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Thread: Fourier transforms

  1. #1 Fourier transforms 
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    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?

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    2. http://crimsonietta.net/scifair/clarinett.jpg
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  3. #2  
    Forum Professor serpicojr's Avatar
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    You might want to try tooling around with some statistical software. It's been a while I've done any stats, but I feel like a useful model to run would be ANOVA. You can enter as many potential independent variables as you like (which could be, e.g., highest frequency, second highest, etc.; some of the ratios you suggested; presence or absence of specific frequencies; whatever you can think of), and then the test will basically sort out which of the variables has the most significant effect on the test variable (whatever measure of memory you used). And you can then select out variables which seem to have little correlation with the end result, and this may weaken or strengthen the effects other variables have. At the end, you're aiming to find a combination in which all of the included variables show a high correlation with the test variable.

    Take all of this with a grain of salt. It's been years since I've done anything like this, and I may remember ANOVA to be more magical than it actually is.


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  4. #3  
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    My guess is, your project is doomed. Music and its effect on the human mind cannot be boiled down to the sum of its component frequencies. That tells you nothing about melody, harmony and things of that nature. If it were that easy, a sound engineer could just mix together various frequencies and get music. More likely you would just get a screeching mess.
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  5. #4  
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    I do realize that there are MANY more variables that would be factored into the "music and effect on mind" - melodic sequence, resonance, volume, tempo, etc.

    What I am doing is basically breaking down each "piece" of this equation. Which is the most beneficial harmonic spectrum is the focus of this study. Later, I will move on to study various intervals, various resonance levels, various volume levels, various tempo, etc. and in the end, hope to piece together all of these findings to determine a type of "ideal" structure for mind-enhancing music.
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  6. #5  
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    Take two sound tracks of the same piece of music, maybe a violin piece. Have one played by a novice student and the other played by a professional. I think it is safe to say these will have a very different effect on the test subject. One may tend to jangle the nerves while the other has a soothing effect. Can any of the objective criteria you listed tell you which sound track is which? If not, I think you are wasting your time.
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  7. #6  
    Forum Isotope Bunbury's Avatar
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    I can't offer any suggestions about how to correlate your data, but as a sort of counter to Harold's prediction of failure, I think that the discovery of no correlation would be a perfectly valid and useful result, and should not be considered a failure. There are many scientific experiments that do not produce the expected results but still represent an increase in our knowledge and understanding of the world. Good luck.
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  8. #7  
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    My focus is on artificially-generated music, and on artificial manipulation of waveforms.

    I'm thinking I may have to declare no correlation, though. I'll run some chi-squared tests later for null hypothesis and try that analysis of variance as well.

    I'm an HS student by the way ;D I need a grade for this, so might as well make it thorough.
    Thanks for all your feedback!
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