Up until now our study of harmony and voice leading has been based on triadic formations. This type of tertian harmony has been very useful in our examination of music of the 18th and 19th century when the confines of traditional syntax was tested. We saw with the formation of free triads that virtually any syntax is possible if the purpose of such syntax is well defined. We concluded our study of singular triadic formations with a quote from Persechetti

"...if each voice has purpose and design, any triad may progress freely and with harmonic meaning"

Chords by Fourths

Basic Quartal Voicing

1. Standard vs. Closed Inverted Quartal Voicing
a. The most distinctly characteristic sound of quartal harmony occurs when all members of the chord are placed a fourth apart. This is standard quartal voicing

b. Notice that as we go into closed inversions of the quartal harmony we always produce a 2nd. These closed inversions may at times sound more like 11th, 13th or other triadic formations with added or suspended tones.

2. Three Note Chords by Fourths

a. Like a triad, 3 note quartal harmony can have 3 types of intervallic arrangements:

1. P4-P4
2. P4-A4
3. A4-P4

Note: A4-A4 would yield an enharmonic 2 note chord.

b. Each 3 note quartal harmony has two inversions and although some of the character is lost by leaving open quartal harmony...

1. Inversions help to prevent harmonic monotony
2. Inversions present a P5th which can be used as a fundamental harmonic structure

c. Open spacing (displacement of a subsequent fourth to a different octave register) and voice doublings increase harmonic expression.

d. Any chord tone may skip to any other tone that is a derivation of quartal harmony if the other tones stay stationary.

e. Like Free triads, free quartal progressions must occur with purpose

f. The upper 4th in quartal harmony clashes with the natural overtone series. As such quartal harmony sounds more vague and ominous in lower registers and brighter and more defined in upper registers. ( compare Brick Impromptu 8vb)

3. P4-P4

a. Each note is of equal harmonic significance. As such any note may be doubled
b. A progression of P4-P4 does not fall within the makeup on any one scale and thus become chromatically "supple"
c. A progression where the root of a P4-P4 follows a diatonic scale will create polytonal potential (see 4-9b)
d. Neither P4 is considered dissonant and thus neither are forced to resolve and any note may skip.

 

4. P4-A4 or A4-P4

a. In quartal harmony containing a TT, the TT is perceived as a dissonance and will have a tendancy to resolve to the closest note of the prevailing harmonic or melodic context.
b. Note: The resolution of the tritone may be up or down as long as its to the closest (remember difference between resolution of d5 vs. A4)

Homework: Assignment 1: Due next class 1. Write a sequential passage for flute, oboe and clarinet. use chords by P4 only 2. Realize your composition with Garritan and submit your score and mp3 to: hmu415@gmail.com

Homework: Assignment 2: Due next class 1. Write a double period for full string ensemble that features a mix of P4-P4, P4-A4, and A4-P4 quartal harmony. Do not include any triadic formations. 2. Realize your composition with Garritan and submit your score and mp3 to: hmu415@gmail.com

Homework: Assignment 3: Due next class 1. Persechetti Application #4 Pg. 106-107 2. Realize your composition with Garritan and submit your score and mp3 to: hmu415@gmail.com

 

5. Movement between Quartal and Triadic Harmony

a. Quartal harmony may be easily approached or left by triads when the uppermost note is prepared.
b. A Triadic Tonic chord may contain the 6th and 9th as the upper quartal voices
c. Quartal harmony can be built on the root of any "dominant" function.
c. As always, Quartal and triadic harmony may move with ease when one voice moves with strong melodic purpose.

 

6. Four-Note Quartal Harmony

a. Basics

1. Adds tremendous resonance
2. Includes 10th above bass in root position.
3. Very useful in inversions because of the greater variety of intervals
4. When using arabic analysis dont confuse ^6 & ^7 (eg. 642 (triadic) vs. 742 (quartal) )

b. Basic concepts of Voice leading

1. Stepwise voice leading in two or more voices can yield a nice resolution to a triadic formation as secondary harmony.
2. When the voice leading from a quartal harmony leads stepwise to a triadic 7th one may create dominant as primary harmony
3. Three note quartal harmony with an octave doubling can also lead to a similar triadic resolutions (as above)
4. When the tritone is present in an 4 note quartal harmony, it can be used as a gravitational force as tritone harmony

a. This is particularly effective when moving from one quartal harmony to another
b. It is also most effective when the tritone appears in the top voices.

c. Compound Construction

1. Combinations of 3rds and 4ths brings new color to quartal harmony
2. A third above a quartal construction adds richness and complexity
3. A third below a quartal construction provides an edge to the quartal harmony
4. Use of a third below or above is an effective coloration of a passing quartal harmony.

d. Multi-note quartal harmony

1. 5 Note P4 quartal harmony spells an inverted m7 with an added 11th
2. 6 Note P4 quartal harmony spells an inverted m7 with an added 11th & 13th
3. 12 different tones may be placed a perfect fouth apart.
4. multi-note quartal harmony will spell triadic formations with added 9ths, 11th, 13th and, as such can act as a pivot to
added note tertian harmony as the ear will not distinuish the two.
5. To maintain a characteristic quartal tonality, one may isolate the quartal elements of a given multi note quartal harmony within an
orchestral timbre.