Theory III


Class Notes 6

Mixture

Please note: All references to "Aldwell Audio " can be found on
"2 CD set to accompany Harmony & Voice Leading 3rd Edition"


All other items can be found in zip file on index page

Homework: Workbook Chapter 23

Preliminaries: a, b, e, k, q
Longer Assignments: #1
Study and Analysis #1

or Textbook all "Exercises" except #2 & #6


So far, we have segregated our study to either tonal and harmonic functions occuring in Major or those occurring in minor. We use the term "Mixture" to define situations in which elements from a minor key are set forth in its parallel major, or, conversely, when we see elements from a major key set forth in its parallel minor.

Combining Modes

1.  Minor in major and vice versa

Remember, I differ from the text in that I use "-" or "+" to refer to a chordal scale degree that has been lowered or raised. For example, the use of -VII in minor (as a modulation to III or as a predecessor to V) indicates that the chord is not built on the leading tone but rather on the minor 7th. This terminology becomes critical in our discussion of mixture. H&VLs method of using "b" and "#" instead of "-" and "+" becomes, by their own admission, a problem in a context that contains mixture. Take, for example an F Major chord in the key of A Major. In its naturally occuring state, F# exists in A Major. Via mixture the chord can be built on a lowered ^6 scale degree yielding an altered VI chord. Even though that altered VI chord is built on a lowered ^6 scale degree It would make no sense to call that altered VI chord a bVI as there are absolutely no flats in either the chord or the prevailing key. H&VL's solution is to apply different rules to the use of the nomenclature "b" and "#" when discussing mixture. In this class we will simply use the same system we have previously: When a tone is lowered from its naturally occuring state we will use the designation "-" and when it is raised we will use the designation "+" Thus the Fmajor chord in the key of A is a "-VI"

2.  -^6 in major

a. The lowered sixth scale degree -^6 is often used


1. in subdominant harmony IV5(-3)
2. in supertonic harmony II 6(-3)


b. When leading from tonic I, the -^6 requires no special preparation as it will lead smoothly as a stepwise ascent from ^5, and a M3 descent from ^1
c. Less common is the d4th ascent from ^3 (note: it is NOT a M3 ascent but infact a d4th)

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3.  -^3 in major

a. The lowered third scale degree -^3 is often used


1. as an altered coloration of tonic harmony from Major to minor (similar to our discussion of minor V)
2. When -^3 is combined with -^6 we can introduce -VI into Major harmony
3. When -VI is used in place of VI in a deceptive cadence, the tonal contrast is dramatically increased as we lead to two different non diatonic tones. Therefore, the deceptive effect is significantly reduced.

4.  +^3 in minor

a. Using the major 3rd in a minor key setting is one of the most frequent instances of mixture. When it is used at the conclusion of a piece or a section, it is known as a "Picardy 3rd"



Note: Throughout the discussion of mixture and in its examples, H&VL presents the use of -^6 and -^3 in Major as having a much stronger tendancy to resolve downward to ^5 and ^2 than their major counterparts ^6 and ^3. To be sure this comes from the very strong 1/2 step pull from the -^6 to ^5 (a very stable tone) and a similar gravitational force of the 1/2 step between -^3 and ^2.

In minor, the use of +^3 and +^6 is not quite as common although one should not shy away from such usages. Again the idea is to be mindful of the voice leading. The +^6 will lead the ear into melodic minor. Of course, the +^3 is a very beautiful and effective "Picardy 3rd"

5.  More extended uses of Mixture

a. Sometimes an entire phrase or even section of a piece will be cast in the parallel minor or major. This was the case with the Music Theory II Final exam where, upon our return to the 1st period statement, you switched modes from Major to minor or from minor to Major

 

6.  VIIº7 in Major

a. We have seen that the -^6 of VIIº7 occurs naturally in minor
b. Introducing the VIIº7 and the -^6 as a form of mixture in Major happens frequently and presents no problems
c. Note: The º7 may appear without preparation as a form of melodic figuration and will resolve as expected (^4 + ^2 may resolve to either +^3 or -^3)

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7.  Secondary Mixture

a. Secondary mixture occurs when the 3rd of a triad is altered but is not the ^3 scale degree.
b. For example, in Major the III would naturally be minor. altering ^5 to a +^5 creates a Major III5/+3
c. Again Note my use of + and - in the arabic figuration.


d. III+ is commonly followed by II6 as part of a cadence or in the larger scale I-III#-V
e. III+ holds a special relationship with V and I:


1. Coming off a V7, the ^5 in the bass can rise by chromatic half step to +^5 similar to the rise from ^5 to ^6 in a deceptive cadence
2. The ^4 as the chordal 7th of V7 can fall to ^3 as expected but now as the root of the III
3. The ^2 may remain the same
4. The resulting III+ can be thought of as an alternate deceptive cadence
5. Interestingly, that "alternate deceptive cadence" just happens to be an applied dominant to the real Deceptive cadence.