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Harmonic Progressions: Arithmetic

Goal: To hear the circle of fifths using arithmetic concepts.

Out of Tempo

Addition

Addition

Beginning

  1. Teacher speaks, “One.“
  2. Students repeat.
  3. Teacher speaks, “Five, one.”
  4. Students repeat.
  5. Teacher speaks, “Two, five, one”
  6. The process repeats until, in reverse the teacher has spoken.

"One, four, seven, three, six, five, one"

Intermediate (focus on four, five, one)

  1. Teacher speaks, “Four, five, one.”
  2. Students repeat.

Advanced

  1. Teacher speaks, "Six, two, five, one."
  2. Students repeat.

Subtraction

Beginning

  1. Teacher speaks, "One, four, seven, three, six, two, five, one."
  2. Students repeat.
  3. Teacher repeats circle of fifths minus the first chord.
  4. Students repeat.
  5. The process repeats until only "five, one" is left.

Intermediate

  1. Teacher speaks the bass notes of the circle of fifths using letters:
    1. "C F B E A D G C" (key of C).
  2. Students repeat.
  3. Teacher removes the first note and repeats the bass line.
  4. Students repeat.
  5. Process repeats until only "G, C" remains.

Advanced

  1. Teacher speaks the bass notes in Solfege first in C, then in other keys.
    1. "Doe Fa Ti Mi La Rey Sol Doe"
  2. Students repeat.
  3. Teacher removes the first note and repeats the bass line.
  4. Students repeat.
  5. The process repeats until only "Sol, Doe" remains.

Multiplication

Beginning

  1. Teacher chooses a four chord progression and repeats it speaking roman numerals four times (tonic, dominant, etc.).
  2. Students repeat four times.
  3. The process repeats repeating the combination different number of times.

Intermediate

  1. Teacher chooses a chord progression and repeats it x times speaking the bass line notes. (1 6 4 5 1, 1 6 4 5 1, 1 6 4 5 1, 1 6 4 5 1)
  2. Students repeat.
  3. The process repeats repeating the combination different number of times.

Advanced

  1. teacher speaks a combination of simple three or four chord progressions in solfege and repeats them x times.
  2. Teacher can also request naming chord type – major, minor, etc. – in a differing tonality.
  3. Students repeat.

Division

Beginning

  1. Teacher speaks, "One, four, seven, three, six, two, five, one".
  2. Students repeat.
  3. Teacher divides the progression in half: "One, four, seven, three," then "six, two, five, one."
  4. Students repeat.

Intermediate

  1. Teacher prompts, “Divide the circle of fifths in pairs of chords.”
  2. Students do so, "One, four," then "seven, three," then "six, two," "five, one."

Advanced

  1. Teacher prompts, “Divide the circle of fifths in pairs, backwards.”
  2. Students do so: "Five, one," then "six, two," "seven, three," "one, four."

In Tempo

Singing, playing, and focusing on bass line of the circle of fifths.

Teacher starts by ‘humming’ or ‘lu-ing’ the bass line. Then adds numbers, letters, solfege, and even the names of the chords sung as a lyric.

Addition

Beginning

  1. Teacher sings – humming on lu , “I“ not numbers, letters, solfege yet.
  2. Students repeat.
  3. Teacher sings, “Five, one.”
  4. Students repeat.
  5. Teacher sings, “Two, five, one.”
  6. The process repeats until, in reverse the teacher has sung.

"One, four, seven, three, six, two, five, one"

Intermediate (focus on four, five, one)

  1. Teacher sings, “Four, five, one.”
  2. Students repeat.

Advanced

  1. Teacher sings, "Six, two, five, one."
  2. Students repeat.

Subtraction

Beginning

  1. Teacher sings, "One, four, seven, three, six, two, five, one."
  2. Students repeat.
  3. Teacher repeats circle of fifths minus the first chord.
  4. Students repeat.
  5. The process repeats until only "five, one" is left.

Intermediate

  1. Teacher sings the bass notes of the circle of fifths using letters:
    1. "C F B E A D G C" (key of C)
  2. Students repeat.
  3. Teacher removes the first note and repeats the bass line.
  4. Students repeat.
  5. Process repeats until only "G, C" remains.

Advanced

  1. Teacher speaks the bass notes in solfege first in C, then in other keys.
    1. "Doe Fa Ti Mi La Rey Sol Doe"
  2. Students repeat.
  3. Teacher removes the first note and repeats the bass line.
  4. Students repeat.
  5. The process repeats until only "Sol, Doe" remains.

Multiplication

Beginning

  1. Teacher chooses a four chord progression and repeats it singing roman numerals four times (tonic, dominant, etc.).
  2. Students repeat four times.
  3. The process repeats repeating the combination different number of times.

Intermediate

  1. Teacher chooses a chord progression and repeats it x times speaking the bass line notes. (1 6 4 5 1, 1 6 4 5 1, 1 6 4 5 1, 1 6 4 5 1)
  2. Students repeat.
  3. The process repeats repeating the combination different number of times.

Advanced

  1. Teacher sings a combination of simple three or four chord progressions in solfege and repeats them x times.
  2. Teacher can also request naming chord type – major, minor, etc. – in a differing tonality – major or minor.
  3. Students repeat.

Division

Beginning

  1. Teacher sings, "One, four, seven, three, six, two, five, one"
  2. Students repeat.
  3. Teacher divides the progression in half: "one four seven three," then "six two five one."
  4. Students repeat.

Intermediate

  1. Teacher prompts, “Divide the circle of fifths in pairs of chords.”
  2. Students do so "one, four," then "seven, three," then "six two", "five one."

Advanced

  1. Teacher prompts, “Divide the circle of fifths in pairs, backwards.”
  2. Students do so: "five, one," then "six, two," then "seven, three," "one, four."