Maximizing Performance and Musical Analgesics: The Correlation between Quantified Music and Electrodermal Activity

Just as how no two people have the same genetic fingerprints, there are no two pieces of music that have the same mathematical measurements.  Regardless, music is said to have alleged benefits such as building valuable brain connections and reduce stress in youth [1].

Imagine if we could harness the power of music in such a way that we could modify our own behaviors just by listening to music.  Medical music (Biofeedback) is already a growing field, but what if instead of just subjectively thinking about the different musical qualities of a music piece, we could actually mathematically define the music that helps ameliorate our medical conditions. It is definitely a hard goal to reach, but this study was intended to be a step into the right direction.

Due to the positive correlation between stress and the Galvanic skin activity, also known as electrodermal activity [3], this study examined the correlation between the sound wave energies of music and the electrodermal activities of a randomized sample of the Monta Vista student body (ages 13-18).

In conclusion, it was clear that music affects people in such different ways so that although I was unable to identify a consistent correlation between my analyzed music and electrodermal activity (EDA), I instead found that each person has different ideal levels of psychological arousal that govern their individual performance level and offer ways to implement music into individualized analgesics.


Born in Mountain View, California, I attend school at Monta Vista High School and other than doing anything sciency, I enjoy competing in abacus (arithmetic) competitions the most.

I truly admire Thomas Edison because even though many people only recognize him for his lightbulb invention, he had actually innovated countless other devices that inevitably shape our society and culture.  

My dream college is Stanford, and I aspire to become a neuroscience engineer when I grow up.

Winning would mean everything to me; there is no greater honor than being recognized by a global community of like-minded individuals while being able to apply my current and future scientific research to help people around the world.  The prizes would not only give me a significant amount of encouragement to continue with my science research but also give me a once-in-a-lifetime opportunity to apply my future work to places that would need it the most.


Introduction: Objectives

Music is said to have alleged benefits such as building valuable brain connections and reducing stress in youth [1]. By quantifying music, my objective was to learn how music affects stress so a mathematical equation can be defined to create music that reduces stress.

Due to the positive correlation between stress and the Galvanic skin activity, also known as electrodermal activity [3], this study examined the correlation between the sound wave energies of music and the electrodermal activities of a randomized sample of the Monta Vista student body (ages 13-18). 

While attempting to quantify the most stress-relieving music, this project provides scientific evidence of the individual psychological differences that posit ways to maximize personal levels of motivation.

Goals and Applications:

  1.  Offer an innovative and mathematical perspective of the relationship between music and stress to determine whether certain types of music can reduce stress and pain.
  2.  By understanding the wave energy of music and its correlation with electrodermal activity, particular compositions of music can be produced to calm the sympathetic nervous system in stressful or dangerous scenarios (especially in schools), thereby increasing the capacity for the brain to use more cognitive functions instead.
  3. Maximize levels of performance.


If music can be defined by its wave energy per unit time, with use of the FFT algorithm, then the electrodermal activity of a test subject would have a positive correlation with the increase of the music’ sound wave energy over time. 



Hearing is one of our biological energy senses, in that sound, like any other form of energy wave, has amplitude, frequency, and energy [2].  Therefore, like light, sound can be measured through the Planck-Einstein equation: E=hf, where h is Planck’s constant of 6.636E10-34, E is the energy of sound, and f is the frequency per unit time [5]. However, music contains multiple frequencies ranges and amplitudes per unit time [2].  The only way to even begin analyzing music is through the Fast-Fourier Transformation [8].

The FFT is a complicated algorithm that uses the Discrete Fourier Transformation (DFT) to decompose a point time domain signal into time domains composed of a single point and then corresponds the frequency to these time domain signals, and finally synthesizes the frequency-domain into a single frequency spectrum [8].

On a psychophysiological basis, hearing works because of the connections between sensory nerves of the peripheral nervous system (PNS) and the perceiving nerves of the central nervous system (CNS) [1, 9]. Since the central nervous system regulates perception, it can also respond to certain perceptual cues, and act on these cues through the sympathetic nervous system (SNS) [1].  This in turn increases the electrolytes released from the sweat glands controlled by the sympathetic nervous system, which results in an increase in the electrodermal activity [7]. Since the electrodermal response (EDR), better known as the Galvanic skin response, is an exosomatic process, Galvanic skin response electrodes are able to detect changes in the electrodermal activity per unit of time [4].  The electrodermal responses were measured in microSiemens and were then corresponded with the wave energy over time and analyzed in order to determine the relationship between the quantified music aspects and the electrodermal activity. 


While EDA does exist in all sweat glands of the human body, as far as current research goes, the most sensitive and therefore the best area to measure the EDA is in the finger phalanges [1]. The finger phalanges are the most EDA-sensitive areas because its nerve fibers connecting to the sweat glands are unmyelinated, thus allowing a greater conductance to the electrodes attached.

Although there are many other indicators of stress, such as heart rate or blood pressure sensors, EDA electrodes were chosen because electrodermal activity has fewer confounding variables.  For example, while breathing abnormally can easily cause fluctuations in heart rate, regardless of what caused the irregular breathing, an electrodermal response is only changed when a physiological response is accompanied by a cognitive interpretation of the stressor [9].

Applications of this experiment

  • Certain types of music can be used as part of treatment for pain or other psychological responses (and be mathematically correlated to do so)
  • Helps people understand their own ideal amount of psychological arousal for tasks (different aspects of music yields different amounts of arousal in humans)

Operationalized Variables

Independent: Sound wave energies of the music selected 

  • Selection of music pieces (Based on my own subjective opinion because the criteria by which the music pieces were selected for should be irrelevant when the music is analyzed)

Music Definition/Analytics: Using the FFT algorithm, the music was analyzed for its intensity of frequency over time. 

With these frequency-domain spectrograms, the raw 3-d data of frequency, intensity/amplitude, and time (per ~ 0.2 seconds) was extracted. The sample amount was set to 5443 samples because the total time of all 5 pieces was 1088.679161 seconds in order to closely match up 0.2 seconds per sample. Row 1 represents the set ranges of frequencies (Hz) while the data values from B2:B5444, BZU2:BZU5444 represent the intensity of each frequency range for that time. Because the data extracted contained 3 dimensions, and the data could only be compared if it had 2 dimensions, the frequency and intensities were used to find the average wave energy of the music over time. The following equation was derived through the modified Planck-Einstein equation because the distance between the signal and the receptor was constant for my experiment.  A graph of all the data points (music wave energy over time) is presented to better visualize the varying amounts of sound wave energy in my music sample.

Dependent: Electrodermal Activities (EDA) of the participants (randomly selected) were measured via galvanic skin electrodes while the participants listened to the analyzed music.

  • Through excel, student numbers from Monta Vista's student directory were corresponded to a computer-generated randomly assigned value.  The values were then sorted based on size and the corresponding student numbers were used to contact the students randomly selected (after approved human consent forms were signed by both the participant and his/her legal guardian), which would ensure a representative sample of the student body at Monta Vista.  It was important that a computer-generated list were used to avoid sample bias. 
  • To reduce situation-relevant confounding variables, all experiments were conducted in the same classroom.
  • Materials: Galvanic Skin Electrodes 

Electrodermal Activity Measurements/Analytics: The raw EDA data collected from the galvanic skin electrodes for each of the 16 participants varied greatly because each participant has different amounts of sweat glands and release different amounts of electrolytes regardless of the stimuli presented, so the EDAs had to be normalized.  The raw EDA values and normalized EDA values of participant 1 are provided below. 

A graph of all the normalized EDA values are provided below to better visualize the change in EDA over time in response to the music.  

Finally, the normalized EDA values (y axis) were compared with the averaged music wave energies (x axis) after time was eliminated as a parameter.  After that, these two sets of data can be analyzed with pearson's correlation coefficient in order to determine the strength of the relationship between the sound wave energy of music and the electrodermal activity of the participants.


Analyzed Data: 

Individual Responses to music:

Pearson's "r" coefficient values:

Comparison of r values to music pieces:


Interpretation of results:

Since this study involves the measuring of human data, r values can be lower and still delineate a correlation, but since the r values varied greatly, my results were inconclusive.

Strong Positive Correlation (0.5 < r < 1):

Participants 1, 6, 8, and 10

Moderate Positive Correlation (0.25 < r < 0.5):

Participants 12, 14, and 16

Strong Negative Correlation (-1 < r < -0.5):

Participants 3 and 13

Moderate Negative Correlation (-0.5 < r < -0.25):

Participants 4, 11, and 15

Weak Correlation (-0.25 < r < 0.25):

Participants 2, 5, 7, and 9

The graph of test subject 16 exemplifies this lack of correlation between music wave energy and electrodermal activity.  This substantiates my conclusion that the correlation between music wave energy and electrodermal activity cannot be reliably determined with such a small sample size.

However, the correlation between electrodermal activity and music wave energy for “Power of Darkness (Halloween)” contradicts the lack of correlation, because of the many significant r values that display a strong negative correlation between electrodermal activity and music wave energy.  However, this still reinforces my conclusion that even though a larger sample size is needed to reliably determine correlation, there is likely a correlation between music wave energy and electrodermal activity to be identified.


The results show that while some students have positive correlations between their electrodermal activities and the wave energies of music, other students have negative or insignificant correlations.  Some of this discrepancy could potentially have resulted from confounding variables.

  1. Although a majority of the test subjects were randomly selected, I eventually had to resort to asking my classmates because not all the randomly selected people were able or willing to participate in this study.  As a result, there is a degree of sample bias, which next time I will reduce by initially randomly selecting more people than needed in order to account for the people that decline to participate.
  2. Although the situation-relevant confounding variables were removed to the best of my ability (by experimenting in the same classroom), the time at which I conducted the experiments varied.  Ranging from lunchtime to afterschool, the test subject might have felt hungry and anxious to leave; ranges of emotions the sympathetic nervous system regulates which could have affected my results.  Next time, I will keep the time at which I conduct the experiments constant.
  3.  Since students respond to music differently, their sympathetic system acts on the perceived responses differently, resulting in variations among their electrodermal activities.  As a result there is no control group available, but next time I would experiment on more students (start earlier) so that the variations in the data would be more balanced.

Although a correlation between music energy and electrodermal activity was not identified, the inconsistent data indicates the myriad of individual psychological processes and preferences. Since individuals naturally seek optimal levels of physiological arousal, stress-relieving music as defined by the wave energy equation may be perceived as more exciting for some than for others, resulting in different electrodermal responses to the same music. These findings are important in supporting the arousal theory of motivation; benefiting society as biological proof that individuals are so unique that people should embrace their own psychological differences instead of conforming to mainstream influences in order to be happy. Further research with quantitative approaches to define music includes increasing sample size and developing more precise Galvanic Skin Response electrodes so the sound wave energies can be better corresponded with more precise electrodermal activity measurements.

These results were debriefed to my test participants afterwards.


Not the end: Although my experiment did not support my hypothesis that an increase in sound wave energy increases EDA, it did provide evidence that music does affect a participant's EDA; only that the way in which music affects EDA is unique to each person.  From this, there are many possible applications of my findings:

  1. Musical treatments: Through specially designed tests that utilize the sound wave equation, a patient's response to the standardized music can be quantified and used so that individual music can be developed to relieve a patient's stress/pain symptoms.


[1] Alberti, Peter W. "Anatomy and Physiology of the Ear and Hearing." N.d. PDF file. 

[2] Audacity. Audacity, n.d. Web. 7 Mar. 2015. .

[3] Braithwaite, Jason J., et al. A Guide for Analysing Electrodermal Activity (EDA) & Skin Conductance Responses (SCRs) for Psychological Experiments. 2013. PDF file.

[4] "Electrodermal activity measurements." BIOPAC. BIOPAC, 24 Dec. 2014. Web. 12 Feb. 2015. .

[5] "Energy of a Photon." PVEducation. N.p., n.d. Web. 4 Dec. 2014. .

[6] "Fast Fourier Transforms." Hyper Physics. N.p., n.d. Web. 30 Jan. 2015. .

[7] Malmivuo, Jaakko. "The Electrodermal Response." Bioelectromagnetism. N.p.: n.p., n.d. Bioelectromagnetism. Web. 1 Mar. 2015. .

[8] NTS Press. FFT Basic Concepts. YouTube. N.p., n.d. Web. 7 Mar. 2015. .

[9] Picard, Rosalind W., Ming-Zher Poh, and Nicholas C. Swenson. A Wearable Sensor for Unobtrusive, Long-Term Assessment of Electrodermal Activity. N.p.: IEEE, 2010. Print. IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING 5.

[10] Sigview. SIGVIEW, 2013. Web. 3 Mar. 2015. .

[11] Smith, Steven W. "Chapter 12: The Fast Fourier Transform." The Scientist and Engineer's Guide to Digital Signal Processing. California Technical, 2011. Web. 7 Feb. 2015. .

[12] Weisstein, Eric W. "Fast Fourier Transform." From MathWorld--A Wolfram Web Resource.


  • I would like to thank Ms. McCarty for her mentorship and permission to use her classroom for my experimentations.
  • I would like to thank Ms. Fallon for her advice, lab demonstrations, and schedules to keep me on track.
  • This project would have been impossible without the financial support of the STEM fund of Monta Vista High School.
  • Special thanks to my parents for emotionally encouraging me every step of the way to finish this project.