Musical Engineering and Discovery with Wavelet Analysis

April 3, 2021   /  

Name: Rephael Berkooz
Major: Mathematics
Minor: Computer Science
Advisors: Dr. Pamela Pierce

This project presents a novel method for extracting musical features via signal processing and wavelet analysis. I begin by exploring the human experience of consuming music, contrasting with digital encoding and playback of music. Starting with the Fourier transform, I construct and explore different modes of encoding music information in time and frequency dimensions. This project also introduces the fundamental limitations of encoding time and frequency information. Building upon these limitations, this project constructs the mathematics of Wavelet Analysis, which allows the representation of digital music information in a format very close to our human understanding of music. Utilizing convolutions and other techniques in signal processing, this project proposes methods for extracting beats and rhythm structure. Furthermore, I propose a method for recommending music based upon these extracted musical features. This music recommendation system enables individuals to choose the degree of similarity between different repeating parts of the recommended songs, such as bass line, rhythm, and melody. My IS project has given me a new way of connecting music with different modes of mathematical analysis, all within the context of the interface between human experience and digital technology.

Rephael will be online to field comments on April 16:
noon-2pm EDT (PST 9-11am, Africa/Europe: early evening) and 4-6 pm EDT (PST 1-3pm, Africa/Europe: late evening)

23 thoughts on “Musical Engineering and Discovery with Wavelet Analysis”

  1. Nice job at your orals, Rephael! Thank you for taking me on this journey–I learned a lot through your investigation. You are ambitious and hard-working. Keep pushing–you will go far. All the best to you – your advisor.

  2. I love how you incorporated your love of music into your Senior Independent Study! Thanks for sharing your findings, and Congratulations!

  3. This is really interesting. The way you came up with the topic is super relatable to me as well. Well done and congratulations!

  4. Very interesting work Rephael. It is always great to see computer science applied to a personal passion! I can see how your work would be very useful as a way to group and organize music based on specific features of the music instead of through broad terminology or genre based classifications. What are your future plans for this work?

    1. Thanks Dr. Guarnera!

      I’m definitely going to keep working on this as a little side project from here on. There’s a lot of work to be done in translating this algorithm into a true recommendation engine, but it would be so cool to turn it into an app that anyone could use to discover new music.

  5. Fascinating topic, Raphael. The animations in your presentation are very clear. Were you able to find any unexpectedly good music related to the song(s) you liked?

    1. Thanks Dr. Guarnera! Wavelet analysis is a bit tricky, but visualizing the process really helps the learning process.

      I haven’t started working with music outside of a library of smaller test sound files, but I ended up finding tons of good music during all the time I spent working in IS. In one way or another, my project did help me discover new areas of music.

  6. What an interesting project that combines music and science, Rephael! I enjoyed your presentation.

    1. Thanks Dr. Visa, I’m glad you enjoyed it!
      One of my favorite parts of the IS process in the math department is the flexibility we get in picking our project topics. It was really an amazing experience to connect two of my interests in a new way.

  7. Your work is so impressive, Reph! Great job and I’m proud of you for finIShing.

  8. Nice project, Rephael! I’ve had the same annoyance with music recommendation algorithms. Its a really nice idea to use convolution to encode features of the music. Were you able to apply the method to any songs you thought should be similar to see the results?

    1. Thank you Dr. Long! I had some very promising results in the test cases that I ran, and I’m hoping to expand it to some larger unstructured music libraries to see its how well it generalizes to sounds that I haven’t heard before.

  9. Impressive work, Rephael! It is really fun to see what you have been working on this year. Thanks for sharing your research. You are an excellent scholar and I look forward to hearing about your future endeavors!

  10. This is an interesting way of analyzing the structure of music, Rephael. Congratulations, and we wish you the best as you pursue what comes next after Wooster!

  11. This is awesome, Reph! A really new and original project and a great way to blend your personal and academic interests. Happy trails!

    1. Thanks so much, I’m so glad you liked it! Happy trails to you to my friend!

  12. Great job Rephael and congratulations. As someone who is interested in music, but knows little about advanced math’s and computer science, this was an interesting watch. I was wondering how this might function to categorize different genres that have similar drum rhythms and patterns? For instance harmonic complexity and such may vary between a metal song and a hardcore electronic song but in both cases rhythmic patterns might be similar. Again, fantastic job!

  13. Amazing work, Reph! I really though the topic was over my head (well, it still is) but your presentation made it very understandable. Congrats!!

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