{"id":52677,"date":"2025-05-01T10:38:23","date_gmt":"2025-05-01T14:38:23","guid":{"rendered":"https:\/\/engineering.jhu.edu\/ams\/?post_type=news&p=52677"},"modified":"2025-09-17T13:25:56","modified_gmt":"2025-09-17T17:25:56","slug":"seeing-sound","status":"publish","type":"news","link":"https:\/\/engineering.jhu.edu\/ams\/news\/seeing-sound\/","title":{"rendered":"Seeing Sound"},"content":{"rendered":"

To help musicians, producers, and even listeners better understand the complex nature of FM synthesis, an applied mathematics and statistics sophomore at the Whiting School of Engineering has developed a set of visualization tools\u2013one of them interactive\u2013that reveal what makes its uniquely rich tones so compelling.<\/span>\u00a0<\/span><\/p>\n

Frequency Modulation synthesis creates sound by layering and combining sine waves\u2014those smooth, pure tones used when people take a hearing test. Musicians bring together those waves to form songs.<\/span>\u00a0<\/span><\/p>\n

\u201cThe formula looks simple\u2014one sine function inside another\u2014but the sounds it makes are surprisingly rich and dynamic,\u201d said Matt Wang.<\/span>\u00a0<\/span><\/p>\n

He shared his findings on April 29 at <\/span>Design Day<\/span><\/a>, the\u00a0 Whiting School of Engineering\u2019s annual event students\u2019 solutions to real-world challenges.\u00a0<\/span>\u00a0<\/span><\/p>\n

To better understand and visualize how FM synthesis works, Wang turned to spectrograms\u2013visual representation of sound frequencies over time.\u00a0<\/span> \"STFT<\/span><\/p>\n

\u201cIf a sound is simple, you see one bright stripe,\u201d Wang explained. \u201cBut FM synthesis showed shifting, layered textures, which corresponded directly to the perceived changes in the audio\u2013vibration and fluctuating tones.\u201d<\/span>\u00a0<\/span><\/p>\n

To help others <\/span>see<\/span><\/i> what they <\/span>hear<\/strong>, Wang created a series of audio-aligned visualizations that animated how FM frequencies evolve over time, <\/span>one<\/span> video<\/span><\/a> shows how key frequency \u201cpeaks\u201d shift and interact offering an intuitive glimpse into the math behind music.\u00a0<\/span>\u00a0<\/span><\/p>\n

\u201cYou can drag through each frame and watch how the frequencies rise and fall. It\u2019s like watching music breathe.\u201d<\/span>\u00a0<\/span><\/p>\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.\u00a0<\/span>\u00a0<\/span><\/p>\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<\/span>\u00a0<\/span><\/p>\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.<\/span>\u00a0<\/span><\/p>\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.\u00a0<\/span>\u00a0<\/span><\/p>\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<\/span>\u00a0<\/span><\/p>\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.\u00a0<\/span>\u00a0<\/span><\/p>\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<\/span>\u00a0<\/span><\/p>\n","protected":false},"template":"","class_list":["post-52677","news","type-news","status-publish","hentry","news_categories-applied-mathematics","news_categories-research","news_categories-student-experience"],"acf":[],"yoast_head":"\nSeeing Sound | Department of Applied Mathematics and Statistics<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/engineering.jhu.edu\/ams\/news\/seeing-sound\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Seeing Sound | Department of Applied Mathematics and Statistics\" \/>\n<meta property=\"og:description\" content=\"To help musicians, producers, and even listeners better understand the complex nature of FM synthesis, an applied mathematics and statistics sophomore at the Whiting School of Engineering has developed a…\" \/>\n<meta property=\"og:url\" content=\"https:\/\/engineering.jhu.edu\/ams\/news\/seeing-sound\/\" \/>\n<meta property=\"og:site_name\" content=\"Department of Applied Mathematics and Statistics\" \/>\n<meta property=\"article:modified_time\" content=\"2025-09-17T17:25:56+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"3 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Seeing Sound | Department of Applied Mathematics and Statistics","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/engineering.jhu.edu\/ams\/news\/seeing-sound\/","og_locale":"en_US","og_type":"article","og_title":"Seeing Sound | Department of Applied Mathematics and Statistics","og_description":"To help musicians, producers, and even listeners better understand the complex nature of FM synthesis, an applied mathematics and statistics sophomore at the Whiting School of Engineering has developed a…","og_url":"https:\/\/engineering.jhu.edu\/ams\/news\/seeing-sound\/","og_site_name":"Department of Applied Mathematics and Statistics","article_modified_time":"2025-09-17T17:25:56+00:00","twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/engineering.jhu.edu\/ams\/news\/seeing-sound\/","url":"https:\/\/engineering.jhu.edu\/ams\/news\/seeing-sound\/","name":"Seeing Sound | Department of Applied Mathematics and Statistics","isPartOf":{"@id":"https:\/\/engineering.jhu.edu\/ams\/#website"},"datePublished":"2025-05-01T14:38:23+00:00","dateModified":"2025-09-17T17:25:56+00:00","breadcrumb":{"@id":"https:\/\/engineering.jhu.edu\/ams\/news\/seeing-sound\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/engineering.jhu.edu\/ams\/news\/seeing-sound\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/engineering.jhu.edu\/ams\/news\/seeing-sound\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/engineering.jhu.edu\/ams\/"},{"@type":"ListItem","position":2,"name":"News","item":"https:\/\/engineering.jhu.edu\/ams\/news\/"},{"@type":"ListItem","position":3,"name":"Seeing Sound"}]},{"@type":"WebSite","@id":"https:\/\/engineering.jhu.edu\/ams\/#website","url":"https:\/\/engineering.jhu.edu\/ams\/","name":"Hopkins Applied Math & Statistics","description":"Department of Applied Mathematics and Statistics","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/engineering.jhu.edu\/ams\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"distributor_meta":false,"distributor_terms":false,"distributor_media":false,"distributor_original_site_name":"Department of Applied Mathematics and Statistics","distributor_original_site_url":"https:\/\/engineering.jhu.edu\/ams","push-errors":false,"_links":{"self":[{"href":"https:\/\/engineering.jhu.edu\/ams\/wp-json\/wp\/v2\/news\/52677","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/engineering.jhu.edu\/ams\/wp-json\/wp\/v2\/news"}],"about":[{"href":"https:\/\/engineering.jhu.edu\/ams\/wp-json\/wp\/v2\/types\/news"}],"wp:attachment":[{"href":"https:\/\/engineering.jhu.edu\/ams\/wp-json\/wp\/v2\/media?parent=52677"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}