Fourier transforms

[Miri]

Okay. So for my research project this year I've used the DFT/FFT algorithm to calculate amplitudes of harmonics in various waveforms. These waveforms had been played to various subjects as they took spatial-reasoning tests to see which waveform enhanced concentration the most (based on the hypothetical claim that "music improves learning").

 

So right now I have 14 graphs I acquired from running FFTs, and I am at a loss of how to find a connection between them. Why are the waveforms on top more beneficial than the ones on the bottom? Absence of 3rd harmonic? High 2nd harmonic? The results are so inconsistent I'm totally lost.

 

So my question is, what would be the most effective way to compare the harmonics amongst these graphs? Each harmonic's amplitude divided by the total of the five highest amplitudes to find a ratio? Each harmonic's amplitude divided by the highest amplitude?

 

-- Most beneficial --

1. http://crimsonietta.net/scifair/oboe.jpg

2. http://crimsonietta.net/scifair/clarinett.jpg

3. http://crimsonietta.net/scifair/violin.jpg

4. http://crimsonietta.net/scifair/trumpet.jpg

5. http://crimsonietta.net/scifair/sawtooth.jpg

6. http://crimsonietta.net/scifair/sine.jpg

7. http://crimsonietta.net/scifair/tensax.jpg

8. http://crimsonietta.net/scifair/organ.jpg

9. http://crimsonietta.net/scifair/organ.jpg

10. http://crimsonietta.net/scifair/guitar.jpg

11. http://crimsonietta.net/scifair/piano.jpg

12. http://crimsonietta.net/scifair/square.jpg

13. http://crimsonietta.net/scifair/banjo.jpg

14. http://crimsonietta.net/scifair/bassoon.jpg

-- Least beneficial --

[Resha Caner]

This is a fascinating idea, but incredibly complex. I have to ask a few questions.

 

1. Have you considered the cause/effect issue? Is music the cause of improved spatial reasoning, or are people with higher spatial reasoning simply more likely to like a certain kind of music?

 

2. Given that question, you need a "control". Maybe you have already done this, but you need some measure of the participant's ability before they take the test. That will help you determine if the music affected them. Then, you should also have a group take the test in complete silence - an absence of music. You may even want to ask participants before they take the test, "Do you like to study with music? If so, what kind?"

 

3. Then, what you are really after here, is not a Fourier analysis, but a statistical analysis. You need to have a proper sample size, and use statistical testing to determine if certain spectral lines in the music cause a statistically significant difference in the result.

 

Does that sound scary? Have fun!

 

Caner