Music theory is the study of musical tones and rhythms for the purpose of understanding how music is made.
I have interest in music theory as I feel that understanding what makes a song sound the way it does helps me appreciate it better, and also helps me make better songs myself, as I can pick out little songwriting tricks and patterns a little easier if I understand music theory.
Beginning music theory is a fairly necessary thing in order for musicians to communicate clearly with one another and write songs. For every learn-by-ear guitarist, there is a bass player who understands the level of theory necessary to make some sense out of the meandering riffs to the end of making intelligible bass lines that match the guitar riffs...or so I hope.
The notes on the guitar are pretty limited, but every note you find on a piano can be found somewhere on the guitar or the bass, except some of the very low ones.
Long ago, Germanic peoples invented a notation for communicating the notes on the keyboard with one another using the alphabet. This system expanded into what we now use in most (if not all) English-speaking societies.
There are seven natural notes and five sharps, or five flats. You see, in standard western tuning, some notes are the same as others. When two notes are written differently, but make the same tone, they are called "enharmonic equivalents."
The seven natural notes are:
A B C D E F and G
The five other notes are represented by sharps and flats. I will use # for sharp and b for flat, because it is easier for me at this point than fishing for the symbols. A sharp is a note that is raised one half step (one fret toward the body of the guitar or one key to the right) and a flat is just the opposite of that, a note that is lowered one half step (so that it is one fret closer to the head of the guitar or one key to the left on the piano).
The five sharps are:
A# C# D# F# and G#
The equivalent flats are
A# = Bb, C# = Db, D# = Eb, F# = Gb, and G#= Ab
So the five flats, which are the same as the five sharps are:
Bb Db Eb Gb and Ab
What's more, you can also write B#, but it will just be the same thing as C, and C is a little simpler, so we don't write B# unless there is a good reason to do so, like if C is somehow already taken. The same goes for E# and F.
You can sharp a sharp to get a double sharp, written here with an "x" symbol. You can flat a flat to get a double flat "bb," and if you flat a sharp or sharp a flat, you just end up where you started.
Some Germanic countries (actually most, from what I understand) use the letter H instead of the letter B, so that the notes in these countries are represented by A H C D E F G. The letter B they use in musical notation is the same as our Bb, so it can get pretty confusing when an Englishman and a German discuss music.
Other European societies use another notation for the notes, which is also familiar to most of us:
Do Re Mi Fa So La Ti
Or some variation of that.
Even music in Indian classical music is represented in a way similar to that:
Sa Re Ga Ma Pa Dha Ni
Anyway, it is confusing, because the music itself has existed for a very long time, but the notation for writing the music down hasn't existed nearly as long.
I'll use the notation that most english speakers use: A B C D E F G with #'s and b's, and the occasional x or bb.
After the letters repeat, I'll call that an "octave." You can have two different keys on the piano that we call "A," that sound different. Since there are seven letter to use, then we repeat the seven letters again, I'll use the term octave, which comes from the prefix oct- for eight of something.
Sometimes the octave number will be part of the name of the note, but usually it is not. For example, the third string of the the guitar is typically tuned to G3, which means that it is the note G in the third octave. above low C. The notes do not stop at any given point going up or down. Below C1 there is a B0. Below C0, there is a B00. Although the human ear stops registering audible frequencies around the fundamental frequency of E00, the brain still detects the pitch from overtones.
Rhythm is another thing to worry about. The length of time that a note is played has to be communicated somehow. The different units of note length are defined relative to the quarter note:
The whole note is held for the time of four quarter notes.
The half note is held for the time of two quarter notes.
The eighth note is only held for half the time of the quarter note.
The sixteenth note is held for one quarter of one quarter note.
The thirty-second note is held for one eighth of a quarter note.
The sixty-fourth note is held for one sixteenth of a quarter note.
Most music utilizes whole notes, half notes, quarter notes, and eighth notes, with regular use of sixteenth notes. Thirty-second and sixty-fourth notes are very rare.
Notes are divided by their timing into "measures." Certain parts of the measure are accented to be just slightly louder than others, and this consistent positioning of the accents gives the song a certain rhythm.
To determine the meter of the song, or the song's pulse, musicians use a time signature.
The time signature is written like a fraction. The number on the top tells you how many beats are in a measure, and the number on the bottom tells you which type of note is considered a beat.
The most common time signature is 4/4 (read four-four time); in fact, it is so common, that it is refered to as "common time." The four on the top means that there are four beats per measure. The four on the bottom means that a quarter note is equivalent to one beat. When in 4/4, you should count "ONE two Three four," as the heaviest accent is one one and the subtler accent is one three.
Other common time signatures are 3/4 and 2/4. In these time signatures, count "one" with a loud accent, and the other number with a medium accent. 3/4 time is common in waltzes, minuettes, and country/western ballads. 2/4 time is common in marches and polkas.
Some other time signatures that you may find without looking too far are 6/8 and 12/8. The time signatures with eighth notes as one beat tend to imply a faster rhythm, but implies a slight accent on all odd numbered beats. 6/8 is common in faster folk dances, double jigs, tarantellas (famously "The Sicilian Tarantella," a traditional Italian song widely represented in movies and television shows during scenes in Italian restaurants). 12/8 time is very common in blues and blues-rock.
Odd time signatures are those that are not considered common in western music. Some examples include 9/12, which is used for Richard Wagner's Walkürenritt (Ride of the Valkries), which may be better known among my generation as Elmer Fudd's "Kill the Wabbit Leimotif." Tchaikovsky's "Limping Waltz" from Pathétique Symphony is written in 5/4, as is Dave Brubeck's "Take Five." Also from Dave Brubeck, "Blue Rondo a la Turk" is written partially in 9/8 time,
So now that we know how to cut the notes up and put them in time, what about which notes to play?
Well, I discussed how there are twelve notes per octave in standard tuning. There are a number of ways to put these notes together.
Two notes put together are called an interval.
The most basic intervals in western music are the whole step and the half step. The basic idea is that two half steps make a whole step, and all of the other intervals can be made from these basic units.
A half step on the guitar is one fret. On the piano, it is the next key over, black or white. The whole step on the guitar is two frets. On the piano it is two keys over, even if the two keys are touching each other.
starting from C, a whole step up is D, then a whole step up from there is E. F is only a half step up from E, because there is no black key between them. But then G is a whole step up from F, and A is a whole step up from G, and B is another whole step up from A.
Staying on the white keys from a lower C to a higher C, you play what is called a scale. The notes you play are C D E F G A B C, and the steps you take are whole, whole, half, whole, whole, whole, half or "wwhwwwh" for short.
The next step is to number the intervals from 1 to 8, so:
C=1 D=2 E=3 F=4 G=5 A=6 B=7 C=8
Or we could repeat that C=1 again, like we said in the first place. I don't like trying to say 1=8, so I'll usually omit the number eight altogether.
I will go one step further by saying a 1 is called a "root" or "unison," and giving ordinal names to the intervals, like second, third, fourth, etc.
Analyzing these notes and intervals, I will put the major scale together with the intervals, so when I say 3, I will thing "major third." To make it less easy, I'll say that the fourth and fifth intervals are extra special, so I won't call them "major," but I'll call the "perfect" instead.
So now I can say that the major scale is 1 2 3 4 5 6 7, or read aloud, "root, major second, major third, perfect fourth, perfect fifth, major sixth, and major seventh."
So now we have a few intervals. The interval between C and F could be called a perfect fourth. If I'm starting someplace other than C, I can still move the same number of steps and it is still a perfect fourth. For example, if I start at D instead of C, I will end up at G instead of F. So the interval between D and G is also a perfect fourth.
If there is a major something, then there is also a minor of it. That's why there are flats. If I ever see b3, for example, I call it "minor third."
Perfect intervals can be flattened to make them diminished, or sharpened to make them augmented. In fact, and interval that is a half step sharper than it is in the major scale is called "augmented." Diminished can also mean that it is a half step flatter than the minor interval.
Once intervals are understood, we can move on to triads, which form tonalities, and scales, which are like a palette of notes from which to choose to make melodies.