Notes "or pitches" are the most absorbing of the elements that make up music. The time elements, like tempo and rhythm, are more of a 'feel' thing. Notes, however, are a more exacting science. The way they blend together, and, more importantly, don't blend together is a never ending source of wonder to me, even after playing for 50 years.
Melody is the 'linear', or horizontal, way of using notes, where they come one at a time with time; Harmony is the vertical way, where notes ring out together as chords.
Scientifically speaking, sound is really molecules of air, moving in waves, that reach our eardrums and translate into all that we hear. The waves are measured in hertz, or 'how many waves hit your eardrum per second'. We can hear tones from about 20Hz (very low) to 17,000 Hz (very high). The note A, second fret of the 4th string, rings out at 440 Hz; the open A string, an octave lower, rings out at 220 Hz; the A note on the thin string, 5th fret rings out at 880 Hz. So, take any note, double its frequency and you have that same note an octave higher; half it, and you have the same note an octave lower.
It's all mathematics. Here's another example: The formula for determining how far apart the frets on a guitar should be is f2 = 21/12 x f1 ... if that's not mathematics, I don't what is. But it's the art of making music that I love, not the science. I find it endlessly fascinating that we can manipulate sound in the ways that we do through musical instruments, that these sounds can affect us so deeply.
If you're at all familiar with the piano, you'll know that those '#/b" notes -- sharp/flat -- are the black keys on the keyboard. Guitars make no distinction between natural notes and the #/b notes, they're all mixed in together and look the same on the fretboard.
Notes are the sound element of Music, what we hear. They're also referred to as 'pitches'. Any sound that holds a certain fundamental frequency is a pitch, like a bell, or a struck wine glass, or an electronic beep. Sounds like sirens or jet engines starting up are not pitches, their sounds are continuous and smooth changes in pitch from either low to high or high to low. Sounds like ocean waves breaking are a combination of all frequencies called "white noise". Music breaks sound down into notes or pitches. Here is how:
• There are 12 notes which repeat, just like the 12 months of the year. Months of the year are named from past to future; notes are named from low to high.
• A 'musical year' is called an octave. The human ear has a range of many octaves, the guitar has a range of 4 and a half or so (electrics, almost 5).
• Notes of the same name in a different octave have a different pitch, but follow the rules as if the same note, just as February is always February, whether it's 1963 or 2013.
• The 12 repeating notes are mere building blocks until a template is introduced, like a stack of bricks waiting for the blueprint to become a house.
• The distance in pitch between any two adjacent notes is called a semitone or half step , on a guitar: one fret. A whole step is (obviously) two half steps, two frets. The idea of "step" is a good analogy as notes in sequence do form a kind of staircase in pitch as illustrated below.
• The distance between any two notes is called an interval. An octave is an interval; a semi tone is an interval (the smallest); a whole step is an interval.
• Intervals are the ruling force within the system of music. These distances between notes allow for melody and harmony and the many different qualities our ears and hearts discern when listening to music.
Below is a graphic showing showing some notes (represented by the blue ovals) rising from bass to treble. Their names are based on the first seven letters of the alphabet: A B C D E F G and they're named from low to high. The green panel encloses one octave of notes, in this case from A to A.
Notice that there are some gaps between the named notes, there are some 'in between' notes. They're named differently, using the symbols 'sharp' and 'flat'.
Because of browser incompatibility, I'll just use the hash sign (#) and a lowercase B (b) for those symbols throughout the site.
# means higher by one semitone, b means lower by one semitone. So a C# is the same note as a Db. It's the note that is "higher than C" and "lower than D". The reason for this duality is of no concern at this stage, it's just a pain in the neck. They're called either one or the other, not both. For example, the note between A and B is either called A#; or Bb. The rule about how to choose which are which is not important at this stage.
You'll also notice in two instances that there is no in-between note. B goes straight to C and E goes straight to F. So here is a graphic now showing all the note names starting and ending at A.
Here's another way of looking at notes. In this image, the lowest note is C (it can be any) and 12 steps later, we're back to C. Notice that both C's are lined up in the same way, illustrating the fact they they are the same note, but one octave apart, which is represented in this analogy by the vertical distance between them. The vertical distance between each step is a "semitone", or (don't let this confuse you) a "half-step". Look at this spiral staircase continuing up and down through three octaves to get the full picture of how notes work. An acoustic guitar has about 4 1/2 octaves of usable notes, an electric a little more.
Those blank steps are the ones that can have two different names, either "sharp" of the name below, or "flat" of the name above. So the step between F and G is either F# or Gb, but whatever it's called, it is in fact the same note. Later on, as you get more into theory, you'll see why this is, but for the time being, there's no real need to worry about it.
These 12 notes (+ their octaves), taken together, are called the Chromatic Scale.