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Harmonic Progressions: Arithmetic

Goal: To prepare improvisations using harmonic progressions, which include tonicization and modulation.

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 Harmony Smorgasbord for ideas.

Addition

Beginning

  1. Teacher sets up as above and prompts, “Student A sings the bass line 1, 5, 1."
  2. Student A does so.
  3. Teacher prompts, “Add a tonicizing leading tone to 5."
  4. Student sings, "1, #4, 5" (or 4, 7, 1 in the new key).

Intermediate

  1. Teacher sets up as above and prompts, “Student B sings the bass line 1, 4, 5, 1."
  2. Student B does so.
  3. Teacher prompts, “Add a tonicizing leading tones to 4 and 5."
  4. Student sings, "1 (down), 3, 4, #4, 5, 1."

Advanced (Using the Circle of Fifths)

  1. Teacher sets up as above and prompts, “Student C sings the bass line C, F, B, E, A, D, G, C" (the circle of fifths downward in C).
  2. Student C does so.
  3. Teacher prompts, "Student C adds a leading tone before each of the notes of the circle of fifths: B C, E F, A# B, D# E, etc."
  4. Student does so.

Subtraction

Using four-part harmonization listed in Smorgasbord as Chorale No. 1.

Beginning

  1. Teacher prompts, “Four students sing this harmonization.”
  2. Students do so.

Intermediate

  1. Teacher prompts, “Three students sing the harmonization without the soprano part.”
  2. Students do so.

Advanced

  1. Teacher prompts, “Three students sing the harmonization without the bass part.”
  2. Students do so.

Multiplication

Changing time signature using four-part harmonization listed in Smorgasbord as Chorale No. 1.

Beginning

  1. Teacher sets up a tempo for the example and prompts, “Four students sing the exercise in three-four time with the rhythm half note/quarter note.”
  2. Students do so.

Intermediate

  1. Teacher sets up a tempo for the example and prompts, “Four students sing the exercise in three-four time, the three lower voices with the rhythm half note/quarter note and the top voice in rhythm patterns of the student’s choice.”
  2. Students do so.

Advanced

  1. Teacher sets up a tempo for the example and prompts, “Four students sing the exercise in four-four time, the three lower voices with the rhythm half note/half note and the top voice in rhythm patterns of the student’s choice.”
  2. Students do so.

Division

Using four-part harmonization listed in Smorgasbord as Chorale No. 1.

Beginning

  1. Teacher sets up as above and prompts, “Four students each beat as two eighth notes.”
  2. Students do so.

Intermediate

  1. Teacher sets up as above and prompts, “Change the time signature to three-four. The first beat is worth two beats and the third is one beat. Four students sing eighth notes for all the beats.”
  2. Students do so.

Advanced

  1. Teacher sets up as above and prompts, “Change the time signature to four-four. Three students sing half/quarter/eighths as assigned. The fourth voice uses two sixteenths/eighth note and a lower neighbor-tone embellishment.”
  2. Students do so.

The process continues until all students have participated and all voices have traded different rhythmic activities.

This approach can be used with other types of music including close harmony and pop harmonizations.