have one electron each (and need two). The oxygen shares two of its electrons with the hydrogens, and the hydrogens share their electrons with the oxygen. The result is a covalent bond between the oxygen and each hydrogen. The oxygen has a complete octet and the hydrogens have the two electrons they each need.

When atoms move closer, their orbitals change shape, letting off energy. However, there is a limit to how close the atoms get to each other—too close, and the nuclei repel each other.

One way to think of this is a ball rolling down into a valley. It will settle at the lowest point. As a result of this potential energy "valley", there is a specific bond length for each type of bond. Also, there is a specific amount of energy, measured in kilojoules per mole (kJ/mol) that is required to break the bonds in one mole of the substance. Stronger bonds have a shorter bond length and a greater bond energy.

The Valence Bond Model
One useful model of covalent bonding is called the Valence Bond model. It states that covalent bonds form when atoms share electrons with each other in order to complete their valence (outer) electron shells. They are mainly formed between non-metals.

An example of a covalently bonded substance is hydrogen gas (H2). A hydrogen atom on its own has one electron—it needs two to complete its valence shell. When two hydrogen atoms bond, each one shares its electron with the other so that the electrons move about both atoms instead of just one. Both atoms now have access to two electrons: they become a stable H2 molecule joined by a single covalent bond.

Double and Triple Bonds
Covalent bonds can also form between other non-metals, for example chlorine. A chlorine atom has 7 electrons in its valence shell—it needs 8 to complete it. Two chlorine atoms can share 1 electron each to form a single covalent bond. They become a Cl2 molecule.

Oxygen can also form covalent bonds, however, it needs a further 2 electrons to complete its valence shell (it has 6). Two oxygen atoms must share 2 electrons each to complete each other's shells, making a total of 4 shared electrons. Because twice as many electrons are shared, this is called a 'double covalent bond'. Double bonds are much stronger than single bonds, so the bond length is shorter and the bond energy is higher.

Furthermore,, nitrogen has 5 valence electrons (it needs a further 3). Two nitrogen atoms can share 3 electrons each to make a N2 molecule joined by a 'triple covalent bond'. Triple bonds are stronger than double bonds. They have the shortest bond lengths and highest bond energies.

Electron Sharing and Orbitals
Carbon, contrary to the trend, does not share four electrons to make a quadruple bond. The reason for this is that the fourth pair of electrons in carbon cannot physically move close enough to be shared. The valence bond model explains this by considering the orbitals involved.

Recall that electrons orbit the nucleus within a cloud of electron density (orbitals). The valence bond model works on the principle that orbitals on different atoms must overlap to form a bond. There are several different ways that the orbitals can overlap, forming several distinct kinds of covalent bonds.

The Sigma Bond
The first and simplest kind of overlap is when two s orbitals come together. It is called a sigma bond (sigma, or σ, is the Greek equivalent of 's'). Sigma bonds can also form between two p orbitals that lie pointing towards each other. Whenever you see a single covalent bond, it exists as a sigma bond. When two atoms are joined by a sigma bond, they are held close to each other, but they are free to rotate like beads on a string.

The Pi Bond
The second, and equally important kind of overlap is between two parallel p orbitals. Instead of overlapping head-to-head (as in the sigma bond), they join side-to-side, forming two areas of electron density above and below the molecule. This type of overlap is referred to as a pi (π, from the Greek equivalent of p) bond. Whenever you see a double or triple covalent bond, it exists as one sigma bond and one or two pi bonds. Due to the side-by-side overlap of a pi bond, there is no way the atoms can twist around each other as in a sigma bond. Pi bonds give the molecule a rigid shape.

Pi bonds are weaker than sigma bonds since there is less overlap. Thus, two single bonds are stronger than a double bond, and more energy is needed to break two single bonds than a single double bond.

Hybridization
Consider a molecule of methane: a carbon atom attached to four hydrogen atoms. Each atom is satisfying the octet rule, and each bond is a single covalent bond.

Now look at the electron configuration of carbon: 1s22s22p2. In its valence shell, it has two s electrons and two p electrons. It would not be possible for the four electrons to make equal bonds with the four hydrogen atoms (each of which has one s electron). We know, by measuring bond length and bond energy, that the four bonds in methane are equal, yet carbon has electrons in two different orbitals, which should overlap with the hydrogen 1s orbital in different ways.

To solve the problem, hybridization occurs. Instead of a s orbital and three p orbital, the orbitals mix, to form four orbitals, each with 25% s character and 75% p character. These hybrid orbitals are called sp3 orbitals, and they are identical. Observe:

$$C\quad  \frac{\uparrow\downarrow}{1s}\;\;   \frac{\uparrow\downarrow}{2s}\;   \frac{\uparrow\,}{2p_x}\;   \frac{\uparrow\,}{2p_y}\;   \frac{\,\,}{2p_z}$$

$$C^{*}\quad \frac{\uparrow\downarrow}{1s}\;\;  \frac{\uparrow\,}{sp^3} \frac{\uparrow\,}{sp^3} \frac{\uparrow\,}{sp^3} \frac{\uparrow\,}{sp^3}$$

Now these orbitals can overlap with hydrogen 1s orbitals to form four equal bonds. Hybridization may involve d orbitals in the atoms that have them, allowing up to a sp3d2 hybridization.

title: General Chemistry/Covalent bonds


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Trigonometry/Inverse Trigonometric Functions

The Basic Idea
In the equation
 * $$y=\sin(x)$$

if we are given $$x$$ we can work out $$y$$.

If we are given $$y$$, can we work out $$x$$ ?

Look at the graph of $$\sin(x)$$ and you will see that for $$y>1$$ or $$y<-1$$ there aren't any answers at all, whilst for other values of $$y$$ there are infinitely many answers.

If
 * $$y=\sin(x)$$

we write the inverse of $$\sin$$ as follows
 * $$x=\sin^{-1}(y)$$

Notice the strange notation. It's just a convention, and does not really fit in well with the convention of $$\sin^2(x)$$ meaning $$\sin(x)^2$$. However, we are stuck with this notation. It is so widely used and so familiar in mathematical work that in practice it does not cause confusion. On many calculators the alternative notation $$\arcsin$$ is used.

A calculator will only give one answer (or error) for $$\sin^{-1}(y)$$. You can get some of the other answers by adding or subtracting multiples of 360°. In a later section we spell out the conventions as to which answer is given by $$\sin^{-1}(y)$$.

arcsin
A common notation used for the inverse functions is the "arcfunction" notation, prefixing the function name by "arc" or sometimes just "a".
 * $$\sin^{-1}(x)=\arcsin(x)=\mbox{asin}(x)$$ ,
 * $$\cos^{-1}(x)=\arccos(x)=\mbox{acos}(x)$$, and
 * $$\tan^{-1}(x)=\arctan(x)=\mbox{atan}(x)$$.

The arcfunctions might perhaps be so named because of the relationship between radian measure of angles and arclength--the arcfunctions yield arc lengths on a unit circle.

The Inverse Functions, Domain and Range
The inverse of sine or cosine for some values has multiple answers and some values does not exist at all. We'd like it if the inverse were a function, but according to the mathematical definition of a function it is not:

 * A function is something that given one value always gives back a unique value as its 'answer'.

$$\sin(x)$$ is a function because given any x it gives back some value. There is not really a function that is an inverse for $$\sin(x)$$ because, for example, $$\sin(20^\circ)$$ and $$\sin(160^\circ)$$ have the same value. The inverse 'function' does not know whether to go back to 20° or 160°.

To deal with this we need some more mathematical language. We have mathematical terminology for what a function operates on and where its values end up. A function like $$\sqrt{x}$$ needs to be accompanied by some agreement as to what values it can operate on and where they end up. By convention $$\sqrt{25}=5$$, though $$x=-5$$ is also a valid solution to $$x^2=25$$. So how do we describe this kind of thing?

 * The domain of a function is the set of values which it is defined on.

The function $$\frac{1}{x}$$ is defined on all values of x except for 0. Its domain is the real numbers excluding zero.

The factorial function, operates on the positive whole numbers. As a function f - $$f(1)=1\ ,\ f(2)=2\ ,\ f(3)=6\ ,\ f(4)=24\dots$$. The factorial function is usually written by writing an exclamation point after a number. So, 3 factorial is usually written as 3! and it is $$3\times 2\times 1=6$$. 4 factorial is written as 4! and it is $$4\times 3\times 2\times 1=24$$.

The domain of the factorial function is the positive whole numbers.

 * The range of a function is the set of values which it can take. The range will depend on the domain too.

Consider the function
 * $$f(x)=x^2$$

If we use ordinary numbers for x like 37.2 or -1001.56 we always find $$f(x)$$ is a positive number (or zero). The range of $$f(x)$$ is the numbers greater than or equal to zero.

Consider the function
 * $$f(x)=2x$$

If we choose the domain of $$f(x)$$ to be the numbers greater than or equal to 1, then the range of $$f(x)$$ is the numbers greater than or equal to two.

More Notation

 * The integers are whole numbers like 1,2,3,4 and also include 0, -1, -2,-3... A symbol we use to indicate the integers is $$\Z$$ . The statement $$x\in\Z$$ means exactly the same thing as x is an integer.

 * The reals include all the integers, and also fractions, and also other numbers like pi, and square root of 2. The reals 'fill in the gaps' between the integers. You'll get a better definition of the reals in a later book. A symbol we use to indicate the reals is $$\R$$ . The statement $$x\in\R$$ means exactly the same thing as x is a real number.

 * A range of numbers in the reals can often be written using interval notation. Here is an example for numbers greater than or equal to zero and less than one: [0,1). The square and round brackets have special meaning. The square bracket means the number is included. A round bracket means the number is excluded.

 * The notation (1.3,100.7] means all numbers between 1.3 and 100.7, including 100.7 but excluding 1.3.
 * The notation [-59.1,12.5] means all numbers between -59.1 and 12.5, including -59.1 and including 12.5.
 * The notation (0,71.2) means all numbers between 0 and 71.2, excluding 0 and excluding 71.2.

 * Function composition is applying one function after another. If we have two functions f and g, we write the composite function, applied to x as: $$f\circ g(x)$$ . This means first apply g to x, then apply f to that result. We can regard $$f\circ g$$ as a new function in its own right.

 * An inverse to a function $$f$$ is written $$f^{-1}$$ . If $$f$$ is the function that adds 12 to a number, then $$f^{-1}$$ is the function that subtracts 12 from a number.

Inverses to Trig functions
Some textbooks 'solve' the problem of inverses for trig functions by defining new functions $$\mbox{Sin}(x)$$, $$\mbox{Cos}(x)$$ , and $$\mbox{Tan}(x)$$ (all with initial capitals) to equal the original functions but with restricted domain.

With suitably restricted domain the functions $$\mbox{Sin}(x)$$, $$\mbox{Cos}(x)$$ , and $$\mbox{Tan}(x)$$ (all with initial capitals) do have inverses which are functions too.

The restrictions to allow the inverses to be functions are standard. Here (and for the rest of this page) we are using radians to measure angles rather than degrees:
 * $$\mbox{Sin}(x)$$ has domain $$\left[-\tfrac{\pi}{2},\tfrac{\pi}{2}\right]$$

 * $$\mbox{Cos}(x)$$ has domain $$[0,\pi]$$ ; and

 * $$\mbox{Tan}(x)$$ has domain $$\left(-\tfrac{\pi}{2},\tfrac{\pi}{2}\right)$$

For each function, the restricted domain includes first-quadrant angles as well as an adjacent quadrant.

Inverses, Really?
It is important to note that because of these restricted domains, the inverse trigonometric functions do not necessarily behave as one might expect an inverse function to behave. While
 * $$\mbox{Sin}^{-1}\left(\sin\left(\tfrac{\pi}{6}\right)\right)=\mbox{Sin}^{-1}\left(\tfrac{1}{2}\right)=\tfrac{\pi}{6}$$ (following the expected $$\mbox{Sin}^{-1}\big(\sin(x)\big)=x$$),
 * $$\mbox{Sin}^{-1}\left(\sin\left(\tfrac{5\pi}{6}\right)\right)=\mbox{Sin}^{-1}\left(\tfrac{1}{2}\right)=\tfrac{\pi}{6}$$.

For the inverse trigonometric functions, $$f^{-1}\circ f(x)=x$$ only when $$x$$ is in the range of the inverse function.

The other direction, however: $$f\circ f^{-1}(x)=x$$ for all $$x$$ to which we can apply the inverse function.

The Inverse Relations
'For completeness', here are definitions of the inverse trigonometric relations based on the inverse trigonometric functions. This section is really mostly about using mathematical notation to express how adding multiples of 360o to an angle gives us another solution for the inverse. Because we are working in radians we're adding multiples of two pi. Some more notation being used here:
 * Curly braces like so {} mean the 'set of', i.e. the set of whatever is inside them.
 * The symbol $$\cup$$ is read as union. The union of two sets is everything that is in either of them.

 * $$\sin^{-1}(x)=\left\{\mbox{Sin}^{-1}(x)+2\pi k\big|k\in\Z\right\}\cup\left\{\pi-\mbox{Sin}^{-1}(x)+2\pi k\big|k\in\Z\right\}$$ (the sine function has period $$2\pi$$, but within any given period may have two solutions and $$\sin(x)=\sin(\pi-x)$$)
 * $$\cos^{-1}(x)=\left\{\pm\mbox{Cos}^{-1}(x)+2\pi k\big|k\in\Z\right\}$$ (the cosine function has period $$2\pi$$, but within any given period may have two solutions and cosine is even: $$\cos(x)=\cos(-x)$$)
 * $$\tan^{-1}(x)=\left\{\mbox{Tan}^{-1}(x)+\pi k\big|k\in\Z\right\}$$ (the tangent function has period $$\pi$$ and is one-to-one within any given period)


text:
Music Theory/Introduction

What is music theory?
Music theory is the study of music; and while the term is often applied to the Western musical tradition (more on that later), there are also music theories in other traditions around the world.

It is of interest to the reader to know that music theory emerged after the actual production of music. There were people making music long before we had ideas of what a major third was, and there were groups singing tribal songs long before we got the idea of a "downbeat". Although these ideas were often practiced before they were understood, to have a knowledge of what they are and how they work reduces their difficulty and increases their potential and flexibility.

What is music?
Music can be many things, and while the subject of what constitutes music has been long debated and argued, we will not be spending considerable time on its definition. Like all art, music is highly subjective and traditional. It is hard to make sense of music from an alien culture or tradition. This book only deals with a subset of music; a very large subset though. We look at the Western Tradition of music as it has evolved from the ancient European civilizations with influences from Africa, the Middle East and Asia. We will also look primarily at written music, rather than music which is only ever performed, but we realize that music notation can almost never capture everything that makes a piece. Sheet music is a limitation that we live with. You will notice the words "sometimes", "usually", "probably", and other similar terms used frequently as music is highly subjective and many "rules" are broken.

Music usually has five basic aspects: rhythm, melody, harmony, dynamics, and timbre.

 * Rhythm : Concerns note length, speed and stress — the "time" aspect.
 * Melody : Concerns a series of notes — the "horizontal" aspect.
 * Harmony : Concerns notes played at once — the "vertical" aspect.
 * Dynamics: Concerns the volume of notes  — the "volume" aspect.
 * Timbre : Concerns the physical sound of notes — the "texture" aspect.

Although the definition presented above may be valid to some, let's not forget the highly subjective nature of "music." That which is "music" to some is "noise" to others. Although we have many definitions, all definitions have their critics. Here is another definition of "music" that may be totally valid. "Music is a set of 'organized sounds' created from a human entity or human-created machinery."

One more definition of music may simply be the "process in finding the solution to the problem of creating an expression of emotion or disdain," which is more analogous towards mathematics. Despite the fact we don't have a universal (intracultural) definition of music we can all agree on, we can analyze music using music theory. Before we dive into music theory, we must first understand the preliminaries.

title: Music Theory/Introduction


text:
Organic Chemistry/Introduction to reactions/Alkyne hydration

Alkynes readily combine with water in the presence of acid (usually sulfuric acid) and mercury(II) salts (usually the sulfate is used) to form carbonyl compounds, in a process known as Kucherov's reaction. In the case of acetylene (ethyne) the product is acetaldehyde (ethanal), while other alkynes form ketones. Terminal alkynes reliably form methyl ketones and symmetric internal alkynes give single ketone products, but mixtures of ketones may form from unsymmetrical internal alkynes.

The intermediate product is an enol (an alkene with a hydroxyl group attached to a doubly bonded carbon), which then transforms to its keto tautomer through keto-enol tautomerisation.

Mechanism
Alkene hydration only requires acid catalysis and proceeds through the most stable carbocation available (Markonikov selectivity), but alkynes are less basic (less easily protonated), as they would generate less stable vinyl cations upon protonation. Both H+ and Hg2+ are catalysts in the hydration of alkynes. The Hg2+ additive presumably adds to the alkyne to form a more stable vinyl cation (β-stabilized) than would be afforded by protonation. As with Markovnikov selectivity in the case of alkenes, the most stable vinyl cation (usually the most highly substituted) is preferred.

Addition to either end of a symmetric alkyne (internal or acetylene/ethyne) gives the same cation and only one carbonyl product is formed, but addition to unsymmetrical alkynes gives two possible cations, and two products are possible. Terminal alkynes selectively produce a methyl ketone owing to a strong preference for the most highly substituted vinyl cation, but unsymmetrical internal alkynes can produce two different vinyl cations, whose stabilities may be similar if the alkyne's substituents are electronically and sterically similar, and therefore two different ketone products would be obtained in a mixture.

After the addition of water and O-deprotonation to an α-mercurated enol, the acid can effect an electrophilic substitution of the Hg2+ by α-C-protonation (ipso-protonation) and elimination of Hg2+ (demercuration), a process akin to electrophilic aromatic substitution (SEAr).[example]. Both routes result in an enol that (usually) tautomerizes to the (usually) more stable keto form, again an acid-catalyzed process.

The α-mercurated enol may instead tautomerize to the (usually more stable) keto form in an acid-catalyzed step involving α-C-protonation and O-deprotonation, but this is mechanistically unproductive; this must be reversed by reprotonation of the carbonyl O to trigger the fragmentation and loss of Hg2+. Both routes start with α-C-protonation; whether this is followed by immediate demercuration or by O-deprotonation, O-reprotonation and demercuration (the "tautomer detour") is indistinguishable. The more direct C-protonation-demercuration route is the most step-economical and suffices to explain the alkyne hydration process. Although both enol and keto forms of the α-mercurated ketone likely co-exist, only the protonated version has mechanistic significance.

Note

 * A specific SEAr analogy to the H+-Hg2+ exchange involved in alkyne hydration is the acid-promoted demercuration of arylmercury(II) salts, triggered by ipso-protonation, while the mercuration of arenes, a substitution of H+ by Hg2+, would be an example of the reverse reaction.


text:
Perl Programming/Operators

= Introduction =

Perl's set of operators borrows extensively from the C programming language. Perl expands on this by infusing new operators for string functions (.=, x, eq, ne, etc.). C by contrast delegates its subset of Perl functionality to a library strings.h, and ctype.h, and includes no such functionality by default compilation. Perl also includes a highly flexible Regex engine inspired by Sed with improvements to standard POSIX regexes, most notably the support of Unicode.

= The operators =

Arithmetic
Most arithmetic operators are binary operators; this means they take two arguments. Unary operators only take one argument. Arithmetic operators are very simple and often transparent.

Binary
All the basic arithmetic operators, addition (+), subtraction (-), multiplication (*), and division (/), and the modulus operator <tt>%</tt> exist. Modulus returns the remainder of a division (<tt>/</tt>) operation.

The exponentiation operator is <tt>**</tt>. It allows you to raise one value to the power of another. If you raise to a fraction you will get the root of the number. In this example the second result when raised to the power of 2 should return 2 (<tt>(2**(1/2))**2 = 2</tt>).

The function <tt>sqrt</tt> is provided for finding a square root. Other fractional powers (i.e., (1/5), (2/13), (7/5), and similar) are suitably found using the <tt>**</tt> operator.

Unary
The auto-decrement (<tt>--</tt>), and auto-increment (<tt>++</tt>) operators are unary operators. They alter the scalar variable they operate on by one logical unit. On numbers, they add or subtract one. On letters and strings, only the auto-increment shift one up in the alphabet, with the added ability to roll-over. Operators that come in post- and pre- varieties can be used two ways. The first way returns the value of the variable before it was altered, and the second way returns the value of the variable after it was altered.

Assignment
The basic assignment operator is <tt>=</tt> that sets the value on the left side to be equal to the value on the right side. It also returns the value. Thus you can do things like <tt>$a = 5 + ($b = 6)</tt>, which will set <tt>$b</tt> to a value of 6 and <tt>$a</tt> to a value of 11 (5 + 6). Why you would want to do this is another question.

The assignment update operators from C, <tt>+=</tt>, <tt>-=</tt>, etc. work in perl. Perl expands on this basic idea to encompass most of the binary operators in perl.

Comparison
Perl uses different operators to compare numbers and strings. This is done, because in most cases, Perl will happily stringify numbers and numify strings. In most cases this helps, and is consistent with Perl's DWIM Do-What-I-Mean theme. Unfortunately, one place this often does not help, is comparison.

Logical
Perl has two sets of logical operators, just like the comparison operators, however not for the same reason.

The first set (sometimes referred to as the C-style logical operators, because they are borrowed from C) is <tt>&&</tt>, <tt>||</tt>, and <tt>!</tt>. They mean logical AND, OR, and NOT respectively. The second set is <tt>and</tt>, <tt>or</tt>, and <tt>not</tt>.

The only difference between these two sets is the precedence they take (See Precedence). The symbolic operators take a much higher precedence than the textual.

Conditionals
Most of the time, you will be using logical operators in conditionals.

In this case, you could safely substitute <tt>and</tt> for <tt>&&</tt> and the conditional would still work as expected. However, this is not always the case.

This, however, is completely different.

Most people prefer to use C-style logical operators and use brackets to enforce clarity rather than using a combination of textual and C-style operators (when possible), which can be very confusing at times.

Partial evaluation
Partial evaluation (or "short circuiting") is the property of logical operators that the second expression is only evaluated, if it needs to be.

This also works with logical OR statements. If the first expression evaluates as true, the second is never evaluated, because the conditional is automatically true.

This becomes useful in a case like this:

Here, if the <tt>foo</tt> subroutine returns false, "foo failed\n" is printed. However, if it returns true, "foo failed\n" is not printed, because the second expression (<tt>print "foo failed\n"</tt>) does not need to be evaluated.

Bitwise
These operators perform the same operation as the logical operators, but instead of being performed on the true/false value of the entire expressions, it is done on the individual respective bits of their values.

 * <tt>&</tt> (bitwise AND)
 * <tt>|</tt> (bitwise OR)
 * <tt>^</tt> (bitwise XOR)
 * <tt>~</tt> (bitwise NOT)

The left and right shift operators move the bits of the left operand (e.g. $a in the case of $a << $b) left or right a number of times equal to the right operand ($b). Each move to the right or left effectively halves or doubles the number, except where bits are shifted off the left or right sides. For example, $number << 3 returns $number multiplied by 8 (2**3).

 * <tt><<</tt> (left shift)
 * <tt>>></tt> (right shift)

String
The string concatenation operator is <tt>.</tt>, not <tt>+</tt> that some other languages use.

There is a repeat operator for strings (<tt>x</tt>) that repeats a string a given number of times.

Comparing strings
To compare strings, use <tt>eq</tt> and <tt>ne</tt> instead of <tt>==</tt> or <tt>!=</tt> respectively. You can also look for a substring with <tt>substr</tt>, or pattern-match with regular expressions.

File Test

 * See Perl Programming/Function Reference

Other
The range operator (..) returns a list of items in the range between two items; the items can be characters or numbers. The type of character is determined by the first operand; the code: print ('A'..'Z'); print ('a'..'z'); print ('A'..'z'); print (1..'a'); print (1..20); print ('&'..'!'); print (10..-10); print "$_\n" foreach (1..10); Outputs (Newlines added for readability): ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz ABCDEFGHIJKLMNOPQRSTUVWXYZ

1234567891011121314151617181920 &

1 2 3 4 5 6 7 8 9 10 Note that the case is defined by the first operand, and that the <tt>1..'a'</tt> and <tt>(10..-10)</tt> operations return empty list.

Precedence
Precedence is a concept that will be familiar to anyone who has studied algebra or coded in C/C++. Each operator has its place in a hierarchy of operators, and are executed in order. The precedence of perl operators is strict and should be overridden with parentheses, both when you are knowingly going against precedence and when you aren't sure of the order of precedence. For a complete listing of the order, check perlop.

The smart match operator
The smart match operator <tt></tt> is new in perl 5.10. To use it, you'll need to explicitly say that you're writing code for perl 5.10 or newer. Its opposite operator <tt>ǃ~</tt> matches smartly an inequality:

The smart match operator is versatile and fast (often faster than the equivalent comparison without <tt>ǃ~</tt> or <tt></tt>). See smart matching in detail for the comparisons it can do. <tt></tt> is also used in the <tt>given/when</tt> switch statement new in 5.10, which will be covered elsewhere.

The doubledollar
A variable, previously referenced with the reference operator can be dereferenced by using a doubledollar symbol prefix:

The arrow operator
If the left hand operand of the arrow operator is an array or hash reference, or a subroutine that produces one, the arrow operator produces a look up of the element or hash:

Perl/演算子

title: Perl Programming/Operators


text:
Study Skills

Table of Contents

 * /Introduction/
 * /Managing Your Time/
 * /Taking Notes/
 * /Reading/
 * /Listening To Lectures/
 * /Memorizing/
 * /Having Discussions/
 * /Tests/
 * /Writing Term Papers/
 * /Alternative Techniques/
 * /Ideas/

title: Study Skills


text:
User talk:Moe45673~enwikibooks

Hewwo :)

--Furrykef 02:56, 14 May 2004 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Moe45673. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Moe45673~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:28, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 05:16, 19 April 2015 (UTC)

title: User talk:Moe45673~enwikibooks


text:
Music Theory/Chord Structures

A chord structure, also called a chord progression or harmonic progression, helps indicate where the melody should go.

The purpose of chord structures
It can be argued that many forms of music are organic, while imposing a rigid "structure" can be hampering. This is a legitimate concern. However, consider that rigid chord structures occur most often in improvisational music (especially jazz), which is usually not rigid in itself. Furthermore, many composers do not consider chord structures much when composing, perhaps trying various things out and just going with what works, or maybe simply having an intuitive understanding of the structures involved. Knowledge of chord structures will help you communicate with other musicians, but is not a must for participating in any kind of jam session. Jamming can begin and end anywhere either with or without structure.

Common chord structures
By far the most common chord structures revolve around, or at least contain, the I, IV, and V chords. This is why it is important to know the Roman Numerals for these scale degrees: they pop up a lot! Many songs use only these three chords (and possibly variations of them). The first we will consider is the classic twelve bar blues based on the 'Blue Scale'.

The twelve bar blues
The twelve bar blues, despite its name, pops up in a variety of genres, from jazz to rock. It has been used in many great songs, such as the theme from the Batman television show. Its most basic structure is this:

I I  I  I  IV IV I  I  V7 IV I  I The roman numerals are also used for different songs. e.g E E E E / A A E E / B A E E. This can be used for any chords but you must use the same pattern repeatedly. That is, the first four bars are the I chord, the next two the IV chord, the next two the I chord again, and so on. It begins on the tonic and ends on the tonic, which is common in many progressions. Many chord progressions start at the tonic, move away to somewhere else, only to come back to the tonic. To complicate this, however, twelve bar blues structures sometimes feature a turnaround at the end, meaning the very last bar is a V7 chord, or it has a I chord followed by a V7 chord. Turnarounds usually occur at the end of a verse or some other section in preparation for the next section. Usually the very last bar of a song will not have a turnaround.

In some genres, such as jazz, seventh chords occur more commonly, so the basic twelve-bar blues might become something more like this:

I I   I  I7  IV IV7 I  I7  V7 IV  I7 I

It can also be modified further. For instance, the tenth bar (the last occurrence of IV) might become another V7 chord. This alteration was often used when adapting the twelve-bar blues to rock and roll.

The II-V-I
In jazz, the II-V-I is probably the most common chord progression. As its name indicates, it goes:

IIm7 V7 Imaj7

As always, the exact type of chords can be modified to give a different feeling, such as in this melodic minor, ascending form only, version:

IIm7b5(9) V7alt Imaj7

Note: Only the IIm7b5(9) and V7alt chords are from melodic minor scales.

The Minor II-V-I
Another commonly used chord progression is the minor ii-V-i. One can derive this from the melodic minor scales shown above, while substituting a IminMaj7 for the IMaj7 chord, or by using three modes from one harmonic minor scale, which produces the following chord progression:

IIm7b5(b9) V7b9(b13) IminMaj7(b6)

Applications of II-V-I's
II-V-Is can be chained together, creating complex progressions. Here's an example:

C     Bm7b5 E7   (I     II  V)  Am7    Dm7   G7   (I     II  V)  C      (etc...)   (I     etc..)

An example of complicated progression that can be created this way is the "Coltrane Changes", where the "I" chords move by Major 3rd intervals. Here's a simple example:

Dm7 G7  Cmaj7    (II V I  ) F#m7 B7 Emaj7    (II V I  ) Bbm7 Eb7 Abmaj7  (II V I  ) Dm7 etc... (I etc...)

The way the II-V-I progression works is that first the II chord moves by 4ths upwards, which very often produces interesting results, and then when moving from the V chord to the I chord the 7th of the V chord descends a half step and becomes the 3rd of the I chord.

II-V-I progressions can also be used in other styles, such as classical.

Two-chord structures
Two-chord structures are much simpler than three-chord structures, of course. However, they are harder to work with! It is more difficult to write an interesting piece with fewer chords, therefore the musicians must get the most they can out of them. One example of this can be found in the song "O Superman" by Laurie Anderson.

One-chord structures
One-chord "structures" are uncommon, but they do exist. For instance, Frere Jacques is a one-chord song because it can be played against a single major chord. More contemporary examples are "On the Road Again" by Canned Heat, numerous rap songs, and so on.

title: Music Theory/Chord Structures


text:
Japanese/Software

Open-source Software

 * Tagaini Jisho is a free, open-source Japanese dictionary and kanji lookup tool that is available for Windows, MacOS X and Linux. Features complete stroke order animations; lets you train entries you are studying and follows your progression. Released under the GPLv3.
 * JFC Japanese flashcard program. Can be used to drill user-created wordlists. Complements JWPce well.
 * JFC for Mac OS X Mac version of Japanese flashcard program. It seems quite undeveloped.
 * PyJflash is both a Japanese flashcard viewer and a spreadsheet-like conversion utility and editor supporting various formats for Windows, Linux and Unix-like OSes. (no longer being maintained)
 * Rikaichan, a pop-up Japanese-English/German/French/Russian dictionary extension for Firefox. It's simple to use, all you have to do is just hover the mouse on top of a Japanese word. It even automatically de-inflects verbs and adjectives, which is useful.
 * jMemorize is flash card software that has some Japanese flash cards made already.

Shareware

 * Learn Japanese the fun way | Nihongoup Japanese educational game and reviewing tool.
 * Stackz! Flashcard type program that lets you drill custom wordlists. Good selection of downloadable wordlists.
 * Kanji Sketch Pad Draw kanji with your mouse and get coached on where you went wrong. Built in information on usage and readings. Automatic revision scheduler based on performance.

Commercial Software

 * Coscom Kanji learning software
 * Popup Japanese Dictionary for Windows, a Japanese dictionary for Windows which allows the looking up of words by copying them to the clipboard. The meaning of the word will be displayed in a popup window. Features include lookup history and export to Anki capability.

Open-source Software

 * gjiten, by Botond Botyanszki, is a Japanese/English/kanji dictionary for GNOME that uses Jim Breen's EDICT and KANJIDIC files.
 * JWPce, by Glenn Rosenthal, is a Japanese word processor for Windows, including a Windows CE version, that's released under the GPL. It includes EDICT dictionaries, kanji information, etc.
 * Moji is an extension for Mozilla Firefox that can look up words and kanji while you browse. It's released under the GPL.
 * PAdict, by Lars Grunewaldt, offers EDICT-based dictionary lookup on the Palm OS without additional libraries. It's released under the GPL.

Freeware

 * JED, a dictionary application for Android, includes stroke order, searching by radicals, romaji and different codes and working with clipboard.

Shareware

 * JEDict is a dictionary program that uses EDICT files to look up kanji. It provides readings, definitions, and radicals. The free version can look up kanji in a basic dictionary, but the registered version ($25) supports additional specialized dictionaries. Only available for Mac OS X.
 * NJStar Communicator/Word Processor Text Processor for Windows, gives the ability to write kanji in ani text input, selecting them with different input methods
 * KanjiQuick is a dictionary program with all data from Spahn/Hadamitzky's Japanese-English Kanji Dictionary (has a Japanese-German version too). It comes with a free EDICT reader, a translation and a TTS- (Text To Speech) module. It can be evaluated for free (MS Windows only).

Open-source Software

 * kdrill, by Philip Brown, is an interactive, intuitive kanji learning program, which is highly scalable to the level of the learner.
 * by Filip Kábrt is the hybrid of learning tool and a dictionary for Chinese and Japanese, supports a lot of dictionary formats including EDICT, supports flash cards, works under Windows.
 * kanatest is a flashcard-like program for learning the kana (hiragana, katakana), available for Linux under GPL.
 * JKana test is a Java version of kanatest.

Freeware

 * KanjiGym Light is a free study aid for the Kanji learning system by James W. Heisig. Available in English, German, French and Spanish for Java and Palm OS.
 * Kotoba! is a free multilingual Japanese dictionary for iPhone and iPod touch devices.
 * Project LRNJ is a role-playing game for Linux, Mac OS X, and Windows that teaches hiragana, katakana, kanji, and some English loan-words. The site also includes a "phrase of the day" in Japanese, which expands from normal writing, progressing from including kanji, to pure hiragana, to katakana, to romaji, to a literal translation, to a sentence with correct English grammar. (warning: some of the character combinations being taught are rather unnatural, like ッマ, and the software is not currently being maintained)
 * Sokushuji App for learning Kanji on the iPhone
 * Obenkyo is the App to learn Kanji on Android, with different test types (includes drawing a kanji), errors highlighting

Shareware

 * iKana is a hiragana and katakana study tool for the Mac by ThinkMac Software. It features flash cards, a speed recognition test and a word romanisation test. Only available for Mac OS X.
 * iKanji is a kanji study tool for the Mac by ThinkMac Software. It features flash cards, a kanji meaning test, kanji readings test and kanji stroke order test. It covers all kanji in Japanese school grades 1 to 6 and JLPT levels 1 to 4. Only available for Mac OS X.

Input methods (typing Japanese)

 * For information about Windows and Macintosh operating systems see: the Penn State site on Working with Japanese.
 * For *nix systems, you're probably best off with uim or SCIM. See uim for Wikibooks documentation on the former.

Other
Jim Breen's site also has a comprehensive list of free and non-free software.

title: Japanese/Software


text:
General Chemistry/Basic Chemical Concepts

 * 1) Properties of Matter
 * 2) Atoms and Molecules
 * 3) Nomenclature
 * 4) Calculations
 * 5) Molar Concepts
 * 6) Stoichiometry [[Image:50%.svg]]
 * 7) Gas Stoichiometry
 * 8) Solution Stoichiometry


text:
Music Theory/Chords

''This is a basic introduction to chords. There is also a complete chord reference.''

Chords are the vertical arrangement of notes from a scale. The study of chords is called Harmony. Harmony is concerned with how one or more notes interact, and how they follow each other. Many people define chords as several notes played simultaneously. It must be pointed out that it is not possible to play music of a chordal nature on the flute, trumpet, or a lone human voice, all three being monophonic instruments. Since obviously monophonic instruments cannot play a stacked chord where the notes are sounded simultaneously; the chords are implied. A simpler way of viewing this is that when chord tones are played as an arpeggio on a monophonic instrument the human ear interprets that there is a harmonic structure. We therefore define a chord as the basic element of harmony. To start with we will look at examples of the most basic chord, the triad.

Triads
The triad is a class of chords, specifically three-note chords formed by this formula: 1-3-5 or root, third, fifth. In this example they are constructed of two consecutive thirds.

There are four kinds:

The major is very consonant; the minor is a bit less so but still consonant for most purposes. The augmented is very dissonant and the diminished is extremely dissonant as it contains a tritone (augmented fourth or, in this case, diminished fifth).

The major and minor triads may have their third omitted, although this is uncommon. If the third of a major or minor chord is omitted, the result is a fifth chord, which is often called a power chord when played on an overdriven guitar.

Triads and Inversions
If we look at a C major triad or three-voice chord it is based on combining a root voice (C) with two other voices at slightly different intervals of a third (E, a major third from C and G, a minor third from E). If we compare the key of C major to the C major chord using the names do, re, mi, fa, so, la, ti, to represent the scale degrees 1, 2, 3, 4, 5, 6, 7, the C major chord is constructed from the notes do, mi, and so. This same relationship is true for all major triads in all corresponding major keys.

These three notes (the root, major third and perfect fifth) can be structured or 'voiced', C-E-G, E-G-C or G-C-E. No matter what order the three notes (called voices) are in they still create a C major chord. It does not matter if the voices are the singers in a choir or the instruments of an orchestra, if the notes are all either C, E, or G we simply have a gigantic sounding C chord.

The two consecutive intervals produced by these voicings would be:
 * C E G = major third, minor third (root position),
 * E G C = minor third, perfect fourth (first inversion),
 * G C E = perfect fourth, major third (second inversion).

If the root (C) is on the bottom this voicing is called root position. If the third (E) is on the bottom it is called first inversion. If the fifth (G) is on the bottom this voicing of the triad is called second inversion.

Since there are only three possible voicings of a triad it is relatively easy to hear them in that they are a common feature of the past two centuries of traditional harmonic structures in Western music. The use of the exponentially more complex voicings arising from 4-voice, 5-voice and larger chords is more challenging. Some 4-voice chords are used in traditional, 'classical' and church music but others such as the diminished seventh were strictly forbidden in early sacred music as they contained the tritone interval; the mathematical halfway point in the octave which acquired the name diabolus in musica (the Devil in music) due to its dissonant qualities. Other 4-voice chords were not used in symphonic and 'classical' music until the French Impressionist era and in modern jazz. All triads and 4-voice chords are built within the octave, or eight-note scale which encompasses the do-re-mi-fa-sol-la-ti-do of the major scale, for instance, or the scale steps 1-2-3-4-5-6-7-8; eight being the octave where the pattern starts over again.

All triadic and therefore, common, chords can be constructed the same way : using the 1 3 5 formula. Take the C scale, for instance:

Seventh Chords and More
Seventh chords are triads with another fourth note a seventh from the root; they're characteristic of jazz music and provide more color than a basic triad.

There are several types: * Many people choose not to recognize half-diminished seventh chords, and prefer to call them minor seventh chords with a flat fifth.

These chords have inversions in the same sense that triads do, except seventh chords have three inversions:

 * The root position of C major seventh: C, E, G, B
 * The first inversion of C major seventh: E, G, B, C
 * The second inversion of C major seventh: G, B, C, E
 * The third inversion of C major seventh: B, C, E, G

Sixth Chords
A slightly less dissonant option than a seventh chord would be a sixth chord, with replaces the seventh with a sixth. Only the major sixth is used because a minor sixth would make a dissonant minor second with the fifth; a minor sixth chord would be built with a major sixth despite it not being a minor interval.

Chord Notation
People very often abbreviate chords into just a couple letters and symbols and put them on sheet music or jazz lead sheets.

Some chord symbols on chords with the root C (the C can be replaced with any note): Extensions or alterations are added directly at the end of the chord symbol, often with parentheses: an A dominant seventh flat-nine chord would look like A7♭9 or A7(♭9). For more than one alteration/extension, use a comma between each extension for clarity.

"Slash chords" are chords written with a slash and a note name after it, like E♭Δ7/F. This communicates an E♭ major seventh chord, but with an F played in the bass. While the E♭ is still the root of the chord, there is an F at the bottom for flavor. This is useful if you want to explicitly mark inversions: the first inversion of a C minor triad would look like Cm/E♭.

Analysis Notation
Theorists very often use Roman numerals in the place of scale degrees when they're talking about chords, so that they can talk about chord patterns that aren't specific to any key. Uppercase numerals indicate major (or augmented) chords and lowercase numerals indicate minor (or diminished) chords, like so: Thus, all of the triads in any major scale could be listed simply as I ii iii IV V vi vii°, and all of the triads in any minor scale as I ii° III iv v VI VII.

Like any scale degree number, you can put a sharp or flat behind a symbol to specify a chord with a root outside of the scale, so in D major a ♭VI chord would be a B♭ major triad.

Applying Chords
The easiest way to apply a triad, or indeed any chord, is to pick one on a polyphonic instrument (such as a piano) and play its three notes simultaneously. This is often how chords occur in actual music: an instrument plays all the notes in the chord at the same time. However, there are other possibilities. The simplest is to arpeggiate the chord, that is, to play its notes one at a time in any order, especially in an ascending or descending order. Often melody can be written around the chord, using notes in the chord as well as the diatonic and chromatic passing notes between the chord tones. When this is done, while there is no accompaniment actually playing a chord, the chord is implied.

Other Chords
Some chords are defined by the relation to the key rather than by any inherent characteristics. The Neapolitan chord, for example, expressed as N in analysis notation, is an ordinary major chord, but its root is the lowered supertonic of the corresponding key, so the Neapolitan of C major is a D♭ major chord. Additionally, the Neapolitan is usually found in first inversion. A borrowed chord is one from the parallel major or minor key. In C major, the parallel key is C minor and borrowed chords include E♭ major, B♭ major, and F minor.

title: Music Theory/Chords


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Diagram of covalent chemical bond (hydrogen)

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Talk:Internet Technologies/Search engine

hmmm That looks a bit suspect. Who the hell is searchenginecity@yahoo.com, and why would I want to email them for information? -- Nojer2 12:16, 14 May 2004 (UTC)

 * I've no idea. I don't see how it's helpful so I've removed it. Angela


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Phoenix/Enemy 1

"Enemy 1" is the first enemy you encounter. It appears on levels 1, 2, and 3. It shoots the equivalent of Weapon 1, a 2x2 pixel bullet, straight forward. It has 2 Hit Points.

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User talk:Alfwatt~enwikibooks

This is my user talk page. I can edit it, and imagine that others can see it as well. Check out my websites: iStumbler.net and dotpublic.com.

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