Scales: Arithmetic

Speaking, singing, playing.

Natural, harmonic, and melodic minor.

Beginning

1. Teacher speaks the number 1 or the first note of a key.
2. Students repeat.
3. Teacher speaks, "1, 2" or the first two notes of a key.
4. Students repeat.
5. Process continues until all eight notes of a minor scale are spoken up the scale and down the scale.

Intermediate

1. Teacher starts on a number other than 1 of a key.
2. Students repeat.
3. Teacher adds a number or solfege above or below the starting number.
4. Students repeat.
5. Process continues until all eight notes of a minor scale are spoken.

Advanced (in different keys)

1. Teacher starts on a letter.
2. Teacher prompts, “continue in the key of…"
3. The students add the remaining notes with accidentals.
4. The students add the remaining notes in scalar order or out of scalar order.

Natural, harmonic, and melodic minor.

Beginning

1. Teacher speaks an entire scale in numbers or solfege.
2. Students repeat.
3. Teacher prompts, “Subtract the last note from the scale.”
4. Students subtract the last note from the scale.
5. This process repeats until all that remains is the first note.

Intermediate

1. Teacher speaks an entire scale in numbers or solfege.
2. Students repeat.
3. Teacher prompts, “Subtract the first note from the scale.”
4. Students subtract the first note from the scale.
5. This process repeats until all that remains is the last note.

Advanced

1. Teacher speaks an entire scale in numbers or solfege.
2. Students repeat.
3. Teacher prompts, “Subtract the notes one at a time out of scalar order.”
4. Students subtract the notes one at a time out of scalar order.
5. This process repeats until only one note is left, whichever it is.

Natural, harmonic, and melodic minor.

Beginning

1. Teacher speaks an entire scale in numbers or solfege.
2. Students repeat.
3. Teacher prompts, “Repeat (multiply) the scale two, three, or four times.”
4. Students repeat the scale two, three, or four times.

Intermediate

1. Teacher speaks an entire scale in numbers or solfege.
2. Teacher prompts, “Each student will repeat the scale two, three, or four times.”
3. Students go around the room and repeat the scale two, three or four times.

Advanced

1. Teacher speaks an entire scale in numbers or solfege at a moderato speed but not in tempo.
2. Teacher prompts, “Speak each note of the scale scale twice as slow.” (Multiplying = augmenting the length of each note.)
3. Students speak each note of the scale twice as slow.

Dividing the octave into different combinations: natural, harmonic, and melodic minor.

Beginning

1. Teacher speaks the eight notes of the scale in numbers or solfege.
2. Students repeat.
3. Teacher divides the octave into four groups of two.
4. Students repeat.

Intermediate

1. Teacher speaks the eight notes of the scale in numbers or solfege.
2. Students repeat.
3. Teacher divides the octave into two groups of four.
4. Students repeat.

Advanced

1. Teacher speaks eight notes of the scale from scale degree 7 – 7, or Ti to Ti.
2. Students repeat.
3. Teacher groups the eight notes in to two groups of four notes resulting in grouping the tri-tone.
4. Students repeat.

Natural, harmonic, and melodic minor.

Beginning

1. Teacher sings a minor scale in a given time signature, one note per measure.
2. Teacher then sings the first tonic note.
3. Students repeat.
4. Teacher adds the next note up the scale.
5. Students repeat.
6. Process continues adding one note at a time either up or down the scale.

Intermediate

1. Teacher sings a minor scale.
2. Teacher sings a note other than the first tonic note.
3. Students repeat.
4. Teacher adds a note on either side of the first sung note.
5. Students repeat.
6. Process continues adding one note at a time either up or down until the scale is ‘complete.’

Advanced

1. Teacher sings a note.
2. Teacher prompts, “Sing that note and turn it in to a new tonic and sing a minor scale.”
3. Students sing the given note and turn it in to a new tonic, then sing the scale.
4. Teacher changes the note, adding another above or below it and prompts, “Sing those notes and add the remainder to complete the scale.”
5. Students repeat the given notes and complete the scale.

Natural, harmonic, and melodic minor.

Beginning

1. Teacher sings an entire minor scale in numbers or solfege.
2. Students repeat.
3. Teacher prompts, “Subtract the last note from the scale.”
4. Students subtract the last note from the scale.
5. This process repeats until all that remains is the first note.

Intermediate

1. Teacher sings an entire minor scale in numbers or solfege
2. Students repeat.
3. Teacher prompts, “Subtract the first note from the scale.”
4. Students subtract the first note from the scale.
5. This process repeats until all that remains is the last note.

Advanced

1. Teacher sings an entire scale in numbers of solfege
2. Students repeat.
3. Teacher prompts, “Subtract the notes one at a time out of scalar order.”
4. Students subtract the notes one at a time out of scalar order.
5. This process repeats until only one note is left, whichever it is.

Natural, harmonic, and melodic minor.

Beginning

1. Teacher sings an entire minor scale in numbers or solfege.
2. Students repeat.
3. Teacher prompts, “Repeat (multiply) the scale two, three, or four times.”
4. Students repeat the scale two, three, or four times.

Intermediate

1. Teacher sings an entire minor scale in numbers or solfege.
2. Teacher prompts, “Each student will repeat the scale two, three, or four times.”
3. Students go around the room and repeat the scale two, three or four times.

Advanced

1. Teacher sings an entire scale in numbers or solfege using a moderate tempo.
2. Teacher prompts, “Sing each note of the scale twice as slow.” (Multiplying = augmenting the length of each note.)
3. Students sing each note of the scale twice as slow.

Dividing in the octave in to different combinations: natural, harmonic, and melodic minor.

Beginning

1. Teacher sings the eight notes of the scale in numbers or solfege.
2. Students repeat.
3. Teacher divides the octave into four groups of two.
4. Students repeat.

Intermediate

1. Teacher sings the eight notes of the scale in numbers or solfege
2. Students repeat.
3. Teacher divides the octave into two groups of four.
4. Students repeat.

Advanced

1. Teacher sings eight notes of the scale from scale degree 7 – 7 or Ti to Ti.
2. Students repeat.
3. Teacher groups the eight notes in to two groups of four notes resulting in grouping the tri-tone.
4. Students repeat.