Rhythm

Webster's Definition: "the aspect of music comprising all the elements (as accent, meter, and tempo) that relate to forward movement"

My Definition: The flow or movement of a piece of music.
          ~It can be a little tough to really describe just what rhythm is - it  often seems to be something simply understood. You feel it and experience it when you listen to music. It often seems that it flows right through you from the music. When it comes to dancing, we say that some people have rhythm and other just don't. Rhythm is just something that's there in music. It simply exists.

It is, however, also a technical term used to describe an element of music. Rhythm is made up of three sub-elements: beat, meter and tempo.

Beat

Beat is really the big thing when it comes to rhythm. Beat is what any listener, no matter how musically knowledgeable, can usually find and follow along. It is the steady pulse of a piece of music.
Oftentimes when we think about beat, we think of drums. Drums and other percussion instruments are generally the main purveyors of the beat in a piece of music - at least in music from the last century or so. In fact, it can be quite difficult sometimes to find the beat in a lot of classical music, simply because of the way that they are composed and the instruments at their disposal. 
We, too, have steady beats: our heartbeats. And just like the way that your beats in a pattern of DA-dum-DA-dum-DA-dum, beats in music are also both strong and weak.

Meter

Meter is simply the way in which those strong and weak beats I just mentioned are organized in a piece of music. Generally, meter is relatively simple. There are three types of simple meters: duple, triple, and quadruple...

• Duple Meter: this type of meter has a pattern exactly like your heartbeat - it goes DA-dum-DA-dum-DA-dum-DA-dum. In counting this meter out, it would go something like "ONE-two-ONE-two-ONe-two" and so on.
• Triple Meter: this type of meter has one more "dum" sound than duple meter. If your heart was in triple meter, it would go DA-dum-dum-DA-dum-dum-DA-dum-dum. If you counted it out, you would say "ONE-two-three-ONE-two-three-ONE-two-three."
• Quadruple Meter: this type of meter is like a double heartbeat - it goes DA-dum-dum-dum-DA-dum-dum-dum-DA-dum-dum-dum. You would count it out like "ONE-two-three-four-ONE-two-three-four."

NOTE: the technical terms for the "DA" and the "dum" are pick-up and downbeat, respectively. The pickup is strong (DA) and the downbeat is weak (dum).

Now, there are also some more complicated types of meter. I won't get into them too much, but they are complex meter, compound meter, polymeter, and mixed meter.

Tempo

The tempo of a piece of music is simply it's speed. It is how fast the beat goes. Whether it is your heartbeat or a musical beat, tempo is measured in BPM. For your heart, this stands for Beats Per Minute. For music, however, it stands for Beats Per Measure.

A great example for rhythm is the White Stripes' "Seven Nation Army." It has a very easy to find and follow beat, is in a simple meter, and has a rather moderate, sometimes fast, tempo.

Pitch

Webster's Definition: "the property of a sound and esp. a musical tone that is determined by the frequency of the waves producing it :  highness or lowness of sound"

My Definition: How high or low a piece of or aspects of a piece of music sounds.

There really doesn't seem to be anything else to know about pitch, now does there? It's the highness or lowness of a piece of music. And that's it...right? Wrong. The idea of pitch is actually a lot more complicated than just  highness and lowness. It's a scientific concept based on frequency and the periodic disturbance of air particles.
So, since pitch is about the highness or lowness of sound, let's discuss the science of sound. Sound is vibration. It is created when air particles are disturbed and the disturbance travels to your ear, where it's perceived as sound. Frequency is basically how fast or slow those air particles are being disturbed.  Higher pitches come from faster frequencies, and lower pitches come from slower frequencies. If you wanted to measure the frequency or pitch of a sound, you would do so in Hertz (Hz), which is a unit of measurement for sound waves.

So, again, pitch is how high or low a sound is. Which, as we just learned, is determined by the frequency of the disturbed air particles that make up sound. The easiest way to visualize pitch in a musical sense is with a piano keyboard. Each key has a different pitch.
Here you can find a great interactive way of seeing all of those different pitches on a piano keyboard.
Note: "MIDI" stands for Musical Instrument Digital Interface. It's basically just a universal program and unit for music on your computer.

Melody

Webster's Definition: "a rhythmic succession of single tones organized as an aesthetic whole"

My Definition: The main character or focus of a piece of music.

Just like in any novel, just because it's the main character, doesn't always mean that it's good or that you'll like it. Melodies can be pleasant, but they can also be unpleasant. If a melody is pleasant, we call it conjunct. If it is unpleasant, we call it disjunct.
Technically speaking, conjunct melodies have notes that are generally close together and pitches that all seem to stay relatively the same. Disjunct melodies have notes that generally kind of jump around all over the place, and differing pitches. Most listeners prefer more conjunct melodies, just like most readers prefer good guys for protagonists.

A couple of examples of melody are Beethoven's "Ode to Joy" (conjunct melody) and "The Star Spangled Banner" (disjunct melody):

When it comes to visualizing melody, we can use something called melodic contour. This is basically just the way that a melody would look if it were a line or shape. Here are two examples of a conjunct and disjunct melodic contour:

Okay, so now that we have gone over all of that, there is just one last aspect of melody that I would like to go over. This is tunefulness. And, well, ya know how sometimes you hear a song and then it's just playing in your head over and over again all day and you can't seem to get rid of it? Or you'll suddenly find yourself humming a catchy commercial jingle? Well, you do these things because the melodies are tuneful. Generally tuneful melodies are conjunct and fairly repetitive in their nature. This is what makes them so memorable. As an example, perhaps the most tuneful song out there is "It's A Small World." I won't post it here though, so as not to torture you with it. But you get the idea.

Harmony

Webster's Definition: "the combination of simultaneous musical notes in a chord"

My Definition: The presence of multiple pitches occurring simultaneously.

Just like melody, harmony isn't necessarily always a good thing. It is simply the occurrence of two or more notes at the same time. It's multiple musical sounds simultaneously. Also like with melody, harmony can also be pleasant or unpleasant. Pleasant harmonies, when the notes sound nice and sweet together, it's called consonant. Unpleasant harmonies, when the notes clash and don't go well together, it's called dissonant.

 Vivaldi's "Spring" is a lovely example of  a consonant harmony.

Wagner's "Die Meistersinger von Nurnberg" has a lot of dissonance in it.

 

Texture

Webster's Definition: "a pattern of musical sound created by tones or lines played or sung together"

My Definition: How much musical "stuff" is present in a piece of music, or the layering of different sounds in music.
          ~Basically, texture describes how many melodies are happening within a piece at any given time.

There are four main types of texture in music: monophonic, homophonic, heterophonic, and polyphonic. 

Monophonic Texture

The word monophony breaks down to mean literally "one sound." In monophonic texture, there is only one melody present. All the singers and musicians play the same melody - basically, everyone is in unison.

 The classic nursery rhyme "Pop Goes the Weasel" is a good example of what monophonic texture sounds like:

Homophonic Texture

The word homophony breaks down to mean "the same sound." Even though there isn't only one melody going on, you really only hear one general sound. That's because there is one main melody going on, with some other little sounds supporting it.There isn't necessarily only one melody going on, but you only hear the one main melody.

A beautiful example of homophonic texture is W.A. Mozart's "Eine Kleine Nachtmusik":

 

Heterophonic Texture

The word heterophony means "different sounds." There are multiple melodies going on, but, again, with one main melody. Heterophonic texture is like a novel - you have a main character supported by a whole cast of characters who serve to improve the story and accent the main character. Heterophony does exactly that, only with melodies instead of characters.

Most popular music today is heterophonic in texture, including my absolute favorite song, "Yellow" by Coldplay:

 

Polyphonic Texture

The word polyphony means "many sounds." In polyphonic texture, there really are many melodies going on at once. There is no main melody, because all of the melodies being played are pretty much equally important. It's like a good ensemble cast. However, it can be a little confusing to listen to at times, what with so much going on at the same time.

A good, classic example of polyphonic texture is J.S. Bach's "Toccata & Fugue in D-Minor":

And there you have it - texture in its many forms!

Timbre & Instrumentation

Webster's Definitions:
           -Timbre: "the quality of tone distinctive of a particular singing voice or musical instrument"
          -Instrumentation: "the arrangement or composition of music for instruments esp. for a band or orchestra"

My Definition: The quality of a sound or tone.

Timbre, really, is just how a song or aspect or a song sounds. So-how a sound sounds. Instrumentation is really just how the different instruments sound and how a composer or musician takes advantage of that sound. Every instrument and person has their own unique timbre. Sometimes things can sound similar, yes, but it's always at least a little different. Timbre is kind of like your musical fingerprint - unique for everyone and everything.
There are a variety of words you can use to describe timbre. You've probably even heard and used a lot of them before. Some examples are raspy, smooth, sweet, pure, harsh, etc. You can use adjectives like these to describe somebody's voice or any other instrument as well.
Really that's all there is to say about timbre and instrumentation. It's just your musical fingerprint and how your voice or instrument or the song in general sounds. And that's really all that there is to know!

Form

Webster's Definition: "manner of coordinating elements"

My Definition: The "shape" of a piece of music, based on the repetition and contrast of the parts of it.

One way to think about form in music is as a plan. It tells you how the song is going to go and where there will be repetition (repeated musical moments) and contrast (noticeable differences in the music). It lays out the movement and sequence of events of a piece of music.
When it comes to analyzing or transcribing the form of a piece of music, we do that much the same way that we would for poetry: we use letters for each line. For the first line of repetition, we use "A." For all the lines of repetition that follow, we use "A" + a prime symbol like ' or '', depending on how slightly different each repetitive line is. For the contrast lines, we use "B," "C," "D," and so on. We use the same prime symbols as  we do for the repetition.
Now, that was probably a bit confusing, so let's listen to an example and give it a try:

"Twinkle Twinkle Little Star" is a classic nursery rhyme that you have  most likely heard and sung before. It has what we could call a simple ABA form.

 

  
Twinkle, twinkle little star,         A

How I wonder what you are.       A'

Up above the world so high,       B

Like a diamond in the sky.         B'

Twinkle, twinkle little star,         A

How I wonder what you are.      A'

And that's how form looks! It's really that simple. If a line sounds like the line before it, go ahead and give it the same letter. If it's clearly different, give it a new letter. And that's exactly what we just did for "Twinkle, Twinkle, Little Star." We planned out the classic nursery rhyme based on how it sounds and its repetition and contrast, which is just what form in music is.