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Meter: Arithmetic

Goal: To use counting to hear, sing, play compound meters through speaking, singing, and playing.

Out of Tempo

Addition

Beginning

  1. Teacher speaks, “1 2 3, 1 2 3.” (six-eight)
  2. Students repeat.

Intermediate

  1. Teacher speaks, “1 2 3, 1 2 3, 1 2 3.” (nine-eight)
  2. Students repeat.

Advanced

  1. Teacher speaks, “1 2 3, 1 2 3, 1 2 3, 1 2 3.” (twelve-eight)
  2. Students repeat.

Subtraction

Beginning

  1. Teacher speaks, “1 2 3, 1 2 3, 1 2 3, 1 2 3.” (twelve-eight)
  2. Students repeat.

Intermediate

  1. Teacher speaks, “1 2 3, 1 2 3, 1 2 3.” (nine-eight)
  2. Students repeat.

Advanced

  1. Teacher speaks, “1 2 3, 1 2 3.” (six-eight)
  2. Students repeat.

Multiplication

Using dotted quarter and eighth notes.

Beginning

  1. Teacher prompts, “Student A, you speak three eighth notes per beat. Student B, you speak one dotted quarter-note per 3 eighth notes. You both speak this at the same time in six-eight time – (2 x dotted quarter notes = six-eight and 6 x eighth notes = six-eight).”
  2. Students do so.

Intermediate

  1. Teacher prompts, “Student C, you speak three eighth notes per beat. Student D, you speak one dotted quarter-note per 3 eighth notes. You both speak this at the same time in nine-eight time – (3 x dotted quarter notes = nine-eight and 9 x eighth notes = nine-eight).”
  2. Students do so.

Advanced

  1. Teacher prompts, “Student E, you speak three eighth notes per beat. Student F, you speak one dotted quarter-note per 3 eighth notes. You both speak this at the same time in twelve-eight time – (4 x dotted quarter notes = twelve-eight and 12 x eighth notes = twelve-eight).”
  2. Students do so.

Division

Beginning

  1. Teacher prompts, “Here are 2 dotted quarter notes. Divide them into 6 eighth notes.”
  2. Students do so.

Intermediate

  1. Teacher prompts, “Here are 3 dotted quarter notes. Divide them into 9 eighth notes.”
  2. Students do so.

Advanced

  1. Teacher prompts, “Here are 4 dotted quarter notes. Divide them into 12 eighth notes.”
  2. Students do so.

In Tempo

Teacher sets up a tempo, compound time signature, tonality, and conducting, using one beat per measure, then more types of beats as students are more comfortable with the exercise. Students use repeating solfege and later can use non-repeating scalar solfege (singing).

Singing and playing.

Addition

Adding a beat.

Beginning

  1. Teacher sets up six-eight in eighth notes as above and prompts, “Sing in dotted quarter notes.”
  2. Students do so.

Intermediate

  1. Teacher sets up nine-eight in eighth notes as above and prompts, “Sing in dotted quarter notes.”
  2. Students do so.

Advanced

  1. Teacher sets up twelve-eight in eighth notes as above and prompts, “Sing in dotted quarter notes.”
  2. Students do so.

Subtraction

Beginning

  1. Teacher sets up twelve-eight in eighth notes as above and prompts, “Sing in dotted quarter notes and remove one beat.”

Intermediate

  1. Teacher sets up nine-eight in eighth notes as above and prompts, “Sing in dotted quarter notes and remove one beat.”

Advanced

  1. Teacher sets up six-eight in eighth notes as above and prompts, “Sing in dotted quarter notes and remove one beat.”

Multiplication

Using dotted quarter and eighth notes.

Beginning

  1. Teacher prompts, “Student A, you sing or play three eighth notes per beat. Student B, you sing or play one dotted quarter-note per 3 eighth notes. You both sing or play this at the same time in six-eight time – (2 x dotted quarter notes = six-eight and 6 x eighth notes = six-eight).”
  2. Students do so.

Intermediate

  1. Teacher prompts, “Student C, you sing or play three eighth notes per beat. Student D, you sing or play one dotted quarter-note per 3 eighth notes. You both sing or play this at the same time in nine-eight time – (3 x dotted quarter notes = nine-eight and 9 x eighth notes = nine-eight).”
  2. Students do so.

Advanced

  1. Teacher prompts, “Student E, you sing or play three eighth notes per beat. Student F, you sing or play one dotted quarter-note per 3 eighth notes. You both sing/play this at the same time in twelve-eight time – (4 x dotted quarter notes = twelve-eight and 12 x eighth notes = twelve-eight).”
  2. Students do so.

Division

Beginning

  1. Teacher sets up six-eight and prompts, “Here are 2 dotted quarter notes. Divide them into 6 eighth notes.”
  2. Students do so.

Intermediate

  1. Teacher sets up nine-eight and prompts, “Here are 3 dotted quarter notes. Divide them into 9 eighth notes.”
  2. Students do so.

Advanced

  1. Teacher sets up twelve-eight and prompts, “Here are 4 dotted quarter notes. Divide them into 12 eighth notes.”
  2. Students do so.