Common period triadic formations used the harmonic series as the cornerstone of their gravitational force. The Tonic I, Dominant V and Subdominant IV all contained the ^1 and/or ^5. Gravitational pull was enhanced by a leading tone ^7 (or +^7 in minor) whose tonal proximity to the tonic added an additional gravitational force towards the tonic. To be sure, the most characteristic tendancy of the ^1-^5 relationship in the overtone series led the western ear to its first two primary chords: The tonic and dominant.

Triads

Cyclical Relationships
The strength of the tonic - dominant relationship became the cornerstone of harmonic progressions in the common period. In addition to the I,IV, and V chords we saw sequential patterns based upon descending or ascending (less frequent) 5ths. We observed the "deceptive nature of other triads containing the ^1 or ^5 and some observed the "cycle of 5ths" when building key signatures. A cyclical relationship is one in which triads progress through constant intervalic steps,

1. The Cycle of 5ths
a. If we examine a progression of P5ths with C key center we observe that our primary chords form the upper and lower harmonic neighbors in the cycle:

b. We also observe the natural formation of:

1. Plagal Cadence
2. Full Cadence
3. II-V-I Cadential progression

2. Beyond the Cycle of 5ths
a. As music departed from the common period, composers began to experiment with the gravitational forces eminating from the harmonic series. To be sure the western ear hears a strong gravitational pull of the tonic-dominant relationship but Cant there be an aesthetic beauty in something that counters the natural gravity of the harmonic series? Is it possible that a gravitational force is created by the fact that notes are ordered in a cyclical series regardless of their intervallic relationship? The answer is undeniably Yes

3. The Cycle of 3rds
a. If we examine a progression of diatonic 3rds with a C key center we observe that our primary chords form the upper and lower harmonic neighbors in the cycle:

b. We also observe the natural formation of equivaltents to:

1. "Plagal" equivalent Cadence = VI-I
2. "Full" equivalent Cadence = III-I
3. "Cadential" equivalent progression = V-III-I

4. The Cycle of 2nds
a. If we examine a progression of diatonic 2nds with a C key center we observe that our primary chords form the upper and lower harmonic neighbors in the cycle:

b. We also observe the natural formation of equivaltents to:

1. "Plagal" equivalent Cadence = VII-I
2. "Full" equivalent Cadence = II-I
3. "Cadential" equivalent progression = III-II-I

5. Other Cycles
a. If we explore the gravitational pull of cycles beyond that of the P5 we find that both the cycle of 3rds and 2nds have a force that at once, may not seem as potent as that of the P5th but still contain a gravitation that when skillfully exploited may yield extraordicnary beauty. Cycles built on the the remaining intervals prove to be but inversions of the P5, diatonic 3rd and 2nd. Thus the cycle on a P4th yields the same primary chords as that of the P5. The cycle on the diatoic 6th and diatonic 7th yield the same primary chords as the cycles on the diatonic 3rd and 2nd respectively. As such, the nature of the altered gravities of the cycle of diatoic 6ths an 7ths is inheranty linked to that of their inversions.

6. Implementation of triadic cycles
a. Skillful implementation of triadic cycles requires the same fundamental concepts we saw when implementing synthetic scales

1. Create cadential patterns around the triad built on the key center
2. Use primary chords to bring the triadic cycle into focus
3. Use "relative" secondary triad to add depth and interest
Note: a relative secondary triad is any triad that does not contain the tritone and contains fewer primary notes than the primary triads forming the upper and lower harmonic neighbors to the tonic.
4. Avoid the tritone when it hinders the tonic-primary relationship.
5. Employ chormatic alterations to bring into focus a tonal center or primary chord

 

In class assignment 1. write an antecedent/consequent phrase that clearly defines a tonal center with triadic formations based on cyclical 3rds

 

7. Triadic cycles within modes and synthetic scales
a. Triadic formations in cyclical relationships may be constructed in any mode or synthetic scale. One should carefully observe the following:

1. The primary chord(s) of the mode or synthetic scale may contradict the primary chord(s) of the cycle.
2. When a primary chord of a cyclical relationship does not contain the characteristic tone(s) of the mode, one must carefully
incorporate the secondary chrods and melodic figurations that do contain the characteristic tone if the character of the mode or synthetic scale is to be preserved.
3. Use "relative" secondary triad to add depth and interest
Note: a relative secondary triad is any triad that does not contain the tritone and contains fewer primary notes than the primary triads forming the upper and lower harmonic neighbors to the tonic.
4. Avoid the tritone when it hinders the tonic-primary relationship.
5. Employ chormatic alterations to bring into focus a tonal center or primary chord

Homework: Assignment 1: Due next class 1. Write a short passage for Horns and Winds that utilizes any mode or synthetic scale you like The passage should demonstrates triadic cyclical 3rds and/or triadic cyclical 2nds as well as preserve the characteristic nature of the mode or synthetic scale. 2. Realize your composition with Garritan and submit your score and mp3 to: hmu415@gmail.com

6. Syntax and Triadic Cycles

1. Use of syntax with Cyclical Triads in diatonic, modal and synthetic formations

a. Determine function of syntax by examining the harmonic role of characteristic tones, and "dominant" structures
b. Identify Tonic,
c. Identify "Dominant-Like" Primary
d. Identify "Intermediate-Like" Secondary
e. Identify all Tritones

2. Redefinition of "Tonic - Dominant" Relationship
3. Redefinition of Cadence

7. Free Triads: Non Cyclical - Non Syntactical Triads

1. Use of mixed cycles produces a non tonic function
2. Tonality is immediately local
3. Bass movements of Major and minor 2nds & 3rds previal.
4. Bass movements of P5ths may be overbearing in their definition of a tonal center
5. Triadic formations tend to be Major or minor to allow the ear to accept the lack of tonal center
6. Bass movements of A4ths is very effective in conjunction with highly chromatic triad progressions
7. Triadic Formations are often root position but inversions may occur.
8. Triadic formations may become sequential independent of or in combination with a sequential bass formation.
9. Triadic formations may result from purposeful counterpoint in two or more voices
10. Triadic formations may result from the reinterpretation of a characteristic note as the ^1, ^3, ^5 (this is particularly useful with orchestral pedals)
11. Triadic formations may result from the assignement of a fixed chordal scale degree on a unadorned scale formation.

8. Seventh and Ninth Chords: Polytriadic formations (see chapter 7)

1. Persechetti, goes into detail about how 7th& 9th chords can move without their dissonance resolving
2. Persechetti, goes into detail about how 7th& 9th chords can move well in cyclical 5ths, 3rds, and 2nds.
3. Persechetti, goes into detail about how 7th& 9th chords can move through inversions and modalities.
4. Polytriadic formations

a. Diatonic
b. Modal
c. Synthetic
5. Triadic formations tend to be Major or minor to allow the ear to accept the lack of tonal center
6. Bass movements of A4ths is very effective in conjunction with highly chromatic triad progressions
7. Triadic Formations are often root position but inversions may occur.
8. Triadic formations may become sequential independent of or in combination with a sequential bass formation.
9. Triadic formations may result from purposeful counterpoint in two or more voices
10. Triadic formations may result from the reinterpretation of a characteristic note as the ^1, ^3, ^5 (this is particularly useful with orchestral pedals)
11. Triadic formations may result from the assignement of a fixed chordal scale degree on a unadorned scale formation.

 

Homework: Assignment 2: Due next class 1. Select or create a mode or synthetic scale formation and build triads in cyclical 3rds. Identify the function of every triad as per the above examples. 2. Write a short passage for Strings that utilizes the mode or synthetic scale from above. The passage should demonstrates triadic cyclical 3rds as well as preserve the characteristic nature of the mode or synthetic scale. It should show a clear understanding of Primary, secondary and cadential functions. Tritone harmony should be handled appropriately. 2. Realize your composition with Garritan and submit your score and mp3 to: hmu415@gmail.com

 

Homework: Assignment 3: Due class after the quiz 2. Write a short passage for any ensemble you like utilizing free triads. The composition should demonstrate a purpose underlying the implementation of your triads. You should try to avoid any implications of a tonal center within the interior of the piece. 2. Realize your composition with Garritan and submit your score and mp3 to: hmu415@gmail.com

 

Up unitl now, our triadic formations have been the result of a given mode or scale formation. It is important to note that as we move further from tonal centers, an underlying scale, mode or tonality is sometimes a resultant factor of the triadic formations.

Have we come full cirlce?

When we begin our exploration of music theory many students conception of harmony is one chord somewhat randomly followed by another. Syntax and synthetic and alternate scale formations are unkown and the beginner often moves freely in their harmonic progressions with blissful innocence. The very first concepts of tonic-dominant and Leading Tone relationships makes the ear aware. The exploration of these relationships through sequencial functions, chromaticism, modality, and synthetic scale formations focuses our ear on that which causes gravitational force. Perceiving cyclical relationships allows us to understand that there is gravity in relationships beyond the tonic-dominant and leading tones. We learn of alternate "dominance" Understanding this gravitational force is the essence to leading the ear to a desired emotional response. We see it over and over again. The deceptive cadence is deceptive because the Leading Tone leads where we expect but the dominant does not. Sequencial formations are sequential because we lead the ear to expect certian combinations of tonic, dominant and LT relationships. Augmented 6th lead to a cadential V because we understand the doubled LT function of the A6. Phrygian modality has a characteristic ^2 which at once makes Primary II and VII. Primary became a term we understood as being a triad we used to "focus" our tonal center. Primary in cyclical relationships furthered that focus to redefine the syntax of our dominant and subdominant. Our ear has been inevitably trained to find focus... the tonic and "dominant" within a world defined by triadic harmony.

So have we come full circle

Well yes and no. Free triadicism does appear to have the youthful innocence of the unenlightened. But it is my hope that your understanding of harmony is now with purpose. If you sit down with your guitar or piano or jotting notes into finale, are you just randomly seaching for chords or is there a deeper purpose. If there is a deeper purpose than you have arrived.

In our text (pg 71) Persechetti states:

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

What happens, though, if we abandon triads..........?