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Triads: Arithmetic

Goal: To set up the improvisation using triads in inverted positions, major, minor, augmented, and diminished (with focus on using whole tone and pentatonic scales to create triads and singing in three-part harmony).

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

Harmonic Triads.

Beginning

  1. Teachers sets up as above and prompts, “Students A, B, and C add one note at a time from root up, singing triad x, y, or z in root position.”
  2. Students do so.

Intermediate

  1. Teachers sets up as above and prompts, “Students A and B, start together and student C adds the remaining chord tone singing triad x, y, or z in root position.”
  2. Students do so.

Advanced

  1. Teachers sets up as above and prompts, “Student A, starts first and students B and C add the remaining two chord tones singing triad w, x, y, or z in root position.”
  2. Students do so.

More Advanced

Use inverted positions following the same additive process.

Subtraction

Beginning

  1. Teacher sets up as above and prompts, “Students A, B, and C sing a root position triad at the same time with my accompaniment. After two measures the student with the third stops singing.”
  2. Students do so.

Intermediate

  1. Teacher sets up as above and prompts, “Students A, B, and C sing a first inversion triad at the same time with my accompaniment. After two measures the student with the third stops singing.”
  2. Students do so.

Advanced

  1. Teacher sets up as above and prompts, “Students A, B, and C sing a second inversion triad at the same time with my accompaniment. After two measures the student with the third stops singing.”
  2. Students do so.

Multiplication

Beginning

  1. Teacher sets up as above and prompts, “Student A sings root, third, fifth, student B sings third, fifth, root, and student C sings fifth, root, third, at the same time, one note per measure repeating the process twice = six measures.”
  2. Students do so.

Intermediate

  1. Teacher sets up as above and prompts, “Student A sings root, third, fifth, student B sings third, fifth, root, and student C sings fifth, root, third, at the same time, in three-four time, slowly, three notes per measure repeating the process four times = four measures.”
  2. Students do so.

Advanced

  1. Teacher sets up as above and prompts, “Student A sings root, third, fifth, student B sings third, fifth, root, and student C sings fifth, root, third, at the same time, one note per measure. After you sing your chord position, all students rotate to the next chord position, and then rotate again to the final chord position. Repeat this entire process four times = thirty-six measures.” For example, student A sings root, third, fifth, then third, fifth, root, then fifth, root, third. Student B and C start third, fifth, root, and fifth, root, third at the same time.
  2. Students do so.

Division

Beginning

  1. Teacher sets up as above and prompts, “Two students sing an octave. Using the whole tone or pentatonic scale, a third student sings a triad up from the lower note of the octave."
  2. Students do so.

Intermediate

  1. Teacher sets up as above and prompts, “Two students sing an octave. Using the whole tone or pentatonic scale, two more students sing two more notes to complete a triad from the lower note of the octave."
  2. Students do so.

Advanced

  1. Teacher sets up as above and prompts, “Two students sing an octave. Using the whole tone or pentatonic scale, two more students sing two more notes downward to complete a triad from the upper note of the octave."
  2. Students do so.