Music theory can be a very daunting subject because it covers such a large span. I always say that music theory is the "math" of music. Like math, music theory covers the simplest concepts to very advanced ones that most people will never learn. In math, I could teach you what 2+2 is, or go into advanced calculus. Music theory starts with concepts so simple that you might not know you know them. For instance, can you identify if a note is low or high? That's "ear training" and essentially "music theory."
I am going to break music theory down into smaller subjects and try to touch on the easiest concepts as well as a few slightly more advanced components within each subject. Keep in mind, all of these subjects overlap quite a bit.
If you crack open a music theory workbook, chances are it will start with material that revolves around reading music. It might start with identifying a treble clef, or learning that a music staff has 5 lines and 4 spaces. It might go into the names of the notes on the staff. Within this category, there's an overlap with rhythm - particularly being able to read rhythms. Beginning students might learn that a quarter note has 1 beat, a half note has 2 beats, and a whole note has 4 beats. That's enough to keep a new music student busy for a while. When combined with note names, that's pretty much all you need to play a song. But a good music teacher will make sure that their students are practicing their "note-naming" and maybe clapping some rhythms in addition to learning songs so that their reading skills stay sharp.
Some might argue that ear training is a subject in itself, but I believe that it has enough overlap with classic music theory that it might as well be invited to the party. Ear training is exactly what it sounds like - training your ears to be able to identify sound qualities - whether that's the type of chord you're hearing (major or minor), or what notes you're hearing.
Melodic Ear Training is training your ear to be able to identify the notes in melodies. This means one note at a time. Solfege is a great tool for melodic ear training. This is the "Do Re Mi" that everyone has heard at some point in their life (if nothing else, from The Sound of Music). When I was in middle school and high school, I didn't understand why anyone would use solfege. It seemed like one of those things teachers do with students to make things fun, and really just made me feel like a baby. But then in college, I finally understood the purpose. Solfege is a great way to connect your voice with the functions of different notes on the scale. It's an amazing tool to use as a vocalist to experience music the way an instrumentalist does. When you sing 3 notes on "ooh," you might not have a clue what you're actually singing. If you challenge yourself to "solfege" the notes, you might sing "Do Mi Sol" and then realize that you're singing the 1, 3, and 5 of a scale, or arpeggiating a major chord. Solfege starts easy and can get really wild once you incorporate chromatic solfege. The easiest way to explain chromatic solfege is that you're adding the black notes on the piano. Normal solfege is based on a major scale - 'Do Re Mi Fa Sol La Ti Do" is the same as "1 2 3 4 5 6 7 1." But if you want to sing every note on the piano including the black notes, you would sing "Do Di Re Ri Me Mi Fa Sol Si La Li Ti Do" ... there's a lot more to this, but you can imagine that once I learned this, solfege no longer made me feel like a baby.
Harmonic Ear Training is training your ear to be able to identify harmonies or chords. This is 2 or more notes at the same time. For instance, if someone plays a chord on the piano, a music student should be able to identify if it's major, minor, diminished, or augmented. When students get more advanced, they will be able to identify even more complicated things like different types of 7th chords (4-note chords that include the 7th degree in some form) and tensions (add-ons to chords to make them even cooler-sounding). This skill is very important for musicians to have, especially if they're playing with other musicians. Jazz musicians play music based on chords and need to be able to identify where in the music they are by using their ears. A good jazz musician should never get lost in a song. If they zone out for a second and forget what they're doing (it happens to the best of us), they should be able to use their ears to identify what chord the rest of the band is playing, and therefore where they are in the song.
Rhythmic Ear Training - Rhythm isn't just for reading, it's also something that you should be able to transcribe as a musician. This means to identify (and write down) the rhythms that you're hearing. This starts early for music students. Most elementary music classes have rhythm sticks or some sort of percussive instrument for playing "follow the leader." They most likely aren't writing those rhythms down, but they are parroting them back to the teacher. That's rhythmic ear training! When that student gets older, they might find themselves dealing with polyrhythms (don't ask!)
Some things are just so mathematical in music theory that they can only be categorized as... theory.
The circle of 5ths is one of the most important concepts to understand in music. Once you understand the Circle of 5ths, everything else makes sense. This is a concept that takes a while to put together, but for those of you that actually want to know, I will try to explain it as simply as I can.
The circle of 5ths is essentially a map of all the keys. At the top of the circle, you will see the key of C. The reason it's at the top is that it's the major key with no sharps or flats. If you're at a piano, play C, and then every white note until you reach the next C. You just played a C major scale. The next key to the right on the circle of 5ths is a G. The G is 5 notes higher than C or "Up a 5th" from C. This is why it's called the circle of 5ths. Why is G important? Because the key of G has 1 sharp. If you play a G on the piano, and then every white note until you reach G, it might sound a little off. But if you play an F# instead of an F, it will sound just like the major scale you're used to hearing. The next key is D because it has 2 sharps, then A because it has 3, and so on. If you start at the top of the circle again and go to the left, it's the same pattern, but going down a 5th and adding another flat each time.
This is a super cool trick for all you music students out there: Did you notice that each time you add a sharp, the previous sharp is still part of the key? For instance, the key of G has an F#, then D has F# and C#, then A has F#, C#, and G#? Well, I've got a trick for you:
Order of Sharps:
"Father Charles Goes Down And Ends Battle"
in other words...
F# C# G# D# A# E# B#
Order of Flats
"Battle Ends And Down Goes Charles' Father"
in other words...
Bb Eb Ab Db Gb Cb Fb
*Did you notice that those sentences are the reverse of each other!? Amazing! If that makes no sense to you, don't worry! The circle of 5ths can be a really scary and confusing concept at first, but most of my students eventually have an "aha" moment after hearing me talk about it for the 100th time.
Why is the Circle of 5ths Important?
The circle of 5ths, aside from being a really cool concept and a pretty-looking diagram, is the ultimate explanation of what keys are, what each key consists of, and how each key is related to each other. The more a student learns about music, the more they come to rely on the circle of 5ths.
Intervals and Inversions
An interval is the distance between 2 notes. The confusing thing about intervals is that when you're counting up the scale, you count the note you're on first. In the wild, that's not how intervals work. For instance, if you have a 1-year-old and a 3-year-old, they are 2 years apart. In music, if you play the 1st degree of a scale and the 3rd, you count the first note you're playing, then continue counting up. So if you're playing C and E, you would sound C D E, and the interval you're playing is a "3rd." Notes next door to each other are a "2nd." Intervals are important to understand for music reading purposes as well as ear-training. Identifying intervals is a very important part of melodic ear training because you use intervals to navigate around a melody - from the note you're on to where you're going. If you're not already confused by intervals, I'll leave you with this... there can also be major and minor intervals! It has to do with the number of half steps. For example, C to C# is a minor 2nd whereas C to D is a major 2nd.
Inversions are the specific order that you're playing notes. They can refer to intervals or to full chords. Inversions of a triad (or 3 note chord) are as follows:
Inversions of an interval are the same concept, but instead of 3 options, there are only 2...
Advanced Concept: If you know your intervals, and you understand the concept of inverting an interval, check this out...
As you might know (or be able to figure out), a 2nd inverted becomes a 7th. For instance, the distance between a C and a D is a 2nd, then if you transfer the C up an octave, the distance between that D and the new C is a 7th. But what you may not have noticed is that each interval and what it inverts to ads to 9. 2+7=9, 3+6=9, etc. But wait, it get's crazier...
So the concept is the same but add in that minors become majors and vice versa. Aside from this being mathematically awesome, these groups also have a very similar vibe. 2nds and 7ths are dissonant and clashy, 3rds and 6ths are very pretty, and 4ths and 5ths both have kind of a regal sound.
Even though this isn't technically music theory, someone who's curious about music theory might also wonder what "technique" is referring to. Technique is referring to the practice of a musician improving their technical facilities. This could mean a violinist practicing their bow-hold, or a pianist practicing finger exercises to improve their dexterity. For pianists, there are 3 very common exercises that incorporate technique as well as theory. These can be played by other instruments as well, but might have to be adjusted for non-harmonic instruments (instruments that can't play more than 1 note at a time):
Arpeggios are playing a chord one note at a time, ascending and descending a certain number of octaves (depending on how advanced the student is). For instance, a 2 octave C major arpeggio would be C E G C E G C (all ascending), and then back down again.
Cadences are a series of chords that would commonly resolve a phrase or a song. There are many different candences, but a common one to practice is (we write them in roman numerals): "I IV I V I." That's 1-4-1-5-1 or in the key of C: "C-F-C-G-C." This helps students understand the function of different chords in different keys and is a great exercise for their dexterity and finger strength.
Inversions can be practiced "broken," "blocked," or both. I have my students practice both on the tonic (1) chord of whatever key we're playing that week. For instance, if they're playing a C major scale and C major arpeggios and C Major cadences, they will be playing a C major inversion, which is taking a C major chord and playing it in every configuration (or inversion) of the chord.
As you can see, music theory is very similar to math but is essential to understanding music as a whole. The good news is that everyone's invited to the music theory club, whether you're able to clap back a rhythm or you're doing a chord analysis on a modal jazz tune.