Triads and Seventh Chords

We have now suffered through the three quizes and we are about to undertake our first steps into music analysis. ;-) Be sure to practice your rhythmic and sofeg sight singing as there will be a section on the midterm that covers this stuff.

Homework: Workbook all of Chapter 4 except pages 27+28

Triads

1.  Triad as a basic chord
a. In Unit 1 we saw defined a triad as a chord with a 5th and a 3rd above the bass note. We now need to expand that definition.

2. Triad Qualities
a.     Since we now know that interval qualities can be defined as Major, minor, augmented or diminished, the quantitative aspect of our previous definition needs to be refined. To be sure, the list of possible triads can go beyond the table below. However, for our purposes now, we shall limit ourselves to the following:

Important note: Some people suggest a method of determining the construction of triads by stacking intervals of a 3rd. That is, they would say a root position Major triad contains a M3 above the bass and a m3 above the M3. This method ignores the fundamental function of each tone in the triad and should be ignored. Always construct a triad by determining the quality of the 5th and the 3rd.

3. Roman Numerals (Major)
a.  If we build a triad on the root (or fundamental tone) of each of the seven scale degrees of diatonic C major then assign each scale degree a roman numeral we get the following:

4. Roman Numerals (minor)
a.  If we build a triad on the root (or fundamental tone) of each of the seven scale degrees of diatonic C natural minor then assign each scale degree a roman numeral we get the following:

5. Roman Numerals (inflected minor)
a.  We saw that the use of the harmonic (raised 7 only) minor allowed us to create a stronger motion to 1 by creating a "leading tone" out of the raised 7th scale degree. When the natural minor triads containing a 7th scale degree have that scale degree raised, we get the following:

b.  We saw that the use of the melodic (raised 6 & 7 ) minor allowed us to create a stronger motion to 1 by creating a "leading tone" out of the raised 7th scale degree while simultaneously eliminating an awkward augmented 2nd between the 6 & 7. When the natural minor triads containing a 6th & 7th scale degree have those scale degrees raised, we get the following: (note I contains neither 6 nor 7 and is not listed below)

c. Since the raised 7th scale degree creates a leading tone that has a very strong gravitational push towards 1, we will se the alteration of the inflected forms of minor on V and VII extremely frequently in music of the classical period. Although less frequent in the classical period, the use of the inflected form of III will become more prominant in later periods.

6. Triads in Inversion
a.  When the root of the triad is the lowest tone, the triad is said to be in "root position". Until now, this has been the primary way we have looked at triads. Just as an interval (like a M3) can be inverted (m6) so too can a triad. When some other tone than the root is in the bass, the triad is inverted. Many people will speak of the "root position" containing the fundamental in the bass, the "first inversion" containing the 3rd of the triad in the bass, and the "second inversion" containing the 5th of the triad in the bass. Whereas this is common, it is more useful to speak of the actual intervalic relationship in any "inversion"

7. 5-3, 6-3, 6-4 chords; figured bass
a.  This system of defining the intervals above the bass tone to determine the traidic position is called "Figured Bass" or "Through Bass" and is a very useful kind of musical shorthand. As one becomes familiar with this system, a single figured bass line is all that is necessary to realize an accompaniment. Similarly, when throughts are flowing quickly in the compositional process, a figured bass line with a melody or rhythmic pattern can quickly preserve the essence of the idea without interrupting the creative flow.

b. When figuring a "five-three" or "six-three" chord, the "three" will be eliminated resulting in just 5 and 6.
NOTE: On page 52 of H&VL the statement "Also the symbol 5-3 is frequently shortened to 6" is wrong. It should read "Also the symbol 6-3 is frequently shortened to 6"

c. A few rules of figured bass:

1. Key signatures apply to figures
2. Modification of key signatures are indicated by the appropriate sign next to the figure
3. An accidental alone without a figure always applies to the 3rd above the bass
4. Figures do not specify the arrangment of tones above the bass

8. 6-3, 6-4 chords as products of melodic motion
a.  When a figure occurs as the result of a temporary melodic motion over a stable bass tone, either the figuration is considered "passing" and may be omitted or the passage can be figured with a horizontal line between each figure. Note: It is very important to determine if the figure is "temporary" and/or "passing"

9. Nomenclature
a.  When we refer to the lowest tone of a triad we will follow the figured bass approach and call the lowest tone the "bass" tone NOT the "root"

10. Harmonic Analysis
a. By using a combination of Roman numerals and figured bass, we have created the tools we need for standard harmonic analysis in music theory. One should note with caution the aforementioned warning about chords derived as products of melodic motion. Analysis of every single chord in a piece, including those that arrive via melodic motion, can be misleading.

9. Remembering Triads
a.  As we saw in 3 and 4 above, Roman numerals represent the chords built on each scale degree. It is critical that you be able to quickly identify the Roman numeral. To do so, look at the C Major scale and construct the triads on each scale degree. The letter names of these 7 triads represent the only 7 triads that exist. (note these letters may always be altered with accidentals)

Seventh Chords

12.  The Melodic Origins of 7th chords
a. All consonant chords are 5-3, 6-3 and some 6-4 triads
b. All Aug. and Dim and some 6-4 triads are dissonant.
c. When a triad contains a 7th (dissonant) the triad also become dissonant.
d. The 7th is derived as a passing tone between the 8th of one chord (the V chord) and the 3rd of another chord (the I chord)
e. the active, unstable, dissonant 7th must resolve by stepwise decent.

13. 7th Chord Qualities
a.     With the exception of the Dominant 7th which occures on the 5th scale degree (the Dominant) The quality of the seventh chord is not nearly as significant to its function as the qualtiy of the triad is to its function.

14. 7th Chords on scale degrees
a.     In Major

a.     In natural minor and some important alternatives

15. Inversions of 7th Chords
a.     In our discussion of triads we saw that there existed an inversion for each tone of the triad such that

b.     If we now add a 7th to the triad we get another inversion as follows:

16. Figured Bass for 7th Chords

a.    It is important to note that the figured bass for any 7th chord will contain the interval representing the 7th of that chord. Thus the abbreviations 7, 6-5, 4-3, and 4-2 all contain the interval above the bass that includes the 7th.