one video<\/a> shows how key frequency \u201cpeaks\u201d shift and interact offering an intuitive glimpse into the math behind music.<\/p>\n\n\n\n\u201cYou can drag through each frame and watch how the frequencies rise and fall. It\u2019s like watching music breathe.\u201d<\/p>\n\n\n\n
Starting with Dexed, a software plugin that emulates the sounds produced by Yamaha\u2019s legendary DX7 synthesizer, Wang dove into the mechanics of FM synthesis by creating and manipulating sounds himself. Dexed lets users adjust six sound generators, called \u201coperators,\u201d each with its own frequency, amplitude, and shape. The way these operators are connected shapes the final sound.<\/p>\n\n\n\n
\u201cOne cool thing I noticed,\u201d Wang said, \u201cwas that pairing a 100 Hz frequency with a slightly different one, like 110 Hz, created richer, more resonant sounds than using something mathematically neat like a 200 Hz frequency. This mismatch seems to add harmonic tension and complexity, which could be part of what makes these FM tones feel so expressive.\u201d<\/p>\n\n\n\n
This observation, though simple, points to the nuanced way our brains perceive timbre and tone. The math might say one thing, but the ear responds to something deeper\u2014less predictable, and more intriguing, he said.<\/p>\n\n\n\n
Beyond visualization, Wang explored reconstructing complex FM sounds with simpler mathematical models. By identifying key frequency \u201cpeaks\u201d and tracking their amplitude and phase over time, he recreated a streamlined version of the original signal using only sine waves. This approach strips the sound down to its mathematical core, helping to reveal what makes FM synthesis so expressive.<\/p>\n\n\n\n
\u201cIt\u2019s like breaking a symphony into a few clear notes and then building it back up,\u201d he said. \u201cI wanted to show that you can recreate something intricate with just a few essential parts\u2014if you understand the math behind it.\u201d<\/p>\n\n\n\n
With smoothing techniques like phase tracking (preserving the position within each waveform cycle) and amplitude normalization (adjusting volume levels to a consistent range), the reconstructed sounds come surprisingly close to the originals.<\/p>\n\n\n\n
\u201cIt\u2019s not perfect,\u201d the student admits, \u201cbut the goal is to make FM synthesis more understandable and explainable through math while also opening doors to creating more intuitive sound design tools for musicians and producers.\u201d<\/p>\n\n\n\n
![\"\"](\"https:\/\/engineering.jhu.edu\/designcenter\/wp-content\/uploads\/2025\/05\/image.png\")
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