{"id":14877,"date":"2023-04-27T13:45:00","date_gmt":"2023-04-27T20:45:00","guid":{"rendered":"https:\/\/dornsife.usc.edu\/news\/?p=14877"},"modified":"2024-08-22T16:23:56","modified_gmt":"2024-08-22T23:23:56","slug":"relationship-between-music-and-math","status":"publish","type":"post","link":"https:\/\/dornsife.usc.edu\/news\/stories\/relationship-between-music-and-math\/","title":{"rendered":"Musical numbers: Math and music nurture a deep and complex relationship"},"content":{"rendered":"\n\n\n    \n                                                    \n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--article-hero \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--article-hero\"\n    \n      >\n\n    \n<div class=\"inner-wrapper\">\n          \n<div class=\"f--field f--image\">\n\n    \n    \n    \n    \n    \n    \n              \n      <img\n                            data-src=\"https:\/\/dornsife.usc.edu\/news\/wp-content\/uploads\/sites\/7\/2023\/04\/math_music_newsite-768x432.jpg\"\n          data-srcset=\"https:\/\/dornsife.usc.edu\/news\/wp-content\/uploads\/sites\/7\/2023\/04\/math_music_newsite-1920x1080.jpg 1920w,https:\/\/dornsife.usc.edu\/news\/wp-content\/uploads\/sites\/7\/2023\/04\/math_music_newsite-1280x720.jpg 1280w,https:\/\/dornsife.usc.edu\/news\/wp-content\/uploads\/sites\/7\/2023\/04\/math_music_newsite-768x432.jpg 768w\"          data-sizes=\"(min-width:1200px) 75vw, (min-width:768px) 83vw, 100vw\"          class=\"lazyload\"\n        \n                  alt=\"An illustration with a monochrome musician playing the saxophone with overlapping circles and other shapes in the background.\"\n        \n        \n                                      \/>\n\n    \n    \n  \n  \n\n<\/div>\n  \n      <div class=\"image-caption\">\n          \n<div class=\"f--field f--description\">\n\n    \n  Musicians as varied in sound as John Coltrane and Johann Sebastian Bach have cited mathematics as inspiration. (Illustration: Sarvani Kolachana.)\n\n\n<\/div>\n    <\/div>\n  \n  <div class=\"text-wrapper\">\n          <nav aria-label=\"Breadcrumb\" class=\"breadcrumbs\">\n        <ul>\n                      <li><a href=\"\/news\/stories\/\">News<\/a><\/li>\n                      <li><a href=\"\/news\/stories\/\/?category=faculty\">Faculty<\/a><\/li>\n                  <\/ul>\n      <\/nav>\n    \n              \n<div class=\"f--field f--page-title\">\n\n    \n  <h1>Musical numbers: Math and music nurture a deep and complex relationship<\/h1>\n\n\n<\/div>\n    \n          <div class=\"subtitle\">\n            \n<div class=\"f--field f--description\">\n\n    \n  Discover how math and music intertwine in creative expression, from John Coltrane\u2019s Circle of Tones to the shared skills needed to master both subjects.\n\n\n<\/div>\n      <\/div>\n    \n           <strong class=\"author-field\"><span >By<\/span><a href=\"mailto:communication@dornsife.usc.edu\">Margaret Crable<\/a><\/strong>\n    \n          <span class=\"post-date-field\">April 27, 2023<\/span>\n      <\/div>\n<\/div>\n\n\n  <\/div><\/div>\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--social-share \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--social-share\"\n    \n      >\n\n    \n  <div class=\"content-wrapper\">\n    <span class=\"a2a_kit a2a_kit_size_32 addtoany_list\" style=\"line-height: 32px;\">\n      <span class=\"title\">\n        Share\n      <\/span>\n                        <a class=\"a2a_button_copy_link\" target=\"_blank\" href=\"\/#copy_link\" rel=\"nofollow noopener\" title=\"Link\">\n            <span class=\"a2a_svg a2a_s__default a2a_s_copy_link\">\n              <svg height=\"19\" viewBox=\"0 0 19 19\" width=\"19\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"m7.43475275 9.52380952-2.17490843 2.26076008c-1.08745421 1.058837-1.68841575 2.518315-1.68841575 4.0350275 0 1.5167124.60096154 2.9475732 1.68841575 4.0350274 1.058837 1.0874543 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xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"m8.14285714 9.42857143c-.17142857 0-.34285714 0-.51428571.08571428l7.28571427 6.34285719c.3428572.2571428.6857143.2571428.9428572 0l7.2857142-6.34285719c-.0857142-.08571428-.2571428-.08571428-.4285714-.08571428zm-1.28571428 1.11428567v.1714286 8.5714286c0 .6857143.6 1.2857143 1.28571428 1.2857143h14.57142856c.6857143 0 1.2857143-.6 1.2857143-1.2857143v-8.5714286c0-.0857143 0-.0857143 0-.1714286l-7.2 6.3428572c-.7714286.6857143-1.8857143.6857143-2.6571429 0z\" fill-rule=\"evenodd\" transform=\"translate(-6 -9)\"\/><\/svg>\n            <\/span>\n            <span class=\"a2a_label visually-hidden\">Email<\/span>\n          <\/a>\n                  <\/span>\n  <\/div>\n\n  <\/div><\/div>\n \n\n\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p>When famed jazz saxophonist, composer and bandleader John Coltrane wanted to illustrate his understanding of music, he turned to mathematics.<\/p>\n<p>Coltrane took the Circle of Fifths, a geometric diagram that sketches out the spatial connections between music notes and expanded it with his own ideas around tonal relationships. His drawing, dubbed Coltrane\u2019s Circle of Tones, has inspired\u00a0<a href=\"https:\/\/roelhollander.eu\/en\/blog-saxophone\/Coltrane-Geometry\/\" target=\"_blank\" rel=\"noopener\">whole essays<\/a>\u00a0on \u201cmusical geometry.\u201d<\/p>\n<p>Mathematics and music may seem like disparate worlds, but they share a profound, symbiotic relationship that stretches back centuries. This connection isn\u2019t a coincidence. Math is woven into the very essence of the art form, from the way we organize musical scales to the physics that dictates an instrument\u2019s sound. Learning one may even enhance one\u2019s ability to master the other.<\/p>\n<p>The relationship between music and math flows both ways. Prominent Princeton University mathematician Manjul Barghava, a renowned tabla drum player and a poet, said in a <a href=\"https:\/\/www.quantamagazine.org\/number-theorist-manjul-bhargava-is-awarded-fields-medal-20140812\/\" target=\"_blank\" rel=\"noopener\"><em>Quanta Magazine<\/em><\/a>\u00a0story, \u201cAll kinds of creative thoughts come together when I think about all three.\u201d<\/p>\n<p>This synergy upends the stereotype that mathematicians are exclusively left-brained scholars, disinterested or incapable of soulful expression.<\/p>\n<p>\u201cMathematicians would actually object to the idea that math isn\u2019t interested in beauty,\u201d says\u00a0<a href=\"https:\/\/dornsife.usc.edu\/cf\/faculty-and-staff\/faculty.cfm?pid=1003338\">Cymra Haskell<\/a>, professor (teaching) of mathematics at the USC Dornsife College of Letters, Arts and Sciences, who plays the fiddle.\u00a0\u201cWhen I write down a proof of a result in mathematics, it feels like a puzzle coming together. There can be an intense pleasure in that, similar to the pleasure I feel when I listen to a beautiful piece of music or gaze at a beautiful painting or go for a walk in the mountains, on the beach or in a wood.\u201d<\/p>\n<h2>Musical numbers<\/h2>\n<figure id=\"attachment_14878\" aria-describedby=\"caption-attachment-14878\" style=\"width: 500px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-14878 size-5x7_500\" src=\"https:\/\/dornsife.usc.edu\/news\/wp-content\/uploads\/sites\/7\/2023\/04\/math_music_instorya-500x406.jpg\" alt=\"A line of people sit playing flutes in an orchestra.\" width=\"500\" height=\"406\" \/><figcaption id=\"caption-attachment-14878\" class=\"wp-caption-text\">Mathematics professor Ken Alexander (wearing red tie) plays flute with the Pacific Symphony Orchestra. (Photo: Courtesy of Pacific Symphony Orchestra.)<\/figcaption><\/figure>\n<p>Western music today is based around sets of 12 notes that rise in pitch, called octaves. The tuning of each note isn\u2019t arbitrary; it\u2019s based on math. Each note within an octave has a frequency about 5.95% higher than the previous one. As a result, each note has twice the frequency of the same note an octave lower. Hence, the measured rise as you play through an octave.<\/p>\n<p>Math is also represented, whimsically, in other areas of classical music. Johann Sebastian Bach\u2019s compositions, for instance, are peppered with the numbers 14 and 41. It\u2019s a reference to numerology, which assigns letters of the alphabet individual numbers; that is, A=1, B=2, C=3 and so forth. Adding the numeric values of the letters in Bach\u2019s name \u2014 B+A+C+H or 2+1+3+8 \u2014 equals 14. And 14 backwards is 41.<\/p>\n<p>Just as musicians benefit from math, mathematicians benefit from music.\u00a0<a href=\"https:\/\/dornsife.usc.edu\/cf\/faculty-and-staff\/faculty.cfm?pid=1003039\">Ken Alexander<\/a>, professor of mathematics at USC Dornsife, was a flutist with Orchestra Nova LA (formely known as the\u00a0<a href=\"https:\/\/ladso.org\/\" target=\"_blank\" rel=\"noopener\">Los Angeles Doctors Symphony Orchestra<\/a>)\u00a0for 30 years. He says there\u2019s a strong connection between the skills needed to play an instrument and those essential to solving math problems.<\/p>\n<p>\u201cWhat\u2019s written on a page of music is just a sequence of pitches and how long you hold each pitch. You have to see that, underneath, there are themes, flows and a cadence in the music. There are all kinds of patterns that you have to identify,\u201d he says.<\/p>\n<p>Identifying patterns is also key to mathematical discovery. \u201cIn math, a lot of great insights and breakthroughs come about when people see how different parts of mathematics are actually related to each other. Pattern recognition is a very central aspect,\u201d he says.<\/p>\n<p>Research supports Alexander\u2019s assertion.\u00a0<a href=\"https:\/\/dornsife.usc.edu\/cf\/faculty-and-staff\/faculty.cfm?pid=1004700\">Assal Habibi<\/a>, an associate professor (research) of psychology, studies how\u00a0<a href=\"https:\/\/theconversation.com\/music-training-speeds-up-brain-development-in-children-61491\" target=\"_blank\" rel=\"noopener\">music training affects cognitive outcomes for children<\/a>\u00a0through the\u00a0<a href=\"https:\/\/dornsife.usc.edu\/labs\/brainandmusic\">Brain and Music Lab<\/a>\u00a0she heads at USC Dornsife\u2019s\u00a0<a href=\"https:\/\/dornsife.usc.edu\/bci\/\">Brain and Creativity Institute<\/a>. She has found that music training enhances executive functions like working memory, which can, in turn, improve mathematical abilities.<\/p>\n<p>\u201cWorking memory is about keeping information in your mind and manipulating that information, like remembering a phone number and being able to repeat it backwards,\u201d she explains. Without a robust memory to retain complex information, the pattern recognition Alexander and other mathematicians prize isn\u2019t so feasible.<\/p>\n<h2>Strength in numbers<\/h2>\n<p>Studying mathematics may seem like a solitary pursuit, but only so much can be done alone, says Alexander. The collaboration between mathematicians to solve a problem mirrors the collaboration between musicians in a band or orchestra. \u201cYou work very intensely, mentally, on your own, and then you come together to try to make something out of what you accomplished individually,\u201d he says.<\/p>\n<p>Musical collaborations aren\u2019t unusual for faculty in the USC Dornsife mathematics department. Haskell says she and a colleague recently played the fiddle together. And Alexander often plays with pianist\u00a0<a href=\"https:\/\/www.cs.usc.edu\/directory\/faculty\/profile\/?lname=Kempe&amp;fname=David\" target=\"_blank\" rel=\"noopener\">David Kempe<\/a>, a computer scientist with the\u00a0<a href=\"https:\/\/viterbischool.usc.edu\/\" target=\"_blank\" rel=\"noopener\">USC Viterbi School of Engineering<\/a>.<\/p>\n<p>Habibi\u2019s research has also demonstrated that music training can enhance social skills, making it an invaluable tool for collaboration.<\/p>\n<p>The children in her study are enrolled in the LA Phil\u2019s\u00a0<a href=\"https:\/\/www.laphil.com\/learn\/yola\/youth-orchestra-los-angeles\" target=\"_blank\" rel=\"noopener\">Youth Orchestra Los Angeles<\/a>\u00a0program. This means they aren\u2019t just learning an instrument on their own. \u201cYou really have to pay attention to others and adjust your playing,\u201d she says. Her research found that social skills are another executive ability amplified by music training.<\/p>\n<p>Can adults reap the cognitive benefits of learning music (and perhaps boost their math skills)? Habibi says yes, although the improvements aren\u2019t as pronounced as they are in children.<\/p>\n<p>Her research found that adults with no prior music training, when enrolled in a choir, boosted their speech perception and attention skills, she says.<\/p>\n<p><a href=\"https:\/\/onlinelibrary.wiley.com\/doi\/full\/10.1002\/hbm.25298\" target=\"_blank\" rel=\"noopener\">Another study<\/a>\u00a0found that older adults with a limited background in music improved their memory after four months of lessons on the keyboard harmonica.<\/p>\n<p>Perhaps being \u201cmath-brained\u201d could have a little something to do with the sound of music.<\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n\n\n\n  \n        \n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--article-related-stories \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--article-related-stories\"\n    \n      >\n\n    \n  <div class=\"inner-wrapper\">\n              \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Related News\n      <\/h2>\n\n\n<\/div>\n    \n                  <article>\n              \n<div class=\"f--field f--cta-title\">\n\n    \n  <h3>\n          <a href=\"https:\/\/dornsife.usc.edu\/news\/stories\/career-options-for-math-majors\/\" \n                        class=\"\" \n      >What can you do with a math degree? The options are nearly infinite<\/a>\n      <\/h3>\n\n\n<\/div>\n        <\/article>\n              <article>\n              \n<div class=\"f--field f--cta-title\">\n\n    \n  <h3>\n          <a href=\"https:\/\/dornsife.usc.edu\/news\/stories\/music-training-speeds-up-brain-development-in-children\/\" \n                        class=\"\" \n      >Music training speeds up brain development in children<\/a>\n      <\/h3>\n\n\n<\/div>\n        <\/article>\n              <article>\n              \n<div class=\"f--field f--cta-title\">\n\n    \n  <h3>\n          <a href=\"https:\/\/dornsife.usc.edu\/news\/stories\/neuroscience-music-lessons-affect-childrens-brains\/\" \n                        class=\"\" \n      >Neuroscientists\u2019 research reinforces music\u2019s impact on the developing brain<\/a>\n      <\/h3>\n\n\n<\/div>\n        <\/article>\n            <\/div>\n\n\n  <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>From Coltrane\u2019s Circle of Tones to the shared skills required for both, discover how math and music intertwine in creative expression.<\/p>\n","protected":false},"author":13,"featured_media":14879,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[23,10,16],"tags":[94,235,106],"class_list":["post-14877","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-arts-and-culture","category-faculty","category-science-and-technology","tag-mathematics","tag-music","tag-neuroscience"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Musical numbers: Math and music nurture a deep and complex relationship<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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