Arduino Theremin Activity #3: Human Hearing (cont)


Overview:

Having demonstrated the outer bounds of human hearing, the Arduino theremin is used to demonstrate the limitations within human hearing. Smaller and smaller intervals show the difficulty of discerning small changes in pitch, and the degree to which this varies at different points in the audio spectrum.

Materials

  • One functioning Arduino theremin (Make Magazine or Open.Theremin)
  • Amplification for theremin
  • One computer with Frequency Analyzer (such as FreqAnalyst hosted in Audacity)
  • Audio spectrum chart 

A keyboard amplifier or set of hi-fi speakers are the best options for reproducing the full range of a theremin. The most cost-effective option is to determine your connectivity needs and search locally (perhaps even at your institution) for second-hand items.

Student Level

5-12

Terminology

  • Spectrum
  • Audio
  • Frequency
  • Pitch
  • Hertz
  • Cents
  • Decibels
  • Interval
  • Cochlea
  • Psychoacoustics 

Suggested Plan

For this demonstration you will not need the upper and lower extremes of your instrument’s range; instead you will want the finest possible control over pitch. If possible, adjust your pitch control so that intervals are more widely spaced.

When ready, demonstrate each of the following intervals first by bending the pitch audibly from one to the other, and then by lowering the volume before changing so that both are heard individually. Keep an eye on your frequency analyzer. 
Starting at a frequency close to each of the following, demonstrate differences of 1 semitone (100cents), 1 quartertone (50 cents), and one eighth tone (25 cents).

  1. 100 Hz
  2. 500 Hz
  3. 1000 Hz
  4. 2000 Hz
  5. 4000 Hz
  6. 8000 Hz
  7. 16,000Hz

[Image: Cents to Hz Conversion Chart] (hard to read)

Remember that your starting frequency need not be exact; within 100 Hz on either side is probably fine. The deviation (either up or down) should be as precise as possible though. 

It should become apparent that discrete tones are more difficult to distinguish from one another than those played continuously, and that smaller differences are harder to detect. It should also become apparent that the smallest differences are easier to detect in some registers than in others. This is related to Lesson 2, where we showed that some frequencies sound louder than others to the human ear.

Related Concepts

  • Interval
  • Consonance/Dissonance
  • Scale
  • Harmony
  • Chord
  • Melody
  • Intonation

Extensions

If two functioning theremins are available the relationship between closely spaced (or mathematically related) frequencies can be illustrated through beating. This demonstrates the importance of phase relationships.

Additional Resources

SFU Acoustic Ecology Handbook – Intervals

SFU Acoustic Ecology Handbook – Frequency response (with audio examples)

SFU Acoustic Ecology Handbook – Loudness Contours

Hein Computing: Intonation

  

A PDF VERSION OF THESE LESSONS CAN BE FOUND HERE

We encourage teachers to use and alter these lesson plans.  But, don’t be shy!  Please let us know what you do and send us photos, videos, or notes.  We’d love to hear from you. education@santafe.edu





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