Those stupid aeroplane questions

Everyone who does Spec will know what I'm talking about. "This aeroplane wants to fly from airfield A to airfield B, but there's a wind blowing from x direction at x velocity. What direction should the plane fly in?" I hate these questions for two reasons. 1) They're annoying. 2) I like planes and I abhor their usage in annoying questions. Unfortunately, if you do Spec you'll have no other choice than to encounter and solve them.

Let's have a look at one of these questions- this time using a helicopter, not an aeroplane. Good riddance to helicopters.

A helicopter can fly at 75m/s in still air. The pilot wishes to fly from airport A to a second airport B, 300km due North of A. If i is a unit vector due East and j a unit vector due North find (in the form ai + bj) the velocity vector that the pilot should set and the time the journey will take if
a) there is no wind blowing,
b) there is a wind of (21i + 10j) m/s blowing.

Part a) is easy. Since there is no wind to affect the movement of the helicopter, the helicopter can just fly directly North for 300km (i.e. with a velocity vector of 75j). You can then use distance / speed to get the time required. You do need to be careful in this one- you have to convert m/s into km/h, or you can convert km into m.

75*3.6 = 270 km/h
300/270 = 1.11 hr = 1 hr 7 minutes (nearest minute)

Alternatively:
300*1000 = 300 000 metres
300000/75 = 4000 seconds = 66.7 minutes (1 d. p.) = 1 hr 7 minutes (nearest minute)

Now part B... that's the part I hate simply because it requires more work. Drawing a diagram can help to visualise the situation.

I have to admit that my diagram is a bit misleading (especially because I've only just realised that I wrote "aeroplane" instead of "helicopter" and "airfield" instead of "airport" out of sheer habit). Unless the journey is complete in exactly 1 second or 1 of whatever unit of time you're using, the resultant of the wind and aircraft vectors will not be equal to the distance to the airport or wherever the question's asking you to go to. The resultant is a scalar multiple of the position vector of the second airport relative to the first- that is, it's in the same direction, but shorter or longer.

Now, the question said that the helicopter can go at 75m/s in still air. This means that the magnitude of the aeroplane's velocity should be 75m/s. If we let the helicopter's velocity be xi + yj m/s, then we can create this equation for x and y:

sqrt(x^2 + y^2) = 75 m/s

Now, as you probably already know, when we have 2 variables, we need at least 2 equations to solve for the variables. We can get another equation by adding together the wind and helicopter vectors- as previously mentioned, the resultant should be a scalar multiple of the position vector of the second airport relative to the first. Sounds like a lot of garble, but it's actually not that complex.

21 i + 10 j + xi + yj = k(300 000j) where k is a constant.

Then just equate the i components and the j components separately.

21 + x = 0
therefore x = -21

10 + y = 300000k

Since this example is quite easy we can get a result for x straight away. We can then substitute it into that equation we had earlier to work out what y is.

sqrt((-21)^2 + y^2) = 75 m/s

y = 72 (reject -72 as we can see from the above diagram that y has to be positive)

Therefore, the velocity vector of the plane is -21i + 72j m/s.

To work out resultant velocity, add wind and helicopter velocities together. You can then work out the magnitude from there and use that to complete the question.

21i + 10j - 21i + 72j = 82j

|82j| = 82m/s = 295.2km/h
300/295.2 = 1.02 hours = 61 minutes (nearest minute)

And that's how you solve an aeroplane question!

That was a relatively simple question, though, since the velocity vector is directly north. Here I'll give a very brief explanation on what to do if the velocity vector isn't directly north. I might expand on it later if I can be bothered.

Write out the position vector of the second location relative to the first in component form. For example, if the airport was actually 300km north-east, you could write it as 300 cos 45 i + 300 sin 45 j. It doesn't matter here whether you use the same units (kilometres or metres) as your velocity vectors, since these numbers are going to be cancelled out soon anyway.

When you equate the velocity vectors to a scalar multiple of the position vector, you'll end up with this:

21 i + 10 j + xi + yj = k(300 cos 45 i + 300 sin 45 j)

Equating i and j components:

21 + x = 300 cos 45 k
10 + y = 300 sin 45 k

Divide the first equation by the second and rearrange it to get an equation for x or y.

(21 + x)/(10 + y) = (300 cos 45 k)/(300 sin 45 k)
(21 + x) / (10 + y) = cos 45 / sin 45
21 + x = (cos 45 / sin 45)(10 + y)
x = (cos 45 / sin 45)(10 + y) - 21

You could then substitute this into the sqrt((-21)^2 + y^2) = 75 m/s equation.

By the way, the equation x = (cos 45 / sin 45)(10 + y) - 21 could be further simplified to x = 10 + y - 21 and then x = y - 11 because cos 45 happens to be equal to sin 45. The only reason I left them unsimplified is because you won't always get nice numbers that can simplify down like that.

Applications of electrolysis

I'll have to admit that I keep neglecting all of the applied stuff when I study chemistry. Now it's time for me to partially make up for that with this little post on the applications of electrolysis.

No diagrams yet, sorry. If you don't know what an electrolytic cell looks like, check out my post on electrolysis.

All right. Let's get down to business.

Electrorefining, also known as electrolytic refining, is the refining of an impure substance using electrolysis (as can probably be inferred by the name). At the anode, you have the metal to be refined, while at the cathode you have a small piece of very pure metal.

The way that electrorefining works is that, at the anode, electrons are removed so that the metal and its impurities become metal ions and dissolve into the electrolyte. At the cathode, only the ions of the metal that you want refined become metal again. All other ions remain in the electrolyte solution, though I think some might come out of solution and form a sort of "anode mud" at the bottom- possibly less reactive substances like gold, silver and platinum. Could someone please clear this up for me?

Electrowinning, or electroextraction, is the process of extracting metal from an electrolyte solution. (Sometimes this is done after electrorefining, to get all of the impurities dissolved in the electrolyte solution which could consist of metals such as zinc and nickel.) The metal ions are reduced at the cathode to become metals again.

Anodisation is a way of coating a substance such as aluminium with an oxide coating in order to protect it. In anodisation, the metal to be anodised is the anode (hence "anodisation"). The electrolyte is a solution such that water is the substance being oxidised at the anode to produce oxygen.

That's it from me... for now. Maybe I should study Spec later... stuff that, I'll let myself relax first.

Colligative properties of solutions

I was just doing a practise test (the 2011 Chemistry 2AB exam, which you can find online) when it occurred to me that I know nothing about this term called "colligative properties of solutions..." so I looked it up!

It turns out that "colligative properties" are all based on how many particles of solute are dissolved in the solution. It doesn't matter what the particles are, just how many of them you have.

The number of particles in a solution affect three colligative properties: vapour pressure, melting temperature and boiling temperature. How much these properties are affected depends on how many particles of solute there are in the solution.

The reason I say particles is because molecules, atoms and ions all count as particles. So if you have, say 1 mole of glucose and 1 mole of sodium chloride, the 1 mole of sodium chloride actually has more particles because it contains 1 mole of Na + ions and 1 mole of Cl - ions (2 moles total) whereas the glucose just has 1 mole of glucose molecules. And, as I said before, it doesn't matter what the particles are, it just matters how many particles you have.

Now, these particles of solute sometimes get in the way of evaporation. You see, if there are solute particles near the top, they'll inhibit any solvent particles beneath them that might want to evaporate. As fewer particles can evaporate, the vapour pressure of the solution is decreased. And, since vapour pressure has to be as high as atmospheric pressure to boil, you have to heat the solution up even more until this happens. Therefore, boiling point is also increased.

Melting point is decreased because the solute particles get in the way of the bonds that need to form for the solvent to solidify.

Next up: applications of electrolysis, another topic I've found that I don't know a whole lot about!

The Romantic Period (c.1830-1900)- Berlioz and his Symphonie Fantastique

Berlioz was a crazy man. He was always obsessed with women, which isn't so crazy in itself, but what is crazy is the measures that he took to get his hands on the women that he wanted. When one woman cheated on him, Berlioz equipped himself with a myriad of weapons and made a complex plot to kill her. Eventually, he travelled to where she was living with her new husband, disguised as a maid, and then changed his mind about killing her- rather anti-climatic, don't you think?

Berlioz's Symphonie Fantastique was written in his quest to get his hands on a woman- a Shakespearian actress named Harriet Smithson, to be exact. Berlioz immediately fell in love with her when he saw her perform the part of Ophelia, and wrote this symphony about the object of his obsession. He got his friends to  practically force her to attend a performance of it, and at the end, he proposed to her. When she appeared indecisive, he drank poison and said that he would only drink the antidote if she agreed to marry him! (I'm not sure if I got all of the details correct, but he was a pretty crazy guy...) Harriet finally agreed to marry Berlioz, but she couldn't live up to the high ideals that Berlioz had held of her, so Berlioz found himself a new woman. Harriet eventually died of alcoholism.

Symphonie Fantastique is programmatic and has five movements, each telling a "chapter" in the story. (By the way, "Symphonie Fantastique" is actually its subtitle- the official title of the symphony is "An Episode in the Life of the Artist.") In the first movement, "Reveries, Passions," Berlioz is listless and unhappy until he meets Harriet. In the second movement, "A Ball," the two dance together. In the third movement, "Scene in the Fields," he sees her with a shepherd boy. In the fourth movement, "March to the Scaffold," he dreams that he has killed her and is awaiting execution. In the fifth and final movement, "Dream of a Witches' Sabbath," he dreams that Harriet comes back as a witch to haunt him. Strange story, don't you think? It certainly presented multiple themes that were common in Romantic-era art and literature- love, death and the supernatural.

Berlioz being Berlioz, he couldn't just write a work about Harriet using just a small ensemble. No, he had to use a giant ensemble, using a myriad of common and uncommon instruments. In his Symphonie Fantastique, he wrote for piccolo, flute, oboes, Eb clarinet, C clarinet, bassoons, trumpets, horns, valved horns, trombones, ophecleides (the predecessor to the tuba), violin I and II, viola, cello, double bass, chimes, bass drum, timpani and cymbals. Such an array of instruments allowed him to make use of a variety of tone colours in Symphonie Fantastique.

In my analysis, I'm going to focus on the 5th movement, "Dream of a Witches' Sabbath."

The movement has five main parts: an introduction, the Dies Irae, the Round Dance, the Dies Irae and Round Dance together and a coda. Throughout all of the parts, plenty of chromaticism can be heard, as well as extreme dynamics (there's a pppp in there somewhere!). 6/8 rhythms are used to give the music a dancelike effect, which can have other side effects, as we shall soon see.

Throughout all five movements of the symphony, Harriet is represented by a theme known as the idée fixe. Since Harriet is meant to be a witch in this movement, the idée fixe is distorted to reflect this. Firstly, it's played on shrill instruments like Eb clarinet and piccolo. It is also played in a fast jig 6/8 rhythm with lots of trills. Both of these changes make the idée fixe sound grotesque.

The Dies Irae ("Day of Wrath"), a traditional Gregorian chant used in funeral masses, is used in this movement, giving a sense of foreboding. It is first played on the low instruments, which makes it sound ominous. Eventually it is given to higher and higher instruments and played using shorter note values (a technique known as "diminution"), making it sound more and more trivial each time.

The Witches' Round Dance is hinted at during the Dies Irae through the use of small fragments of the Round Dance theme. When the Round Dance gets going properly, however, it gets going in a fugue, adding to the ritualistic nature of such a dance.

Other musical ideas can be heard in this work. In the introduction, you can hear sounds that represent shrieking and witches' heckling. There are loud chords heard every so often throughout the piece that could represent a witches' shout. Last but not least, there are the bells that could represent a clock tolling midnight.

I probably need to expand my analysis further, but I'll do it when I've got a score in front of me. Right now, it's 8.56pm and I have orchestra tomorrow, so I need to go to sleep. TTFN!

The Romantic Period (c.1830-1900) - Music and Society

The Romantic era was, in some respects, a reaction to the Classical era that preceded it. While the Classical period favoured form and structure, the Romantic period favoured a greater range of emotions. The arts became more emotional, and centred on a range of themes, including love, nature, death, passion, freedom and the supernatural. Artists and composers began to be inspired by other art forms- for example, a composer might write music based on a painting that he or she had seen. During the Romantic period, the idea of "beauty in the eye of the beholder" developed. Previously, structure, form and proportion were seen to be the epitome of beauty, and those who didn't appreciate it were thought to have not had enough education. Now, in the Romantic period, beauty was seen as something that one had to perceive for oneself, not something that could be taught.

Many important events happened during the Romantic period inspired music and art of the time. The French Revolution inspired many people with its hope of freedom and democracy. The Industrial Revolution increased the quality and availability of instruments, resulting in an expanded orchestra. Many other theories and ideas were also developed, but once again I need to go back through all of my notes and do some extra reading here.

Romantic music favoured emotion over balanced phrases. That's not to say that all Classical music was all about balanced phrases and no emotion and all Romantic music was about emotion and no balanced phrases- all I mean to say is that emotion became more important. More woodwinds, including extended woodwinds like piccolo and cor anglais, were used for their tone colours. More extreme dynamics were used, partly due to the increased capacity of instruments to handle larger dynamic ranges. Starting towards the end of the Classical period, there began to be deviations from traditional forms- for example, symphonies could have more than four movements (Berlioz's Symphonie Fantastique had five). There was also a greater amount of thematic unity between movements- that is to say, ideas in one movement were more likely to be repeated in the other movements. Some music was programmatic- that is, it told a story, but not as explicitly as an opera or an oratorio would. Berlioz used motifs known as idée fixe to represent the characters in his programmatic works.

Now let's look at some composers of this period!

Berlioz was an interesting fellow. I'll talk about him in a future post.

Liszt, who was Beethoven's student, was a great pianist and a good composer. One of his famous piano works is Liebesträume, or Dreams of Love. (I can play it, but not very well.)

Brahms was also a pretty famous composer. I'm sure you've heard of Brahms' Lullaby at some point! He wrote two sonatas for clarinet and piano- I played the second movement of his second sonata for my recent performance exam, and I'm eyeing the first movement of the first sonata for next year. My clarinet teacher is thinking of the final movement of the first sonata, though.

Saint-Saëns was another composer of the Romantic period. He wrote a musical suite called Carnival of the Animals in which each movement represented an animal. He also wrote a sonata for clarinet and piano. I played the first movement of that sonata for my Semester 1 performance exam.

Grieg was another Romantic-era composer, famous for writing his Peer Gynt suite. I'm sure you've all heard some of the movements from this suite, like Morning and In the Hall of the Mountain King.

Chopin wrote lots of music for piano, including his Raindrop Prelude, his Polonaise in A and his Funeral March. One guy in my class claimed that Chopin was the "best composer to have ever lived" or something along those lines. We all asked, "According to who?"

Next up: Berlioz and his Symphonie Fantastique!

The Classical Era (c.1750-1830) - Mozart's Symphony no. 40

Now, even if you don't recognise this symphony by its rather vague title, you will recognise it when you hear it.

Let's first talk about Mozart the composer. Mozart, as you probably already know, was a child prodigy. He was composing and performing at a young age (again, I need to go back through my handouts to work out exactly what age he was composing at). His older sister Nannerl was also pretty damn good too, but Mozart quickly overshadowed her. As children, Mozart's father arranged for trips around Europe to show off his children to the courts of Europe. What a childhood!

Mozart wrote a hell of a lot of music during his lifetime. Some of it was composed for people that he worked for, as during those times a lot of composers still had to work in the service of noble families. At one point, though, he had trouble looking for work, and started having financial difficulties. In addition, he had kidney failure (I think it was kidney failure anyway), so not only did he have financial difficulties, but his health was also failing. At this time, a cloaked figure came asking him to write a Requiem (a funeral mass). The cloaked guy probably wanted it for his wife or something, but as Mozart was already sick, he became obsessed with the idea that the cloaked figure was a messenger telling him to write a requiem for his own death! Mozart, still poor at the time of his death, was buried in an anonymous grave.

Mozart wrote his final three symphonies, 39, 40 and 41, in 1788, three years before his death. (I feel like I need to say something else here, like I need to elaborate on that sentence, but I can't think of anything to say.)

Now, for this post, I'm going to be concentrating on his Symphony no. 40. Symphony no. 40 was scored for flute, oboe, Bb clarinet (yay!), bassoon, violins I and II, cello, double bass, and horns. (Cello and double bass share the same line of music.) It is in sonata form- that is, it has an exposition, development and recapitulation.

In the first theme of the exposition, you have the ever-famous 3-note motif in G minor. This three-note motif is repeated a few times before being followed by an upward leap of a minor 6th (my textbook refers to this as the "rocket theme"). The accompaniment has lots of repeated quavers reminiscent of the sturm und drang movement as seen in music. Towards the end of the first theme, there are a few pedal notes in the oboes and bassoons, before leading into the bridge with its broken chords in the lower parts and arpeggiated chords (not sure if that's how you're meant to describe them) in the violins. At the end of the bridge is a bar of dramatic silence to build up tension- another sturm und drang technique. The second theme is in Bb major, the relative major, and is softer and gentler, as the 2nd theme of many sonata-form works tend to be. This theme is characterised by a descending chromatic line. Adding to the "gentleness" of this theme is the fact that the woodwinds get more of a chance to shine. Towards the end there is a long drawn-out crescendo which my textbook refers to as a "steamroller effect," then there's a codetta in which the 3-note motif is played in imitation between the clarinet and bassoon. Right at the end of the codetta the cello and double bass repeatedly play the dominant and tonic notes in order to reinforce the perfect cadence (V - I) that is to conclude the exposition.

The development, true to its name, takes the two themes introduced in the exposition and develops them. The first theme is first developed. It is given an unexpected ending, and the theme is also fragmented (I think this basically means that only part of the theme is used) and played over and over again in a descending sequence. Contrasting dynamics are used- these descending sequences were played piano, but are soon interrupted by a forte entry by all of the instruments at once. A different fragment is then played in another descending sequence, with those repeated quavers beneath in that sturm und drang style. The instruments are then suddenly cut away to leave only flute, clarinet, bassoon and violin I, all playing piano. Clarinet 2 and bassoon play a pedal note while the other instruments have some kind of interplay where they echo each other playing the melody. Soon, some more instruments come in, and the descending 3-note motif in the violins is contrasted with an inverted 3-note motif in the woodwinds. Soon the dynamics suddenly jump back to forte and all of the strings come in with the 3-note motif, sometimes inverted, sometimes in its original form, while the woodwinds play ascending and descending arpeggiated chords reminiscent of the bridge passage in the exposition. The end of the development has the 3-note motif in sequential imitation in the woodwinds with some chromaticism reminiscent of the second theme of the exposition. Soon the development is finished and it's back to the recapitulation.

The 1st theme of the recapitulation is very similar to the first theme of the exposition, but towards the end it is altered slightly to lead into a slightly longer bridge section in which the arpeggiated chords are played in the bass lines and the violins have sequential quaver runs. The second theme appears this time in G minor. The coda of the recapitulation is also a bit longer than the codetta of the exposition, before the whole work draws to a close with a perfect cadence followed by a few G minor chords.

Wow, I'm not actually too bad about writing on and on about music. It might actually come in handy during my Music Lit test tomorrow. It had better do, because I feel that I'm actually quite shaky on the Classical and Romantic periods.

The Classical Period (c.1750-1830) - Music and Society

I must admit my notes on the Classical period are rather lacking in comparison to my notes from the previous periods. I mean, seriously, my Baroque period page was totally covered in STUFF while my Classical period page is rather bare. Maybe I should go back through the handouts I got and add stuff.

The Classical period saw yet another return to the styles of Ancient Greek and Roman times. Balance, symmetry and proportion were all important ideals in art. Musical phrases were balanced and music had more homophony, a stark contrast to the long-winded polyphonic phrases that were appearing in the late Baroque. Although music was a lot more controlled, it wasn't necessarily devoid of emotion. The works inspired by the Sturm und Drang (storm and stress) literary movement, such as Mozart's Symphony no. 25, are obvious examples, but there are many others. Some composers even put witty parts into their music- think Haydn and his Surprise Symphony.

The concerto developed further in this period, and chamber music also became more popular. All different types of chamber ensembles were formed, like string quartets and clarinet quintets. A new popular genre, the symphony, developed from the overtures of Baroque oratorios and operas (which were also called sinfonias). Classical symphonies have four movements: fast, slow, moderate dance-like tempo, fast.

Another important structural form that took off was sonata form (not to be confused with a sonata which is a multi-movement work for instruments). Sonata form is a bit like a musical "essay." It has an exposition, a development and a recapitulation. During the exposition, both themes are introduced (the first usually being in the tonic key and the second either in the dominant key or relative major key), unless the piece is monothematic (only has one theme). They are connected by a short bridge passage, and the second theme is concluded by a short codetta. During the development, the themes are developed further: given unexpected twists and turns, modulated, or otherwise tweaked in a variety of different ways. Finally, during the recapitulation, both themes are reintroduced in the tonic key. The whole work is concluded with a coda.

I can't believe that I've forgotten to talk about this. During the classical period, more instruments were developed. More woodwinds and brass instruments were used as a result of this, though strings were still more dominant in many musical works (unless they were works that specifically featured woodwind or brass instruments, like concertos). The piano was a very important instrument that was developed during this period. Unlike its predecessors, it could play using graduated dynamics. Because of this, Classical-era music generally did away with the Baroque style of terraced dynamics and began using graduated dynamics instead- that is, dynamics with crescendos and decrescendos. The trombone was another new instrument that was developed during this time, if I remember correctly. Also, the orchestra's best instrument was invented during this time: THE CLARINET.

Now, I was going to say that if you hadn't heard of lots of Classical-era composers, you must be living under a rock... until I realised that I actually don't know that many myself! There are some composers that I know but I don't know what era they composed in- is that a good enough excuse? Anyway, here I go with the composers that I do know about.

I'm pretty sure you've heard about Mozart. I won't talk about him so much now, I'll save that for another post.

Haydn was another big giant of that era. He is often considered to be the "Father of the Symphony" because he wrote over 100 symphonies, including the "Surprise Symphony." (I must confess that the first time I listened to this symphony was on Nintendogs. Yes, I'm so very cultured.) Haydn taught Beethoven for a short period, but the two didn't get along very well.

I know that Salieri and Albrechtsberger were also composers of that period, but all I know about them is that they also taught Beethoven.

Beethoven and Schubert were two Classical-era composers that are generally credited for making the transition to the Romantic period that followed the Classical period.

... I REALLY need to learn more to make up for my shameful lack of knowledge. I'm going to finish the posts on the Classical and Romantic periods (both of which I know rather little about...) and then read some more and learn some more to touch up these posts. Ah well, you never stop learning I guess!

The Baroque Period (c.1600-1750) - Handel's Messiah (1742)

So... Handel's Messiah. If you haven't heard of it, you've been living under a rock.

What? You don't recognise the title "Messiah?" Well, does this famous chorus sound at least a little familiar to you?

Handel, although usually a secular composer, was so inspired to write this piece that he completed it in 24 days! It was written to be performed during Lent, as operas couldn't be performed during Lent, and this particular oratorio tells a story that is very important to the Christian faith. In fact, the latter part is exactly why this oratorio was first met with criticism: people didn't like that a secular composer wrote an oratorio about the most important sacred story- an oratorio which was going to be performed in secular venues such as concert halls! However, it met wider acceptance when it was performed to raise funds for an orphanage. People then said that the Messiah "fed the hungry, clothed the poor and mended the sick."

The Messiah used (I really should be writing in the present tense as it can still be performed today, but meh) a standard SATB choir with soloists. Some solos could be sung by different voices if need be. Instrument-wise, the Messiah used the standard string instruments (violin I and II, violas, cellos, double basses), an organ, and trumpets and timpani to be used in important moments such as in the Hallelujah Chorus.

The Messiah can be divided into three main sections. Part 1 is the Prophecy, or Christmas section. Part 2 is the Crucifixion, or Easter section, at the end of which is the Hallelujah Chorus. The final section is about the redemption of the world through faith.

The main parts of an oratorio include the overture, recitatives, arias and choruses. Here I am going to give an example of each in The Messiah.

The overture used in The Messiah is a French overture. French overtures have two sections. The first is slower, homophonic and uses dotted rhythms. FYI, in the Baroque period, they liked to lengthen the dotted part and shorten the non-dotted part of the dotted rhythms. The second section is faster, lighter and uses some polyphony. It's fugal and uses sequential imitation between higher and lower parts while lower parts occasionally have long held notes, or pedal points. (That's not to say that they only have pedal points, however- they have a fair few faster notes too. In fact, the pedal points are somewhat of a rarity.)

Recitatives basically allow the soloist to move the story along. The singing style is simple because it's intended to get meaning across. There are two types of recitatives: secco, which uses minimal accompaniment, and accompagnato, which uses much more accompaniment. The Angel Recitatives are examples of both kinds of recitatives. The recitative accompagnato "And lo, the angel of the lord came upon them" uses a rippling string figure reminiscent of angels' wings.

Arias allow the soloist to reflect on the emotions related to the story told in the recitatives, and as such, the singing style uses a lot more emotions. An example of an aria in Handel's Messiah is Rejoice Greatly. This aria uses Da Capo Aria form (ABA) and ritornello (short recurring instrumental passages). In this aria, the B section is in a minor key to reflect the seriouslness of the words ("He is the righteous Saviour, and He shall speak peace unto the heathen"). There is a lot of exchange between the singer and the violins. The singer has a lot of melismas, some of which are extremely long.

Choruses allow the whole choir to comment on the action, just like choruses in Greek Theatre which allowed groups of actors to comment on the action in the play. The most well-known chorus in Handel's Messiah is the Hallelujah Chorus. It's traditional to stand up when this chorus is played, the reason being is that during one performance the King decided to stand up, so everyone stood up with him. It is unknown as to why the King stood up, but from then on it became tradition for everyone to stand up during this very powerful piece of music.

The Hallelujah chorus uses a mixture of homophonic and polyphonic textures. Homophony is used to emphasise words. Instrument usage is also varied depending on the part of the text- for example, "For the Lord God Omnipotent" is lightly scored when compared to "Hallelujah" which has fuller instrumentation. During the polyphonic parts, imitative polyphony in rising sequences is used. The whole chorus ends in a plagal cadence- the traditional "Amen" cadence.

That's the main points for The Messiah. If you have anything more to add, feel free to comment!

The Baroque Period (c.1600-1750) - Society at the Time

After the Renaissance period came the Baroque period, with composers with names that you'd probably recognise such as Bach and Handel. In fact, Bach was such a musical giant that the Baroque period is generally said to end in 1750, the year of his death.

First of all, let's have a look at what society was like back in the Baroque period. Pretty much all European countries were still absolute monarchies, ruled by kings like Louis XIV who loved music and employed lots of musicians to write music for them. A lot of music was commissioned by nobility or by the developing middle classes which consisted of doctors and wealthy merchants. The Church was less important again (it's a trend that continues with every subsequent period) so much more music and art were secular rather than sacred. The arts, including architecture, still conformed to the whole idea of balance and symmetry, but everything became more detailed and every available space was taken up with action. The word "baroque" comes from a Portuguese word meaning "misshapen pearl" and is a reference to the architecture of the time (whether the architecture was really deserving of this description or not is up to you). More women were composing and performing, and there were also more amateur musicians too.

Secular music really began to flourish in the Baroque period. New forms were created, such as operas, oratorios, concertos, sonatas and cantatas, while keeping the old forms intact. There was also a whole array of new instruments available to play this music, including keyboard instruments such as organs, harpsichords and clavichords, the latter used mainly in the home. Other new instruments included valveless trumpets, French horns, timpani, string instruments and a few woodwind instruments- I think oboes and bassoons were invented at around this time. Instrumental music became as important as choral music in the late Baroque period, possibly due to the increased diversity of instruments. The introduction of equal temperament tuning also helped things along a little, as it allowed instruments to play in all different keys (initially you'd have to change some of the metal tubing or something of that nature to play in a different key).

Baroque music liked to be one of two things: either consistent or containing lots of contrasts. Terraced dynamics (dynamics without crescendos or decrescendos between different dynamic levels), largely due to the capabilities of the instruments, created massive dynamic contrasts. The all-new concerto form had contrasts between a small group or individual versus the whole ensemble (which was also known as tutti or ripieno). Baroque music achieved consistency through its much stronger sense of rhythm and structure, with forms such as ritornello (instrumental interludes), binary, ternary, rondo and Da Capo arias (essentially ternary form with arias). Ground bass, or ostinatos, or a repeating bass line, was also used- think Pachelbel's Canon with its repeating D, A, B, F#, G, D, G, A repeated some 52 times or somewhere around there.

Let's see... what were some other features? Well, homophony was popular in the late Renaissance and early Baroque, but by the time of the late Baroque, polyphony was still popular, and so were long drawn-out melismas. Baroque composers also liked imitation, which is where one line plays the same thing that another line just played. (Sequential imitation is like imitation, but the melody or melodic fragment is repeated at a different pitch.) Word painting was still used, and dissonance was more often in order to convey expression. Lots of ornamentation was also used, just like how buildings of the time were intricately decorated.

Now to the genres of music! Operas and oratorios were both very important forms of entertainment at the time. Opera, a form that took off thanks to the operas of Monteverdi, combined music and acting in onstage productions. They came in two varieties: opera seria (serious Italian opera) and opera buffa (comic opera), both of which used secular stories. Oratorios were sort of like operas, but no acting was involved. People didn't pretend to be the characters, they simply sang about them. Oratorios used sacred stories and were performed in the vernacular, the local language. During Lent, operas were banned, so oratorios were usually performed instead. Handel's Messiah is a very famous oratorio.

Cantatas, part of the Lutheran Church service, was a multi-movement work unified by a chorale or hymn tune. It had arias, recitatives and choruses (more on what these parts are later). It involved solo singers and choirs.

Sonatas came in two forms: sonata da chiesa (serious church sonatas) and sonata da camera (dance-like chamber sonatas).

Concertos, as mentioned before, were multi-movement works that had a small group or individual against the whole ensemble.

(I really need to find out more about cantatas, sonatas and concertos to flesh out their sections above... ah well. Apparently next year we're going to be studying concertos.)

Last but not least, there were a lot of important composers in the Baroque period. Here's a run-down for you. Once again, my knowledge is seriously lacking.

Purcell was a British composer. He wrote an opera called Dido and Aeneas which was originally written to be performed by the students of a girls' school, as well as a myriad of other works.

Scarlatti, who is one of my piano teacher's favourite composers, wrote a lot of sonatas for keyboard instruments. He was a good harpsichordist.

Vivaldi was an amazing violinist at his time. He wrote the very famous solo concerto The Four Seasons.

Pachelbel wrote his Canon in D, infamous to cello players and famous to everyone else.

Bach wrote a lot of music, mainly sacred. He was German, and he stayed in Germany all his life. He was an organist and composer, but in his time he was known mainly for his organ playing. His works included the Brandenburg Concertos; a cantata known as Sleepers, Awake (Watchet Auf), which was based on a Protestant chorale tune; and the Well-Tempered Clavier, a collection of preludes and fugues in every key. Of course, he wrote many other works besides these.

Handel was also German, but he travelled a lot more. In fact, he was working for some noble guy in Germany until he asked for a year's leave to go to England. He enjoyed England so much he didn't come back, but then, ironically enough, his old master came to England and became the English King! As a way of apology, Handel wrote the Water Music and had his orchestra play it on a barge in the Thames when the Royal Family was also going down the river on the 17th of July 1717 (17/7/1717... that's a lot of 1s and 7s!). The King enjoyed it so much that he forgave Handel. Also, unlike Bach, Handel composed mainly secular music. His main exception was his oratorio Messiah, which I'm going to talk about in greater detail in my next post.

The Renaissance Period (c.1450-1600) - Palestrina's Pope Marcellus Mass (1567)

I mentioned Palestrina and his mass in my last post. In this post, I'm going to expand on what I told you earlier.

Palestrina was a composer of sacred music, and a pretty damn loyal one at that. In fact, he actually wrote a few secular tunes, but afterwards he wrote that he "blushed and grieved to have written love songs." He wrote 100+ masses, as well as some spiritual madrigals. His music is pure and a capella, just like most other sacred works of the time. As well as composing, Palestrina also worked as an organist and choirmaster.

Palestrina is also occasionally considered to be the "saviour of polyphony" because of his Pope Marcellus Mass. He wrote his work during the time of the Counter-Reformation (see The Renaissance Period (c. 1450-1600) - Music and Society). Palestrina managed to use polyphony while avoiding the use of secular songs as a cantus firmus and keeping the text clear, which some say helped to appease the Council of Trent.

Here are the lyrics to the Gloria section of the Pope Marcellus Mass (or Missa papae marcelli, as the Italian name goes):

Gloria in excelsis Deo
et in terra pax hominibus
bonae voluntatis.
Laudamus te.
Benedicimus te.
Adoramus te.
Glorificamus te.
Gratias agimus tibi propter
magnam gloriam tuam.
Domine Deus, Rex caelestis,
Deus Pater omnipotens.
Domine Fili
unigenite, Jesu Christe.
Domine Deus, Agnus Dei,
Filius Patris.
Qui tollis
peccata mundi,
miserere nobis.
Qui tollis peccata mundi,
suscipe depecationem nostram.
Qui sedes ad dexteram Patris,
miserere nobis.
Quoniam tu solus sanctus.
Tu solus Dominus.
Tu solus Altissims.
Jesu Christe, cum Sancto Spiriu
in gloria Dei Patris.
Amen.

Simple, no? Oh, all right, here's an English translation, but I can't bothered putting all the line breaks in, so I'm just going to type it all out in a big paragraph.

Glory be to God on high, and on Earth peace to men of good will. We praise Thee. We bless Thee. We adore Thee. We glorify Thee. We give Thee thanks for Thy great glory. Lord God, heavenly King, God the Father Almighty. O Lord, the only-begotten Son, Jesus Christ. Lord God, Lamb of God, Son of the Father. Thou that takest away the sins of the world, have mercy on us. Thou that takest away the sins of the world, receive our prayer. Thou that sittest at the right hand of the Father, have mercy on us. For thou alone art holy. Thou only art the Lord. Thou alone art most high. Jesus Christ, along with the Holy Spirit in the glory of God the Father. Amen.

Pretty serious religious stuff, right? No wonder the Church didn't want secular songs and overly complex polyphony! What compositional devices could be used without spoiling the effects that the Council of Trent wanted?

First of all, Missa papae marcelli is completely choral- no noisy instruments involved. The voices involved were Cantus, Altus, Tenor I, Tenor II, Bass I and Bass II. Cantus and altus were often done by boys, countertenors or castrati  (see The Renaissance Period (c.1450-1600) - Composers and Performers).

Secondly, Palestrina did whatever he could to make the text heard. The Pope Marcellus Mass is mainly syllabic- only one note per syllable. Some parts are neumatic (a few notes per syllable), but melismas (lots of notes per syllable) tend to be reserved for towards the end in the closing "Amen," which also has quite a lot of polyphony and embellishment (after all, everyone already knows what the words are there). Palestrina also made sure that each syllable would be introduced separately in order to make the text clearer.

Palestrina not only made words clearer, he also emphasised some of them. He used homophony (multiple voices moving all at once) to emphasise important words such as Jesu Christe and Domine Deus. He also made use of the different voices for emphasis, only using the entire choir for important words. Hocket was another technique used- in some places the text is also broken up between multiple voice parts, again for emphasis.

Palestrina used some other compositional devices in his work such as cori spezzati, or split choirs. In the introduction, Tenor II and Bass II are roughly grouped together and Tenor I and Bass I are also roughly grouped together. These parts sing alternately at the start. Different rhythms are also used- some syncopation exists throughout the piece. Palestrina also utilises a full, consonant harmony throughout the piece, making use of parallel 10ths and 3rds.

That's the main rundown of the Gloria of Palestrina's Pope Marcellus Mass. Here's a Youtube video for you.

The Renaissance Period (c.1450-1600) - Composers and Performers

So who was around to write such complex polyphonic music in the Renaissance Period? Quite a few people, actually, and this time, we actually know more of their names. I'm pretty much just going to list some of them with a fact or two about each. (I'll admit that these facts are taken from my notes, which are probably taken from the textbook, so they are pretty vague. Maybe one day I should get around to actually learning about them.)

Jacques Arcadelt wrote both secular and sacred music. He wrote in a simpler, lyrical style than many other composers in this age of complex polyphony.

Giovanni Gabrieli was the first to specify dynamics and instruments in his music. It's possible that he helped the shift from the Renaissance period to Baroque period.

Josquin des Prez also wrote secular and sacred music. In the realm of sacred music, he wrote Ave Maria, Virgo Serena, while in the realm of secular music he wrote many motets and chansons, including Mille Regretz. He focused on the text and having all voices in equality. His music had expressive harmonies and serene melodies.

Guillaume du Fay wrote with well-defined melodies and rhythms. His music contained some of the elements of the medieval style.

Alessandro Striggio wrote a mass in 40 parts. The mass actually got lost for many years because some idiot librarian filed it under "Strusco's mass in 4 parts."

William Byrd was another famous British composer who wrote works such as The Earl of Oxford's March (we played a band arrangement of this once, very fun).

Giovanni Pierluigi da Palestrina was another very important composer of the day. I'll write more about him in a later post.

Now for the people who were there to perform the music! In this time of learning, most well-to-do people could play an instrument or sing well. There were also performers who were employed in churches, cities and courts, just like in the medieval period. Now here's a sad story for you: since women still weren't allowed to sing in churches (some did become professional singers, just not in churches), and they needed someone to sing high parts, churches often used boys to sing these high parts. The issue was that eventually these boys would grow up and lose their nice childlike voices, so what did the church do? The Church had some of them castrated so that the boys would keep their childlike voices. These singers were known as castrati. When women were finally allowed to sing in church, the Vatican issued an apology to all of those boys who were castrated. I'm not sure how many there were, exactly, but there were a lot.

Next up: Palestrina and his Pope Marcellus Mass!

The Renaissance Period (c. 1450-1600) - Music and Society

Okay, I'm going to talk about the Renaissance period now. This time, I'm going to break it up. This post will just be about the style of music in the Renaissance period and society at the time. Rather broad, I know, but we'll see how it goes.

The word "renaissance" means "renewal" or "rebirth." The "renewal" referred to here is a renewed interest in the culture, arts and sciences of Greek and Roman times. The arts, including architecture, conformed with Greek ideals of balance and symmetry. Art had more depth and realism, and the human body was now considered to be an object of beauty. Scientific inquiry and exploration became the big thing of the time, and the Renaissance period saw great discoveries and inventions like Galileo's invention of the telescope, Columbus discovering America, and the all-important invention of the printing press which provided people with a greater access to education. Humanism is the term that refers to the celebration of human achievements. Amidst this period of scientific enquiry, the Church became slightly less important than it was in the preceding period, but it was still pretty important.

Music was centred around the same genres as medieval music was, but with some changes of course. Sacred music underwent some radical changes following the introduction of polyphony (multiple voices singing different lines at the same time) towards the end of the medieval period. There were now Masses based on secular tunes, like the L'homme armé mass (I forgot who wrote this one, though), and some composers started introducing instruments. Secular music expanded somewhat because of the declining importance of the Church, and more of it was written down. The most popular forms of secular music included dance music, chansons and madrigals. Italy and England had madrigals, the English version being simpler and lighter than the Italian version. Madrigals, sung by 3-8 voices, were entertaining songs about popular themes such as love. They made good use of word painting, which is where the meaning of the words is reflected in the music- for example, a harsh dissonance for "death" or an ascending scale for "heaven." (Wow, talking about "death" and "heaven" in the same sentence sounds so morbid. Ah well.) One well-known madrigal was Fair Phyllis, written by an English composer called John Farmer.

As instruments still weren't very common and choral music became increasingly more complex, the Renaissance period is often considered to be the "golden age of choral music." (That's not to say that instrumental music didn't make any advances, however- there was some purely instrumental music, and most music didn't actually specify instruments, so you could use voices or instruments or a combination of both- it was all up to the performer.) Polyphony was very popular, with complex harmonies, increasing in number and complexity until a very important event known as the Counter-Reformation (more on that later). Perfect intervals were used less frequently, as now the sweeter sound of 3rds and 6ths were more popular. Imitative polyphony (where one line "imitates" another) became more popular. Antiphonal music, which is where groups come in in alternation, was also popular. It was during this period that harmonies also began to centre on triads and music began to have more of a fixed meter.

Now, back to the Reformation and Counter-Reformation. The Reformation all started when Martin Luther, a priest, nailed his 95 theses to the doors of his church in Wittenberg (you can read a translation of them at http://www.spurgeon.org/~phil/history/95theses.htm). This wasn't such a forceful act as you may believe- the church doors were often used as a kind of noticeboard, and Martin Luther wasn't really being disparaging of the Church. All he really wanted was to see some reforms which he thought would make the Church better: translating the Bible into the vernacular and allowing the congregation to sing in Church. He was especially critical of the practice of "indulgences" which is where people pay the Church to absolve themselves of their sins. Martin Luther just wanted to inspire scholarly debate, but instead the full-fledged Reformation took place.

Eventually some priests thought that the Reformation was all going a bit too far and so they formed the Council of Trent. The Council of Trent proposed different reforms in a process known as the Counter-Reformation. One aspect that the Council of Trent targeted was music. They were opposed to complex polyphony that obscured the text, the use of noisy instruments in Church, the use of secular texts as a cantus firmus, and even the attitude of the singers in church, which they described as "irreverent." Indeed, some of the members of the Council of Trent would have advocated a change back to the simple monophony of the Middle Ages, but that obviously didn't happen. One of the influences preventing this was Palestrina's Pope Marcellus Mass, which I'm going to talk about in a later post. Stay tuned...

The Medieval Period (c. 450-1450)

In music, we don't just do theory and practical. We also have to study music history. This here is a post on the first period that we studied: the medieval period.

The medieval period is often dated from AD 450 (the fall of the Roman empire) to 1450, but these are rough dates only. Not that much is known about medieval music, because not much music got written down, and much of what did get written down was anonymously written by monks so we don't even know that many composers of the period. That's not to say that we don't know anything about the medieval period, however. In this post I'm going to write down everything that I know, or think that I know.

Society at that time was ruled by two main powers: the monarchs and the Church. Of these two powers, the Church was the most important. Even the kings and queens had to pay attention to what the priests had to say. As well as being the centre of worship, the Church was also the centre of education at that day, and we all know how powerful knowledge is. Many children were sent to their local monastery at a young age to live a life devoted to prayer and study.

Because the Church was so important to society, society had to give a lot back to the Church. During that time, families had to give a tenth of what they owned to the Church (I think this was called a "tithe" or something like that). If a family had ten children, they had to give the tenth child to the church. Hildegard of Bingen was the tenth child of a noble couple (even the nobility had to give back to the Church), so she was given to a convent where she later became a nun. She had visions, which the Church accepted as authentic, which gave her so much authority that she could even challenge the priests. Hildegard of Bingen was a very learned woman and she wrote treatises on medicine and science. She also wrote poetry, some of which she set to music.

Which reminds me. Most music written in the medieval period was written for the Church because of the support and patronage of the Church. Much of this music was written in Gregorian chant, so-called because it was all codified and written down by Pope Gregory I. Gregorian chant is essentially a flowing line of music that moves mainly by step. It has no beats, but simply follows the natural rhythms and patterns of speech. It was purely vocal and was meant to make the singers (mainly men as later in the medieval period only men were allowed to sing in Church) experience feelings of reverence or something like that (I can't quite remember). As it consisted of only one melodic line with no accompaniment, it is classified as being monophonic.

Hildegard composed in a style similar to Gregorian chant, but because she hadn't received the same kind of musical training that the boys had received, her melodies had some other defining features to them, such as upward leaps of a fifth which create a feeling of expansiveness and repeating melodic motives, a feature seen in music today that was very rare in Hildegard's time. Hildegard used her musical talent to write a morality play called the Ordo virtutum. She also made sure that her music was written down, and it is thanks to this act that her works can still be performed today.

Anyway, that's enough about Hildegard for now. I'll talk about some other composers later, but maybe I should get back to the music in general.

As I said before, most music was written for the Church and was therefore sacred music. Sacred music was written for worship. The most important service of the Church is known as the Mass, and has different texts that were set to music. The texts are further grouped into two parts: the Proper and the Ordinary. The Ordinary texts are used day in, day out, while the Proper texts change each day depending on the occasion. (There are other Church services known as Offices if I remember correctly, but I won't talk about them now.) The liturgy is the name for the order and structure of Church services.

I'm going to focus on the Ordinary texts, because they're the same throughout the year. There are five Ordinary texts: Kyrie, Gloria, Credo, Sanctus and Agnus Dei. The words to the Kyrie are in Greek rather than Latin, hinting at Christianity's roots back to Greek times. The words of the Kyrie are "Kyrie eleison, Christe eleison, Kyrie eleison" which means "Lord have mercy, Christ have mercy, Lord have mercy." The Gloria is pretty self-explanatory: "Gloria in excelsis Deo" means "Glory to God in the highest." The words of the Credo mean "I believe in only one God," while "Sanctus" simply means "Holy." Finally, the words of the Agnus Dei mean something along the lines of, "Lamb of God, who taketh away the sins of the Earth, have mercy on us." (I think there's another one called "Ite, missa est"- Go, it is dismissed- at the end of the service, but I'm not sure if it was actually a text or whether it was just something that the priest said. Perhaps someone can enlighten me on this one.)

More sacred music was written down than secular music. Music was written down using a system of dots known as neumes, which eventually evolved into the system that we have today. At that time, instead of being based on major/minor tonalities, music was based on a series of different scales, known as modes. I can't remember which modes were used in churches at that time though.

Although most sacred music was monophonic as mentioned earlier, as the medieval period wore on people got rather tired of a single line and tried to add in extra lines. Early attempts to add extra lines to music were all based on original Gregorian chants. In organum, plainchant was sung in one voice while a different line was sung in another voice. The original plainchant that the organum was based on is called a cantus firumus. There were also motets were multiple texts were sung simultaneously, and sometimes sacred and secular texts were combined. Some composers later wrote Masses using secular tunes as the cantus firmus.

Early polyphony often relied on perfect intervals like 5ths and octaves, or on simple oblique motion where one voice sings a drone note and another voice sings a melody on top, but eventually it became more complicated. Polyphony probably helped bring about musical notation, as it was necessary to notate more exact meters and notation for the many complex rhythms which worked against each other at times.

Apart from church music, there was some secular music as well, though a lot of it wasn't written down. The main performers of secular music of the day were either travelling musicians or musicians employed in cities and courts. Jongleurs and minstrels were versatile entertainers, and could provide lots of kinds of entertainment other than simply music. Trouvères, troubadours and minnesingers entertained courts in northern France, southern France and Germany, respectively. They were poet-musicians who were often members of aristocracy and royalty. Musicians often accompanied their noble lords to wars, such as the Crusades or the Hundred Years' War, to keep them entertained and to keep morale high. During these wars,  musicians often picked up new musical ideas from musicians from other countries.

Secular music was primarily for entertainment. There as dance music, as well as music that told stories, like ballads. Popular story themes included love, crusades and political issues. Secular songs were sung in the vernacular, or the local language of the people, rather than the Latin of the church. Also, unlike sacred music, secular music sometimes used instruments. Instrumental parts were often improvised, so we don't know too much about what it sounded like. There were soft instruments, like the recorder, pipe, lute and harp, and loud instruments, like the shawm (a type of oboe) and sackbut (a type of trombone). There were also percussion instruments, like nakers and tabors (types of drums).

That's pretty much it about the medieval period- oh, wait, I've just remembered something. Earlier on, I said I'd mention some more medieval composers! Well, I only have two more here in my notes. Guillaume de Machaut wrote both sacred and secular music in the style of Ars Nova ("New Art"-  there was also an "Ars Antiqua"). He was a poet and a cleric as well as a musician, and he worked in the courts of France. He wrote polyphonic chansons (songs). Rambaut de Vaqueiras was a troubadour and he wrote a piece of dance music known as Kalenda Maya (the First of May).

Wow, that was quite a lot about a period that I actually don't have that much information about! I'll be back later to talk about Renaissance music!

Electrolysis

Today I'm going to talk about electrolysis, the final thing that you need to learn about redox in Year 11 Chemistry.

Remember how I said that sometimes reactions might not occur, depending on where the elements sit on the Standard Reduction Potentials chart? (See Redox Equations if you can't remember.) Well, I lied (or at least I think I did...). It is possible to make these reactions occur, but they won't occur spontaneously. That's where electrolysis comes in- an electrical current is passed through a substance to make a reaction occur. For example, you can electrolyse sodium chloride to give you sodium and chlorine, and I'm pretty sure you can also electrolyse water to give hydrogen and oxygen.

To electrolyse something, you need some equipment: mainly a battery, some wires, and inert substances such as graphite. Oh, and you also need the solution that you want to electrolyse. The solution is known as the electrolyte while the inert substances are the electrodes.(You can have electrodes that aren't made of inert substances, but if they aren't inert then they might react in the electrolysis process. Sometimes this comes in handy, like in electroplating which I'll tell you about in a future post, but most other times you'll want to keep the electrodes inert.)

Here's a nice little diagram of how to set up the equipment:

Now, the way I think this works is that the battery provides electrons for oxidation and reduction processes to occur. Electrons flow through the battery from the positive end to the negative end, then out the negative end into the rest of the circuit, then back up the positive end. Therefore, electrons are flowing into the electrode known as the cathode, making the cathode negatively charged, and flowing out of the electrode known as the anode, making the anode positively charged. Because of this, positively- and negatively- charged ions flow to the cathode and the anode, respectively.

How will I remember all this?! you might ask. Well, you could try my Chemistry teacher's trick. The anode is positive because it starts with an A and getting an A+ is a really good thing, while the cathode is negative because it starts with a C and that's just average. Also you might find it interesting (though not really that helpful) that positive ions, also known as cations, flow to the cathode, while negative ions, also known as anions, flow to the anode. There's also another acronym that might help you remember stuff:

AN OIL RIG CAT
At the Anode, Oxidation, which Is Loss takes place while Reduction which Is Gain takes place at the Cathode.

Writing half-equations for electrolysis of molten salts is the same as writing half-equations anywhere else (see Redox Equations for more info). If you're using solutions, however, things get a bit trickier, as a solution indicates that water comes into it as well. In this case, you need to write down all of the possible oxidation reactions and all of the possible reduction reactions. FYI, here are the oxidation and reduction reactions for water:

Oxidation: 2H₂O -> O₂ + 4H⁺ + 4e^-

Reduction: 2H₂O + 2e^- -> H₂ + 2OH^-

(By the way, Wikipedia pointed out to me that if you combine these two equations you get 2H₂O -> H₂ + O_{2 : the electrolysis of water.)}

Then you need to go back to the good ol' Standard Reduction Potentials table and look at those numbers on the side. Compare the standard reduction potentials of the two elements that might possibly be oxidised/ reduced. The element you need is the one with the highest standard reduction potential. (Be careful, though, as some of the reactions might be listed the other way around on your sheet. If this is the case, then you need to change the sign on the standard reduction potential value from positive to negative or vice versa. It may be easier just to look for the highest absolute value.)

(Actually I need to double check that last paragraph- this is the section where I get all confused with what's what. I'm sure it's not that confusing. One day I'll sort it out... though I can get some consolation from the fact that solutions isn't strictly required knowledge in Chemistry 2AB...)

How to Deal with Qualified Drivers

Qualified Drivers- the bane of every Learner Driver. Some qualified drivers are retards, but I get the feeling that many learners who hate the qualified drivers (hereafter referred to as Q-drivers) tend to hate them just because they're there. I've decided to write this guide to combat the average learner's fear (for lack of a better word) of Q-drivers. After all, being able to handle traffic is all part of being a driver- and yes, that means being able to handle the fact that there are other Q-drivers around and some of them are pretty nasty towards L-drivers.

Q-drivers come in all different varieties. There's the nice ones and the indifferent ones, the tailgaters and the show-offs. And yes, there's the smart Q-drivers and the idiotic Q-drivers. Just because you have your driver's licence doesn't mean that you're a smart, safe, courteous driver. Conversely, just because you're still on your Ls doesn't mean that you're a dumb, dangerous, discourteous driver. L-drivers have as much right to be on the road as Q-drivers do, provided that they have L-plates, their learner's permits and a supervisor. I'm going to repeat that again, just to stress my point: you have as much right to be on the road as any Q-driver, so you deserve to be afforded the same amount of respect and courtesy as a Q-driver. Don't let other people's attitudes get in your way of becoming good at driving.

One thing that I found really helped me in becoming used to other Q-drivers is by pretending that I am one- one that follows the road rules, anyway. Since I got into this frame of mind, other benefits compounded on this. I've been beeped at a couple of times by impatient drivers, but because I don't see myself as that L-driver that all of the Q-drivers hate, I just go, "bloody impatient driver" and go on my merry way. Of course, this tactic might not work for you as everyone's mind is different.

If you get a tailgater, you could try some of the tactics that I've gathered from Q-drivers. (However, if you try one of these, you should be sure that the driver behind is definitely a tailgater and that it isn't a case of the car just appearing to be close when you look at it in the rearview mirror.) Here are some tactics:

1. Tap the brake pedal not so much that you start slowing down, but enough so that the brake lights come on.
2. Let go of the accelerate pedal.
3. Use the windscreen spray thingo. If the wind's right the water might blow onto their windscreen. My mum did this on the freeway to a jerk who was tailgating her...
4. If there's an intersection nearby, indicate so that they think that you're turning and will slow down to allow you to turn.
5. If there's a place where they can overtake, slow down to allow them to overtake. However, tailgaters will probably overtake on their own as soon as they have the opportunity to do so.
6. You could always simply ignore the tailgater. Or you could pull faces at them in your rearview mirror. Whatever.

Whatever you do, though, NEVER NEVER NEVER go over the speed limit just to appease a Q-driver. If there's a camera nearby, it's you who'll end up with the fine, not them.

And that's pretty much it for my article on how to handle Q-drivers. If you're still struggling you could try and drive an automatic so that you don't have to worry about Q-drivers and gears at the same time. I'll have to admit that I'm learning on automatic (both my parents have automatics) so I don't have any advice for you if you stall your car in the midst of a whole bunch of Q-drivers. I can, however, offer some consolation: the Q-driver in front of me stalled their car at an intersection. If Q-drivers can stall their cars then really there's nothing that hateful about L-drivers stalling their cars either.

As always, if you have anything else to say on the matter, please leave a comment!

How to Turn Left

Hiya all, today I'm going to post about driving.

When you start learning how to drive, even the simplest little tasks like turning left and right can seem daunting, so I've composed a nice little guide on how to turn left.

First of all, your preparation is pretty important. You should slow down as much as possible before you turn as it is easier to control your car at a lower speed. As my driving instructor says, cars are like men: they can only do one thing at a time. They can slow down, or they can turn, but they can't really do both at the same time, so make sure you do most of your slowing down before you get to the road you want to turn into. 15-25km/h is a good speed for turning at, less if it's raining.

When you turn left, the position of your car is also important. Most suburbian roads widen out at the end for a reason, and that reason is to help you turn left! Make full use of that curvy bit to help you turn. Here's a diagram (I even labelled the car for you, hehe):

The trick is that, to get in this position in the first place, you would already have had to have put some turn on the wheel. That way, when you actually make the turn, you don't have to turn the wheel much more.

Of course there are some roads that won't enable you to do this, but most of the time you can get a nice left-hand turn position going. Even when you're not turning left at the end of the road but down some other random road instead, you'll still find that there are curvy bits where the roads intersect and you can use these to your advantage.

I have another tip for you and that is in regards to steering. If you find that you can't steer sharply enough, try this steering method. To turn left, grab the top of the wheel with your left hand and pull anticlockwise. Push up anticlockwise with your right hand. Repeat the process as needed. To turn right, just reverse the directions.

To sum up- here are the steps that you should be taking when you do a left-hand turn on a normal suburban road:

1. Check your mirrors
2. Start slowing down
3. As you slow down, indicate that you're about to turn left.
4. Get into the left-hand turning position.
5. If you're on a terminating road about to enter a different road, you need to stop and check for traffic in the left lane. If it's all clear, then you can go.

By the way, if visibility is good, as in REALLY good and you can see for quite a while down the road, and you can see that there aren't any cars coming, then you don't need to stop completely at the end of a terminating road unless there's a stop sign. (You must stop before stop signs- even if you're stopped behind a car stopped at a stop sign, once that car moves off, you need to stop AGAIN at the stop sign BEFORE you move off. I learned this the hard way with my driving instructor- at least I didn't learn the hard hard way in a driving test...)

Hopefully that helps you all with turning left... if anyone has any other tips, or if there's anything incorrect in this post, let me know!

Radicals 足 刀 日

I said I was going to post 3 a day, but I kind of didn't stick to that promise. Ah well.

Here are 3 more radicals for you to learn today.

足， ⻊ = foot

This character exists as a standalone character, but it has a slightly different form that appears on the left hand side of some characters, particularly those to do with feet.

足 - foot
跑 - run
踢 - kick (踢足球 - play football/soccer)
跃 - leap, jump
蹦 - leap, jump, spring
跳 - leap, jump, spring, bounce (the list of English translations keeps growing...)
跟 - with, to follow
踩 - step on, trample

刀，刂 = sword, knife

One way of remembering that the two characters are related is that the second one is really just the first one with the top bit removed and the left bit squished a bit closer towards the right bit- wait, that wasn't really all too helpful... There's also a third form that I don't know how to type and can't find one that I can copy or paste (though to be honest I'm not really looking very hard). It looks like the top of the character 色 or 龟.

刀 - sword, knife
剪 - scissors, shears
色 - colour
龟 - turtle
兔 - rabbit
划 - stroke (of a Chinese character), to scratch
切 - cut
免 - avoid, avert, escape (免费 - free of charge)
刚 - just
别 - other, don't

日 - sun, day

This character evolved from a pictograph. I'm sure you can find its origins on a quick Google search.

日 - sun, day
旧 - old
旦 - dawn
晓 - dawn, daybreak
显 - apparent, obvious, show, display, illustrious and influential
明 - bright (昆明 - Kunming, capital of Yunnan Province in China, which is where the Hanyu Qiao Chinese Proficiency Competition is going to be held this year)
时 - time
旭 - rising sun
早 - early, morning
晚 - night
量 - to measure
晴 - sunny

Redox equations

This is possibly the reason why I hate redox so much. The actual equations themselves aren't too bad, it's just working out whether a reaction occurs or not. My brain always gets mixed up reading that stupid reduction potentials chart... argh...

Anyway. The first two types of redox reactions that I'm going to talk about are metal and halogen displacement reactions.

In metal displacement reactions, a metal reacts with a metal ion in such a way that the originally solid metal becomes an ion and the original metal ion becomes a solid metal. Confused yet?

For example, if you have solid potassium reacting with a solution of sodium chloride (i.e. sodium ions and chloride ions), you'd end up with solid sodium and a solution of potassium chloride (i.e. potassium ions and chloride ions). The net ionic equation would look like this:

K + Na⁺-> Na + K⁺

In this reaction, K has been oxidised and Na has been reduced.

Note that if you had solid sodium and a solution of potassium chloride, they would not react. But how can you tell just by looking at the reactants if you're going to have a reaction or not? This is where the Standard Reduction Potentials table at the back of your data sheet comes in.

The closer an element is to the bottom of the table, the more it wants to be oxidised and become a positive ion. For the most part, groups I and II elements (alkali metals and alkaline earth metals) are at the very bottom and directly above them is mainly transition elements (with exceptions such as aluminium and water which randomly snuck in). I'm very curious as to why this is so, but I'm too lazy to look it up myself.

When you have the reactants of a metal displacement reaction, take a look at the Standard Reduction Potentials chart. Which element has the strongest desire to be a positive ion? If it's already a positive ion, no reaction will occur. If it isn't, then a reaction will occur. That's basically how it works.

Halogen displacement reactions are the opposite of metal displacement reactions. Here's an example:

F₂ + 2Br^- -> 2F^- + Br₂

Now, when working out whether a reaction will occur or not, you have to do the opposite of what you did with the metal displacement reactions as this time we're dealing with negative ions, not positive ones.

If the bottom of the table lists the elements that want to be oxidised and become positive ions, then it also follows that the top of the table lists the elements that want to be reduced to negative ions. When working out halogen displacement reactions, work out which element has the strongest desire to be a negative ion. Then think about whether that element is already a negative ion or not. If it's already a negative ion, then no reaction will occur. If not, then a reaction will occur.

(By the way, there are ways to force the reactants to react even when they don't really want to, but I'm not going to go into that for now.)

Now, next up is half equations. In Chemistry 2AB, you only have to deal with the dead easy half equations, but there's also acidic conditions and stuff that you can learn about too.

You can write half equations for any kind of redox reaction, whether it be metal displacement, halogen displacement, or a myriad of other types of reactions that I don't know the names of. As long as an element is being reduced and another is being oxidised, you can write half equations.

Basically, you write separate equations for the reductant and the oxidant. Then you add in electrons to balance the charges.

F₂ + 2e^- -> 2F^- 

2Br^- -> Br_{2 +} 2e^-

Just make sure that the number of Fs or Brs or whatever are balanced on either side of the equation, and then chuck in some electrons to balance the charges as well.

You can also write balanced net ionic equations as well simply by adding together the two half-equations and then cancelling off the electrons on either side. If the two half-equations involve different numbers of electrons, however, care needs to be taken.

If you have different numbers of electrons in the two equations, what you first need to do is multiply each by a certain number so that the number of electrons are the same. For example, if you have 3 electrons in the first equation and 2 in the second, you can multiply the first equation by 2 and the second by 3 so that you have 6 electrons in both equations. Then you can add the two equations together, cancelling out the electrons on both sides. It's just like simultaneous equations in maths really.

Earlier, I mentioned half equations in acidic conditions. Normally, when you have a question asking for these, it's because you have some crazy polyatomic ion like the chromate ion. The steps for working out these are as follows:

1. Balance the number of atoms on each side (except for hydrogen and oxygen- we'll get to them later).

MnO₄^- -> Mn²⁺

2. Add water in order to balance out the number of oxygen atoms.

MnO₄^- -> Mn²⁺ + 4H₂O

3. Add hydrogen ions (acidic conditions, remember?) to balance out the number of hydrogen atoms.

MnO₄^- + 8H⁺ -> Mn²⁺ + 4H₂O

4. Calculate overall charge on each side.

In above equation, the left hand side has an overall charge of +7 while the right hand side has an overall charge of +2.

5. Add electrons to balance out the charges.

MnO₄^- + 8H⁺ + 5e^- -> Mn²⁺ + 4H₂O

So that's pretty much all you need to know and more on redox equations! Next up- electrolysis!

Basics of Redox

Argh I hate redox. I'm not too bad at it, but it annoys me for some reason. Anyway, rant over, it's time for me to try and explain it.

Now, redox is all about the transfer of electrons. When an atom gains electrons and thus has its charge reduced, we say that it has undergone reduction. When an atom loses electrons, we say that it has undergone oxidation. The word "oxidation" comes from the fact that there are lots of cases in which the addition of oxygen makes another atom lose electrons.

When do redox reactions occur? Well, you know very well that the transfer of electrons happens when atoms become ions. (If you didn't already know this, go here to find out more.) But there are other times when electrons are transferred too. It's easier to explain this by talking about oxidation numbers, so that's what I'm going to talk about first.

You can assign each element in a compound an oxidation number. If it's just a single element you're looking at, like Fe or O2 or Na, the oxidation number is 0. Hydrogen usually has an oxidation number of +1, but if it's a metal hydride, then it has an oxidation number of -1. (And, as said before, if it's on its own, like in H2, then it has an oxidation number of 0.) Similarly, oxygen usually has an oxidation number of -2, but there are a few exceptions where this is different (I'll have to check what the exceptions are). In ionically-bonded compounds, the oxidation number of each monoatomic ion (ion with only one atom (ion?), like Na+) is simply the charge on the ion (for example, the oxidation number of Na in NaCl is +1 because Na has a +1 charge). Assign these elements their oxidation numbers first.

Now, in a neutrally-charged compound, all of the oxidation numbers have to add to 0. Similarly, in a charged compound or polyatomic ion, all of the oxidation numbers have to add to the charge on the ion or compound. Simple, isn't it?

Now I'm going to talk about carbonic acid, H2CO3. Let's start off by assigning it some oxidation numbers.

Since this isn't a metal hydride, the oxidation number of H is +1. That was easy, wasn't it?

Now, CO₃<sup>2- has a -2 charge. Therefore, the oxidation numbers of C and O need to add up to -2. Each O has an oxidation number of -2. Three Os have a combined oxidation number of -6. C must have an oxidation number of 4 because 4-6 = -2, the overall charge on the ion.

That wasn't too hard, was it? (If it was, don't feel stupid, just ask me to clarify.) Now for two more examples: carbon dioxide and water.

Water's easy. Each H has an oxidation number of +1 (the two Hs combined have an oxidation number of +2) and O has an oxidation number of -2. The overall charge is 0.

Carbon dioxide isn't much harder. Each O has an oxidation number of -2, and because carbon dioxide is neutral, the oxidation number of C has to balance out the oxidation number of the Os. The oxidation number of C is therefore 4.

Now, the decomposition reaction of carbonic acid to carbon dioxide and water is not a redox reaction. Why? Well, it's because none of the elements has changed oxidation number! If any of the elements had changed oxidation number, then it would be a redox reaction. (Sorry, I thought this decomposition reaction would be a redox reaction as well, but soon realised that it wasn't. One day I'll put a better example up.)

In a redox reaction...

The element that loses electrons, thereby obtaining a higher oxidation number, has been oxidised and is known as the reducing agent or reductant (as it reduces the other element).

The element that gains electrons, thereby having its oxidation number reduced, has been reduced and is known as the oxidising agent or oxidant (as it oxidises the other element as it is being reduced).

Remember that if electrons are being lost then they have to have somewhere to go to, and vice versa (if electrons are being gained the atom needs to gain them from somewhere).</sup>

By the way, there's a nice little mnemonic to help you remember which is the oxidant and which is the reductant. It's OIL RIG. It stands for Oxidation Is Loss of electrons, Reduction Is Gain of electrons.

I'm too tired to do any more for now. At least I've done the first four dot points here (explain oxidation and reduction as electron transfer, calculate oxidation numbers, identify and name oxidants and reductants and identify redox reactions using oxidation numbers). I think I'm good for now. Only 5 dot points left and I'll have gone through pretty much the whole Chemistry 2AB course- unless you count all of the Applied Chemistry stuff, of course.

Naming and Drawing Organic Compounds

Because I'm pretty lazy, I just photocopied my Chemistry holiday homework for this one.

Sorry that it's on a slight angle.

Rightio, let's start with 1a. It's always a good place to start!

First things first- identifying which homologous series the structure belongs to. There's only single bonds here, so it's an alkane and will therefore end with an -ane ending.

Secondly, we work out what the longest carbon chain is. No, it's not 4, it's actually 6. There's three on the top row, and then the third one joins on to the three on the bottom row. (Due to the nature of single bonds, rotations and flips and whatnot don't change the order of bonding- sorry, couldn't think of a clearer term. Anyway, diagrams don't even accurately show where the atoms are in relation to each other.) Therefore, we know that there's a hex- in there somewhere. So far, we've got ourselves "hexane."

But what about that extra CH3 joined on to the third atom? Well, that's called a "alkyl group." Because there's only one C atom, it's "methyl-." (If there were two carbons, it'd be ethyl-. Three would make it propyl-, and so on.)

Now, we also have to assign the alkyl group a number so that we know where to find it on the chain! Counting in one direction, the alkyl group's on the 3rd carbon. Counting in the other direction, it's on the 4th carbon. Always work with the lower numbers. Since 3 is lower than 4, we'll stick with 3. Finally, since there's only one methyl group, we don't need to worry about adding di- or tri- before the "methyl." (You don't need to add mono- either- if there's no prefixes, it's implied that there's only one.) Therefore, the final name is 3-methylhexane. Yay!

We can write this all down as a series of steps:

1. Figure out which homologous series the structure belongs to. This will give the suffix.
2. Count the number of carbons in the longest carbon chain.
3. Figure out the names and locations of all attachments to the chain that aren't hydrogen atoms. (This includes alkyl groups and halogens like bromine and iodine.) If there's more than one of anything, indicate this with a prefix like di- or tri-. Also, when giving locations of groups, make sure to give all the attachments the lowest possible numbers. List all attachments in alphabetical order.

Let's try these steps with 1e.

Homologous series- Alkane, as all single bonds. Hence -ane ending.

No. of carbons- 10, so dec-.

Extra bits and pieces:

1 x Chlorine at 2

1 x Fluorine at 5

3 (tri-) x Methyl at 3, 3 and 9

1 x Propyl at 5

Final name: 2-chloro-5-fluoro-3,3,9-trimethyl-5-propyldecane

I won't give worked examples of the other ones because I have to wake up at 6am tomorrow and I'm not a morning person, but I will give some pointers.

NO2 goes by the prefix nitro- and NH2- goes by the prefix amino-. However, you don't really have to worry about these in 2AB Chemistry.

You also don't need to worry about cycloalkyl groups in 2AB (as seen in 3c). They work pretty much the same way as an alkyl group. The trick is knowing whether you're dealing with a cycloalkane with alkyl groups or an alkane with cycloalkyl groups.

You do need to worry about cycloalkanes with alkyl groups. Labelling these is exactly the same as labelling alkanes with alkyl groups. The only difference is that cycloalkanes obviously don't have ends. The numbering goes clockwise. Just try and make it so that each alkyl group or halogen has the lowest numbering possible. Halogens should get preference for the lowest numbers.

Now for drawing hydrocarbons. I'm going to pick a semi-hard example so that I'll cover pretty much everything and will only have to explain once. The example I'm going to pick is 2i: 2,2-dichloro-6-methyl-4-propylheptane.

Drawing hydrocarbons is easier, in my opinion. Here are my steps:

1. Draw all of the carbons required.

2. Draw bonds between them according to the functional group.

3. Add all of the other bits and pieces on.

4. Draw on all of the hydrogen atoms. Yes, you have to do this step. My Chem teacher told us that this guy from another class offered his brother $5 if he would draw on all of the hydrogen atoms for him. The brother looked at how many he had to draw and said, "Not worth it!"

Obviously, you need to draw all of the bonds on but I kind of ran out of room and couldn't be bothered rearranging stuff.

So that's pretty much all of the basic stuff on naming and drawing organic compounds. I've only really covered alkanes, but alkenes and alkynes aren't too different. The only thing is that you need to put the location of the double and triple bond just before the -ene or -yne suffix (e.g. but-2-ene). If you want me to clarify, just ask!