# 4 Sample exercises

Procedures for completing various exercises related to Lesson 7 follow.  Click on the exercise of your choice, or go through each, one after another. Try to complete each step of an exercise before checking the response.

• Analyze a triad (Problem 1)

• Analyze a triad (Problem 2)

• Construct a triad given the root and quality

• Construct a triad given the third and quality

• Construct a triad given the 5th and quality

#### Procedure for analyzing a triad

Problem 1: Analyze the following triad by root and quality: 1. Determine the letter name of the root

### 2. Analyze the third on the bottom (root to third)

### B-D is a minor third because it contains one natural half step;
in the key of B major, B to D-sharp is major, so B to D is minor;
or the 3rds built on B E A D are minor, so B-D is minor.

3. Analyze the fifth (root to 5th)

### B-F is a d5 because there are 2 natural half steps; therefore B to F-sharp is a P5;
all natural fifths are perfect except B to F (which is diminished); therefore B to F-sharp is perfect;
in the key of B major, B to F-sharp is a P5.

Solution

### B minor

A triad built on B and constructed of a minor third and perfect fifth is a B minor triadYou can also check to make sure the 3rd on top is major.  D to F-sharp is a M3. #### Procedure for analyzing a triad

Problem 2: Analyze the following triad by root and quality 1. Determine the letter name of the root

### 2. Analyze the third on the bottom (root-3rd) G to B is a major 3rd because there are no natural half steps; therefore G-flat to B-flat is also a M3;
in the key of G-flat major, G-flat to B-flat is a major 3rd;
the thirds built on G, C and F are major; therefore G-flat to B-flat is a M3.

3. Analyze the fifth (root to fifth) G to D is a perfect fifth because all 5ths are perfect except B to F; therefore G-flat to D is an A5;
or in the key of G-flat major, G-flat to D-flat is a perfect 5th; therefore G-flat to D is an A5.

Solution

A triad built on G-flat and constructed of a major third and augmented fifth is a G-flat augmented triad. You can also check to make sure the 3rd on top is major.  B-flat to D is a M3. #### Procedure for constructing a triad, given a root and quality

Problem 3: Construct the following triad above the given root: 2. Add an accidental to the 3rd if necessary. A minor triad has a m3 on the bottom.
E-flat to G is a M3; therefore E-flat to G-flat is a m3;
or the thirds built on B E A D are minor; therefore E to G is minor and E-flat to G-flat remains minor.
3. Add an accidental to the 5th if necessary. A minor triad has a P5 from the root to the fifth.
E to B is a P5; therefore E-flat to B-flat remains a P5.

#### Procedure for constructing a triad, given a third and quality

Problem 4: Given the 3rd, construct the following triad 1. Add notes for the root and 5th of the chord.
2. Add an accidental to the root if necessary. A major triad has a M3 on the bottom.
D to F is a m3; therefore D-flat to F is a M3.
Caution: Do not change the given note. In this case, F.
Students often make the mistake of writing a M3 above D (F-sharp) rather than writing a M3 below F (D-flat).

3. Add an accidental to the 5th if necessary. A major triad has P5.
D to A is a perfect 5th, therefore D-flat to A-flat remains a perfect 5th.
To check, a major triad has a m3 on top.  F to A-flat is a m3.

#### Procedure for constructing a triad, given a fifth and quality

Problem 5: Given the 5th, construct the following triad: 2. Add an accidental to the root if necessary. A diminished triad has a d5.
C to G is a P5; therefore C-sharp to G is a d5.
Do not change the given note (G). Use your hands so you realize the bottom note needs to be raised.

3. Add an accidental to the 3rd if necessary. A diminished triad has a m3 on the bottom.
C to E is a M3.  C-sharp to E is already a m3.  No accidental is necessary.