Musical Intervals Lab

The Following Information is Provided to the Student

Question: How do the sounds produced by two nearby keys (within seven half-steps apart) on the piano keyboard sound when played together? Are certain frequency ratios more pleasing than others?

Purpose: To play nearby notes (not more than 7 keys apart) on the piano keyboard in order to determine if there are certain frequency ratios which sound more pleasing than others.

A complete lab write-up includes a Title, a Purpose, a Data section, and a Conclusion/Discussion. The Data section should include the provided table. The Conclusion/Discussion section should identify the collection of frequency ratios associated with notes which sound pleasant when played simultaneously. Specific trials in the Data section should be referenced as supporting evidence. If additional data need to be collected, then it should be added to the Data section.

Scoring Ruberic

S8.	Musical Intervals Lab	Score
_____	Included, labeled and organized all parts of the lab report.	_____ / _____
_____	Data section includes the completed table with some note pairs which sound good and some which sound bad. May include class data; class data is labeled as such and organized. Results are reasonably accurate.
_____	Conclusion/Discussion identifies the frequency ratios which are associated with consonant and dissonant sounds; specific examples and reasoning is provided to support the conclusion. Conclusions are consistent with either individual data or class data reported in the Data section.

Materials Required

Computer interfaced microphone; toy music keyboard; Frequency Cheat Sheet (See Aux Musical Scales).

Description of Procedure

Students adjust the settings of a piano keyboard to play the flute. They then simultaneously play two keys and listen carefully to the sound. They make a judgment of the relative pleasantness of the two sounds when played together. A sample of the sound is captured with the computer interfaced microphone; a sketch of the repeating section of the waveform is drawn. The frequencies of the two sounds are recorded and the ratio of the high frequency to low frequency is calculated. Students repeat the process for several key combinations, making an effort to experiment with various frequency ratios.

Alternative Materials and Procedure

If a computer interfaced microphone is not available, the lab can still be performed; the waveform column of the data table will have to be skipped. If only a single keyboard is available, then the experiment can still be performed as a demonstration lab.

Safety Concerns

There is always a higher than usual level of risk associated with working in a science lab. Teachers should be aware of this and take the necessary precautions to insure that working environment is as safe as possible. Student horseplay (especially the use of meter sticks as swords) and off-task behaviors should not be tolerated.

Suggestions, Precautions, Notes

Toy keyboards can often be purchased at department stores for $10 or less. The best prices can be found during the Christmas season. They typically have 30 or more keys stretching across nearly three octaves. The inexpensive variety typically have synthesized sounds for a variety of musical instruments. There are usually a few other features which give students great pleasure and teachers much aggravation.
It might be useful to construct a Frequency Cheat Sheet similar to the one provided here. Tape it to the underside of each keyboard as a quick student reference. Reduce its size when printing so that it fits the width of the keyboard.
Of all the synthesized sounds on the keyboard, the flute sound tends to be the most pure. While students enjoy experimenting with the different sounds, best results on this lab are typically obtained when the keyboard is set to play the sound of the flute.
With very little guidance and simply working on their own, students will usually conclude that keys with frequency ratios of 5:4 (1.25), 4:3 (1.33), and 3:2 (1.5) produce relatively pleasing sounds. The take home lesson is that sounds whose frequencies have simple whole number mathematical relationships are perceived by the ear as being pleasing. These sounds typically have relatively clean waveforms associated with them.
Many students will not be able to make judgments of the pleasantness of two sounds without an initial demonstration. Before passing out the keyboards, describe the purpose and then play two notes which are an octave apart (e.g, C₄ and C₅); these two notes sound pleasant when played together. Then play two notes like C₄ and A₅^b; these two notes sound unpleasant or dissonant.

Links

Connections to The Physics Classroom Tutorial:
The following reading is a suitable accompaniment to this lab:
http://www.physicsclassroom.com/Class/sound/u11l3a.cfm