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Harmonic Progressions: Arithmetic

Goal: To prepare 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 (adding a raised scale degree)

  1. Teacher sets up as above and prompts, “Sing these notes: 1, 3, 5, 5, #4, 5.”
  2. Students do so.

Intermediate

  1. Teacher sets up as above and prompts, “Sing these notes: 1 3 5, 7 2 5, 1 2 #4, 7 2 5 (now 3, 5, 1 in the new key)."
  2. Students do so.

Advanced (to the relative minor)

  1. Teacher sets up as above and prompts, “Sing these notes: 1, down to #5 6, 3 down to #5 6, 5 up to #5 6."
  2. Students do so.

Subtraction

Refer to the Chorale No. 1 in Harmony Smorgasbord.

Beginning

  1. Teacher plays through this example – one line at a time, then all together.
  2. Class sings it by ear with the teacher playing along.
  3. Teacher prompts, “Sing it again without the bass line.”
  4. Students do so.

Intermediate

  1. Teacher plays through this example – one line at a time, then all together.
  2. Class sings it by ear with the teacher playing along.
  3. Teacher prompts, “Sing it again without the soprano line.”
  4. Students do so.

Advanced

  1. Students sing only the two inner voices a cappella – without the teacher accompanying them.

Multiplication

Refer to the Chorale No. 1 in Harmony Smorgasbord.

Beginning

  1. Teacher plays through this example.
  2. Class sings it with the teacher playing along.
  3. Teacher prompts, “Sing it again turning each chord in to a full measure of two-four time.”
  4. Students do so.

Intermediate

  1. Teacher plays through this example.
  2. Class sings it with the teacher playing along.
  3. Teacher prompts, “Sing it again turning each chord in to a full measure of three-four time.”
  4. Students do so.

Advanced

  1. Teacher plays through this example.
  2. Class sings it with the teacher playing along.
  3. Teacher prompts, “Sing it again turning each chord in to a full measure of six-eight time.”
  4. Students do so.

Division

Refer to the Chorale No. 1 in Harmony Smorgasbord.

Beginning

  1. Teacher plays through this example.
  2. Class sings it with the teacher playing along.
  3. Teacher prompts, “Sing it again turning each quarter note chord in to two eighth notes per beat.”
  4. Students do so.

Intermediate

  1. Teacher plays through this example.
  2. Class sings it with the teacher playing along.
  3. Teacher prompts, “Sing it again turning each quarter note chord into four sixteenth notes.”
  4. Students do so.

Advanced

  1. Teacher plays through this example.
  2. Class sings it with the teacher playing along.
  3. Teacher prompts, “Sing it again turning each quarter note chord into an eighth note – sixteenth note combination"
  4. Students do so.

More Advanced

Continue the same process but change individual voices, not all four voices at a time.