appliedharmony.com uses a fairly standard symbol based on Roman numerals. These exercises have been prepared in order to improve our user’s relative pitch from a harmonic point of view so we will never talk specifically about pitch classes but intervals from a pitch center which is usually called the tonic.
Finally, keep in mind that, unless otherwise stated, harmonic analysis of these exercises not only refers to the chords played by a specific instrument but harmony produced by chord tones played by all instruments in a given time, including the lead vocal.
Level 1
Diatonic Chords in Major Key. Triads and V7. Basically in Root Position with a Stable Harmonic Rythm.
Since a tonal center, scale-degree triads in a major key shall be labeled as follows: III-III-IVVVI-VIIº, whether the exercise is in one key or another.
Example in C major:
Example in E major:
And so on in any major key.
Therefore, each major triad (major third and perfect fifth) is referred to by the scale-degree of its root labeled by a Roman numeral. There are three major triads in major keys, above the first, fourth and fifth scale-degree chords, which will be labeled as I, IV and V, respectively.
A minor triad (minor third and perfect fifth) is referred to by the scale-degree of its root labeled throughout a Roman numeral but adding a minus sign. There are three minor triads in major keys, above the second, third and sixth scale-degree chords, which will be labeled as II-, III- y VI-.
A diminished triad (minor third and diminished fifth) is labeled adding a circle to its scale-degree numeral (º). There is only one diminished triad in major keys, above the seventh scale degree, so it will be labeled as VIIº.
Dominant seventh chords may appear in level 1 exercises above the fifth scale degree, that is to say, a major triad with chordal seventh minor, whose label will be V7.
Examples in C major and A major:
Finally, a chord may appear with a note other than the root in the lowest part. In that case, we would say the chord is inverted. Inverted chords will be labeled writing the note which appears in the bass after a slash. A triad which is not in root position can be in first inversion (if the third is the bass) or in second inversion (if the fifth is the bass).
Example in C major:
Seventh chords can be in third inversion.
Example in G major:
When there are two chords in the same box, they usually have the same length. However, sometimes they don’t last the same. In such case, we will use the symbol \ to indicate the beats in which the box could be divided. Each beat labeled by a \ has the same harmony as the previous beat.
Examples using bars:
Level 2
Diatonic Chords in Major and Minor Keys. Triads, V7 and Secondary Dominants. Inverted Chords, Easy Examples of Modal Mixture (Minor in Major), sus4 and sus2 chords.
Exercises in minor key are included. Traditionally, nine pitch-class appearing in minor mode are analyzed by grouping them into three forms of minor scale of seven notes each - natural, harmonic and melodic minor-, but actually chords derived from any of the three may appear in the same exercise.
Example in C minor:
C NATURAL MINOR
C HARMONIC MINOR
C MELODIC MINOR
As for the symbol, the major difference compared to the major key is that in minor key scale degrees are not always at the same distance, perfect or major, from the tonic.
For example, in a major key
- the interval from the tonic to the third scale-degree is a major third,
- from the tonic to the fourth scale degree, perfect fourth,
- from the tonic to the seventh scale degree, major seventh,
- and so on.
However, in a minor key, there are some scale degrees which do not meet this requirement as major key does.
In a natural minor scale
- the third scale degree is a minor third below the tonic, in the previous example, C (tonic) to E
(third grade), - the interval from the tonic to the the sixth scale degree (C to A) is a minor sixth,
- and from the tonic to the seventh scale degree (from C to B), minor seventh.
To indicate that the root of these three chords is an interval of minor third, minor sixth and minor seventh respectively is included in the label a , so there can be no doubt about which is the root. These chords will then be defined completely thanks to the rest of the symbol. In the natural minor scale, therefore, being these three major chords, they will be labeled easily as III, VI and VII.
In the harmonic minor scale, however, the interval from the tonic to the seventh scale degree is a major seventh, so we no longer use the flat, and being a diminished chord the label will be VIIº.
In C minor this accidental should be precisely a flat, but we have to understand that the flat written in its label does not determine a specific flat, natural or sharp but a specific intervallic, i.e., the flat is used to indicate that it is a semitone less than perfect or major interval. Therefore, this symbol can be generalized to any key, regardless of the necessary accidentals in each case.
Example in A minor:
A NATURAL MINOR
A HARMONIC MINOR
A MELODIC MINOR
In addition to the augmented chord (major third and augmented fifth) that is built above the third scale degree in the harmonic and melodic minor scales, in level 2 may appear other triads whose origin historically comes from two suspensions very often used by the composers. They are the sus4 and sus2 chords and in some cases it is useful to consider them as independent chords, especially in jazz and popular music.
Examples in C:
Finally, secondary dominants are labeled according to the chord in which they tend to resolve and not the secondary dominant root.
Example in C:
Level 3
Diatonic and Non-Diatonic Chords in Major and Minor Modes, triads and seventh chords. Modal mixtures (Minor in Major).
Seventh chords above any scale-degree may appear in this level. Minor seventh will be labeled adding a 7 after triadic symbol and Maj7 will be added to indicate a major seventh.
Examples in C major:
Diminished triad plus minor seventh —known as half-diminished seventh chord— is labeled as -7 ̄5 when its function is subdominant or predominant (e.g. seventh chord above second scale-degree in minor tonality) and adding ø when its function is a dominant (e.g. above the leading- tone).
Examples in C major and F major:
Chordal sixth above a triad is labeled as add6. Similarly, a ninth above a triad is labeled as add9.
Also, extended dominants can be found in level three. Its symbol will indicate the diatonic chord in which tends to resolve as well as the number of steps which would be necessary to arrive following a standard way (if you want more information about this specific symbol, see this article in Spanish: Cifrado analítico de los dominantes por extensión):
Examples in C major and G minor:
Sometimes a chord whose analysis is not referenced to the principal tonality but regarding chord in which the secondary dominant resolve could appear before a secondary dominant. In that case, rather than labeling the secondary dominant as we noted above, both chords are analyzed directly with respect to the objective chord using brackets.
Examples in C major and G major:
V7/VI is not used in the first example because brackets indicate that this chord is the inverted dominant of the chord which is just after the bracket. Similarly, it is not necessary to label V7/IV in the second example.
Also, sometimes it is necessary to refer to the tonic, rather than to the root of the chord. In this case, we use the ^ sign above the Arabic number. For instance, 
is a perfect fourth above the tonic, regardless of which is the root of the chord at that particular time. A typical case for using so would be in some pedal points.
Example in C major:
Finally, chords with no third, also known as Power Chords, are labeled adding5.
Level 4
Quadtriadic Harmony. Modal Harmony. No tonal centric systems. Centric Ambiguity (Tonal Pairing).
Some level 4 exercises are based on quadtriadic harmony (also known as jazz harmony; but we prefer the term ‘quadtriadic’ harmony to the more common term ‘jazz’ harmony because this system is not exclusive to jazz, and because jazz does not always use quadtriadic harmony). In any case, the point is that while the triadic harmony is based on three-note chords, the basic unit in a quadtriadic context is the four-note chord.
Quadtriadic harmonization in C major:
Quadtriadic harmonization in A minor:
A NATURAL MINOR
A HARMONIC MINOR
A MELODIC MINOR
If extensions are added, they will be labeled writing each specific interval.
Examples in C major:
In non-tonal but with a pitch center exercises, being a usual mode or not, each chord is labeled using that pitch center as the first scale-degree, provided that this chord has no specific function subject to a different degree to the reference center.
Symbol chords examples in a C pitch center system:
Dominant substitutes can appear in level four –also known as tritone substitutes–, which will be labeled as SubV7. Augmented-sixth Chords will be labeled in the same way. For example, a German augmented-sixth chord is labeled by SubV7/V. (For more information, see the following article in Spanish: Augmented sixth chord and SubV7/V).
Examples in C major:
Some exercises have some degree of ambiguity as relates to their tonic. An attentive listening would allow us at least two possible correct analysis depending on how we localize the tonic, in one scale-degree or another. There are many terms to express this, like centric ambiguity, tonal pairing, double tonic or bifocal tonality. In these cases, the exercises have two variants, a and b. To avoid confusion, note that it could be analyzed from two different tonics, but in each of the two variants of the exercise only one is correct.