Skip to main content

Chromatic Intervals: Arithmetic

Goal: To set up improvisations using chromatic intervals. (These exercises should be started out of tempo and then can be turned into 'in tempo’ versions. Refer to the Interval, Scale and Melody "Smorgasbords" for ideas.)

Out of Tempo

Addition

Beginning

  1. Teacher sets up as above and prompts, “Starting from x, add a half step up, then return to x, then add another half step up until you reach an octave.” For example: C, C#/C, D/C, D#/C, E/etc. First time teacher plays with the student, second time the student sings a cappella.
  2. Students do so.

Intermediate

  1. Teacher sets up as above and prompts, “Starting from x, add a half step down, then return to x, then add another half step down until you reach an octave.” For example: C, B/C, Bb/C, A/etc. First time teacher plays with the student, second time the student sings a cappella.
  2. Students do so.

Advanced

  1. Teacher sets up as above and prompts, “Two students start from x at the same time, one adds a half step up the other adds a half step down, then both return to x, then both add another half step up/down until you reach an octave.” For example: C, B /C, Bb/C, A /etc.; C, C#/C, D/C, D#/etc. First time teacher plays with the students, second time the student sings a cappella.
  2. Students do so.

Subtraction

Beginning

  1. Teacher sets up as above and prompts, “Student A starts on note x, sings up an octave, sings down a half step, leaps down to the note a half step above note x, leaps up to the note two half steps above the original octave and continues to ‘shrink’ the interval distance.” For example: "Doe, Doe, Ti, Doe#, Tib, Re, La," etc., until arriving at "Fa#."
  2. Students do so.

Intermediate

  1. Teacher sets up as above and prompts, “Student B starts on note x, sings down an octave, sings up a half step, leaps up to the note a half step below note x, leaps down to the note two half steps below the original octave and continues to ‘shrink’ the interval distance.” For example: "Doe, Doe, Doe#, Ti, Tib, Rey," etc., until arriving at "Fa#."
  2. Students do so.

Advanced

  1. Teacher sets up as above and prompts, “Students A and B start on note x an octave apart and sing, at the same time, both the beginning and intermediate version of this exercise until they both arrive at a unison F#."
  2. Students do so.

Multiplication

Seconds, fourths, and sevenths

Beginning

  1. Teacher sets up as above and prompts, “Student A sings Doe, Reyb (flat), student B sings the same Doe, then down to Ti."
  2. Students do so.

Intermediate

  1. Teacher prompts, “Student C sings Doe, Reyb (flat), Solb (flat), Student D sings Doe, Ti, Fa#."
  2. Students do so.

Advanced

  1. Teacher prompts, “Student E sings Doe, Reyb (flat), Solb (flat), Ti, Student F sings Doe, Ti, Fa#, Doe#."
  2. Students do so.

Division

Beginning

  1. Teacher sets up as above and prompts, “I play a perfect fifth and student A sings a minor second above or below one of the two notes of the perfect fifth.” For example: teacher plays "Doe" and "Sol." Student sings "Ti" or "Do#," "Fa#" or "Sol#."
  2. Student does so.

Intermediate

  1. Teacher sets up as above and prompts, “I play a perfect fourth and student B sings a minor second above or below one of the two notes of the perfect fourth.” For example: teacher plays "Doe" and "Fa." Student sings "Ti" or "Doe#, "Mi" or "Fa#."
  2. Student does so.

Advanced

  1. Teacher sets up as above and prompts, “I play a perfect fourth and fifth and student C sings minor seconds above or below the notes I’m playing.” For example: teacher plays "Doe," "Fa," and "Sol." Student sings "Ti" or "Doe#," "Mi" or "Fa#," "Sol#."
  2. Student does so.