Tonal music generally prioritizes the pitches in a single key, and chromatic alterations up to this point have been analyzed according to their relationship in that key. Vertical structures have been identified by Roman Numeral functions in the key, with the exception of Augmented 6th and Neapolitan chords. These structures also have a key relationship, but their usage relies on linear resolution of altered tones to diatonic chords in the key. As a general rule, the chromaticism we have explored thus far can be explained within the constructs of functional harmony. Creative composers in the 19th century experimented with sonorities that make sense to the ear, but are non-functional. Several of these are identified below.
Passing chords, also known as embellishing chords, do not belong the key of the moment. Rather, they add an element of color to a progression. One of the more common passing chords is the Common Tone Diminished 7th (ct º7 ), also known as an Embellishing Diminished 7th (emb º7 ). It is easily constructed by starting with a tonic triad, moving the 3rd down a half-step to #2, moving the doubled 5th to the #4 and 6th scale degrees, and retaining the tonic on top. The retained tonic pitch becomes the root of the chord of resolution in most instances. Passing chords are typically located on weak beats, rhythmically. If Roman Numerals were to be assigned, they might be #ii º7 – I, or #iv º7 – V, when resolving to the tonic or dominant chords in the key. The common tone diminished 7th chord (ct º7) does not function in the same way as a secondary leading-tone chord (viio7/X).
Chords whose roots are a third apart may be used in in non-functional “progressions.” There are two basic types of third relationships. A pair of chords forming the chromatic mediant relationship have roots either a M3rd or m3rd apart, share a common tone, and are both major or minor triads of the same quality. They can be used in a tonal context to create a common-tone modulation. In a doubly chromatic mediant relationship, the two triads are of different qualities and share no common tones. With smooth voice leading, chains of chords with third relationships can create engaging progressions. This can counteract the reliance on the circle of fifths that governs most functional harmony.
Like secondary dominant chords, secondary subdominant chords are altered chords with a subdominant function in relation to a key other than the tonic. They are most often applied to the IV or V chord in a major key, and to the iv chord in a minor key. The half-diminished 7th chord built on the second scale degree in minor (ii ±7) is a commonly used secondary subdominant. It typically resolves to the V7 chord, and is used extensively in Jazz music as part of a secondary ii7 – V7 package. The lowered 5th on the ii ±7 chord is retained as a common tone as a flat 9th on the V7 chord in conventional voice leading.
The linear approach to harmony, taken to it’s extreme, can yield sonorities that make sense to the ear, but are non-functional. The traditional Roman Numeral functions, categorized as Tonic (T), Subdominant (S), and Dominant (D), are not useful to explain chords that are mutations of diatonic chords in a key. The movement of a chord member in a linear fashion, often downward by half-step, is a basic tenet of linear harmony. The process may not yield a chord that exists in the key, and cannot be explained in the context of diatonic functions.
A good example of linear harmony is found in Prelude No. 4, Op. 28, by Frederic Chopin.