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Music Theory 101

I wanted to write a simple music theory introduction. I am going to explain the notes, how to read them and how to from basic chords, which are the basis of every song you've ever heard.
The most basic thing to know is the note names. As I stated in my first post, there are 12 notes named from A to G (the white notes) with some "accidentals" or sharps and flats in between (these are the black notes). The distance between two notes that are next to each other is called a half step. So the distance between C and C# is one half step. The notes are shown here to the left in what is called the staff. The staff is the set of 5 lines in which the notes are placed. The placement of these notes are what tell you what the note name is. So whenever you see a note on the bottom line of the top staff, you know that you are looking at an E. As you can see, on the far left of the top staff is a symbol call the treble clef which indicates where on the piano the note is. The symbol on the bottom is called a bass clef and indicates you will be playing an octave lower than the treble clef. With these notes you can form what are called chords. Chords are basically two or more notes played together, but in order to form a chord which sounds good, there are some basic rules that one must follow. A scale can be made starting on any note. There are many types of scales, but I am only going to talk about the major scale right now because almost all of pop/rock music is written in a major scale. In order to make a major scale you just need to follow a simple formula. If you want to make a C major scale, you will start on a C and move up 2 half steps to get your next note (D). Another 2 half steps to get your next note (E). You will continue in this fashion. The order of steps is as follows, starting on C. 2 2 1 2 2 2 1. You should hit all the white notes if you do this right. In order to make a different scale all you do is start on a different note and follow the same formula. So if you want an A major scale, you simply start on A and follow the 2 2 1 2 2 2 1 formula. You can then form chords in these scales, or keys (a song played using the C scale is said to be in the key of C). To make a C major chord, you start with the C scale and you will play the first, third, and fifth note of the scale (C,E,G). To make a C minor chord you simply move the middle note down one half step. (C,Eb,G). You can do this to make any major or minor chord.

These are the very basics of music theory. If you are interested in learning more, or if you have any questions, leave a comment about it, and I'll respond ASAP.

The Infinite

The idea of infinity is one of the most fascinating concepts in mathematics. I could talk for pages and pages about it, but I am going to focus on few fun and interesting infinity facts.
Everybody has an intuitive idea of what a set is. You could say this is my set of fine china, and the only things that would belong to that set would be the things you consider your fine china. There are an infinite number of examples for sets and I want to look at a couple interesting ones.
The set of the natural number (1,2,3,4,5,....) is an easy set to grasp; it's just the counting numbers going on forever. It is easy to see that there are an infinite number of numbers in this set. Now lets look at another set, the set of the natural numbers squared (1,4,9,16,25,...). Now, this too is obviously an infinite set, the numbers continue on forever. So, would you say that these two sets are the same size, i.e. they have the same number of numbers, or is one bigger than the other? Some people would say that they are clearly different sizes because the second set is missing all kinds of numbers (2,3,5,6,7,8,10,11,...) are all numbers that are not a part of the second set and the first set contains all of these numbers, and all of the numbers in the second set, so there must be more numbers in the first set.
I am going to claim that there are the same exact number of elements in the first set as in the second set, and I will prove it to you right now.

Let's try to match up the elements from the first set to elements of the second set. How will we do this? Well an easy way is to just match the number from the first set to its square in the second set.

1-1
2-4
3-9
4-16
5-25
.
.
.
And so on.
So you can see that if we continued this forever, there will always be a number in the second set for each and every number in the first set; it's square to be exact. And if there is an exact matching from one set into another, than those two sets are the same size.
I wanted to talk about this example because it shows what kinds of crazy things can happen when you move from the finite to the infinite. Things become quite bizarre and unintuitive, but very interesting.

Sheet Music List

All right, I am going to start the long process of posting as much sheet music as I can. I am going to start with the more popular stuff and then I'll go from there.

Sheet Music
Augustana-Boston
Avenged Sevenfold-Warmness of the Soul
Coldplay-Amsterdam
Coldplay-Clocks
Coldplay-Don't Panic
Coldplay-Everything's Not Lost
Coldplay-Fix You
Coldplay-God Put a Smile Upon Your Face
Coldplay-Ladder to the Sun
Coldplay-Politik
Coldplay-Shiver
Coldplay-Speed of Sound
Coldplay-Spies
Coldplay-The Scientist
Coldplay-Trouble
Coldplay-Yellow
Dido-Thank You
Gary Jules-Mad World
Elton John-Can You Feel The Love Tonight
Elton John-Candle in the Wind
Elton John-Your Song
Enya-Only Time
Eric Clapton-Wonderful Tonight
Evanescence-Breathe No More
Evanescence-Hello
Five For Fighting-100 Years
Five For Fighting-Superman
The Fray-How to Save a Life
Guns'n'Roses-November Rain
Guns'n'Roses-Sweet Child o' Mine
Eagles-Hotel California
Keane-Everybody's Changing
Metallica-Nothing Else Matters
Muse-Bliss
Muse-New Born
Pink Floyd-Comfortably Numb
Pink Floyd-Echoes
Star Wars-Imperial March
Star Wars-Raiders March

ebooks
29 Jazz Rythyms
36 Christmas Carols
Christmas Favorites
Music Theory
Pink Floyd
Rolling Stones

The World According to Beethoven and Euclid

We are surrounded by two things everyday... Math and Music. Most of the time we don't even notice the math or we just choose to ignore it. But we notice music everywhere... Sometimes as soon as our radio alarm clock goes off in the morning we are surrounded by it. Little do we realize however that in that music are some of the most beautiful and symmetric numerical systems. From simple arithmetical processes to things as complicated as Group Transformations, music is full mathematics.

I have grown to love and appreciate most everything about both of these worlds and would like to just talk about anything having to do with either of them (not necessarily how they complement each other). Any questions you might have, some observations, fun facts, homework help, anything to do with math and music is fair game and I would love to hear your insight and provide my own so everyone grows to appreciate, just a little, the beauty of math and music.

Also, as a piano player who is always looking for a new song to play, I know how frustrating and expensive it is to find pieces of sheet music out there and I myself have become a very avid electronic sheet music collector. I have tens of thousands of sheets of music that I have acquired and would love to share with everyone. I will begin to post the sheets I do have and if there is something you would like that you don't see just let me know and I either have it or will do my best to find it. I have accumulated many resources for that.

For my first journey into the World of Math and Music, I would like to show you the beauty of the mathematical structure which underlies the basics of Western music theory.

The Western musical system consists of 12 tones, or notes. We give these notes names using letters A B C etc. and we go all the way up to G and then we start at A again. Now this only accounts for 7 notes and the other 5 come from things called accidentals which are noted by the #(sharp) sign or the b(flat sign). These notes are just multiples of frequencies. The lowest note on the piano is an A and it's frequency is 27.5. To get A# you simply multiply my the 12th root of 2 and you get 29.135 and you keep doing this and after doing it 12 times you will get 55 which is 27.5x2. When you get a multiple of a frequency then it is the same note. So 27.5 (A) is the same note as 55 (A), just one octave apart. So every note you hear in music is just some frequency and is derived from this.

Now if we lay out a little chart of the notes and do a little mathematical modeling we will begin to see some very interesting things:

C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B C

And if we now associate numbers to all of these we get this:

C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B C
0 1 2 3 4 5 6 7 8 9 10 11 0

Now if we imagine adding one number to another as moving that number up the piano that many notes then we can see that if you take


0+1=1 This means that 0(or C) moved up one note is C#.
You can do this with any numbers as many times as you want as long as you mod out by 12, which means if you get a number higher than 12 when you add, simply divide that number by 12 and the remainder is your new number.

9+11=20 20/12= 1 with a remainder of 8, so 8 is our new number. So when you move A up 11 notes you will land on G#. And this works for any number of additions.

3+7+4+9=23=11mod12 This means that if you take D# and move it up 7 notes, then 4 more, then 9 more, you will land on a B.

You can even do this with whole chords.

C major = {C,E,G} = {1,5,8} I will say that when you add a number to a chord, you are adding that number to each note in the chord.

So C major, plus 7 = {1+7,5+7,8+7} = {8,0,3} which is a G# major chord.

An interesting note about this is that if you add a number to a major chord you will get a major chord and if you add a number to a minor chord you will get a minor chord.

There are so many interesting applications to this and if you notice any or if you see any other structures you think are interesting comment about it and we can see if we could make a whole post out of it.

I will also be working on compiling a list of sheet music, but if there's anything you want now, just let me know and I will tell you if I have it or not, and if I do I will get it to you ASAP