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Harmonic Progressions: Arithmetic

Goal: To hear, sing, and play harmonic progressions with inverted chords while focusing on minor keys, using three forms of minor.

Out of Tempo

Addition

Beginning

  1. Teacher sings “lu” or plays the notes of a minor tonic chord and prompts, “Sing this harmony and add the first inversion.”
  2. Students do so.

Intermediate

  1. Teacher sings “lu” or plays the notes of a major dominant chord and prompts, “Sing this harmony and add the first inversion.”
  2. Students do so.

Advanced

  1. Teacher sings “lu” or plays the notes of a minor tonic chord and prompts, “Sing this harmony and add the first inversion of the major dominant.”
  2. Students do so.

Subtraction

Beginning (Harmonic Minor)

  1. Teacher sings or plays one, five, one.
  2. Students repeat.
  3. Teacher prompts, “Remove the third and fifth.”
  4. Students do so.

Intermediate (Harmonic Minor)

  1. Teacher sings or plays one, five first inversion, one.
  2. Students repeat.
  3. Teacher prompts, “Remove the upper two notes of each chord.”
  4. Students do so, singing the bass line.

Advanced (Natural Minor)

  1. Teacher sings or plays one, five first inversion, one.
  2. Students repeat.
  3. Teacher prompts, “Remove the upper two notes of each chord.”
  4. Students do so, singing the bass line.

Multiplication

Beginning

  1. Teacher sings or plays minor tonic, major dominant in first inversion four times and prompts, “You sing the bass line only."
  2. Students do so.

Intermediate

  1. Teacher sings or plays minor tonic in first inversion, then the major dominant in second inversion four times and prompts, “You sing the bass line only.”
  2. Students do so.

Advanced

  1. Teacher plays IV, V, I in minor using melodic minor and prompts, “Sing this progression in first inversion.”
  2. Students do so.

Division

Beginning

  1. Teacher plays the outer sixth of three progressive first inversion triads and prompts, “Sing the note ‘in the middle’ of each chord.”
  2. Students do so.

Intermediate

  1. Teacher plays the outer sixth of three progressive second inversion triads and prompts, “Sing the note ‘in the middle’ of each chord.”
  2. Students do so.

Advanced

  1. Teacher plays the outer sixth of three progressive first and second inversion triads and prompts, “Sing the note ‘in the middle’ of each chord switching the inversions.”
  2. Students do so.

In Tempo

Teacher chooses a tempo, time signature, minor tonality in keys other than c minor, using the three forms of minor focusing on progressions that include inverted chords. Students sing one note per measure until they become comfortable with the exercise.

Addition

Beginning

  1. Teacher sets up as above and prompts, “Here is progression x. Sing the bass line.”
  2. Students do so.

Intermediate

  1. Teacher plays the progression four, five, one and prompts, “Sing the bass line of four, five, one in harmonic minor using first inversion.”
  2. Students do so.

Advanced

  1. Teacher plays the progression four, two, five, one and prompts, “Sing the bass line of four, five, one in harmonic minor using first inversion.”
  2. Students do so.

Subtraction

Beginning: The Circle of Fifths

  1. Teacher sets up as above and plays one, four, seven, three, six, two, five, one in first inversion.
  2. Students repeat.
  3. Teacher prompts, “Start the circle on four first inversion and continue singing the bass line only.”
  4. Students do so.
  5. The process repeats until only five to one remains.

Intermediate

  1. Teacher sets up as above and plays one, four, seven, three, six, two, five, one in second inversion.
  2. Students repeat.
  3. Teacher prompts, “Start the circle on four first inversion and continue singing the bass line only.”
  4. Students do so.
  5. Process repeats until only five to one remains.

Advanced

  1. Teacher sets up as above and plays one, four, seven, three, six, two, five, one in combinations of first and second inversion.
  2. Students repeat.
  3. Teacher prompts, “Start the circle on four second inversion and continue singing the bass line only.”
  4. Students do so.
  5. Process repeats until only five to one remains.

Multiplication

Beginning

  1. Teacher sets up as above and plays minor tonic, major dominant in first inversion four times and prompts, “You sing the bass line only."
  2. Students do so.

Intermediate

  1. Teacher sets up as above and plays minor tonic in first inversion, the major dominant in second inversion four times and prompts, “You sing the bass line only.”
  2. Students do so.

Advanced

  1. Teacher sets up as above and plays four, five, one in minor using melodic minor and prompts, “Sing this progression in first inversion.”
  2. Students do so.

Division

Dividing a chord between three students.

Beginning

  1. Teacher sets up as above and prompts, “Three students sing the bass line of progression x.”
  2. Students do so.

Intermediate

  1. Teacher sets up as above and prompts, “Two students sing the bass line and one student sings the next higher chord tone of progression x.”
  2. Students do so.

Advanced

  1. Teacher sets up as above and prompts, “One student sings the bass line, one student sings the ‘middle note, and one student sings the highest chord tones of progression x.”
  2. Students do so.