Alphonse Nguyen

I’ve decided to summarize some of the important points that the Royal Conservatory of Music expects you to know for their Harmony exams (grades 3-5). The reason why I’m doing this is because I think that it’s essential for every composer to have a strong foundation of the theory behind music. However, you are not obliged to follow all the guidelines that I’m presenting. In fact, as a composer, you are expected to break the rules as you see fit. For this reason, my review will not be extensive.

1) INTRODUCTION

Every note of the scale has an associated name and number. Get to know them well.

• [I] Tonic
• [II] Supertonic
• [III] Mediant
• [IV] Subdominant
• [V] Dominant
• [VI] Submediant
• [VII] Leading Note
• [I] Tonic

For example, in the C major scale, IV would be F while the submediant would be A.

Now in the melodic minor scale, the submediant and leading note are raised while ascending and are lowered while descending. This is extremely important to know in harmony, as this can produce different versions of the chord. So keep that in mind for the rest of this article.

2) TRIADS

A triad consists of three notes, e.g. the C major triad = CEG. If the key in this example was C major and we came upon the C major triad, it would be known as the tonic, denoted by the Roman numeral ‘I’ (and if we were in the key of C major but we came upon GBD instead, we would denote the dominant with ‘V’, etc).

The lowest note of the triad gives you the bass along with the identity of the notes’ arrangement. So if C happens to be the lowest note, CEG is considered to be in root position. But if E were to be the bass, i.e. EGC, then the triad is in first inversion, whereas if G were the bass, then the triad would be in second inversion.

Note that the inversions are symbolized with Arabic numerals, and that we tend to use the shortened method of naming triads.

3) CHORDS AND SATB

As mentioned earlier, a triad consists of three notes, but you may extend it to four notes, in which case it would be known as a chord. So if you are given a D major triad (DF#A), you may repeat the D to convert it into a D major chord (DF#AD). Four-note chords are important when you compose for SATB (soprano, alto, tenor, bass), because each note of the chord is sung by one of those voices. Soprano and alto are written in the treble clef, while tenor and bass are in the bass clef.

Although you now have four notes to work with, you would still name/classify chords exactly the same way you would with triads (e.g. AbCFC would still be known as an F minor chord in first inversion).

I’m not going to put much emphasis in writing for SATB (that’s an entire article in itself), but here are some general points:

• Keep the voices in their appropriate range. A bass singer obviously can not reach an octave past middle C, so do not write beyond what is possible.
• Try not to stretch the distances between voices, or the music may sound empty and weak. You should generally keep the soprano and alto parts within an octave range of each other, same with the alto and tenor. But the interval between the tenor and bass can go up to a 12th.
• Don’t cross voices or overlap them.
• Avoid parallel/consecutive 5ths and octaves (unless you are deliberately aiming for a medieval sound).

4) TONIC [I]

The rule for a tonic chord is to never omit the 3rd (the ‘E’ in a C major chord) and to never double it. You may double the root or the 5th. In first inversion (‘E’ is the bass), you may still double the root (C) or the 5th (G), but the repeated note would ideally be in the soprano voice.

C+: CEGC (doubled root) or CEGG (doubled 5th)
C-: CEbGC (doubled root) or CEbGG (doubled 5th)

Optional: you may triple the root (omitting the 5th) if you want a stronger finish.

To add variety to your music, you may use the 7th (B) instead of doubling the root or the 5th.

In the example above, two notes were raised by the natural sign. This must be symbolized accordingly, but for convention I will use a # (whereas to signify that a note has been lowered, I will use a flat). Of special interest, the final chord in the example above is known as the ‘Tierce de Picardie’. Essentially you are converting the C minor chord into a C major chord when you raise the 3rd (conversely, in a major key, the tonic may be made minor by lowering the 3rd, i.e. I b3).

Caution: CEGBb should actually be considered to be the dominant 7th of F (IV).

And finally, inversions of I7 are possible (see the V7 section).

5) DOMINANT [V]

C+: V is GBD
• In root position or first inversion, you can double the root (G) or 5th (D).
• The leading note (B) should resolve upwards to the tonic (C), and it should not be omitted or doubled. Additionally, in a minor key, you must make it absolutely clear if the leading note has been raised or not.
• The supertonic (D) may resolve to the tonic or mediant (E).

6) DOMINANT 7THS, 9THS, 11THS, 13THS

C+: V7 is GBDF
• The subdominant (F) should resolve downwards to the mediant (E), while the leading note (B) should still resolve upwards to the tonic (C).
• In cases where you do not wish to use all four notes of the chord, you may double the root and omit the 5th.
• There are now three inversions, so you should memorize the notation below. Also, the first inversion is the only position in a minor key where you cannot clarify that the 3rd has been raised, since it is the bass.

C+: V9 is GBFA
• Omit the 5th.
• Keep the 9th (A) in the soprano voice. It may resolve downwards to the dominant (G) or it may act as an appoggiatura by moving upwards to the leading note (B).

C+: V11 is GBFC
• Omit the 5th and 9th.
• This chord is generally considered to be weak.

C+: V13 is GBFE
• Omit the 5th, 9th, and 11th.
• Keep the 13th (E) in the soprano voice. It may act as an appoggiatura moving down to the supertonic (D), or it may resolve directly to the tonic (C).

7) SUBDOMINANT [IV]

C+: IV is FAC
C-: IV is FAbC
• In root position or first inversion, you can double the root (F) or 5th (C). Doubling the 5th is particularly strong because of the tonic.
• Do not omit the 3rd.

The last chord in the example above may be considered to be the dominant 7th of Bb (bVII).

8) SUPERTONIC [II]

C+: II is DFA
C+: II7 is DFAC
• For II, double the root (for a darker sound) or double the 3rd (for a brighter sound). In first inversion, double the 3rd.
• For II7, resolve the 7th downwards. Also, you may use all four notes, or you may instead double the root (omit the 5th) or double the 3rd (omit the 5th).
• The 5th can be raised or lowered in a major or minor key, which gives rise to many harmonic possibilities.

In the above example, DFAbC is known as a half-diminished chord (the interval from D to F is -3, F to Ab is -3, but Ab to C is +3), while DFAbCb would be known as a full-diminished chord (every interval in the chord is a minor 3rd).

Further harmonic colours are obtained when you flatten the bass (i.e. Neapolitan):

Lastly, the following diminished 7th chord may decorate the tonic:

9) LEADING NOTE [VII]

C+: VII is BDF
• This diminished chord is considered to be weak, and is often found in first inversion.
• It could be used as a passing chord or as a substitute for the second inversion of V7.
• You may double the 3rd (D).
• The bass can be raised or lowered, but be clear in your notation.

Caution: BbDFAb should actually be considered to be the dominant 7th of Eb (bIII).

10) SUBMEDIANT [VI]

C+: VI is ACE
• Double the root or the 3rd.
• In first inversion, double the 3rd.
• The bass can be raised or lowered.

Caution: AbCEbGb should actually be considered to be the dominant 7th of Db (bII).

And lastly, the following diminished 7th chord may decorate the dominant:

11) MEDIANT [III]

C+: III is EGB
• Double the root. In first inversion, double the 3rd.
• The 5th (B) is the leading note, so it may be raised or lowered.

Caution: EbGBbDb should actually be considered to be the dominant 7th of Ab (bVI).

12) SECONDARY DOMINANTS

I’ve briefly touched on this in previous examples, but basically you will come across some chords that do not belong at all to the key you are working in. In fact, they belong to a completely different key, which is completely fine.

For example, let’s look at DFAC, which is II7 in C major. But if I raise the F to F#, there is no way you can justify that F# in the key of C major. Instead, DF#AC functions as the dominant 7th to G (we pretend that the G temporarily acts as the tonic). As such, we symbolize DF#AC as V7/V or V7 of V (V7 being DF#AC, which is the dominant 7th of G; V being the dominant, G, of C major).

13) AUGMENTED 5THS

Many chords have an interval of a perfect 5th when you from the root to the fifth note. But when you raise the 5th, you augment the interval, and this gives you a new sound to play around with.

• I#5 goes to IV
• IV#5 goes to II
• V#5 goes to I

14) AUGMENTED 6THS

• Italian: F# Ab C
• French: F# Ab C D
• German F# Ab C Eb

Normally they are found in first inversion, and they often resolve to the dominant:

15) NON-CHORD NOTES

These notes do not belong to a chord, but they decorate the melody:

• Passing note: unaccented, fills in an interval of a 3rd (diatonically) or a 2nd (chromatically) or a 4th (double passing notes), moves up or down stepwise, may move in 3rds or 6ths (harmonic passing notes)
• Appoggiatura: accented, diatonic or chromatic, moves up or down stepwise into the chord, may be approached by step or by leap or from the previous chord, may move in 3rds or 6ths (harmonic appoggiaturas),
• Auxiliary note (aka neighbour note): unaccented, goes up or down diatonically or chromatically but always returns to the note it originally came from, may move in 3rds or 6ths (harmonic auxiliary notes)
• Incomplete auxiliary note: unaccented, similar to the auxiliary in that it remains in the chord, but it will land on a different note of the same chord
• Anticipation: anticipates the next note of the upcoming chord, occurs usually in the soprano
• Changing notes: a combination of an auxiliary + appoggiatura or a combination of an upper and lower auxiliary, may move in 3rds or 6ths (harmonic changing notes)
• Suspension: a tied appoggiatura that is prepared, suspended, then resolved
• Echapee: the escape note is unaccented, goes one step up then down a 3rd, or goes one step down then up a 3rd (echapee 13 comes from V13, where the supertonic moves to the mediant, which is the 13, then resolves down to the tonic)
• Cambiata: an upside-down echapee, where you move down a 3rd then up a note, or up a 3rd then down a note
• Pedal point: the bass contains a sustained note or a chord (this is the pedal point), while in the upper voices you can have whatever (dissonant) notes you want

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