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Learning Outcomes

Students will be able to

● determine an approximate constant of proportionality by analyzing data in a table

● determine whether two quantities are in a proportional relationship

●define the terms below

Common Core Standards: 7.RP.2.a, 7.RP.2.b, 7.RP.2.c

Vocabulary: Pitch, musical scale, octave, sound wave, vibration, frequency, period, hertz (Hz), subscript

Materials: Per student: pencil; Notes and Frequencies activity sheet; for Activity Extension only: Rhythm Patterns: 3/4 worksheet

Preparation: Ask for a student volunteer to bring in an instrument to class to demonstrate a note in different octaves and a scale. Connect with students’ science teacher to determine students’ familiarity with the physics of sound. You may consider teaching this activity jointly.

Procedure

1. Introduction and Time Signatures (10 minutes, whole group)

Note: This step builds on the activity related to Using Ratios in Music with Jake Shimabukuro. If students have not completed that activity, begin at Step 2. 

Review the 4/4 (“four-four”) time signature. Then, record 3/4 on the board and ask:

● How many beats do you think are in a measure in a 3/4 (“three-four”) time?

● How many beats does a quarter note get?

Give students without a music background an opportunity to respond; as needed, ask others to explain or clarify.

Show students the video. Pause at 1:04.

Engage students in tapping out rhythms in 3/4 time: Have half the group tap three even beats and the other half tap alternating measures of quarter and eighth notes.

2. Video: Pitch (10 minutes, whole group) 

Ask the student volunteer to play a low “A” and a high “A” on the instrument that he or she brought to class.

Establish that one of these notes has a lower pitch and the other one a higher pitch. Both are “A” in the musical scale, but they are several octaves apart.

Have the volunteer play an ascending and a descending scale. Ask students to say in which example the pitches are increasing.

Prompt to find out what students understand about sound waves. As needed, briefly review or introduce the terms vibration, frequency, period, and Hertz (Hz).  

Play the rest of the video, starting at 1:05 and pausing as follows:

● At 1:35, check that students are correctly interpreting the terms and diagrams on the screen.

● At 2:08, ask students, Will A at 880 Hz be higher or lower than A at 440 Hz? Why? Will the period of the sound wave for A 880 be longer or shorter than that of A 440? 

● At 3:10, ask students to answer the question (What is the ratio between A 440 and A 1760?) before Mr. Shimabukuro reveals the answer.

3. Frequency Ratios and Conclusion (10 minutes, pairs) 

Divide the class into pairs, and distribute the activity sheet, calculators, and pencils. Explain to the class that the chart is similar to that in the video (3:12–3:19); the subscript represents the octave.

Review the instructions with the class, noting that students should round to the nearest whole number. 

As students work in pairs, circulate to encourage them to observe patterns in the chart:

● Is the ratio of notes in consecutive octaves always about 1:2?

● Is the ratio of notes that are three octaves apart always the same?

● How does the ratio change when distance between octaves increases?

As time permits, gather the group to share what students noticed about the chart.

Activity Extension: Have students complete the activity extension worksheet.

This activity is based on work developed at TERC.