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Triads: Arithmetic

Goal: To build triads melodically and harmonically using arithmetic concepts.

Out of Tempo

Addition

Beginning

  1. Teacher speaks, “Major third plus minor third = major triad."
  2. Students repeat.
  3. Teacher speaks, “Minor third plus major triad = minor triad."
  4. Process repeats for diminished and augmented triads.

Intermediate

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

Advanced

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

Subtraction

Beginning

  1. Teacher speaks, “Perfect fifth minus a minor third = major third.”
  2. Students repeat.
  3. Teacher speaks, “Perfect fifth minus a major third = minor third.”
  4. Students repeat.
  5. Process repeats.

Intermediate

  1. Teacher speaks, “8 half steps minus 1 half step = 7 = Perfect 5th."
  2. Students repeat.
  3. Teacher speaks, “7 half steps minus 1 half step = 6 = Diminished 5th.”
  4. Students repeat.
  5. Process repeats.

Advanced

  1. Teacher prompts, “Turn a major triad into a minor triad.”
  2. Students answer, “Subtract a half step from the third of the triad.”
  3. Teacher prompts, “Turn a minor triad into a diminished triad.”
  4. Students answer, “Subtract a half step from the fifth of the triad.”

Multiplication

Beginning

  1. Teacher speaks, “Root, third, fifth.”
  2. Teacher prompts, “Repeat x (four) times."
  3. Students repeat x times.

Intermediate

  1. Teacher speaks, “Root, fifth, third” four times.
  2. Teacher prompts, “Repeat x times."
  3. Students repeat x times.

Advanced (Downward to the root – not inverted positions)

  1. Teacher speaks, “Fifth, third, root."
  2. Teacher prompts, “Speak down from the fifth, third, root x times.”
  3. Students repeat x times.
  4. Process continues altering the number of x times the triad is spoken.

Division

Unequal divisions except for the augmented triad

Beginning

  1. Teacher prompts, “Divide a major triad into two intervals.”
  2. Students answer, “Major third and minor third.”
  3. Process continues for all four triads.

Intermediate

  1. Teacher prompts, “Divide the major triad in to half steps.”
  2. Students answer, “7.”
  3. Process continues for all four triads.

Advanced (Chromatic half steps)

  1. Teacher speaks, “Doe, Rey-flat, Rey, Mi-flat" through "high Doe.”
  2. Teacher prompts, “Divide these into combinations of triads.”
  3. Students answer, “Doe, Mi-flat, Sol,” for example.
  4. Process continues, where for example no root can be repeated.

In Tempo

Sung

Addition

Beginning

  1. Teacher sings, “Doe Rey Mi, Mi Fa Sol, Doe Mi Sol Mi Doe.”
  2. Students repeat.

Intermediate

  1. Teacher sings, “1, 2, 3; 3, 4, 5; 1, 3, 5, 3, 1.”
  2. Students repeat.

Advanced

  1. Teacher sings to scale tones, “Major third, minor third, major/minor chord."
  2. Students repeat.
  3. Process repeats for all triads.

Subtraction

Beginning (Adjacent triads)

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

Intermediate (Adjacent triads)

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

Advanced (Non-adjacent triads – singing to the fifth)

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

Multiplication

Beginning (Major)

  1. Teacher sings, “Doe Mi, Doe Mi, Doe Mi, Doe Mi; Mi Sol, Mi Sol, Mi Sol, Mi Sol."
  2. Students repeat.
  3. Teacher prompts, “What kind of triad was that?”
  4. Students answer, “Major.”
  5. Process continues for all triad types.

Intermediate (Root, fifth, third)

  1. Teacher sings, “Doe Sol, Doe Sol, Doe Sol, Doe Sol; Sol Mi, Sol Mi, Sol Mi, Sol Mi" (minor for example).
  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 within the repetitions)

  1. Teacher sings, “Doe Mi (major), Doe Mi (minor), Doe Mi (major), Doe Mi (minor), then Mi Sol (minor), Mi Sol (major), Mi Sol (minor), Mi Sol (major)."
  2. Students repeat.
  3. Teacher prompts, “Which triads were sung.”
  4. Students answer, “First major, then minor.”
  5. Process continues with all triad types.

Division

Beginning

  1. Teacher sings a perfect fifth, “Doe, Sol.”
  2. Teacher prompts, “Divide the fifth into major triad.”
  3. Students sing, “Doe, Mi, Sol.”
  4. Process repeats for minor triads.

Intermediate

  1. Teacher sings a perfect fifth down, “Sol, Doe.”
  2. Teacher prompts, “Divide the fifth into minor triad.”
  3. Students sing, “Doe, Mi, Sol.”
  4. Process repeats for minor triads.

Advanced (Up and down)

  1. Teacher sings diminished or augmented fifth, “Doe, Sol.”
  2. Teacher prompts, “Divide the fifth into minor triad.”
  3. Students sing, “Doe, Mi, Sol.”
  4. Process repeats for augmented and diminished triads, up and down.