{"id":16912,"date":"2026-08-12T15:29:00","date_gmt":"2026-08-12T05:29:00","guid":{"rendered":"https:\/\/geoffreychen.com\/?p=16912"},"modified":"2026-08-12T23:18:08","modified_gmt":"2026-08-12T13:18:08","slug":"can-mathematics-explain-why-music-moves-us","status":"publish","type":"post","link":"https:\/\/geoffreychen.com\/zh\/can-mathematics-explain-why-music-moves-us\/","title":{"rendered":"\u6570\u5b66\u80fd\u89e3\u91ca\u97f3\u4e50\u4e3a\u4ec0\u4e48\u6253\u52a8\u4eba\u5417\uff1f"},"content":{"rendered":"<\/p>\n<p><em>\u300a\u542c\u89c1\u6570\u5b66\u300b\u00b7\u201c\u58f0\u97f3\u600e\u6837\u8fdb\u5165\u8eab\u4f53\u4e0e\u5fc3\u7075\u201d\u00b7 \u7b2c\u5341\u7bc7<\/em><\/p>\n<p>\u5df4\u8d6b\u300a\u54e5\u5fb7\u5821\u53d8\u594f\u66f2\u300b\u4ece\u548f\u53f9\u8c03\u5f00\u59cb\uff0c\u7ecf\u8fc7\u4e09\u5341\u4e2a\u53d8\u594f\uff0c\u6700\u540e\u5199\u7740 <em>Aria da capo<\/em>\uff1a\u548f\u53f9\u8c03\u4ece\u5934\u518d\u6765\u3002\u82e5\u6f14\u594f\u8005\u4e0d\u4f5c\u6539\u52a8\uff0c\u8fd4\u59cb\u548f\u53f9\u8c03\u7684\u97f3\u7b26\u4e0e\u5f00\u5934\u76f8\u540c\uff1b\u5f55\u97f3\u4e2d\u7684\u58f0\u6ce2\u751a\u81f3\u53ef\u4ee5\u901a\u8fc7\u526a\u8f91\u505a\u5230\u5b8c\u5168\u590d\u5236\u3002\u53ef\u662f\u5f88\u5c11\u6709\u4eba\u4f1a\u628a\u7ed3\u5c3e\u7ecf\u9a8c\u4e3a\u201c\u521a\u624d\u5df2\u7ecf\u542c\u8fc7\uff0c\u6240\u4ee5\u4fe1\u606f\u4e3a\u96f6\u201d\u3002\u7ecf\u8fc7\u5361\u519c\u3001\u821e\u66f2\u3001\u6162\u677f\u3001\u70ab\u6280\u4e0e quodlibet\uff0c\u90a3\u6bb5\u548f\u53f9\u8c03\u50cf\u4ece\u8fdc\u5904\u8fd4\u56de\u3002\u6750\u6599\u76f8\u540c\uff0c\u542c\u8005\u5df2\u7ecf\u4e0d\u540c\u3002<\/p>\n<p>\u8fd9\u4e2a\u65f6\u523b\u9002\u5408\u68c0\u9a8c\u672c\u7cfb\u5217\u6700\u5927\u7684\u8bf1\u60d1\u3002\u65e2\u7136\u9891\u7387\u3001\u6bd4\u4f8b\u3001\u8c03\u5f8b\u3001\u8282\u62cd\u548c\u9884\u671f\u90fd\u53ef\u6570\u5b66\u63cf\u8ff0\uff0c\u6211\u4eec\u662f\u5426\u7ec8\u5c06\u5f97\u5230\u4e00\u4e2a\u516c\u5f0f\uff0c\u8ba1\u7b97\u97f3\u4e50\u4e3a\u4ec0\u4e48\u4ee4\u4eba\u611f\u52a8\uff1f\u7b54\u6848\u53d6\u51b3\u4e8e\u201c\u89e3\u91ca\u201d\u662f\u4ec0\u4e48\u610f\u601d\u3002\u6570\u5b66\u80fd\u591f\u63ed\u793a\u4f7f\u671f\u5f85\u3001\u91cd\u590d\u548c\u5dee\u5f02\u6210\u4e3a\u53ef\u80fd\u7684\u7ed3\u6784\uff1b\u5fc3\u7406\u5b66\u4e0e\u795e\u7ecf\u79d1\u5b66\u53ef\u4ee5\u7814\u7a76\u8eab\u4f53\u600e\u6837\u54cd\u5e94\uff1b\u4f46\u4e00\u6bb5\u97f3\u4e50\u5bf9\u4e00\u4e2a\u5177\u4f53\u4eba\u7684\u610f\u4e49\uff0c\u8fd8\u5305\u542b\u8bb0\u5fc6\u3001\u6587\u5316\u3001\u6ce8\u610f\u3001\u6f14\u594f\u4e0e\u4eba\u751f\u5904\u5883\u3002\u628a\u8fd9\u4e9b\u5c42\u6b21\u5168\u90e8\u538b\u6210\u4e00\u4e2a\u6570\uff0c\u4e0d\u4f1a\u5f97\u5230\u66f4\u6df1\u89e3\u91ca\uff0c\u53ea\u4f1a\u4e22\u5931\u95ee\u9898\u3002<\/p>\n<h2>\u4ece\u6982\u7387\u770b\uff0c\u60ca\u8bb6\u4e0d\u662f\u58f0\u97f3\u7684\u56fa\u5b9a\u5c5e\u6027<\/h2>\n<p>\u4e00\u4e2a\u4e8b\u4ef6\u662f\u5426\u51fa\u4e4e\u610f\u6599\uff0c\u53d6\u51b3\u4e8e\u542c\u8005\u5728\u5f53\u65f6\u7ed9\u5b83\u591a\u5927\u6982\u7387\u3002\u4fe1\u606f\u8bba\u5e38\u7528 <code>-log\u2082 P(event | context)<\/code> \u8868\u793a\u4e8b\u4ef6\u5728\u7279\u5b9a\u8bed\u5883\u4e2d\u7684\u4fe1\u606f\u91cf\uff1a\u6982\u7387\u8d8a\u4f4e\uff0c\u60ca\u8bb6\u5ea6\u8d8a\u9ad8\u3002\u82e5\u67d0\u4e2a\u7ec8\u6b62\u5f0f\u5728\u98ce\u683c\u4e2d\u6781\u5e38\u89c1\uff0c\u5b83\u51fa\u73b0\u65f6\u4fe1\u606f\u91cf\u8f83\u4f4e\uff1b\u82e5\u548c\u58f0\u8f6c\u5411\u7f55\u89c1\uff0c\u5374\u4ecd\u80fd\u88ab\u524d\u6587\u7406\u89e3\uff0c\u9884\u6d4b\u8bef\u5dee\u4f1a\u589e\u52a0\u3002<\/p>\n<p>\u516c\u5f0f\u7684\u91cd\u8981\u4e4b\u5904\u662f\u628a\u60ca\u8bb6\u5199\u6210\u5173\u7cfb\uff0c\u800c\u4e0d\u662f\u5199\u6210\u97f3\u7b26\u7684\u5929\u6027\u3002\u540c\u4e00\u4e2a C \u5927\u548c\u5f26\u5728\u66f2\u9996\u3001\u5c5e\u4e03\u4e4b\u540e\u3001\u9065\u8fdc\u8f6c\u8c03\u4e2d\u548c\u7ed3\u5c3e\u8fd4\u59cb\u5904\uff0c\u6982\u7387\u4e0e\u610f\u4e49\u4e0d\u540c\u3002\u5bf9\u719f\u6089\u53e4\u5178\u8c03\u6027\u7684\u542c\u8005\u548c\u7b2c\u4e00\u6b21\u63a5\u89e6\u8be5\u98ce\u683c\u7684\u4eba\uff0c\u5185\u90e8\u6a21\u578b\u4e5f\u4e0d\u540c\u3002<\/p>\n<p>\u73b0\u4ee3\u8ba1\u7b97\u6a21\u578b\u53ef\u4ee5\u4ece\u97f3\u4e50\u8bed\u6599\u5b66\u4e60\u97f3\u7b26\u3001\u548c\u5f26\u4e0e\u8282\u594f\u7684\u6761\u4ef6\u6982\u7387\uff0c\u518d\u6bd4\u8f83\u6a21\u578b\u7684\u9884\u6d4b\u4e0e\u4eba\u7684\u671f\u5f85\u5224\u65ad\u3002\u8fd9\u4e9b\u65b9\u6cd5\u80fd\u5b9a\u4f4d\u4f5c\u54c1\u4e2d\u76f8\u5bf9\u53ef\u9884\u6d4b\u4e0e\u610f\u5916\u7684\u65f6\u523b\uff0c\u4e5f\u80fd\u7814\u7a76\u719f\u6089\u5ea6\u600e\u6837\u964d\u4f4e\u67d0\u4e9b\u4e0d\u786e\u5b9a\u6027\u3002\u7136\u800c\u6a21\u578b\u7684\u6982\u7387\u6765\u81ea\u8bad\u7ec3\u8d44\u6599\u548c\u8868\u793a\u9009\u62e9\uff1a\u628a\u97f3\u4e50\u7f16\u7801\u4e3a\u97f3\u7ea7\u3001\u7edd\u5bf9\u97f3\u9ad8\u3001\u548c\u5f26\u6807\u7b7e\u6216\u58f0\u5b66\u7279\u5f81\uff0c\u4f1a\u5f97\u5230\u4e0d\u540c\u4e16\u754c\u3002\u6982\u7387\u4e0d\u662f\u4f5c\u54c1\u79d8\u5bc6\u542b\u4e49\u7684\u5ba2\u89c2\u6284\u672c\uff0c\u800c\u662f\u4e00\u4e2a\u5177\u6709\u660e\u786e\u89c6\u89d2\u7684\u53ef\u68c0\u9a8c\u6a21\u578b\u3002<\/p>\n<h2>\u6109\u60a6\u53ef\u80fd\u6765\u81ea\u9884\u6d4b\u6210\u529f\uff0c\u4e5f\u53ef\u80fd\u6765\u81ea\u9884\u6d4b\u88ab\u6709\u610f\u4e49\u5730\u4fee\u6b63<\/h2>\n<p>\u97f3\u4e50\u82e5\u5b8c\u5168\u7b26\u5408\u9884\u6d4b\uff0c\u53ef\u80fd\u4ee4\u4eba\u5b89\u5fc3\uff0c\u4e5f\u53ef\u80fd\u53d8\u5f97\u5e73\u6de1\uff1b\u82e5\u6bcf\u4e2a\u4e8b\u4ef6\u90fd\u4e0d\u53ef\u9884\u6d4b\uff0c\u53ef\u80fd\u523a\u6fc0\uff0c\u4e5f\u53ef\u80fd\u65e0\u6cd5\u5f62\u6210\u6574\u4f53\u3002\u8bb8\u591a\u7406\u8bba\u56e0\u6b64\u5173\u6ce8\u53ef\u9884\u6d4b\u6027\u4e0e\u60ca\u8bb6\u4e4b\u95f4\u7684\u52a8\u6001\u5e73\u8861\u3002\u91cd\u590d\u8ba9\u6a21\u578b\u53d8\u5f3a\uff0c\u504f\u79bb\u4f7f\u8bef\u5dee\u83b7\u5f97\u663e\u8457\u6027\uff0c\u540e\u7eed\u53c8\u53ef\u80fd\u8bc1\u660e\u504f\u79bb\u5c5e\u4e8e\u66f4\u5927\u7ed3\u6784\u3002<\/p>\n<p><a href=\"https:\/\/www.nature.com\/articles\/s41583-022-00578-5\" target=\"_blank\" rel=\"noopener\">\u5173\u4e8e\u97f3\u4e50\u4e0e\u5927\u8111\u7684\u7efc\u5408\u7efc\u8ff0<\/a>\u628a\u9884\u6d4b\u89c6\u4e3a\u8fde\u63a5\u97f3\u4e50\u77e5\u89c9\u3001\u52a8\u4f5c\u3001\u60c5\u7eea\u4e0e\u5b66\u4e60\u7684\u91cd\u8981\u80fd\u529b\u3002<a href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC6386687\/\" target=\"_blank\" rel=\"noopener\">\u97f3\u4e50\u5956\u8d4f\u9884\u6d4b\u8bef\u5dee\u5b9e\u9a8c<\/a>\u5219\u663e\u793a\uff0c\u5728\u7279\u5b9a\u5b66\u4e60\u4efb\u52a1\u4e2d\uff0c\u97f3\u4e50\u7ed3\u679c\u76f8\u5bf9\u4e8e\u9884\u671f\u7684\u597d\u574f\u4e0e\u5956\u8d4f\u76f8\u5173\u795e\u7ecf\u6d3b\u52a8\u53ca\u540e\u7eed\u9009\u62e9\u6709\u5173\u3002\u8fd9\u4e9b\u7814\u7a76\u4f7f\u201c\u671f\u5f85\u5f71\u54cd\u6109\u60a6\u201d\u5177\u6709\u53ef\u68c0\u9a8c\u5185\u5bb9\u3002<\/p>\n<p>\u4f46\u4e0d\u80fd\u628a\u5b83\u4eec\u7f29\u6210\u201c\u591a\u5df4\u80fa\u5c31\u662f\u97f3\u4e50\u611f\u52a8\u201d\u6216\u201c\u6700\u4f73\u97f3\u4e50\u7b49\u4e8e\u56fa\u5b9a\u6bd4\u4f8b\u7684\u60ca\u8bb6\u201d\u3002\u5b9e\u9a8c\u4efb\u52a1\u3001\u53d7\u8bd5\u8005\u3001\u66f2\u76ee\u548c\u6d4b\u91cf\u5b9a\u4e49\u9650\u5236\u7ed3\u8bba\u3002\u5956\u8d4f\u3001\u60c5\u7eea\u3001\u5ba1\u7f8e\u5224\u65ad\u3001\u5bd2\u6218\u548c\u4e2a\u4eba\u610f\u4e49\u4e5f\u4e0d\u662f\u540c\u4e00\u4e2a\u53d8\u91cf\u3002\u67d0\u4eba\u53ef\u80fd\u88ab\u60b2\u75db\u97f3\u4e50\u6df1\u6df1\u6253\u52a8\u800c\u4e0d\u60f3\u628a\u611f\u53d7\u79f0\u4e3a\u6109\u60a6\uff1b\u53e6\u4e00\u4eba\u53ef\u80fd\u6b23\u8d4f\u7ed3\u6784\u5374\u6ca1\u6709\u5f3a\u70c8\u60c5\u7eea\u3002<\/p>\n<p>\u9884\u6d4b\u7406\u8bba\u6700\u597d\u7528\u6765\u8bf4\u660e\u97f3\u4e50\u4e3a\u4f55\u80fd\u591f\u8c03\u8282\u6ce8\u610f\u548c\u5f20\u529b\uff0c\u800c\u4e0d\u662f\u5ba3\u5e03\u6240\u6709\u611f\u52a8\u7684\u5355\u4e00\u539f\u56e0\u3002<\/p>\n<h2>\u91cd\u590d\u4fdd\u5b58\u6750\u6599\uff0c\u5374\u6539\u53d8\u5b83\u6240\u5728\u7684\u65f6\u95f4<\/h2>\n<p>\u4ece\u4fe1\u53f7\u89d2\u5ea6\u770b\uff0c\u7cbe\u786e\u91cd\u590d\u6ca1\u6709\u589e\u52a0\u65b0\u6837\u672c\uff1b\u4ece\u97f3\u4e50\u7ecf\u9a8c\u770b\uff0c\u91cd\u590d\u603b\u53d1\u751f\u5728\u201c\u5df2\u7ecf\u542c\u8fc7\u201d\u4e4b\u540e\u3002\u7b2c\u4e00\u6b21\u9648\u8ff0\u5efa\u7acb\u8bb0\u5fc6\uff0c\u7b2c\u4e8c\u6b21\u8ba9\u542c\u8005\u6bd4\u8f83\uff0c\u66f4\u591a\u91cd\u590d\u53ef\u80fd\u5f62\u6210\u4e60\u60ef\u3001\u4eea\u5f0f\u3001\u538b\u8feb\u6216\u671f\u5f85\u3002\u91cd\u590d\u9879\u76f8\u540c\uff0c\u5173\u7cfb\u9879\u589e\u52a0\u3002<\/p>\n<p>\u300a\u54e5\u5fb7\u5821\u53d8\u594f\u66f2\u300b\u7684\u7ed3\u6784\u5c24\u5176\u6e05\u695a\u3002\u5f00\u5934\u548f\u53f9\u8c03\u4e0d\u662f\u4e00\u4e2a\u7b80\u5355\u65cb\u5f8b\u4e3b\u9898\uff0c\u4e09\u5341\u4e2a\u53d8\u594f\u4e3b\u8981\u5171\u4eab\u5176\u4f4e\u97f3\u4e0e\u548c\u58f0\u6a21\u578b\uff0c\u5e76\u5404\u81ea\u5f62\u6210\u72ec\u7acb\u6027\u683c\u3002Peter Williams \u7684<a href=\"https:\/\/www.cambridge.org\/core\/books\/abs\/bach-the-goldberg-variations\/movements\/3940510C02AE2E5C2A881641C9C254EE\" target=\"_blank\" rel=\"noopener\">\u4f5c\u54c1\u7814\u7a76<\/a>\u63d0\u9192\u6211\u4eec\uff0c\u548f\u53f9\u8c03\u672c\u8eab\u66f4\u50cf\u5bf9\u57fa\u7840\u548c\u58f0\uff0f\u4f4e\u97f3\u6a21\u578b\u7684\u4e00\u6b21\u4e30\u539a\u8bbe\u7f6e\uff0c\u800c\u4e0d\u662f\u540e\u6765\u9010\u97f3\u88c5\u9970\u7684\u88f8\u4e3b\u9898\u3002<a href=\"https:\/\/imslp.org\/wiki\/Goldberg-Variationen%2C_BWV_988_%28Bach%2C_Johann_Sebastian%29\" target=\"_blank\" rel=\"noopener\">\u4e50\u8c31<\/a>\u5728\u7b2c\u4e09\u5341\u53d8\u594f\u540e\u660e\u786e\u56de\u5230 <em>Aria da Capo<\/em>\u3002<\/p>\n<p>\u8fd4\u59cb\u65f6\uff0c\u542c\u8005\u53ef\u80fd\u5df2\u4e0d\u8bb0\u5f97\u6bcf\u4e2a\u53d8\u594f\u7ec6\u8282\uff0c\u5374\u4fdd\u5b58\u4e86\u65c5\u7a0b\u7684\u957f\u5ea6\u3001\u901f\u5ea6\u5dee\u5f02\u3001\u5361\u519c\u6b21\u5e8f\u548c\u7b2c\u4e8c\u5341\u4e94\u53d8\u594f\u7b49\u5c40\u90e8\u91cd\u91cf\u3002\u548f\u53f9\u8c03\u7684\u6bcf\u4e2a\u505c\u987f\u56e0\u7ed3\u5c3e\u4f4d\u7f6e\u800c\u83b7\u5f97\u65b0\u7684\u5c3a\u5ea6\u3002\u6570\u5b66\u53ef\u4ee5\u8bf4\u6750\u6599\u76f8\u540c\uff0c\u5f62\u5f0f\u4f4d\u7f6e\u4e0d\u540c\uff1b\u5fc3\u7406\u5b66\u53ef\u4ee5\u8bf4\u5148\u524d\u4e8b\u4ef6\u6539\u53d8\u4e86\u8bb0\u5fc6\u4e0e\u9884\u6d4b\uff1b\u97f3\u4e50\u7ecf\u9a8c\u5219\u628a\u201c\u56de\u6765\u201d\u542c\u6210\u4e00\u79cd\u4e0d\u53ef\u7531\u5f00\u5934\u5355\u72ec\u62e5\u6709\u7684\u610f\u4e49\u3002<\/p>\n<h2>\u4e2a\u4eba\u8bb0\u5fc6\u4e0d\u662f\u4f5c\u54c1\u5916\u90e8\u7684\u566a\u58f0<\/h2>\n<p>\u4e00\u9996\u97f3\u4e50\u53ef\u80fd\u4e0e\u846c\u793c\u3001\u5bb6\u5ead\u3001\u5b66\u4e60\u65f6\u671f\u6216\u67d0\u4e2a\u4eba\u76f8\u8fde\u3002\u540e\u6765\u542c\u89c1\u51e0\u4e2a\u97f3\uff0c\u60c5\u7eea\u4f1a\u88ab\u81ea\u4f20\u8bb0\u5fc6\u8fc5\u901f\u6539\u53d8\u3002<a href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC2758676\/\" target=\"_blank\" rel=\"noopener\">\u97f3\u4e50\u8bf1\u53d1\u81ea\u4f20\u8bb0\u5fc6\u7684\u795e\u7ecf\u7814\u7a76<\/a>\u53d1\u73b0\uff0c\u719f\u6089\u5ea6\u3001\u81ea\u4f20\u663e\u8457\u6027\u548c\u60c5\u611f\u53cd\u5e94\u5f7c\u6b64\u76f8\u5173\uff0c\u5e76\u6d89\u53ca\u591a\u79cd\u8bb0\u5fc6\u4e0e\u81ea\u6211\u76f8\u5173\u8fc7\u7a0b\u3002<\/p>\n<p>\u8fd9\u7c7b\u610f\u4e49\u65e0\u6cd5\u4ece\u603b\u8c31\u76f4\u63a5\u8ba1\u7b97\u3002\u4e24\u4f4d\u542c\u8005\u63a5\u6536\u76f8\u8fd1\u58f0\u6ce2\uff0c\u53ef\u4ee5\u56e0\u751f\u6d3b\u8054\u7cfb\u5f97\u5230\u76f8\u53cd\u53cd\u5e94\u3002\u4e2a\u4eba\u8bb0\u5fc6\u5374\u4e5f\u4e0d\u662f\u5e72\u6270\u201c\u7eaf\u97f3\u4e50\u201d\u7684\u5076\u7136\u6742\u8d28\u3002\u97f3\u4e50\u4e4b\u6240\u4ee5\u80fd\u5728\u793e\u4f1a\u751f\u6d3b\u4e2d\u627f\u62c5\u54c0\u60bc\u3001\u5e86\u5178\u3001\u5b97\u6559\u3001\u8eab\u4efd\u548c\u4eb2\u5bc6\u5173\u7cfb\uff0c\u6b63\u56e0\u4e3a\u5b83\u80fd\u591f\u4e0e\u60c5\u5883\u4e00\u8d77\u4fdd\u5b58\u548c\u5524\u56de\u3002<\/p>\n<p>\u5f53\u7136\uff0c\u4e0d\u80fd\u56e0\u6b64\u8bf4\u6240\u6709\u89e3\u91ca\u90fd\u53ea\u5728\u4e2a\u4eba\u6545\u4e8b\u91cc\u3002\u8fd4\u59cb\u3001\u7ec8\u6b62\u3001\u6e10\u5f3a\u548c\u8282\u62cd\u7b49\u7ed3\u6784\u4f1a\u7cfb\u7edf\u5851\u9020\u8bb8\u591a\u4eba\u7684\u65f6\u95f4\u7ecf\u9a8c\uff1b\u4f5c\u54c1\u4e0e\u8868\u6f14\u8bbe\u5b9a\u53ef\u80fd\u6027\u3002\u4e2a\u4eba\u5386\u53f2\u4e0d\u662f\u4ece\u96f6\u521b\u9020\u58f0\u97f3\u542b\u4e49\uff0c\u800c\u662f\u5728\u4f5c\u54c1\u63d0\u4f9b\u7684\u7ed3\u6784\u4e2d\u6539\u53d8\u663e\u8457\u6027\u3001\u8054\u60f3\u4e0e\u4ef7\u503c\u3002<\/p>\n<h2>\u201c\u5927\u8c03\u5feb\u4e50\u3001\u5c0f\u8c03\u60b2\u4f24\u201d\u4e3a\u4ec0\u4e48\u4e0d\u591f<\/h2>\n<p>\u628a\u97f3\u4e50\u60c5\u7eea\u505a\u6210\u53ef\u8ba1\u7b97\u7279\u5f81\u65f6\uff0c\u4eba\u4eec\u5e38\u4f7f\u7528\u8c03\u5f0f\u3001\u901f\u5ea6\u3001\u54cd\u5ea6\u3001\u97f3\u8272\u4e0e\u8282\u594f\u3002\u7edf\u8ba1\u4e0a\uff0c\u67d0\u4e9b\u7279\u5f81\u4e0e\u5524\u9192\u5ea6\u6216\u6b63\u8d1f\u60c5\u611f\u5224\u65ad\u6709\u5173\uff0c\u4f46\u4efb\u4f55\u5355\u4e00\u5bf9\u5e94\u90fd\u4e0d\u53ef\u9760\u3002\u5feb\u901f\u5c0f\u8c03\u97f3\u4e50\u53ef\u4ee5\u6fc0\u70c8\u3001\u8bd9\u8c10\u6216\u72c2\u70ed\uff1b\u7f13\u6162\u5927\u8c03\u97f3\u4e50\u53ef\u4ee5\u5e84\u4e25\u3001\u758f\u8fdc\u751a\u81f3\u54c0\u4f24\u3002\u548c\u58f0\u8bed\u5883\u3001\u65cb\u5f8b\u65b9\u5411\u3001\u53d1\u97f3\u3001\u6587\u5316\u5b66\u4e60\u4e0e\u6587\u5b57\u6807\u9898\u90fd\u4f1a\u6539\u53d8\u89e3\u91ca\u3002<\/p>\n<p>\u66f4\u6839\u672c\u5730\u8bf4\uff0c\u97f3\u4e50\u201c\u8868\u8fbe\u60b2\u4f24\u201d\u3001\u542c\u8005\u201c\u8bc6\u522b\u60b2\u4f24\u201d\u3001\u542c\u8005\u201c\u81ea\u5df1\u611f\u5230\u60b2\u4f24\u201d\u548c\u542c\u8005\u201c\u559c\u6b22\u8fd9\u6bb5\u60b2\u4f24\u97f3\u4e50\u201d\u662f\u56db\u4e2a\u4e0d\u540c\u95ee\u9898\u3002\u82e5\u6570\u636e\u96c6\u53ea\u8ba9\u53c2\u4e0e\u8005\u9009\u62e9 happy\/sad \u6807\u7b7e\uff0c\u6a21\u578b\u5b66\u5230\u7684\u662f\u8be5\u4efb\u52a1\u4e2d\u7684\u5206\u7c7b\uff0c\u4e0d\u662f\u60c5\u611f\u672c\u8eab\u7684\u5b8c\u6574\u7406\u8bba\u3002<\/p>\n<p>\u6570\u5b66\u6a21\u578b\u9700\u8981\u53d8\u91cf\uff0c\u53d8\u91cf\u9700\u8981\u64cd\u4f5c\u5b9a\u4e49\u3002\u6210\u719f\u7814\u7a76\u4e0d\u4f1a\u56e0\u4e3a\u91cf\u5316\u5c31\u5fd8\u8bb0\u5b9a\u4e49\u8303\u56f4\u3002\u6570\u5b57\u53ef\u4ee5\u6bd4\u8f83\u91cd\u590d\u5b9e\u9a8c\uff0c\u4e5f\u53ef\u80fd\u628a\u65e0\u6cd5\u8fdb\u5165\u91cf\u8868\u7684\u6df7\u5408\u60c5\u7eea\u3001\u8eab\u4f53\u611f\u548c\u4e2a\u4eba\u610f\u4e49\u6682\u65f6\u6392\u9664\u3002\u6392\u9664\u6709\u65f6\u662f\u7814\u7a76\u6240\u5fc5\u9700\uff0c\u4f46\u4e0d\u80fd\u5728\u7ed3\u8bba\u4e2d\u5047\u88c5\u88ab\u6392\u9664\u8005\u4e0d\u5b58\u5728\u3002<\/p>\n<h2>\u6f14\u594f\u4f7f\u540c\u4e00\u7ed3\u6784\u627f\u62c5\u4e0d\u540c\u627f\u8bfa<\/h2>\n<p>\u8fd4\u59cb\u548f\u53f9\u8c03\u7531\u4e0d\u540c\u6f14\u594f\u8005\u3001\u4e0d\u540c\u4e50\u5668\u6216\u4e0d\u540c\u901f\u5ea6\u6f14\u594f\uff0c\u4f1a\u6539\u53d8\u542c\u8005\u7684\u65f6\u95f4\u7ecf\u9a8c\u3002\u7fbd\u7ba1\u952e\u7434\u4e0e\u73b0\u4ee3\u94a2\u7434\u7684\u8d77\u97f3\u548c\u8870\u51cf\u4e0d\u540c\uff1b\u94a2\u7434\u5bb6\u53ef\u4ee5\u901a\u8fc7\u89e6\u952e\u3001\u58f0\u90e8\u5e73\u8861\u548c\u505c\u987f\u5851\u9020\u56de\u8fd4\uff1b\u662f\u5426\u53cd\u590d\u5404\u6bb5\u53c8\u6539\u53d8\u6574\u90e8\u4f5c\u54c1\u7684\u6bd4\u4f8b\u3002\u603b\u8c31\u89c4\u5b9a\u4e86\u8bb8\u591a\u5173\u7cfb\uff0c\u5374\u4e0d\u89c4\u5b9a\u4e00\u5207\u53ef\u542c\u7ec6\u8282\u3002<\/p>\n<p>\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48\u53ea\u5206\u6790\u4e50\u8c31\u6216\u53ea\u5206\u6790\u5f55\u97f3\u90fd\u4e0d\u5b8c\u6574\u3002\u4e50\u8c31\u8ba9\u8de8\u6f14\u594f\u7ed3\u6784\u53ef\u89c1\uff0c\u5f55\u97f3\u5305\u542b\u5177\u4f53\u65f6\u95f4\u4e0e\u97f3\u8272\uff0c\u73b0\u573a\u8fd8\u5305\u542b\u7a7a\u95f4\u3001\u5171\u540c\u6ce8\u610f\u548c\u6f14\u51fa\u4e0d\u53ef\u9006\u6027\u3002\u611f\u52a8\u53ef\u80fd\u6765\u81ea\u4f5c\u54c1\u7ed3\u6784\uff0c\u4e5f\u53ef\u80fd\u56e0\u67d0\u6b21\u6f14\u594f\u6070\u597d\u8ba9\u7ed3\u6784\u53d8\u5f97\u53ef\u95fb\u3002<\/p>\n<p>\u6211\u4eec\u4e0d\u5fc5\u5728\u201c\u4f5c\u54c1\u51b3\u5b9a\u4e00\u5207\u201d\u548c\u201c\u542c\u8005\u4efb\u610f\u6295\u5c04\u201d\u4e4b\u95f4\u9009\u62e9\u3002\u97f3\u4e50\u7ecf\u9a8c\u662f\u4e00\u9879\u5173\u7cfb\u4e8b\u4ef6\uff1a\u5199\u4e0b\u7684\u53ef\u80fd\u6027\u3001\u53d1\u51fa\u7684\u58f0\u97f3\u3001\u8eab\u4f53\u9884\u6d4b\u3001\u5df2\u6709\u8bb0\u5fc6\u4e0e\u5f53\u524d\u5904\u5883\u5728\u4e00\u6bb5\u4e0d\u53ef\u91cd\u590d\u7684\u65f6\u95f4\u4e2d\u76f8\u9047\u3002<\/p>\n<h2>\u6570\u5b66\u80fd\u89e3\u91ca\u5230\u54ea\u91cc<\/h2>\n<p>\u73b0\u5728\u53ef\u4ee5\u7ed9\u51fa\u660e\u786e\u5224\u65ad\u3002<\/p>\n<p>\u6570\u5b66\u80fd\u591f\u89e3\u91ca\u97f3\u4e50\u7684\u8bb8\u591a<strong>\u6761\u4ef6<\/strong>\u3002\u5b83\u8bf4\u660e\u632f\u52a8\u600e\u6837\u53e0\u52a0\u3001\u9891\u7387\u6bd4\u600e\u6837\u5f62\u6210\u97f3\u7a0b\u3001\u8c03\u5f8b\u4e3a\u4ec0\u4e48\u5fc5\u987b\u53d6\u820d\u3001\u8282\u62cd\u600e\u6837\u5efa\u7acb\u5468\u671f\u3001\u58f0\u90e8\u7ebf\u7d22\u600e\u6837\u76f8\u5173\uff0c\u4e5f\u80fd\u7528\u6982\u7387\u63cf\u8ff0\u9884\u671f\u4e0e\u60ca\u8bb6\u3002\u8fd9\u4e9b\u4e0d\u662f\u5916\u56f4\u77e5\u8bc6\uff0c\u800c\u662f\u97f3\u4e50\u5f97\u4ee5\u6210\u4e3a\u53ef\u7ec4\u7ec7\u58f0\u97f3\u7684\u91cd\u8981\u9aa8\u67b6\u3002<\/p>\n<p>\u6570\u5b66\u8fd8\u80fd\u5e2e\u52a9\u68c0\u9a8c\u67d0\u4e9b<strong>\u673a\u5236<\/strong>\u3002\u6a21\u578b\u53ef\u4ee5\u9884\u6d4b\u54ea\u4e9b\u8282\u594f\u8f83\u6613\u5206\u7ec4\u3001\u54ea\u4e9b\u9891\u8c31\u8f83\u7c97\u7cd9\u3001\u54ea\u4e9b\u4e8b\u4ef6\u5728\u67d0\u4e2a\u98ce\u683c\u8bed\u6599\u4e2d\u8f83\u5c11\u89c1\u3002\u5b9e\u9a8c\u518d\u68c0\u67e5\u8fd9\u4e9b\u9884\u6d4b\u662f\u5426\u4e0e\u884c\u4e3a\u548c\u751f\u7406\u53cd\u5e94\u76f8\u7b26\u3002<\/p>\n<p>\u4f46\u6570\u5b66\u4e0d\u80fd\u5355\u72ec\u7ed9\u51fa\u97f3\u4e50\u5bf9\u4e00\u4e2a\u4eba\u7684<strong>\u610f\u4e49<\/strong>\u3002\u610f\u4e49\u4e0d\u662f\u9690\u85cf\u5728\u58f0\u6ce2\u4e2d\u7684\u989d\u5916\u53d8\u91cf\uff0c\u7b49\u7740\u66f4\u5f3a\u7b97\u6cd5\u63d0\u53d6\u3002\u5b83\u5f62\u6210\u4e8e\u7ed3\u6784\u600e\u6837\u88ab\u4e00\u4e2a\u6709\u8eab\u4f53\u3001\u6709\u5386\u53f2\u3001\u5904\u5728\u5173\u7cfb\u4e0e\u6587\u5316\u4e2d\u7684\u542c\u8005\u7ecf\u5386\u3002\u6211\u4eec\u53ef\u4ee5\u7ee7\u7eed\u7814\u7a76\u5176\u4e2d\u89c4\u5f8b\uff0c\u5374\u4e0d\u5e94\u628a\u89c4\u5f8b\u8bef\u5199\u6210\u5bf9\u4e2a\u4f53\u7ecf\u9a8c\u7684\u66ff\u4ee3\u3002<\/p>\n<p>\u8fd9\u4e0d\u662f\u4e3a\u97f3\u4e50\u4fdd\u7559\u4e00\u4e2a\u62d2\u7edd\u7814\u7a76\u7684\u795e\u79d8\u9886\u57df\u3002\u76f8\u53cd\uff0c\u5b83\u8981\u6c42\u66f4\u4e25\u683c\u7684\u89e3\u91ca\uff1a\u6bcf\u4e2a\u6a21\u578b\u90fd\u8981\u8bf4\u660e\u5bf9\u8c61\u3001\u5c3a\u5ea6\u548c\u9057\u6f0f\u3002\u4e00\u4e2a\u6a21\u578b\u53ef\u4ee5\u5f88\u597d\u9884\u6d4b\u5e73\u5747\u6109\u60a6\u8bc4\u5206\uff0c\u5374\u4e0d\u80fd\u56e0\u6b64\u58f0\u79f0\u5df2\u89e3\u91ca\u54c0\u60bc\uff1b\u8111\u6210\u50cf\u53ef\u4ee5\u5b9a\u4f4d\u76f8\u5173\u6d3b\u52a8\uff0c\u5374\u4e0d\u80fd\u66ff\u5f53\u4e8b\u4eba\u8bf4\u660e\u90a3\u6bb5\u97f3\u4e50\u4e3a\u4f55\u4e0e\u67d0\u4eba\u76f8\u8fde\u3002<\/p>\n<h2>\u542c\u89c1\u6570\u5b66\uff0c\u6700\u7ec8\u662f\u542c\u89c1\u5173\u7cfb\u7684\u8fb9\u754c<\/h2>\n<p>\u672c\u7cfb\u5217\u4ece\u4e00\u4e2a\u97f3\u9ad8\u600e\u6837\u5f62\u6210\u5f00\u59cb\uff0c\u7ecf\u8fc7\u516b\u5ea6\u3001\u6cdb\u97f3\u3001\u534f\u548c\u3001\u8c03\u5f8b\u3001\u94a2\u7434\u3001\u8282\u594f\u548c\u590d\u8c03\uff0c\u6700\u540e\u56de\u5230\u4e00\u4e2a\u542c\u8005\u3002\u4e00\u8def\u4e0a\u7684\u6570\u5b57\u90fd\u975e\u5e38\u771f\u5b9e\uff1a440 \u8d6b\u5179\u30012:1\u30013:2\u3001\u5341\u4e8c\u6b21\u65b9\u6839\u3001\u62cd\u901f\u4e0e\u6982\u7387\u3002\u5b83\u4eec\u8ba9\u7ed3\u6784\u53ef\u6bd4\u8f83\u3001\u53ef\u5236\u9020\u3001\u53ef\u6f14\u594f\u3002<\/p>\n<p>\u6570\u5b57\u5374\u6ca1\u6709\u81ea\u884c\u6210\u4e3a\u97f3\u4e50\u3002\u8033\u8717\u9009\u62e9\u9891\u7387\uff0c\u795e\u7ecf\u7cfb\u7edf\u7ec4\u7ec7\u5bf9\u8c61\uff0c\u8eab\u4f53\u9884\u6d4b\u8282\u62cd\uff0c\u6ce8\u610f\u5206\u79bb\u58f0\u90e8\uff0c\u8bb0\u5fc6\u6539\u53d8\u91cd\u590d\uff0c\u6587\u5316\u63d0\u4f9b\u53ef\u5b66\u4e60\u7684\u8bed\u6cd5\uff0c\u4e2a\u4eba\u5728\u5177\u4f53\u65f6\u523b\u627f\u62c5\u610f\u4e49\u3002\u6bcf\u4e00\u5c42\u90fd\u4f9d\u8d56\u524d\u4e00\u5c42\uff0c\u53c8\u4e0d\u80fd\u88ab\u524d\u4e00\u5c42\u5b8c\u5168\u53d6\u4ee3\u3002<\/p>\n<p>\u5f53\u300a\u54e5\u5fb7\u5821\u53d8\u594f\u66f2\u300b\u7684\u548f\u53f9\u8c03\u56de\u6765\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u8bf4\u5b83\u4e0e\u5f00\u5934\u76f8\u540c\uff0c\u4e5f\u53ef\u4ee5\u8bf4\u5b83\u5df2\u7ecf\u4e0d\u540c\u3002\u4e24\u53e5\u8bdd\u90fd\u51c6\u786e\uff0c\u56e0\u4e3a\u5b83\u4eec\u6d4b\u91cf\u7684\u5bf9\u8c61\u4e0d\u540c\u3002\u6570\u5b66\u4fdd\u5b58\u4e86\u540c\u4e00\u5173\u7cfb\uff0c\u65f6\u95f4\u521b\u9020\u4e86\u65b0\u7684\u4f4d\u7f6e\u3002\u97f3\u4e50\u4e4b\u6240\u4ee5\u6253\u52a8\u4eba\uff0c\u5f80\u5f80\u6b63\u53d1\u751f\u5728\u8fd9\u4e24\u79cd\u771f\u7406\u76f8\u9047\u4e4b\u5904\u3002<\/p>\n<h3>\u4e3b\u8981\u8d44\u6599\u4e0e\u8fdb\u4e00\u6b65\u8046\u542c<\/h3>\n<ul>\n<li><a href=\"https:\/\/www.nature.com\/articles\/s41583-022-00578-5\" target=\"_blank\" rel=\"noopener\">Vuust \u7b49\uff1a\u300aMusic in the Brain\u300b<\/a><\/li>\n<li><a href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC6386687\/\" target=\"_blank\" rel=\"noopener\">\u97f3\u4e50\u5956\u8d4f\u9884\u6d4b\u8bef\u5dee\u4e0e\u5b66\u4e60\u7814\u7a76<\/a><\/li>\n<li><a href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC2758676\/\" target=\"_blank\" rel=\"noopener\">\u97f3\u4e50\u8bf1\u53d1\u81ea\u4f20\u8bb0\u5fc6\u7684\u795e\u7ecf\u7ed3\u6784\u7814\u7a76<\/a><\/li>\n<li><a href=\"https:\/\/www.cambridge.org\/core\/books\/abs\/bach-the-goldberg-variations\/movements\/3940510C02AE2E5C2A881641C9C254EE\" target=\"_blank\" rel=\"noopener\">Williams\uff1a\u5bf9\u300a\u54e5\u5fb7\u5821\u53d8\u594f\u66f2\u300b\u548f\u53f9\u8c03\u4e0e\u5404\u4e50\u7ae0\u7684\u7814\u7a76<\/a><\/li>\n<li><a href=\"https:\/\/imslp.org\/wiki\/Goldberg-Variationen%2C_BWV_988_%28Bach%2C_Johann_Sebastian%29\" target=\"_blank\" rel=\"noopener\">\u5df4\u8d6b\u300a\u54e5\u5fb7\u5821\u53d8\u594f\u66f2\u300b\u4e50\u8c31\u4e0e\u5f55\u97f3\u8d44\u6599<\/a><\/li>\n<\/ul>\n<p><strong>\u7ee7\u7eed\u9605\u8bfb\uff1a<\/strong><a href=\"https:\/\/geoffreychen.com\/zh\/category\/piano\/hearing-mathematics\/\">\u6d4f\u89c8\u300a\u542c\u89c1\u6570\u5b66\u300b\u7cfb\u5217\u6587\u7ae0<\/a><\/p>\n<p>\u5982\u679c\u4f60\u4e5f\u60f3\u628a\u8fd9\u4e9b\u5173\u4e8e\u8046\u542c\u3001\u7406\u89e3\u4e0e\u7ec3\u4e60\u7684\u60f3\u6cd5\u5e26\u5230\u7434\u952e\u4e0a\uff0c\u53ef\u4ee5\u8bd5\u8bd5\u6211\u5f00\u53d1\u7684 <a href=\"https:\/\/apps.apple.com\/us\/app\/scoreflow\/id6796205656\" rel=\"noopener\" target=\"_blank\">ScoreFlow<\/a>\uff0c\u8ba9\u4e50\u8c31\u9605\u8bfb\u4e0e\u65e5\u5e38\u7ec3\u4e60\u8854\u63a5\u5f97\u66f4\u81ea\u7136\u3002<\/p>\n<p>","protected":false},"excerpt":{"rendered":"","protected":false},"author":17897162,"featured_media":0,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":true,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_geoff_meta_description_en":"Examines whether math can explain why music moves us, arguing it can model structure and expectation but not the personal meaning of feeling.","_geoff_meta_description_zh":"\u63a2\u8ba8\u6570\u5b66\u80fd\u5426\u89e3\u91ca\u97f3\u4e50\u4e3a\u4f55\u8ba9\u4eba\u611f\u52a8\uff0c\u8ba4\u4e3a\u5b83\u80fd\u523b\u753b\u7ed3\u6784\u4e0e\u9884\u671f\uff0c\u4f46\u65e0\u6cd5\u5355\u72ec\u7ed9\u51fa\u4e2a\u4eba\u5c42\u9762\u7684\u610f\u4e49\u4e0e\u60c5\u611f\u4f53\u9a8c\u3002","_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[787296608],"tags":[787296647,787294457,787296626,787296646,787296649,787294464,787296620,787296614],"class_list":["post-16912","post","type-post","status-publish","format-standard","hentry","category-hearing-mathematics","tag-music-and-emotion-zh","tag-787294457","tag-hearing-mathematics","tag-how-sound-enters-the-body-and-mind","tag-music-and-emotion","tag-predictive-processing","tag-hearing-mathematics-zh","tag-how-sound-enters-the-body-and-mind-zh",""],"translatepress_titles":{"en_AU":"Can Mathematics Explain Why Music Moves Us?","zh_CN":"\u6570\u5b66\u80fd\u89e3\u91ca\u97f3\u4e50\u4e3a\u4ec0\u4e48\u6253\u52a8\u4eba\u5417\uff1f"},"jetpack_publicize_connections":[],"jetpack_likes_enabled":false,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p1ar9H-4oM","jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/posts\/16912","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/users\/17897162"}],"replies":[{"embeddable":true,"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/comments?post=16912"}],"version-history":[{"count":2,"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/posts\/16912\/revisions"}],"predecessor-version":[{"id":17177,"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/posts\/16912\/revisions\/17177"}],"wp:attachment":[{"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/media?parent=16912"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/categories?post=16912"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/geoffreychen.com\/zh\/wp-json\/wp\/v2\/tags?post=16912"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}