Arithmetic

Mathematical concepts transfer well in to improvisational pedagogies because of their omnipotence in music and everywhere else for that matter. Arithmetic can be applied directly to both aural and written improvisation prompts. An arithmetical improvisation could be ‘landscaped’ (introduced) with the teacher calling out mathematical type while the student is performing an improvisation prompt.

Rhythm

Addition

1. Clap four beats left to right once.
2. Add another four beats.
3. Add four more beats.

Subtraction

1. Clap 8 beats
2. Take away 4 beats
3. Take away 2 beats

Multiplication

1. Repeat a given rhythm, pitch, or chord 2, 3, and 4 numbers of times.
2. The use of the repeat sign with instructions to repeat 2, 3, or 4 times.

Division

1. Clap two slow beats (quarter notes)
2. Clap two equal divisions of the beat (eighth notes)
3. Clap four equal divisions of the beat (sixteenth notes)
4. Clap in to three equal divisions of the beat (triplet 8th notes)

Melody

Addition

1. Choose two notes
2. Add one note
3. Add one more note

Subtraction

1. Choose 4 notes
2. Remove 1 note
3. Remove 1 more note

Multiplication

1. Choose 4 notes
2. Repeat the notes two, three, or four times

Division

1. Sing a scale
2. Sing the scale in two groups of four notes
3. Sing the scale in four groups of two notes

Harmony

Addition

1. Sing or Play two chords from a progression such as a cadence
2. Add one chord at a time to the combination

Subtraction

1. Sing or Play an entire multi-chord progression
2. Remove one of the chords
3. Substitute a different chord for the chord that was removed

Multiplication

1. Sing or Play a chord progression
2. Repeat the entire progression
3. Repeat each chord of the progression

Division

1. Sing or Play an entire multi-chord progression and divide it into sub groups.
2. This is a great way to discuss tonic, pre-dominant, and dominant chord functions.