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Triads: Arithmetic

Goal: To set up melodic improvisations using triads in all positions with focus on mixture and chromatic mixture.

Out of Tempo

All Levels

“Out of Tempo” exercises are not presented separately in Ear Training III and Ear Training IV improvisations. Should any exercise prove difficult performed in tempo, out of tempo versions of the materials in Ear Training III and Ear Training IV can be modeled on Ear Training I and Ear Training II approaches to out of tempo improvisations.

In Tempo

Teacher sets up a tempo, time signature, tonality, and rhythms.

Phrases can be four to thirty-two measures in length depending on the student’s ability.

Start with one note per measure and add different rhythms as students become more comfortable with the exercise. For more confident students, use non-repeating notes and rhythm patterns.

Students sing one, two, three, or four notes per measure.

Speaking, singing, playing.

Refer to the Triad Smorgasbord for ideas.

Addition

Beginning

  1. Teacher sets up as above and prompts, “Singing one note per measure, each student adds a chord tone of a major triad from bottom up."
  2. Students do so.
  3. Teacher prompts, “Singing one note per measure, using the third of the same major triad, each student adds a chord tone creating a new major triad from bottom up.”
  4. Students do so.

Intermediate

  1. Teacher sets up as above and prompts, “Singing one note per measure, each student adds a chord tone of a major triad from top down."
  2. Students do so.
  3. Teacher prompts, “Singing one note per measure, using the third of the same major triad as the new fifth, each student adds a chord tone creating a new major triad from top down.”
  4. Students do so.

Advanced

  1. Teacher sets up as above and prompts, “Singing one note per measure, each student adds a chord tone of a diminished triad from top down."
  2. Students do so.
  3. Teacher prompts, “Singing one note per measure, using the third of the same diminished triad as the new fifth, each student adds a chord tone creating a minor triad from top down.”
  4. Students do so.

Subtraction

Beginning

  1. Teacher sets up as above and prompts, “Remove the third of this chord and sing a new major chord upward using the removed note as the root.”
  2. Students do so.

Intermediate

  1. Teacher sets up as above and prompts, “Remove the fifth of this chord and sing a new diminished chord upward using the removed note as the root.”
  2. Students do so.

Advanced

  1. Teacher sets up as above and prompts, “Remove the root of this chord and sing a new diminished chord downward using the third of the chord as the new fifth.”
  2. Students do so.

Multiplication

Beginning

  1. Teacher sets up as above and prompts, “Sing in four-four: CE EE EE EE, EbG GG GG GG, creating a new major third.”
  2. Students do so.

Intermediate

  1. Teacher sets up as above and prompts, “Sing in four-four: EbG GG GG GG, GbBb BbBb BbBb BbBb, creating a new major third.”
  2. Students do so.

Advanced

Process continues in a similar way creating new major thirds from top, down.

For example: C down to Ab becomes A down to F.

Division

Beginning

  1. Teacher sets up as above and prompts, “I’m playing a perfect fifth. Student A sings an upward major triad from the missing major third of the perfect fifth.”
  2. Student A does so.

Intermediate

  1. Teacher sets up as above and prompts, “I’m playing a perfect fifth. Student B sings a downward major triad from the missing major third of the perfect fifth.”
  2. Student B does so.

Advanced

  1. Teacher sets up as above and prompts, “I’m playing a diminished fifth. Student C sings an upward major triad from the missing minor third of the diminished fifth.”
  2. Student C does so.