Music Theory is a large category, and I thought it would be a good idea to go over some of what this category covers. Please note that this is not a comprehensive list, and I'm sure professional colleagues will find many things I have either omitted or forgotten, but I think this will help a lot of you to figure out what you know, and what needs work.
This list is sorted by types of theory, and the various levels. The only section that is, in my opinion, inexcusable not to master for every single music student is the section on fundamentals. That said, I still recommend most students to explore as much as they can on all the other areas, at least level 1 of each. As you go, keep track of where you think you are on this list, and what you should improve or begin learning.
Here's the list!
Category 1: Fundamentals
This is the category that is a prerequisite for getting any benefit from the other categories. I've noted levels under what you should know, but you need to master every level before continuing study of another category, except where noted.
Knowing Rhythmic notations
Level 1: Notes and rests: whole, half, quarter, eighth, dotted half, dotted quarter
Level 2: Notes and rests: 16th, 32nd, 64th (and understanding how this progression
continues), triplets based on quarters and eighths, dotted 8ths
Level 3: Notes and rests: other tuplets (like duplet, quintuplet), other dotted and
double-dotted notes
Knowing names of notes on a staff
Level 1: Treble and Bass Clef: notes on the staff
Level 2: Treble and Bass Clef: notes at least 3 ledger lines below and above each
staff
Level 3: Alto and Tenor Clef through 3 ledger lines up and down (only really
needed for composers, arrangers, orchestrators, conductors, string players)
Common musical terms, dynamic signs, tempos (no levels)
Understanding of Time Signatures
Level 1: 2/4, 3/4, 4/4, 3/8. 6/8, 2/2
Level 2: 9/8, 12/8, 3/2, 6/4, knowledge of other simple/compound meters
Level 3: 5/8, 5/4, 7/8 and other asymmetrical meters
Key Signature Recognition (no levels: All major and minor keys)
Recognizing Types of Scales
Level 1: Major, natural minor, harmonic minor, melodic minor, chromatic; Also
names of scale note functions (Tonic, Dominant, etc)
Level 2: Pentatonic, Whole Tone, Blues, Church Modes (Dorian, etc)
Level 3: Some familiarity with non-Western modes
Recognizing Intervals
Level 1: General 2nd, 3rd, 4th, 5th, 6th, 7th, and octave
Level 2: Major, minor, perfect versions of the above (plus tritone)
Level 3: All other augmented and diminished intervals
Recognizing Types of Chords
Level 1: Major and minor triads in all inversions
Level 2: All inversions: Dominant 7th, Major 7th, Minor 7th, Diminished 7th, Half-
Diminished 7th, Diminished and Augmented Triads
Level 3: minor-Major 7th; types of 9th, 11th, 13th chords; sus-chords,
Level 4: non-traditional chords (can be learned in the Harmony section)
Basic Forms
Level 1: Knowledge of Phrases; Forms: Binary, Rounded Binary, Ternary
Level 2: Theme and Variations, Sonata Allegro, 5 and 7 part Rondos
Level 3: Inventions, Fugues, Song Form & Trio (or Minuet & Trio)
NOTE BEFORE CONTINUING: Unless you intentionally study Music Theory as a class or have a teacher with a passion for the subject, most students never go beyond the fundamentals. And the fundamentals encompass what can be years of study! If you feel like you're still working on this and that going on would be daunting, no worries. Keep working. The good news is: once you have a full measure of confidence in the fundamentals, the transition to these other branches of theory are all very manageable.
Category 2: Part Writing and Voice Leading
The craft of constructing a melody and harmony (or harmonizing a pre-existing melody) in 3 or 4 voices at first might seem antiquated, especially for modern composers, given that it is a practice meant to serve a Baroque and Classical way of composing. However, even in modern music, the understanding of smooth voice leading not only comes in handy for writing practical choral music, but also leads to smooth ensemble voicing even within a woodwind, brass, or string section. It also leads to an understanding of how to smoothly move from any chord to another. The great part is that it trains you in composing without the aid of hearing it played first on an instrument.
If you're not a composer, it's also a great exercise for learning how smooth voice-leading works, and this will help you more reliably predict what to play when sight reading 3 and 4 part textures and larger.
LEVEL 1: Learning how to read figured bass, knowledge of diatonic chords and
chord progressions.
LEVEL 2: Add an inner voice to 3 other parts already written for you.
LEVEL 3: Add 2 inner voices to a bass line and soprano melody.
LEVEL 4: Add 3 parts above a bass line (including melody) or completely
harmonize a melody.
LEVEL 5: Complete 4 part construction from scratch.
Category 3: Harmony and Analysis
Again, this step is not going to be easy or particularly beneficial until you have not only mastered the Fundamentals, but have at least begun working on Level 3 of Part Writing. This is when you take pieces of music and analyze what's there. What you do is up to you (or your professor) as the main objective for studying the music. Here is a sample of some things you could analyze.
Identify all harmonies, and identify all the non-chord tones, either with letter names or with Roman numerals.
Identify the form, both the large overall macro form, and the structure within smaller sections. (For example: Für Elise by Beethoven is a 5-part Rondo of ABACA. The famous A section itself (the part that all your non-piano friends seem to learn) is divided ABA Ternary.
Theme and Variations: How is the theme varied in each variation? Technically, you should be able to find the melody, chord progression, or bass line as something in common with the original theme.
Detailed melodic analysis. Look at every idea. Is it a restatement or modification (inversion, retrograde, modal change, rhythmic change) of an earlier motive or theme, or is it completely new?
It's not easy to assign levels here since some types of analyses could overlap with others. That said, here's how you might determine your level.
LEVEL 1: Analyzing smaller forms with limited and traditional harmony mostly
within the scale.
LEVEL 2: Working with more advanced tonal harmony such as 7ths, secondary
dominants and diminished, augmented 6th chords. Larger forms. More
detailed melodic analysis.
LEVEL 2A: Jazz scores: analyzing within the Jazz language of chord names.
LEVEL 3: Atonal and Polytonal harmonic analysis, knowledge and experience with
tone rows, experience with a system like Hanson, Vector, or other.
Category 4: Counterpoint
This branch of theory deals primarily with polyphonic music, and is equal parts analytical and hands-on construction. Counterpoint simply means note-against-note. The analysis is looking at how multiple melodic lines relate. Typically, it's categorized into what are called 5 species: 1st: 1 note vs 1 note. 2nd: 2 notes vs 1 note. 3rd: 4 notes vs. 1 note. 4th: a specific type of suspension-resolution between voices. 5th: Liberal mixture of all types of combinations.
PREREQUISITES: This type of theory makes no sense until you've mastered notation, full knowledge of all kinds of intervals, harmonic analysis, chord progressions, and some melodic analysis.
LEVEL 1: Analysis of easier Baroque keyboard works, write in 2 parts.
LEVEL 2: Analysis of Bach Inventions: Compose your own.
LEVEL 3: Write with 3 parts, analyze similar music.
LEVEL 4: Write in 4-parts, analyze similar music.
LEVEL 5: 3 and 4 voice fugues - both analysis and composition
LEVEL 5A: Study in Renaissance, Classical, Romantic, and Modern counterpoint
Category 5: Orchestration
As a pure branch, this needs very little prerequisites beyond the fundamentals. You can, of course, incorporate analysis of all kinds when studying an orchestra piece, but you can otherwise begin this at any point. I don't have any specific levels. Just know that a Schubert Symphony is much simpler in terms of orchestration than Tchaikovsky, who is much simpler than Ravel, who is simpler than Penderecki. The closer to now you get, up to a point, the more advanced the orchestration. It is highly recommended that you study this with some form of orchestration textbook and as many written scores as you can find for analysis.
Some things to know:
Score order of instrument families, and knowledge of those families
Common European translation of instrument names
Experience with transposed instruments (and how to transpose to C)
Knowledge of instrument ranges, both practical and possible
Knowledge of instrument strengths and weaknesses as well as special effects
Again, professional theorists can no doubt find other branches and elements they would deem important. How much theory you need beyond the fundamentals is naturally up to you and your goals. However, I would strongly encourage you to have the curiosity to explore as much theory as you can make time for.
If you are looking for someone to guide you, send me a message, and let's talk about how you can get more solid in the world of music theory!