Royal Conservatory of Music (RCM) Theory Exam Guide

I have recently had the privilege of writing the Royal Conservatory of Music (RCM) Grade 6 Theory exam at 98% with 30 minutes of time left. During my studies, I have collected a number of tips, tricks, and shortcuts that help me preserve as much time as I could which I'd like to share here. The rest of this post is divided into subsections correlating to each exam section. As I continue to progress through my piano studies, I will update this post with new tips pertinent to each grade.

Background knowledge

Circle of Fifth

One of the most important things to know when doing theory exams is to know your circle of fifth like the back of your hand1. This will speed up your responses by a large margin.

I like mnemonics, but most mnemonics I found on the internet were more difficult to remember than the circle itself. They are long sentences which don't make much sense: "Caroline Gets Drunk And Eats ButterFlies". Who's Caroline, and why is she eating butterflies? This mnemonic is more appropriate as a passphrase.

I remember the circle of fifth as follows:

See Gee Day Beef, plus a C# which I don't know how to memorize. I have resolved to just remember that it's a C# at the end.

Eff Bead Gee See. Again, I just memorized the Gb and Cb at the end through repetition.

Scale degrees

When talking about scale degrees (e.g. major 3rd, perfect 5th, etc.), you can remember them by imagining a pair of pants.2

perfect       1   4---5   8
              |   |   |   |
              |   |   |   |
major/minor   2---3   6---7

The top layer is diminshed-perfect-augmented while the bottom layer is diminished-minor-major-augmented. Each step (e.g. from diminished to perfect to augmented) is a half step up or down.

Refresh on the relationship between scale degrees. This is beyond the scope of this article.

Building scales

One of the skills that has improved my speed in these exams has been building scales in my head with the following rule: WWHWWWH. TODO

Transposition in major keys

There are two kinds of questions in this section:

The keys are all major in this exam.

Name the keys when interval is given

With circle of fifth firmly in your head, we can now easily tackle the first part. To name a key (which will be a major key in this exam), just refer to the circle of fifth. This should be fast enough if you only count the number of sharps or flats and count through the mnemonic.

To find the transposed key, I ignore all sharps and flats and only pay attention to the key letter (C, D, E, …).

Let's assume the initial key is E major and we are transposing by a dim4 (diminished 4). I start with E in my head, then move up 4 note letters: E-F-G-A. 4th interval is therefore A. So we now know the transposed scale is either Ab/A/A# major (we don't have A# major in this case, so it's either Ab or A).

To determine the accidental on the transposed key, I like to go through the major scale note by note by going through the note distances (W is whole note, H is half note):

These are the note distances for a major scale. Remember this as it's paramount to saving time when figuring out which notes belong to which scale.

Back to our example: I start with E, go through W-W-H to get to the 4th note of the E major scale: E + whole note = F#, F# + whole note = G#, G# + half note = A. Looks like A is the 4th note in the major scale, therefore A is the perfect 4th interval in the E major scale. The question is asking us for a diminished 4th, so we go down from A by a half step and get to Ab. Therefore, the answer is Ab.

When this thought process is practiced, it looks like the following, which should take about 5-10 seconds when practiced. The key is knowing the circle of fifth and WWHWWWH (2 whole then 3 whole, separated by half).

  1. I see 4 sharps in the key signature and the question says it's a major key: See Gee DAE (pronounced Day) -> key is E major.
  2. WWHWWWH for major scale gives me E-F#-G#-A for perfect 4th
  3. go down a half step and it's Ab major

Name the interval when both keys are given

Similar to the above, for this type of question, you would look at the initial key signature, then the transposed key signature and determine the interval. For example, if you have 5 sharps, you will be in the key of Cee Gee DAE [B]eeF: B major. Let's assume the transposed key is given as 3 flats: Cee Eff [B]EAD: Bb major. From B to B flat, we quickly go through our major scale starting from the initial scale going up by WWHWWWH steps: B-C#-D#-E-F#-G#-A#-B.

Here's the tricky part. Bb and A# are enharmonic equivalents and sound the same. However, picking one over the other changes the name of the interval, thus your answer. For this part, we ignore the accidental altogether. If the transposed key is Bb, our interval starts from B. If our transposed key had the signature of A# minor or Db major and was, in fact, a minor key, then we would choose to work with A. Therefore, since our transposed key signature indicates the major key of Bb, our interval anchors in B.

from B to B is a perfect 8. However, our transposed key is Bb which is half a step lower than B. Therefore, our interval becomes diminished 8, which is the answer.

Let's go over another example. 3 flats to 6 flats, both major scales:

  1. 3 flats = Eff B[E]AD = Eb major scale
  2. 6 flats = Eff BEAD [G]C = Gb major scale
  3. WWHWWWH = Eb-F-[G]-Ab-Bb-C-D-Eb (remember we are looking for the same key letter name as our transposed scale, here it's G)
  4. G is major 3rd, therefore Gb is minor 3rd.

Rhythm and Meter

identify time signature

To identify the time signature, it's most helpful to first identify the bottom number: the note value grouping. You are given 4 bars of notes, which should generally given you a good idea of the note grouping. The first thing you'll notice is whether the time is compound or simple. If notes are in groups of three or there are dots everywhere, it's likely compound. If not, simple time. Once you know it's compound vs simple, then you have to decide the bottom number first. For simple it's 2, 4, or 8; for compound it's 4, 8, or 16.

If it's compound time, look at the basic note of each group. If 16th notes are grouped into three (or if you have a dotted 8th note, or a dotted 16th attached to a 32nd and another 16th), the basic note would be 16th. Same applies to other note values. Once you figure out the bottom number, then count the number of notes that would fit in a bar and you have the top number.

Let's go through a few examples.

Here you can see a few dots, indicating this is likely compound time. quarter notes can't attach together, but you notice the 8th notes are attached in two, indicating the quarter note is likely the "base" note we are dealing with. With these two bits of info, it's likely the bottom number (beat value) is 4.

The top number for time signature will be 9, since there are 9 quarter-note-equivalent in each bar. It's easier to count the beats in the second bar.

In this example, there are groups of 3, indicating likely compound rhythm. 8th notes are grouped, and we have a dotted quarter which you can think of as 3 8th notes. Therefore the base note is 8. There are 12 beats (or "pulses" in this case) in each bar, so time signature is 12/8.

The scariest, but just as easy. There are dots and groups of 3 which means compound rhythm. There a group of 3 16th notes, so it's very likely the bottom number is 16. And counting the pulses, you'll get 6 for a time signature of 6/16. Another clue as to the basic beat is the attachment of an 8th note to a 16th note. In cases like this, it's helpful to imagine the 8th note as 2 16th notes, yielding another group of 3 of 16th notes.

Complete bars with rests

Here is the sequence of things you should go through:

  1. Complete the pulse3
  2. Complete the beat
  3. Never combine two and three (beat or pulse)4

The first thing you should do in this type of question is look at the time signature to see what is the basic beat or pulse (bottom number of the time signature).

When given an incomplete pulse in compound time (or beat in simple time, doesn't make a difference), complete that first. For example, if you have a 16th note in a 6/8 time signature, complete the pulse by adding a 16th rest (16th + 16th = 8th, which is the pulse in 6/8 time signature). Similarly, if you have a dotted quarter in 4/4 time, complete it by adding an 8th rest.

Once that is done, complete the beat. In 6/8 time, for example, where you are given 3 8th notes, you can add a dotted quarter rest to complete the second beat.

At this time, feel free to combine anything except the second and third item of any groupings.

Let's look at a few examples.

basic beat is 8. the first 2 notes combine to give an 8th note, so we don't need to complete it. The last note is an 8th, which doesn't need to be completed. The middle part is missing 4 (total beats/pulses) - 2 (already accounted for) = 2 beats or pulses. Let's add 2 8th rests. Notice the second and third "items" (in this case pulses) can't be combined. The convention here is that you can't combined a weaker pulse or beat with a subsequent stronger one, but thinking about strong and weak takes time, so just don't combine 2 and 3.

First beat is complete (8th + 16th = 3 x 16th = 3 pulses = one beat). second beat is complete as well (imagine it like 3 x 16th notes = one beat). Third beat is not complete, so let's complete its pulses first: we have dotted 16th = 16th + 32nd, so we're missing a 32nd rest to complete the second pulse (each pulse is a 16th note value). Then we need to add a rest for the third pulse within the beat as well. This completes the third beat. The last beat is already complete. So we add a 32nd rest and a 16th rest. Noticed we can't combine the 2nd and 3rd pulses, so the 32nd rest and 16th rest will remain separated.

Scales and key signature

Name the scale

Given a scale without a key signature, you have a choice between major, harmonic minor, melodic minor, and natural minor. Let's look at the difference.

A major key follows WWHWWWH. Minor keys always start with WH. Therefore, if the second and third notes in the scale are one whole step apart, it's a major scale, select that and move to the next question.

If the distance between 2nd and 3rd note is a half step, it's a minor scale. Then you need to pick between natural, harmonic, or melodic. Look at the top of the scale, if the 7th note (second to last going up) is different when going up the scale than when going down, it's melodic.

Otherwise, if the 7th and 8th notes are apart by a half step, then it's harmonic. If they are a whole step apart, it's a natural minor scale.

name relative major or minor of a key signature

Know your circle of fifth. Start by assuming a major key and sing it: Eff BEAD or Cee Gee DAY Bee. Once you know the major scale, take the tonic note and go down 3 half steps to get the relative minor key. For example, the relative minor of E major is C# minor (three half steps lower). Db major's relative is A# minor (three half steps lower).

Pick whichever the question is asking. Once again, know the circle of fifth like the back of your hand. You really only need to know the major keys because you can easily derive the relative minor of every key this way (3 half steps lower).

identify scale degree name, assume major or minor

Identify the key (know the circle of fifth, and the relative minor rule with 3 half steps lower). Once you know the key, see where the given notes fits. This is just memorization. Fortunately, in the online exam, the scale degree names are listed in order, so you really don't have to even know the scale degree names. The tonic is the top-most choice, leading tone and subtonic are the last two, mediant is the third, you get the picture. That's the case in all the questions in this category.

Also, forget about considering sharps and flats in the scale, most of the time it's no relevant whether F is sharp or natural in E major as long as you know F is the second note when starting on E. So, instead of being bogged down by sharps and flats, only focus on the note name itself. For example, given B major key signature with note F, you know it's B major (circle of fifth, know it, love it, belive it), so in your mind, start with B-C-D-E-F, HEY there it is, the fifth note. What's the scale degree name of fifth note? it's dominant of course! Did I need to know if C is raised in B major scale? Not at all.

In many of these questions in RCM theory, you never actually need to know the accidental status of a note in a scale, thinking of it slows you down, so focus on the note name: A B C D E F G.

Intervals

Name the interval

To name the interval, you need to remember a #pair-of-pants. Once you are wearing the said pair of pants, then assume the bottom note in the interval is the tonic of the major scale. For example, given two notes E and G, imagine you are dealing with these notes on the E major scale.

You don't need to actually go through whatever scale you're thinking of. The purpose of this exercise is to remind you of the oh-so-valuable WWHWWWH mnemonic. If the second note fits within WWHWWWH, then it's perfect or major. If not, then it's minor, augmented, or diminshed.

Let's see how this works. You are given E and G#. WWHWWWH dictates the major or perfect notes as E-F#-G#….oh, G# is on there! It's 3 notes apart total (counting starts with the tonic, so a third is E(1)-F#(2)-G#(3)), so it's a major 3rd.

Given Bb and A. WWHWWWH: Bb-C-D-Eb-F-G-A-Bb. Look like we have A as the 7th note, and 7 is at the bottom of the pair of pants, so we have major 7.

G and Db. WWHWWWH: G-A-B-C-D-E-F#-G. We see D (focus on the notes names first to identify the scale degree) is the fifth. We know from pair of pants that 5th can be perfect, dim, or aug. In this case, we don't have Db on the major scale, so it's not perfect. Db is half step lower than what we expect the perfect to be, which means Db is dim5.

Name diatonic vs chromatic

Visualize this on a piano in your mind, or if you have a keyboard in front of you it would make this type of question exceedingly easy and fast. I've found visualization to be the fastest way through this type of question.

Chords and Harmony

Identify the chord

To make things fast, make sure you know how to quickly identify the root note and inversion of each chord. If all three notes in a triad are a third apart and look uniformly spaced, it's root position and the bottom-most note is the root note. If the top-most note is the furthest apart (more than a third away from the other two notes), then the top-most note is the root note and you're in first inversion. If the bottom-most notes is furthest away, then the middle note is the root note and you're in second inversion. Try to draw a few chords and go through this thought process to be able to quickly identify these properties.

The first type of question asks you to identify scale degree triad and its inversion. First move the separated (outlying) notes around to turn the chord into the root position. I just take the note that is more than a third away from the other two by an octave down or up and the chord turns into the root position. Now you know the root note. If there are four notes, then it's easy, it's a dominant 7th chord.

Then read the key signature and, once again, circle of fifth. Once you know the major or minor key, then figure out the scale degree name. For example, if the key signature is that of E major and question assumes major key, then if the root note is G, that will be the third scale degree. So, you will have a mediant triad. If the question assumes a minor key, you are in C# minor key and G is, ummm, C-D-E-F-G, 5th scale degree, so dominant triad.

To identify the inversion. If all the notes are thirds apart, it's root. You can also tell by the uniform shape of the chord. In first and second inversions, one note is further apart. If the furthest note is at the top, it's first inversion. If the furthest note is at the bottom, it's second inversion.

For open position chords, I take the top most notes and bring the down by one octave and turn it into the closed position. Then I rearrange them in my mind like above to find the root. Once the chord is in root position (in your mind, or written down on a scratch paper), then if the distance between the first two notes is 2 whole steps, it's a major chord, if it's 1.5 steps (whole and a half), then its minor triad. Again, if it's four notes, it's just dom7, no need to do any of the rearranging. You'd find the inversion based on the what you did before for the closed position (the furthest note).

To figure out the functional chord symbols, look at the root note, that's the name of the chord, then look at the distance between first and second notes. If it's 2 whole steps, it's major, if it's 1.5 steps, it's minor. For this question, you don't need to read the key signature. Just turn the chord into root position first.

Cadence

To identify the cadence (authentic vs half), you can take shortcuts. Just look at the last chord, if it's I or i, it's authentic, otherwise, it's half. First, look at the key signature and figure out the key and whether it's major or minor. If the root note (rearrange the chord to arrive at the root position) is tonic, then it's authentic cadence (doesn't matter what the previous chord is). Similarly, if the last chord is dominant, then it's half cadence.

To determine the cadence as asked by subsequent questions, find the root note of the first and second chords and match them up to tonic or dominant. Note whether the question is assuming minor or major.

Resources

I have found the RCM study guides to be a fantastic resource in reviewing the theory. The practice unit tests along with practice final exam give quite a few opportunities to learn and improve. I have identified most of the above patterns through repetition while doing the practice unit tests.

If you have found any other valuable tips or tricks, send me an email at feedback at amoradi dot org and mention the title of this article. I'll be happy to include it with attribution here.

Footnotes


  1. The circle of fifth is far more useful than just figuring out key signatures. I highly recommend a deeper dive like is done by John Carlos Baez or Gracie Terzian's youtube channel.↩︎

  2. This idea came from my teacher Nina Maxwell.↩︎

  3. Pulses vs beats. In simple meter, we only have beats (no "pulses"). For example, 4/4 has 4 beats, 4/8 has 4 beats each being an 8th note, 2/4 has 2 beats each being a quarter note. Compound meter is a bit more interesting as each beat consists of pulses. 6/8 time is composed of 2 beats, but 6 pulses (each beat has 3 pulses), 12/16 has 4 beats (12 divided by 3 = 4) each having 3 pulses. The number of beats in a compound meter is pulses divided by 3. This has major implications on the forward sensation and movement associated with the music (e.g. dance). You can intuitively find the beat by how often you feel compelled to bob your head!↩︎

  4. This idea came from my teacher Nina Maxwell.↩︎