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)
BD is a minor third because it contains one natural half step;
in the key of B major, B to Dsharp is major, so B to D is minor;
or the 3rds built on B E A D are minor, so BD is minor.
3. Analyze the fifth (root to 5th)
BF is a d5 because there are 2 natural half steps; therefore B to Fsharp is a P5;
all natural fifths are perfect except B to F (which is diminished); therefore B to Fsharp is perfect;
in the key of B major, B to Fsharp is a P5.
Solution
B minor
A triad built on B and constructed of a minor third and perfect fifth is a B minor triad. You can also check to make sure the 3rd on top is major. D to Fsharp is a M3.


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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 (root3rd)
G to B is a major 3rd because there are no natural half steps; therefore Gflat to Bflat is also a M3;
in the key of Gflat major, Gflat to Bflat is a major 3rd;
the thirds built on G, C and F are major; therefore Gflat to Bflat 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 Gflat to D is an A5;
or in the key of Gflat major, Gflat to Dflat is a perfect 5th; therefore Gflat to D is an A5.
Solution
Gflat augmented triad
A triad built on Gflat and constructed of a major third and augmented fifth is a Gflat augmented triad. You can also check to make sure the 3rd on top is major. Bflat to D is a M3.


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Procedure for constructing a triad, given a root and quality

Problem 3: Construct the following triad above the given root:
1. Add notes for the 3rd and fifth of the triad.
2. Add an accidental to the 3rd if necessary.
A minor triad has a m3 on the bottom.
Eflat to G is a M3; therefore Eflat to Gflat is a m3;
or the thirds built on B E A D are minor; therefore E to G is minor and Eflat to Gflat 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 Eflat to Bflat remains a P5.


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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 Dflat 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 (Fsharp) rather than writing a M3 below F (Dflat).
3. Add an accidental to the 5th if necessary.
A major triad has P5.
D to A is a perfect 5th, therefore Dflat to Aflat remains a perfect 5th.
To check, a major triad has a m3 on top. F to Aflat is a m3.


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Procedure for constructing a triad, given a fifth and quality

Problem 5: Given the 5th, construct the following triad:
1. Add noteheads for the root and 3rd.
2. Add an accidental to the root if necessary.
A diminished triad has a d5.
C to G is a P5; therefore Csharp 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. Csharp to E is already a m3. No accidental is necessary.

