Triads: Arithmetic

Beginning

1. Teacher speaks, “Minor third plus perfect fourth = First inversion major triad.”
2. Students repeat.
3. Teacher speaks, “Perfect fourth plus major third = Second inversion major triad.
4. Process repeats for minor, diminished, and augmented triads.

Intermediate

1. Teacher speaks, “3 half steps plus 5 half steps = First inversion major triad.”
2. Students repeat.
3. Teacher speaks, “5 half steps plus 4 half steps = Second inversion major triad.”
4. Students repeat.
5. Process repeats for minor, diminished, and augmented triads.

Advanced

1. Teacher prompts, “In first inversion, turn a major triad into an augmented triad.”
2. Students answer, “Add a half step to the fifth of the triad.”
3. Teacher prompts, “In first inversion turn a minor triad into a major triad.”
4. Students answer, “Add a half step to the third of the triad.”

Process repeats for other triads in inverted positions.

Beginning

1. Teacher speaks, “In second inversion turn a major triad in to a minor triad.”
2. Students answer.

Intermediate

1. Teacher speaks, “In second inversion turn a minor triad in to a diminished triad.”
2. Students answer.

Advanced

1. Teacher speaks, “In second inversion turn an augmented triad in to a major triad."
2. Students answer.

Beginning: First Inversion

1. Teacher speaks, “Third, fifth, root”
2. Teacher prompts, “Repeat x times.”
3. Students repeat x times.

Intermediate

1. Teacher speaks, “Fifth, root, third x times."
2. Teacher prompts, “Repeat x times.”
3. Students repeat x times.

Advanced

1. Teacher speaks, “Third, fifth, root/fifth, third, root.”
2. Teacher prompts, “Repeat x times.”
3. Students repeat x times.
4. Process continues altering the number of x times the triad is spoken.

Teacher sets up a tempo, time signature, tonality, singing numbers or solfege in first or second inversion in keys other than C major or minor.

Singing, playing, one note per measure until students are comfortable with the exercise.

Beginning (First inversion)

1. Teacher sings in numbers or (fixed-Do) solfege, “3 4 5, 5 6 7 8, 1 2 3.”
2. Students repeat.

Intermediate (Second inversion)

1. Teacher sings, “5 6 7 8, 1 2 3, 3 4 5.”
2. Students repeat.

Advanced (First and second inversion up and down)

1. Teacher sings, “3 4 5, 5 6 7 8, 1 2 3, 3 2 1, 8 7 6 5, 5 4 3” then "5 6 7 8, 1 2 3, 3 4 5, 5 4 3, 3 2 1, 8 7 6 5."
2. Students repeat.
3. Process repeats for all triad types.

Beginning (adjacent triads – first inversion)

1. Teacher sings, “3, 5, 8” (major), then “3, 5, 8" (minor).
2. Students repeat.
3. Teacher prompts, “What type of triads?"
4. Students answer, “Major to minor”

Intermediate (adjacent triads – second inversion)

1. Teacher sings, “5, 8, 3” (augmented), then “5, 8, 3" (major).
2. Students repeat.
3. Teacher prompts, “What type of triads?"
4. Students answer, “Augmented to major.”

Advanced (non-adjacent triads –singing to the outer chord tone)

1. Teacher sings, “3, 8, 5” (major), then “3, 8, 5" (diminished).
2. Students repeat.
3. Teacher prompts, “What type of triads?"
4. Students answer, “Major to diminished.”

Beginning

1. Teacher sings, “3, 5, 8,” x times.
2. Students repeat.
3. Teacher prompts, “What kind of triad was that?”
4. Students answer, “Major”
5. Process continues for all triad types.

Intermediate

1. Teacher sings, “5, 8, 3” x times.
2. Students repeat.
3. Teacher prompts, “What kind of triad was that?”
4. Students answer, “Minor.”
5. Process continues for all triad types.

Advanced (switching triad types and inversions)

1. Teacher sings, “3, 5, 8" (major for example) and "5, 8, 3" (minor for example).
2. Students repeat.
3. Teacher prompts, “Which triads were sung.”
4. Students answer, “Major first inversion, and then minor second inversion.”
5. Process continues with all triad types and inversions.

Outer interval is given, middle note is the answer.

Beginning

1. Teacher sings a major sixth using numbers or solfege, 3 to 8, for example.
2. Teacher prompts, “Divide the sixth into an inverted triad.”
3. Students sing, “3, 8, 5.”
4. Process repeats for all triad types.

Intermediate

1. Teacher sings a minor sixth down, using numbers or solfege, 8 down to 3, for example..
2. Teacher prompts, “Divide the sixth into major triad.”
3. Students sing, “8, 3, 5”
4. Process repeats for all triad types.

Advanced (up and down)

1. Teacher sings "3, 8 / 8, 3."
2. Teacher prompts, “Divide the sixth to create an inverted triad.”
3. Students sing, “3, 8, 5 / 5, 8, 3.”
4. Process repeats for all triad types and inversions, up and down. Can be done mixing triad types and inversions.