Intervals: Arithmetic

Interval number.

Beginning: Natural Minor (up and down)

1. Teacher counts speaking, “1 to 3, then 3 to 1 = a minor third.”
2. Students repeat.
3. Teacher counts speaking, “1 to 6, then 6 to 1 = a minor sixth.”
4. Students repeat.
5. This process continues until “1 to 7, then 7 to 1 = a minor seventh.”

Intermediate: Harmonic Minor (down and up)

1. Teacher counts speaking, “8 to 7, then 7 to 8 = a minor second.”
2. Students repeat.
3. Teacher counts speaking, “8 to 6, then 6 to 8 = a major third.”
4. Students repeat.
5. This process continues until “8 to 1, then 8 to 1 = an octave.”

Advanced: Melodic Minor (up and down)

1. Teacher counts speaking, “1 up to 6, 8 down to 6.”
2. Students repeat.
3. Teacher counts speaking, “1 up to 7, 8 down to 7. ”
4. Students repeat.
5. Process repeats until “1 up to 8, 8 down to 1.”

Focusing on fifths, sixths, sevenths, in support of minor scales.

Beginning (Subtracting 1 half step from an interval)

1. Teacher speaks, “9 half steps – 1 half step = minor sixth.”
2. Students repeat.
3. Teacher speaks, 8 half steps – 1 half step = perfect fifth.”
4. Students repeat.
5. Process repeats using the following intervals: diminished fifth, perfect fifth, augmented fifth, minor sixth, major sixth, minor seventh, major seventh.

Intermediate (subtracting half steps from an octave in support of minor keys)

1. Teacher speaks, “12 half steps – 3 or 4 half steps = minor or major third.”
2. Students repeat.
3. Teacher speaks, “12 half steps – 5 or 6 half steps = perfect fourth or augmented fourth.”
4. Students repeat.
5. Process repeats using the following intervals: diminished fifth, perfect fifth, augmented fifth, minor sixth, major sixth, minor seventh, major seventh.

Advanced (using scale degree numbers to identify harmonic minor intervals)

Process repeats as above.

1. Teacher speaks, “In harmonic minor, from the third scale degree down to the raised seventh scale degree is a diminished fourth.”
2. Students repeat.
3. Teacher speaks, “In harmonic minor, from the sixth scale degree down to the raised seventh scale degree is a diminished seventh."
4. Process repeats to identify differences in interval content in natural, harmonic, and melodic minor forms.

Beginning (teacher demonstrates, prompts, students repeat with 1 equalling a half step)

1. 6 x 1 = tri-tone
2. 8 x 1 = minor sixth
3. 10 x 1 = minor seventh

Intermediate

1. 6 x 1 = tri-tone
2. 7 x 1 = perfect fifth
3. 9 x 1 = major sixth

Advanced

1. 6 x 1 = tri-tone
2. 10 x 1 = minor seventh
3. 11 x 1 = major seventh

Using scale degree numbers.

Beginning

1. Divide the octave in 2 = 6 = tri-tone = which scale degrees?
2. Students answer.

Intermediate

1. Divide the octave in 4 = 3 half steps = minor thirds = which scale degrees?
2. Students answer.

Advanced

1. Divide the octave in 3 = 4 half steps = major thirds = which scale degrees?
2. Students answer.

Keys other than c minor: focus on interval inversion.

Beginning: Natural minor/up and down/from low to high/high to low.

1. Teacher sings numbers or solfege, "1, 3," then speaks, “minor third up/major sixth down” in tempo (adding a measure in time).
2. Student repeats.
3. Teacher sings numbers or solfege, "1, 8," then speaks, “minor sixth up/major third down” in tempo (adding a measure in time).
4. Student repeats
5. Teacher sings numbers or solfege, "1, 10," then speaks, “minor seventh up/major second down” in tempo (adding a measure in time).

Intermediate: Harmonic minor/up and down/from low to high/from high to low

1. Teacher sings numbers or solfege, "1, 3," then speaks “minor third up/major sixth down” in tempo (adding a measure in time).
2. Student repeats.
3. Teacher sings, "Do, La," then speaks “minor third” in tempo (adding a measure of time).
4. Student repeats.
5. Process continues until "Do, Do" (downward).

Advanced: Melodic minor/up and down

1. Teacher sings numbers or solfege, "1, 3," then speaks “minor third up/major sixth down” in tempo (adding a measure in time).
2. Student repeats.
3. Teacher sings numbers or solfege, "1, 9" up, then "1, 8" down, then speaks “major sixth up/minor third down” in tempo (adding a measure in time).
4. Student repeats.
5. Teacher sings numbers or solfege, "1, 11" up, then "1, 10" down, then speaks “major seventh up/major second down” in tempo (adding a measure in time).

Some students may not have the range to sing all interval inversions. Therefore starting in another key is helpful.

Using half steps.

Beginning: Natural minor

1. Teacher sings 1 up to 1 down to flat 7.
2. Students repeat.
3. Teacher sings 1 up to 1 down to flat 6.
4. Students repeat.

Intermediate: Harmonic minor

1. Teacher sings 1 up to 1 down to raised 7.
2. Students repeat.
3. Teacher sings 1 up to 1 down to raised 7 down to flat 6.
4. Students repeat.

Advanced: Melodic minor

1. Teacher sings 1 up to raised 6, then to high 1 down to flat 6.
2. Students repeat.
3. Teacher sings 1 up to raised 7, then to high 1 down to flat 7.
4. Students repeat.

Repeat each interval two to four times in tempo.

Beginning: Natural minor

1. Teacher sings low 1 up to high 1, low 1 up to flat 7, low 1 up to flat 6, low 1 up to 5.
2. Students repeat.
3. Teacher sings high 1 to low 1 up to flat 7, high 1 to low 1 up to flat 6, high 1 to low 1 up to 5.
4. Students repeat.

Intermediate: Harmonic minor

1. Teacher sings low 1 up to high 1, low 1 up to raised 7, low 1 up to flat 6, low 1 up to 5.
2. Students repeat.
3. Teacher sings high 1 to low 1 up to raised 7, high 1 to low 1 up to flat 6, high 1 to low 1 up to 5.
4. Students repeat.

Advanced: Melodic minor

1. Teacher sings high 1 down to low 1 up to raised 6 then low 1 to high 1 down to flat 6.
2. Students repeat.
3. Teacher sings high 1 down to low 1 up to raised 7 then low 1 to high 1 down to flat 7.
4. Students repeat.

Beginning: Natural minor

1. Teacher plays an octave and prompts, “Sing flat 3, flat 6, flat 7.”
2. Students do so.

Intermediate: Harmonic minor

1. Teacher plays an octave and prompts, “Sing flat 3, flat 6 and raised 7.”
2. Students do so.

Advanced: Melodic minor

1. Teacher plays an octave and prompts, “Sing flat 3, raised and raised 7, then flat 7 and flat 6 downward from the top of the octave.”
2. Students do so.