MUS 112 Study Guide J (Chapter 10)

Harmonic Progression; Leading Tone & Supertonic Triads

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1. The term "harmonic progression" refers to the order in which chords follow one another.

2. Root Movement:  Progression from one chord to another is always described in terms of root movement–the intervallic distance between the roots of two successive chords, regardless of the actual bass notes.  "Technically," there are only three intervallic distances:  the fifth, the third and the second; the fourth, sixth and seventh are merely inversions of these.

3. Root movement by fifth accounts for a large percentage of motion.  This is the movement of the authentic cadence (V-I), which is so effective in establishing a sense of key.

4. Harmonic Progression:  The frequency of root movement by fifth has been established, such as V-I.  What chord, or chords, then, lead to V?  The logical answer would be the ii chord, since it is a "fifth" away from V.  Counting back by fifths, the following progression emerges; it is called a circle progression because it cycles through the circle of fifths:

Full Circle Progression (major):  I-IV-vii^o-iii-vi-ii-V-I

Note:  Except in a circle progression, the vii^o chord typically functions as a dominant chord, progressing to I.  This is because, e.g., in the key of C, vii^o = BDF, which is three of the notes in a V⁷ chord = GBDF.  The vii^o functions as an incomplete dominant seventh chord.

5. Common progressions:

ii:  to V or vii^o

IV:  to ii, V, or vii^o

vii^o:  to I

In a minor key, ii and IV in the above list will be ii^o and iv.  But when scale degree 6 in either triad progresses to 7 in the following triad, ii (minor) and IV (major) will be used to avoid the interval of an augmented second.

When a triad skips in the direction of tonic:  vi-V, iii-IV, iii-ii⁶

When a triad moves away from tonic:  V-vi, vi-iii-IV

A common progression interrupted by a tonic triad:  ii-I-V, for example

The progression ii^o-vii^o (two successive diminished triads) is not useful, i.e., avoid it.

6. Harmonic Progressions in Minor Keys:  In minor, iv and VII are included in the series of progressions by fifths.  Since these two are minor and major triad, respectively, they can progress by perfect fifth–iv to VII and VII to III.

7. Full Circle Progression (minor):  i-iv-VII-III-VI-ii^o-V-i.  Note that VII is built on the b7 scale degree (C minor: BbDF).  vii^o is built on #7 (C minor: BDF).

8. Following is a useful list of common progressions:

9. Other Common Types of Progressions: There are three additional categories of harmonic progression. The progression standing alone is infrequently used, but in special situations it can be useful.

First inversion in succession:  When a bass line moves by step and each note is the third of a chord, any resulting succession of chords is acceptable.

Harmonic sequence:  A series of three chords or more, with a regularly recurring pattern of root movements in which any resulting pair of triads is acceptable.  While the pattern "descending fifth/ascending fourth" is common, virtually any pattern is possible.

Chromatic bass line:  When the bass line ascends or descends by a series of half steps, any resulting chord succession is usually satisfactory.

10. The Diminished Triad:  consists of two stacked minor thirds; together these produce the interval of the d5, which when inverted becomes the A4.  Because of the tritone, the diminished triad is considered dissonant.

Only in first inversion is there no tritone directly associated with the bass note.  For this reason, the diminished triad is used almost exclusively in first inversion.

As a diatonic triad, the diminished triad is found on the leading tone (vii^o) in both major and minor, and on the supertonic (ii^o) in minor.

11. The Leading-Tone Triad:  is diminished in both major in minor, e.g., in G major or G minor it is spelled F#AC.  It functions as a "dominant" triad, since it usually progresses to tonic.  And remember that it also contains three of the four notes of the V⁷ chord (in GM or m: DF#AC).  The leading-tone triad, vii^o, has two principal uses:

Between the tonic and its first inversion, or reverse.  The aural effect is similar to the passing six-four, but the use of I-vii^o6-I⁶ is more frequent and can be considered the preferred choice.

Following the subdominant triad when the melody ascends.  Using IV-vii^o6 instead of IV-V avoids any real or implied parallel motion, and, so, is the usual choice in this circumstance.

In the progression table, the progression vii^o-V was not included.  That is because vii^o may often be analyzed as an incomplete dominant chord.  Two dominant-class chords typically do not appear consecutively.

12. The Supertonic Triads:  The supertonic triads (ii in major and ii^o in minor) have much in common with the subdominant triad.  Not only do ii and IV (ii^o and iv) have two notes in common, but when ii and ii^o are found in first inversion, which is most of the time, they have the same bass note as the root of IV (iv).  In addition, both triads commonly resolve to V or I, so are considered to be subdominant in function.  Like V versus V⁷, ii and ii^o are used far less frequently than ii⁷ and ii^ø7.

13. Typical uses of the supertonic triad:

Most common usage is first inversion.  It usually leads to V-I or to I.  As a preparation for the dominant, it is used much more frequently than IV (iv).

With root in bass, is useful only in major keys, but still much less so than in first inversion.  Root position in minor is rarely used since it is a diminished triad.

The ii in a minor key.  When a voice line ascends at the point where a supertonic triad is used, scale degree 6 (fifth of the triad) must be raised to #6 to progress to #7 without incurring the augmented second.

14. Writing the Diminished Triad:  Only the use of first inversion of the diminished triad will be considered at this time.  Root position is used in harmonic sequence, and second inversion is very rare.

The usual voice distribution for any diminished triad in first inversion is:  two 3rds (bass note doubled), one root and one fifth.  Exception:  When the triad is found with the fifth in the soprano (infrequent), the fifth is usually doubled (two 5ths, one root, one third).  This voicing creates the resolution problem of resolving both fifths (flat 6 scale degree) downward (parallel octaves) or resolving one fifth up to the leading tone, which creates the augmented second.

15. Writing to and from the Diminished Triad:

Doubled notes:  Since usually found in first inversion, the part-writing guidelines for other triads in inversion apply.  Approach and resolve the doubled note whenever possible by contrary or oblique motion.

Unequal fifths:  This terms describes a diminished fifth preceded or followed by a perfect fifth in the same pair of voices.  The visual effect is parallel fifths, but since they are unequal in size they are acceptable, except between two outer voices.

vii^o6 with the fifth in the soprano:  As a soprano tone, the fifth of the vii^o triad (or any diminished triad) usually descends.  But the fifth in the soprano may ascend when found in a melody line moving in similar motion with the bass at the interval of a tenth.

Why vii^o should sometimes not be considered an incomplete V⁷:  In progressing to the tonic, the seventh of the V⁷ usually resolves down, whereas in the vii^o triad, the fifth (same note as the seventh of V⁷) usually resolves up, allowing the doubled note to resolve by contrary motion.

16. Writing the Supertonic Triad:  In the commonly used ii and ii^o, the third is usually doubled (subdominant scale step).  Since this triad usually precedes dominant harmony, and in first inversion uses the same bass note as IV (in root position), the supertonic harmony is classified as having a subdominant function.

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