Intro to Prolongation

TH101 - Seth Monahan

HARMONIC PROLONGATION AN INTRODUCTION This handout serves a double purpose. First, it will help you become comfortable with the principle of harmonic “prolongation” (also called “expansion”)—a concept that addresses musical hierarchy and structure in a more abstract sense than we’ve seen so far. Second, it will introduce you to a few idiomatic uses of 6/3 chords, expanding your harmonic vocabulary with several new progressions that feature harmonic “prolongation.” This material is CRUCIAL for everything else we will do this semester; I urge you to read it carefully and more than once.

           

Example 1a CLICK TO PLAY

  



Bß:

Example 1b

CLICK TO PLAY

  Bß:



   

        V#

I







 

 

 

I I

V#

I

I

 

       

Non-Chord Tones: SHOW HIDE

/

Neighbor motion: SHOW HIDE

/

(N)

Example 1. Mozart, Piano Sonata in Bß, K. 281, mvt. I, mm. 89-90

HARMONIC PROLONGATION: AN INTRODUCTORY EXAMPLE NON-HARMONIC TONES & MUSICAL HIERARCHY When we look at a passage of music “hierarchically,” our goal is to determine which of its elements are more structurally important than others. We began to ask these sorts of questions in Week 7, when we distinguished between non-harmonic tones and the “underlying” chordal structure that they embellished. To briefly review, compare Examples 1a and 1b above. Example 1a shows a short Mozart excerpt with Roman numeral analysis underneath. Example 1b shows a chordal reduction of that passage. Listen to both recordings; you should be able to hear 1b preserving the essential harmonic data, but with less “clutter.” What are the differences between Examples 1a and 1b? Most obviously, each half-bar has been reduced to a single harmonic unit one quarter-note long, laid out in four voice chorale style. You’ll also notice that a few notes have been omitted entirely from Example 1b: specifically the nonharmonic tones—embellishing notes that do not belong to the surrounding chord. Can you find the non-harmonic tones in each chordal span? (To see them, click “show” to the right of the staff.) By removing these non-harmonic tones, we are making a hierarchical decision: we are saying that these notes are less structurally important than those around them; they are not part of the underlying harmonic “skeleton.” These relationships are often expressed using metaphors of “depth”: we say that the non-harmonic tones are more “superficial,” while the chord tones are part of the “deeper” structure.

PROLONGATION & 6/3-CHORDS (p. 2) TH101 - Seth Monahan

NON-HARMONIC TONES & MUSICAL HIERARCHY (cont’d.) Before moving on, let’s consider a few important properties of these two non-chordal passing tones. First, notice that each one is harmonically dissonant against the surrounding chord; each creates a tension that then resolves when the melody moves on to a chord tone. Second, notice that each has a clear melodic logic. They don’t just pop up randomly; each non-chord tone is part of a coherent linear motion, much like the dissonances in second and third species counterpoint. (This would be equally true of most other non-harmonic tones as well—neighbor notes, appogiaturas, etc.) PROLONGATIONAL CHORDS Now it’s time to go a step further. One of the most important aspects of musical hierarchy is that we can address it at various “levels.” The analysis above dealt with the most superficial level of hierarchy, the difference between local harmonic structures and the non-harmonic tones that embellish them. But we can also address musical hierarchy on another, more abstract (or “deeper”) level: one in which entire chords serve to embellish other chords or harmonies. Let’s return now to Example 1b. Notice that there are two layers of analytic notation. The top layer reproduces the Roman numerals in Example 1a. The bottom layer presents an analysis that goes conceptually deeper into the structure than the one above it. This “second level” analysis has two elements: 1)

A Roman numeral “I” and a horizontal line that goes across all three chords, connecting both instances of tonic.

2)

A parenthetical “N” below the V# chord on beat 2.

Together, these two symbols make an important hierarchical claim about the passage. They claim that the middle chord—the V#—is less structurally important than the tonic chords that surround it. More specifically: 3)

The horizontal line extending from the first tonic chord to the second claims that on a deeper conceptual level, the tonic is “active” throughout the entire progression. True, it is displaced momentarily by the middle V# chord, but this does not affect the “tonic-ness” that pervades the entire progression. We say in such cases that the tonic is prolonged or expanded for the entire duration of the horizontal line.

4)

At the same time, the parenthetical “N” specifies the function of the V# chord within this prolongation: it is a “neighbor” chord, used to embellish the structural tonic chord. It is so named for the neighbor-note motion in the bass voice (Bß – A – Bß).

Chords that serve to embellish and/or prolong more structurally important harmonies are often named after the linear motion of their basslines. “Neighbor chords” are one important family of prolongational chords; another is the “passing chord,” which we will see below. Because these terms are borrowed from the language of counterpoint, prolongational chords with neighbor/passing bass motions are often called “contrapuntal” chords. Listen to the passage and its reduction several times. Can you hear the V# chord in a subsidiary role, carrying less “weight” than the tonic chords that enclose it? It may helpful to use an analogy with non-harmonic tones. Like a non-harmonic tone, the “neighbor” V# above is a foreign element that creates a tension or dissonance within the harmony it embellishes (in this case, the tonic). And like many non-harmonic tones, it is governed by a clear linear logic—here, the neighbor motion in the bass.1 One could also point to the clear passing motion in the soprano voice, connecting the F and D of the tonic chord. But the “official” name always derives from the bass.

1

TH101 - Seth Monahan

EXPANSION IDIOMS USING 6/3-CHORDS This section introduces six idioms for expanding/prolonging either tonic or dominant. All of them involve 6/3 chords, which are entering your vocabulary now for the first time.

PROLONGING HARMONIES THROUGH INVERSION Not all prolongational chords are of the contrapuntal (i.e. passing or neighbor) variety discussed above. In fact, the simplest way of expanding a root-position triad is just to pair it with its own first-inversion counterpart. Example 2a expands tonic using a I6 chord. Notice again that a “second level” analysis shows, with its horizontally extending line, that the tonic is “prolonged” throughout the entire progression. Example 2b shows that we can do the same thing with the dominant, expanding V with V6. (Later in the course, we will expand ii and IV in similar ways.) Example 2c shows a longer progression that combines both tonic and dominant expansions of this sort, once again with a “second level” analysis clarifying the prolongations. This layer reminds us that while there are literally six chords in the excerpt, on a deeper level the harmony only moves twice: from I to V and back again. Listen to each of these examples (and those below) several times, “focusing” your hearing first on the top analytic level, and then on the bottom. Can you can hear the “deeper,” slower rate of harmonic change modeled by the second-level analysis?

Example 2a

# & # 44 ˙˙

CLICK TO PLAY

˙˙

? ## 4 ˙˙ 4 D:

˙˙

I I

Example 2c

CLICK TO PLAY

Example 2b

w w

Ifl

CLICK TO PLAY

˙˙

w w

? ## 4 4

˙ ˙

˙ ˙

D:

Vfl V

V

I I

I

b2 ˙ &b 4 ˙ ? bb 24 ˙˙ Bß:

# & # 44

w w

I I

œœ œ œ

œ œ œ œ

œ œ œ œ

Ifl

I

Vfl V

œœ œ œ

˙˙ ˙ ˙

V

I I

˙ ˙

w w

VOICE EXCHANGES: SHOW HIDE

/

There are two additional points to consider before moving on: OUTER-VOICE COUNTERPOINT Notice that in each of the examples above, the soprano voice moves along with the bass voice. This creates a more musical effect than just moving the bass voice alone. Note also that most of the outer-voice intervals are imperfect consonances, which tend to sound more vibrant than perfect ones.) In Example 2a, the soprano moves in parallel tenths with the bass. In the first bar of Example 2b, the soprano and bass “trade” notes in contrary motion: over Cƒ becomes Cƒ over A. This special technique is known as a “voice exchange”; it is sometimes highlighted in analysis by drawing a large “X” that connects the exchanged notes. Can you find the voice-exchanges in Example 2c?

PROLONGATION & 6/3-CHORDS (p. 4) TH101 - Seth Monahan

STRUCTURAL WEIGHT When we expand a triad by intermingling its ! and £fl versions, there is only a minor difference in structural weight between them. (They are, after all, the same group of notes.) There will generally be only a small fluctuation of stability, with the first-inversion chords being slightly less stable than the root-position ones.

EXPANSIONS USING CONTRAPUNTAL CHORDS You learned on page 2 that “contrapuntal” chords are prolongational harmonies named after the melodic functions of their bass lines (i.e. passing or neighbor). Like all prolongational harmonies, they function as embellishing chords. But they only do so in certain special contexts. This brings us to a critical point: chords are not “prolongational” inherently; they are prolongational when they are used for that purpose. In other words, the same chord can be “embellishing” in one context and “structural” in another. For this reason, our focus here will not be on individual chords in a vacuum. Rather, we will focus on short, two- or threechord progressions in which 6/3 chords are idiomatically used to prolong either tonic or dominant..2 This handout presents five such idioms; you will learn more regularly throughout your theoretic training. In each of the following examples, the prolongational 6/3 chord is marked with an asterisk (*). Be sure to pay close attention to the differences between the first- and second-level analyses in each. EXPANDING TONIC WITH A PASSING CHORD: viio6 •

Example 3 shows that viio6 can be used as a passing chord (P) to connect I and I6, producing a smooth, stepwise bass (^1 - ^2 - ^3 or ^3 - ^2 - ^1).

•

Below, the soprano voice performing voice exchanges (see p. 3) with the bass. This is optional. Another common soprano line for this progression is ^1 - ^7 - ^1.

•

See The Complete Musician 3rd ed., pp. 152–3 for rules on resolving the tritone in viio6.

Example 3 CLICK TO PLAY

3 ˙ &4 ˙ ? 3 ˙˙ 4 C:

I I

*

œ œ œ œ

Ϫ Ϫ Ϫ Ϫ

viiøfl

Ifl

(P)

* œj œJ œj œ J

œ œ œ œ

viiøfl I (P)

˙™ ˙™ ˙™ ˙™ V

V

EXPANDING TONIC WITH A NEIGHBOR CHORD (I): V6 •

Example 4 (next page) shows how V6 can be used as a neighbor chord (N) to embellish a root-position tonic, again with a smooth, stepwise bass (^1 - ^7 - ^1).

•

The leading tone (^7) in V6 must not be doubled under any circumstance.

•

V6 is not always enclosed by two tonic chords, as it is here. Sometimes it simply comes before or after the tonic. In these cases it is called an “incomplete” neighbor chord (IN).

A language analogy may be helpful: we don’t just want to learn new musical “words”; we must also learn how to use them properly within a musical “sentences.”

2

PROLONGATION & 6/3-CHORDS (p. 5) TH101 - Seth Monahan

EXPANDING TONIC WITH A NEIGHBOR CHORD (I): V6 (cont’d.)

3 œ œ œ &4 œ œ œ œ ? 3 œœ œ œœ 4 *

Example 4 CLICK TO PLAY

C:

I I

Vfl

I

˙˙ ˙ ˙

œ œ œ œ

Ifl

I

(N)

˙™ ˙™ ˙™ ˙™

V

V

EXPANDING TONIC WITH A NEIGHBOR CHORD (II): viio6 •

It is also possible to embellish tonic with an upper neighbor, using viio6. This progression gives you a ^1–^2–^1 bass motion. It is used less often than the lower neighbor because ^2 does not have the same “pull” back to tonic as the leading tone in V6 (see Example 4).

EXPANDING TONIC WITH AN “ARPEGGIATING” CHORD: IV6 •

Example 5 presents a less common type of prolongational chord—one whose bass participates in a series of leaps. Here, we see that IV6 is used as a linking chord between I and I6. But rather than connecting them by step, as viio6 did above, this bassline goes from ^1 to ^3 “the long way,” by leaping down a third (to ^6) and then a fourth. This type of embellishing chord is called an “arpeggiating” chord, after its leaping bassline.

•

This idiom nearly always appears with the rising ^3 - ^4 - ^5 soprano line shown here. It also appears more often in major than minor. *

Example 5 CLICK TO PLAY

& 43 œ œ œ œ ? 3 œœ œ 4 œ C:

I I

œ œ œ œ

IVfl Ifl (ARP)

˙ ˙ ˙ ˙

œ œ œ œ

IV

Ifl

IV

I

˙™ ˙™ ˙™ ˙™ V V

EXPANDING DOMINANT WITH A PASSING CHORD: IV6 •

Above, you learned that viio6 can serve as a passing chord to connect I and I6. This same principle allows us to use IV6 as a passing chord to connect V and V6, with a smooth stepwise bass (^5 - ^6 - ^7 or ^7 - ^6 - ^5).

•

As always, the leading tone in V and V6 must not be doubled. In minor, you must use raised ^6 and ^7 .

•

This progression nearly always involves a RISING bass; the “reversed” version is rare.

Example 6 CLICK TO PLAY

3 & 4 œœ œ œœ ? 43 œœ œœ œœ

œœ œ œ

œœ œ œ œ œ œ

C:

V

IVfl Vfl

I I

Ifl

I

V

*

(P)

˙˙ ™™ ˙™ ˙™ I I

PROLONGATION & 6/3-CHORDS (p. 6) TH101 - Seth Monahan

SUMMARY It is important that you memorize all of the idioms presented in this handout, both in terms of their Roman numeral sequence and their specific scale-degree bass lines. (For example, if you see a bass line that moves ^1 - ^2 - ^3, you should immediately recognize this as a possible tonic expansion with a passing viio6.) Committing these progressions to memory now will also aid you in your aural skills classes, where several of these progressions turn up as the basis of “harmonic paradigms” that you will have to master. The following bass-line flow-chart is intended to help you memorize the four “contrapuntal chord” idioms presented on pages 4–5. Note again that several chords appear here with two distinct functions. IV6 can prolong either tonic or dominant, while V6 can prolong tonic (as a neighbor) or be linked (as a structural chord) to V with a passing chord.

TONIC PROLONGATION

V ^5

IVfl ^6

tion g mo passining only!) (ris

I

Vfl

^1

^7 neighbor motion

neighbor motion

viiøfl

Ifl ^3

^2

tion g mo !) passinr direction (eithe

IVfl ^6 “arpeggiation”

DOMINANT PROLONGATION

Ifl ^3

Example 7. Flow chart showing prolongational progressions to expand tonic or dominant using contrapuntal (passing/neighboring/arpeggiating) chords.

A FEW WORDS ON DOUBLING: There is no single, inviolable rule for doubling in 6/3-chords, except that you must never double the leading tone (^7). It is also good to keep the following guidelines in mind: •

Avoid doubling the chordal fifth of 6/3 chords. Prefer to double the root or third.

•

Usually, doubling scale degrees ^1, ^2, ^4, or ^5 is preferable to doubling ^3 and ^6 (Though these can be doubled in a pinch.) But never, ever double the leading tone!