So far, we have looked at the use of individual structures in tertian, quartal and secundal harmony. We now turn our attention to Polychords: The simulataneous combination of two or more chords from different harmonic areas. Our study of polychords will focus on tertian structures with out a key center but you are encouraged to explore the same principles with quartal, secundal and mixed harmonic structures as well.

Polychords

When discussing polychords, it is important to distinguish each chord in the harmony. As such we will refer to each chord of the harmonic structure as a chordal unit.

A. Polytonality vs. Polyharmony

1. Polyharmony = the clear and present existence of two or more segregated series of chordal units sounding simultaneously
2. Polytonality = the clear and present existence of two or more segregated key areas in which polyharmonic chordal units exist.

a. Polyharmony does not have to be polytonal. Polychords that are not polytonal afford a greater array of harmonic possabilities.
b. Polytonal chord structures are polyharmonic

 

 

 

B. Polychords and the harmonic series

As we have seen throughout this semester, we are redefining the way we perceive music and we must listen carefully to determine if what we rationalize is, infact, what we hear. Persechetti's rationale for resonance in polyharmonic structures is based on the relationships of simultaneous overtone series. If the harmonic series is an organic, resonanting series and we are going to exist in a truly polyharmonic context than there is great rationale for saying that the resonance of a polyharmonic structure is directly correlated to the simultaneous overtones present in that structure. In my ear, this rationale rings true. Let your ear guide your rationale.

1. The first closed triad in the overtone series is the 64 and thus has a most natural triadic resonance
2. By building an overtone series on each pitch of the 64 we get a set of 3 overtone series that represents the full harmonic spectrum of our triadic resonance.

3. We recall that the intervallic order of the overtone series is P8-P5-P4-M3-m3-m3(completes dom7th)-M2-M2-M2
4. Resonance above the original 64 is determined by harmonic proximity of a note within the set to the original 64. Those notes in the lower partials carry more resonance than those in the upper partialsIn order:

5. Persechetti then orders each unique note within the set of resonance in ascending P5ths. This formation places the notes in an order beginning with the most consonant to the most dissonant. This forms the basis of his discussion of the quality of major and minor polyharmonic structures.

C. Polychordal Characteristics

1. Placing chordal units well apart clarifies the polychord
2. Placing chordal units close together obscures the polychord
3. Isolate choral units via register, rhythm, orchestration etc..
4. Consonant outter voices provide a stability.
5. Dissonant outter voices provide tension
6. Wider spacing in the lower polychord provides natural resonance and stability even in open position.

 

Note: Persechetti's discussion of consonance, dissonance and resonance of polychords deviates from the naturally occuring order of tones found within the original set of harmonic series found in the fundamental triad. My ear is not convinced by his argument. For example, Persechetti states

"A polychord may be made up of any kind of triads. When it is constructed of major triads it is most consonant and resonant, becoming progressively less so as minor, then augmented, and finally diminished triads are included"

If this were the case, than a C major 64 chord as the lower unit against an F# major triad as the upper unit would sound more consonant and resonant than the same C major 64 chord against a G minor triad as the upper unit. In my ear, this simply is not the case. In my ear, the more lower partials the upper unit of the polychord contains of the lower unit's harmonic eries set, the more consonant the tonality of the polychord. In the above example, the F# major has tones found in the 6th 8th and 10th partials of the Cmajor 64's overtone set. The G minor, on the other hand, has partials found in the 1st, 2nd and 6th partials of the Cmajor 64's overtone set

 

D. Polychordal Consonance and Dissonance

1. The more lower partials the upper unit of the polychord contains of the lower unit's harmonic eries set, the more consonant the tonality of the polychord.

In Class Assignment 1: 1. Create various polychords with various voicings. Analyze the relative consonance and dissonace of each.

Homework Assignment 1: Due next class 1. Write an chordal passage that uses primarily consonant polychordal harmony. Clearly define each chordal unit by assigning it a unique and clearly distinguishable orchestration. You may write for any instruments that you like 2. Write an chordal passage that uses polychordal harmony without regard to its consonant or dissonant hierarchy. Clearly define each chordal unit by assigning it a unique and clearly distinguishable orchestration. You may write for any instruments that you like 5. Realize your composition with Garritan and submit your score and mp3 to: hmu415@gmail.com

 

D. Polychordal Counterpoint

1. Polyharmonic direction is determined by the counterpoint of the chordal units (called counterchords) and is derived as two part counterpoint from

a. The outter voices (top voice of upper unit and bottom voice of lower unit)
b. The roots of both chordal units
c. The outter voices can function as the root, third or fifth of a major, minor, diminished or augmented triad.

In Class Assignment 2: 1. Create a polychordal harmonic progression. Establish a good primary chord then concern yourself more with the purpose of the progression than with the relative consonance or dissonance relationship between choral units.

d. Prolonged passages of pure polychords can be tiresome. One may combat this with

a. Ornamentation
b. Unison interpolation
c. Two voice interpolation
b. Triadic or quartal interpolation
e. Omission of Notes of either chordal unit
f. Use of Polychord as harmonic pillar

 

E. Polychordal Syntax

1. Polyharmonic Syntax is almost always devoid of a key center. As such we will again refer to syntax with the following designations:

a. Primary Polychord: Most resonant. Contains the relatively more consonant tones of the overtone set.
b. Secondary Polychord: Less Resonant. Contains relatively fewer consonant tones of the overtone set.
c. Leading Polychord: Used in a similar manner as other leading functions to lead to Primary See Notes 5

1. Leading Harmony with Tritone. Tritone actively resolves in or out pulling us away from Primary or Secondary functions
2. Leading Harmony with resolution of implied Leading Tone
3. Leading Harmony Resolving through a doubled Leading tone
4. Leading Harmony Resolving through the preparation of a reinterpreted dissonant 4th
5. Leading Quartal Harmony: Interpreting the m7th as an applied "chordal 7th"
6. Leading & Primary Harmony: Via Descending 5th Bass

Homework Assignment 2: Due next class 1. Write an antecedent/consequent phrase pair that demonstrates usage of polychordal harmony with purpose. 2. Clearly define primary, secondary and leading functions of your harmony and use the various techniques discussed above to avoid a tiresome harmonic framework. 3. Your piece should be orchestrated for String ensemble and any other group of instruments you like. 4. Realize your composition with Garritan and submit your score and mp3 to: hmu415@gmail.com