{"id":40632,"date":"2023-02-12T20:29:12","date_gmt":"2023-02-12T12:29:12","guid":{"rendered":"https:\/\/swarma.org\/?p=40632"},"modified":"2023-02-12T20:29:12","modified_gmt":"2023-02-12T12:29:12","slug":"%e7%9b%b8%e7%94%b1%e6%96%b0%e5%a3%b0-%e4%bb%8e%e7%bb%9f%e8%ae%a1%e5%8a%9b%e5%ad%a6%e8%a7%92%e5%ba%a6%e7%9c%8b%e9%9f%b3%e5%be%8b%e5%8f%91%e5%b1%95","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=40632","title":{"rendered":"\u76f8\u7531\u201c\u65b0\u58f0\u201d\u2014\u2014\u4ece\u7edf\u8ba1\u529b\u5b66\u89d2\u5ea6\u770b\u97f3\u5f8b\u53d1\u5c55"},"content":{"rendered":"
\n
\n
\n
\n

<\/p>\n<\/section>\n

\n
\n
\n
\n
\n
\n

<\/section>\n<\/section>\n
\n
\n

\u5bfc\u8bed<\/strong><\/p>\n<\/section>\n<\/section>\n

\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
\n
\n

\u4e3a\u4ec0\u4e48\u97f3\u4e50\u521b\u4f5c\u9700\u8981\u57fa\u4e8e\u4e00\u7cfb\u5217\u89c4\u5219\uff1f\u4e3a\u4ec0\u4e48\u4ee5\u8fd9\u4e9b\u65b9\u5f0f\u521b\u4f5c\u5c31\u5bb9\u6613\u5f97\u5230\u60a6\u8033\u7684\u97f3\u4e50\uff1f\u7269\u7406\u5b66\u5bb6\u7ed9\u51fa\u7684\u7b54\u6848\u662f\u2014\u2014\u76f8\u53d8\u2014\u2014\u58f0\u97f3\u4ece\u5608\u6742\u5230\u548c\u8c10\u7684\u8fc7\u7a0b\uff0c\u4e0e\u5206\u5b50\u4ece\u65e0\u5e8f\u5230\u6709\u5e8f\u7684\u8fc7\u7a0b\u60ca\u4eba\u5730\u76f8\u4f3c\u3002\u672c\u6587\u4ecb\u7ecd\u4e86\u4e00\u9879\u7ecf\u5178\u7814\u7a76\uff0c\u7528\u7edf\u8ba1\u529b\u5b66\u6846\u67b6\u6765\u89e3\u91ca\u4e3a\u97f3\u5f8b\u662f\u600e\u6837\u4ece\u65e0\u5e8f\u97f3\u7b26\u4e2d\u6d8c\u73b0\u7684\u3002\u539f\u6765\u97f3\u5f8b<\/span><\/strong>\u7684\u80cc\u540e\u6709\u6df1\u523b\u7684\u7269\u7406\u4e0e\u6570\u5b66\u7ea6\u675f\uff0c\u800c\u4e0d\u53ea\u662f\u4eba\u7c7b\u968f\u610f\u7684\u53d1\u660e\u3002<\/span><\/strong><\/p>\n


<\/span><\/strong><\/p>\n

\u96c6\u667a\u4ff1\u4e50\u90e8\u4e3b\u529e\u7684\u201c\u590d\u6742\u79d1\u5b66\u4e0e\u827a\u672f\u201d\u7814\u8ba8\u4f1a<\/a>\uff0c\u6b63\u5728\u6301\u7eed\u8fdb\u884c\u4e2d\uff0c\u6c47\u805a\u5404\u9886\u57df\u5185\u7684\u884c\u52a8\u8005\u4e0e\u601d\u60f3\u8005\u2014\u2014\u5305\u62ec\u79d1\u5b66\u5bb6\u3001\u827a\u672f\u5bb6\u3001\u5b66\u8005\u53ca\u76f8\u5173\u4ece\u4e1a\u8005\uff0c\u5c55\u5f00\u8de8\u5b66\u79d1\u7814\u8ba8\uff0c\u5e76\u5408\u4f5c\u4ea7\u51fa\u3002\u7814\u8ba8\u4f1a\u6bcf\u6708\u4e00\u671f\uff0c\u6301\u7eed\u81f32023\u5e746\u6708\uff08\u5ef6\u957f\u81f37\u6708\uff09\u3002\u5728\u7814\u8ba8\u4f1a\u7b2c\u4e09\u671f\u201c\u97f3\u4e50\u590d\u6742\u6027\u3001\u8303\u7574\u8bba\u4e0e\u58f0\u97f3\u827a\u672f\u201d<\/a>\u4e2d\uff0c\u5bf9\u672c\u6587\u6240\u6d89\u7814\u7a76\u505a\u4e86\u5177\u4f53\u4ecb\u7ecd\u3002\u52a0\u5165\u7814\u8ba8\u4f1a\u5373\u53ef\u67e5\u770b\u56de\u653e\u89c6\u9891\u5e76\u5165\u7fa4\u4ea4\u6d41\u3002<\/span><\/strong><\/p>\n<\/section>\n

\n


<\/p>\n<\/section>\n

\n

\u5173\u952e\u8bcd\uff1a\u7edf\u8ba1\u529b\u5b66\u3001\u5341\u4e8c\u5e73\u5747\u5f8b\u3001\u534f\u548c\u97f3\u3001\u5e73\u5747\u573a\u8fd1\u4f3c\u3001\u76f8\u53d8\u3001\u6d8c\u73b0<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\n
\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
<\/section>\n<\/section>\n
\n

\u7f57\u5929\u9e9f<\/span> <\/span>| \u4f5c\u8005<\/strong><\/span><\/span><\/p>\n

\u4e01\u4e9a\u98de\u3001Xiangying Shen<\/span> <\/span>| \u5ba1\u6821<\/strong><\/span><\/strong><\/span><\/p>\n

\u9093\u4e00\u96ea<\/span> <\/span>| <\/strong><\/span>\u7f16\u8f91<\/strong><\/p>\n


<\/strong><\/p>\n


<\/p>\n<\/section>\n

<\/qqmusic><\/section>\n

<\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

0. \u5e8f<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

<\/section>\n
\u65e9\u5e74\u95f4\uff0c\u6bd5\u8fbe\u54e5\u62c9\u65af\u53d1\u73b0\uff0c\u62e8\u52a8\u7434\u5f26\u6240\u53d1\u51fa\u7684\u58f0\u97f3\u4e0e\u7434\u5f26\u7684\u957f\u5ea6\u6709\u5173\uff0c\u97f3\u9ad8\u4e0e\u5f26\u957f\u6210\u53cd\u3002\u800c\u8fd9\u91cc\u7684\u97f3\u9ad8\uff0c\u6307\u7684\u5c31\u662f\u58f0\u97f3\u7684\u9891\u7387\u3002\u540c\u65f6\uff0c\u4eba\u4eec\u8fd8\u53d1\u73b0\u5f53\u9891\u7387\u4e4b\u6bd4\u4e3a<\/span>1:2<\/span>\u7684\u4e24\u4e2a\u58f0\u97f3\u540c\u65f6\u53d1\u51fa\u7684\u65f6\u5019\uff0c\u8fd9\u4e24\u4e2a\u97f3\u542c\u8d77\u6765\u662f\u201c\u534f\u548c<\/span>\uff08<\/span>Consonant<\/span>\uff09<\/span><\/span>\u201d\u7684\u3002\u4eba\u4eec\u6839\u636e\u8fd9\u4e24\u4e2a\u7279\u70b9\uff0c\u6309\u7167\u97f3\u4e50\u6f14\u594f\u9700\u8981\uff0c\u7814\u7a76\u51fa\u4e86\u591a\u79cd\u201c\u5f8b\u6cd5\u201d\u6765\u6807\u6ce8\u4e0e\u8bb0\u5f55\u52a8\u542c\u7684\u97f3\u4e50\uff0c\u8fd9\u4e9b\u5f8b\u6cd5\u5c31\u88ab\u79f0\u4e3a\u201c\u97f3\u5f8b\u201d\u3002\u97f3\u5f8b\u5b9e\u9645\u4e0a\u5c31\u662f\u5728\u9891\u7387\u4e3a<\/span>1:2<\/span>\u7684\u4e24\u4e2a\u97f3\u4e4b\u95f4\u7ee7\u7eed\u7ec6\u5206\uff0c\u4ee5\u8fbe\u5230\u7528\u8fd9\u4e9b\u97f3\u5c31\u53ef\u4ee5\u8bb0\u5f55\u5c3d\u53ef\u80fd\u591a\u97f3\u4e50\u7684\u76ee\u7684\u3002<\/span><\/section>\n

\u867d\u7136\u4e2d\u897f\u65b9\u97f3\u4e50\u79cd\u7c7b\u7e41\u591a\u3001\u5404\u5177\u7279\u8272\uff0c\u4f46\u4e2d\u897f\u65b9\u97f3\u5f8b\u53d1\u5c55\u7684\u5386\u7a0b\u4e0e\u7ed3\u679c\u5374\u60ca\u4eba<\/span>\u5730\u76f8\u4f3c\u3002\u5c3d\u7ba1\u6587\u5316\u4ea4\u6d41\u5728\u5176\u4e2d\u53d1\u6325\u4e86\u5f88\u5927\u4f5c\u7528\uff0c\u4f46\u8fd9\u4f3c\u4e4e\u5e76\u4e0d\u662f\u4e2d\u897f\u65b9\u97f3\u5f8b\u76f8\u4f3c\u7684\u5168\u90e8\u539f\u56e0\u3002\u5728<\/span>2019<\/span>\u5e74\u4e00\u7bc7\u9898\u4e3a\u300a<\/span>The structure of musical harmony as an ordered phase of sound: A statistical mechanics approach to music theory<\/span>\u300b\u7684\u6587\u7ae0\u4e2d\uff0c\u4f5c\u8005<\/span>Jesse Berezovsky<\/span>\uff0c\u51dd\u805a\u6001\u7269\u7406\u5b66\u5bb6\uff0c\u4ea6\u662f\u4e00\u540d\u4e2d\u63d0\u7434\u624b\uff0c\u4ed6\u8ba4\u4e3a\u97f3\u5f8b\u7684\u6700\u7ec8\u5f62\u6210\u4f3c\u4e4e\u5177\u6709\u4e00\u5b9a\u7684\u7269\u7406\u610f\u4e49\uff0c\u4e5f\u8bb8\u4e0e\u67d0\u79cd\u76f8\u53d8\u6709\u5173\u3002<\/span><\/span><\/p>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

1. \u4e50\u7406\u57fa\u7840 \u97f3\u5f8b\u53d1\u5c55<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

<\/section>\n

\u4e3a\u4e86\u80fd\u591f\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u7bc7\u6587\u7ae0\uff0c\u6211\u4eec\u9700\u8981\u82b1\u4e00\u4e9b\u7bc7\u5e45\u6765\u7b80\u5355\u4ecb\u7ecd\u4e00\u4e9b\u4e50\u7406\u77e5\u8bc6\u4ee5\u53ca\u97f3\u5f8b\u53d1\u5c55\u7684\u5386\u7a0b\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u58f0\u97f3\u7684\u7ec4\u6210<\/span><\/strong><\/span><\/p>\n


<\/span><\/strong><\/span><\/p>\n

\u58f0\u97f3\u7684\u4ea7\u751f\u6e90\u81ea\u4e8e\u7269\u4f53\u7684\u632f\u52a8\u3002\u5f53\u6f14\u594f\u4e50\u5668\u3001\u62cd\u6253\u4e00\u6247\u95e8\u6216\u8005\u6572\u51fb\u684c\u9762\u65f6\uff0c\u4ed6\u4eec\u7684\u632f\u52a8\u4f1a\u5f15\u8d77\u4ecb\u8d28<\/span>\u2014\u2014<\/span>\u7a7a\u6c14\u5206\u5b50\u6709\u8282\u594f\u7684\u632f\u52a8\uff0c\u4f7f\u5468\u56f4\u7684\u7a7a\u6c14\u4ea7\u751f\u758f\u5bc6\u53d8\u5316\uff0c\u5f62\u6210\u758f\u5bc6\u76f8\u95f4\u7684\u7eb5\u6ce2\uff0c\u8fd9\u5c31\u4ea7\u751f\u4e86\u58f0\u6ce2\uff0c\u8fd9\u79cd\u73b0\u8c61\u4f1a\u4e00\u76f4\u5ef6\u7eed\u5230\u632f\u52a8\u6d88\u5931\u4e3a\u6b62\u3002<\/span><\/span><\/h2>\n

<\/span><\/section>\n

\u7eaf\u97f3 (Pure tone) \u4e0e\u590d\u97f3 (Complex tone)<\/span><\/strong><\/span><\/p>\n


<\/span><\/strong><\/span><\/p>\n

\u7eaf\u97f3<\/span> (Pure tone) <\/span>\u5c31\u662f\u6700\u57fa\u672c\u7684\u58f0\u6ce2\uff0c\u5373\u6807\u51c6\u7684\u6b63\u5f26\u6ce2<\/span> (\u56fe1-1)<\/span>\uff0c\u4f46\u662f\u53ef\u4ee5\u88ab\u4eba\u8033\u542c\u5230\u7684\u7eaf\u97f3\u5728\u81ea\u7136\u754c\u4e2d\u51e0\u4e4e\u4e0d\u5b58\u5728\uff0c\u81ea\u7136\u754c\u7684\u58f0\u6ce2\u53ef\u4ee5\u88ab\u5206\u89e3\u6210\u9891\u57df\u7a7a\u95f4\u4e2d\u5404\u79cd\u9891\u7387\u7684\u6b63\u5f26\u4fe1\u53f7\u7684\u7ebf\u6027\u53e0\u52a0\u3002\u6211\u4eec\u542c\u5230\u7684\u51e0\u4e4e\u6240\u6709\u58f0\u97f3\u90fd\u662f\u4e00\u5927\u7fa4\u6b63\u5f26\u4fe1\u53f7\u7684\u7ec4\u5408<\/span> (\u56fe1-2)<\/span>\uff0c\u5373\u590d\u97f3<\/span> (Complex tone)<\/span>\u3002\u590d\u97f3\u4e2d\u632f\u5e45\u6700\u5927\u7684\u90a3\u4e2a\u6ce2\u7684\u9891\u7387\u88ab\u79f0\u4e3a\u8fd9\u4e2a\u97f3\u7684\u201c\u57fa\u9891\u201d\u3002<\/span><\/p>\n


<\/span><\/p>\n

<\/p>\n

 <\/span><\/em>\u56fe1-1.<\/span> \u7eaf\u97f3\u65f6\u57df\u6ce2\u5f62\u56fe<\/span><\/span><\/p>\n


<\/span><\/em><\/span><\/p>\n

<\/p>\n

 \u56fe1-2.\u590d\u97f3\u65f6\u57df\u6ce2\u5f62\u56fe<\/span><\/p>\n


<\/p>\n

\u6cdb\u97f3(harmonics)<\/span><\/strong><\/span><\/p>\n


<\/p>\n

\u53e4\u5e0c\u814a\u4eba\u53d1\u73b0\u4e86\u4e00\u4e2a\u6709\u8da3\u7684\u73b0\u8c61\uff0c\u62e8\u5f04\u4e00\u4e0b\u7434\u5f26\uff0c\u8fd9\u6839\u7434\u5f26\u9664\u4e86\u53d1\u51fa\u4e00\u4e2a\u54cd\u4eae\u7684\u97f3\u8c03\u5916\uff0c\u8fd8\u4f1a\u53d1\u51fa\u4e00\u4e2a\u6bd4\u8fd9\u4e2a\u97f3\u8c03\u9ad8\u516b\u5ea6\u4e14\u632f\u5e45\u66f4\u5c0f\u7684\u534f\u548c\u97f3\u3002\u5728\u97f3\u4e50\u7406\u8bba\u4e2d\uff0c\u82e5\u4e00\u4e2a\u97f3\u7684\u57fa\u9891\u4e3aF\uff0c\u5219\u5b83\u5230\u5b83\u9891\u7387\u4e24\u500d<\/span>\uff082F\uff09<\/span>\u7684\u8fd9\u4e2a\u8303\u56f4\u5c31\u79f0\u4e3a\u201c\u516b\u5ea6\u201d\u3002\u201c\u9ad8\u516b\u5ea6\u201d\u7684\u610f\u601d\u4fbf\u662f\u57fa\u9891\u9891\u7387\u4e3a\u539f\u6765\u7684\u4e24\u500d\u3002\u6362\u53e5\u8bdd\u8bb2\uff0c\u4ed6\u4eec\u5728\u516b\u5ea6\u97f3\u7a0b\u7684\u8f83\u4f4e\u97f3\u8c03\u4e2d\u53d1\u73b0\u4e86\u8f83\u9ad8\u97f3\u8c03\u3002\u800c\u6cdb\u97f3\u7684\u82f1\u6587\u4e3a\u4ec0\u4e48\u4f1a\u662f\u201cHarmonics\u201d\uff0c\u8fd9\u662f\u56e0\u4e3a\u7434\u5f26\u632f\u52a8\u4ea7\u751f\u7684\u58f0\u97f3\u5c31\u662f\u65e0\u6570\u7b80\u8c10\u6ce2\u7684\u53e0\u52a0\uff0c\u6700\u7ec8\u5f62\u6210\u952f\u9f7f\u72b6\u7684\u97f3\u8272\u3002\u6cdb\u97f3\u4e2d\u7684\u57fa\u9891\u5c31\u662f\u9891\u7387\u6700\u4f4e\u7684\u90a3\u4e2a\u97f3\u7684\u9891\u7387\uff0c\u6cdb\u97f3\u4e5f\u662f\u4e00\u79cd\u7279\u6b8a\u7684\u590d\u97f3\u3002<\/span><\/p>\n


<\/span><\/p>\n

<\/span><\/p>\n

\u56fe1-3. \u62e8\u52a8\u7434\u5f26\u4ea7\u751f\u7684\u201c\u952f\u9f7f\u201d\u97f3\u8272<\/span><\/p>\n


<\/span><\/em><\/span><\/p>\n

\u58f0\u4e0e\u4eba<\/span><\/strong><\/span><\/p>\n


<\/span><\/strong><\/span><\/p>\n

\u632f\u52a8\u5177\u6709\u4e09\u4e2a\u5f88\u5173\u952e\u7684\u7279\u6027\uff1a\u9891\u7387\u3001\u632f\u5e45\u4ee5\u53ca\u76f8\u4f4d\u3002\u4e00\u4e2a\u58f0\u97f3\u7684\u9891\u7387<\/span>\uff08\u4e5f\u5c31\u662f\u524d\u6587\u6240\u8bf4\u7684\u57fa\u9891\uff09<\/span>\u51b3\u5b9a\u4e86\u8fd9\u4e2a\u58f0\u97f3\u6709\u591a\u201c\u9ad8\u201d\u3002\u58f0\u6ce2\u7684\u632f\u5e45\u51b3\u5b9a\u4e86\u8fd9\u4e2a\u58f0\u97f3\u6709\u591a\u201c\u54cd\u201d\u3002\u76f8\u4f4d\u5219\u4ee3\u8868\u4e86\u58f0\u97f3\u5f00\u59cb\u53d1\u51fa\u7684\u4f4d\u7f6e\u3002\u97f3\u5f8b\u662f\u4e3a\u8bb0\u5f55\u97f3\u7684\u201c\u4f4d\u7f6e\u201d\u800c\u5b58\u5728\u7684\u5f8b\u5b66\uff0c\u6240\u4ee5\u97f3\u5f8b\u7814\u7a76\u7684\u91cd\u70b9\u5c31\u662f\u58f0\u6ce2\u7684\u9891\u7387\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u4eba\u8033\u80fd\u542c\u5230\u7684\u58f0\u6ce2\u9891\u7387\u8303\u56f4\u662f20\u8d6b\u5179\u523020000\u8d6b\u5179<\/span>\uff08\u6bcf\u79d2\u632f\u52a820000\u6b21\uff09<\/span>\u3002\u58f0\u6ce2\u7684\u9891\u7387\u8d8a\u5927<\/span>\uff08\u6bcf\u79d2\u632f\u52a8\u7684\u6b21\u6570\u8d8a\u591a\uff09<\/span>\uff0c\u542c\u8d77\u6765\u5c31\u8d8a\u201c\u9ad8\u201d\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u4f46\u662f\uff0c\u6211\u4eec\u5bf9\u97f3\u9ad8\u7684\u7ebf\u6027\u53d8\u5316\u5e76\u6ca1\u6709\u90a3\u4e48\u654f\u611f\uff0c\u800c\u5bf9\u97f3\u9ad8\u7684\u6307\u6570\u53d8\u5316\u66f4\u654f\u611f\u3002\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u6709\u5982\u4e0b\u4e24\u4e2a\u7cfb\u5217\u7684\u58f0\u97f3\uff1a<\/span><\/p>\n


<\/span><\/p>\n

\u7cfb\u52171\uff1a<\/span><\/strong><\/span><\/p>\n

200Hz\u3001400Hz\u3001600Hz\u3001800Hz\u30011000Hz\u30011200Hz\u30011400Hz\u30011600Hz<\/span><\/strong><\/span><\/p>\n

\u7cfb\u52172\uff1a<\/span><\/strong><\/span><\/p>\n

200Hz\u3001400Hz\u3001800Hz\u30011600Hz<\/span><\/strong><\/span><\/p>\n

\uff08\u6bcf\u4e2a\u5355\u97f3\u6301\u7eed\u65f6\u95f4\u4e3a3s\uff0c\u540c\u65f6\u7531\u4e8e\u5355\u97f3\u7684\u58f0\u97f3\u8f83\u4e3a\u523a\u8033\uff0c\u8bf7\u8bfb\u8005\u964d\u4f4e\u97f3\u91cf\u3002\uff09<\/span><\/p>\n


<\/section>\n
\n
<\/div>\n<\/section>\n
\n
<\/div>\n<\/section>\n
\uff08\u6bcf\u4e2a\u5355\u97f3\u6301\u7eed\u65f6\u95f4\u4e3a3s\uff0c\u540c\u65f6\u7531\u4e8e\u5355\u97f3\u7684\u58f0\u97f3\u8f83\u4e3a\u523a\u8033\uff0c\u8bf7\u8bfb\u8005\u964d\u4f4e\u97f3\u91cf\u3002\uff09<\/span><\/section>\n

<\/section>\n
\u5bf9\u4e8e\u4eba\u8033\u6765\u8bf4\uff0c\u53ea\u6709\u7cfb\u52172\u7684\u58f0\u97f3\u542c\u8d77\u6765\u50cf\u662f\u5177\u6709\u76f8\u7b49\u8ddd\u79bb\u7684\uff0c\u542c\u8d77\u6765\u50cf\u662f\u4e00\u7ec4\u201c\u7b49\u5dee\u201d\u97f3\u9ad8\u3002\u53ef\u662f\u5b9e\u9645\u4e0a\u7cfb\u52172\u7684\u58f0\u97f3\u662f\u4e00\u7ec4\u7b49\u6bd4\u97f3\u9ad8\u3002<\/span><\/section>\n

<\/span><\/section>\n

\u534f\u548c\uff08Consonant\uff09\u4e0e\u4e0d\u534f\u548c\uff08Dissonant\uff09<\/span><\/strong><\/span><\/h2>\n

<\/span><\/strong><\/span><\/section>\n
\u534f\u548c<\/span>\uff08Consonant\uff09<\/span>\u7528\u6765\u5f62\u5bb9\u4eba\u4eec\u542c\u5230\u4e24\u4e2a\u97f3\u65f6\u7684\u611f\u53d7\uff0c\u4eba\u4eec\u5c06\u4e24\u4e2a\u97f3\u4e4b\u95f4\u7684\u97f3\u9ad8\u5dee\u79f0\u4f5c\u97f3\u7a0b\u3002\u6240\u6709\u542c\u8d77\u6765\u60a6\u8033\u3001\u878d\u5408\u7684\u97f3\u7a0b\uff0c\u53eb\u534f\u548c\u97f3\u7a0b\uff0c\u4e5f\u8bf4\u8fd9\u4e24\u4e2a\u97f3\u662f\u534f\u548c\u7684\uff1b\u800c\u542c\u8d77\u6765\u6bd4\u8f83\u523a\u8033\uff0c\u5f7c\u6b64\u4e0d\u5f88\u878d\u5408\u7684\u97f3\u7a0b\u53eb\u505a\u4e0d\u534f\u548c<\/span>\uff08Dissonant\uff09<\/span>\u97f3\u7a0b\u3002\u6240\u4ee5\u5927\u5bb6\u53ef\u4ee5\u53d1\u73b0\uff0c\u534f\u548c\u4e0e\u4e0d\u534f\u548c\u90fd\u662f\u63cf\u8ff0\u4eba\u7684\u611f\u53d7\uff0c\u6240\u4ee5\u6700\u65e9\u5f97\u5230\u7684\u54ea\u4e9b\u97f3\u7a0b\u534f\u548c\uff0c\u54ea\u4e9b\u4e0d\u534f\u548c\uff0c\u90fd\u662f\u901a\u8fc7\u8bb0\u5f55\u65e0\u6570\u4eba\u7684\u611f\u89c9\u5f97\u6765\u7684\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u90a3\u4e48\u54ea\u4e9b\u97f3\u7a0b\u662f\u534f\u548c\u7684\u5462\uff0c\u6211\u4eec\u9996\u5148\u6765\u770b\u770b\u4e24\u4e2a\u5355\u97f3\u76f8\u4e92\u4f5c\u7528\u4ea7\u751f\u7684\u7ed3\u679c\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/span><\/section>\n
\u56fe1-3. \u5728\u4e00\u4e2a\u4e34\u754c\u5e26\u5bbd\u5185\u4e24\u4e2a\u97f3\u7684\u4e0d\u534f\u548c\u7a0b\u5ea6<\/span><\/section>\n

<\/section>\n
\u56fe1-3\u8868\u793a\u4e24\u4e2a\u5355\u97f3\u76f8\u4e92\u4f5c\u7528\u7684\u7ed3\u679c\u3002\u7eb5\u5750\u6807\u4e3a\u534f\u548c\u3001\u4e0d\u534f\u548c\u5ea6\u3002\u6a2a\u5750\u6807\u8868\u793a\u4e24\u4e2a\u7eaf\u97f3\u4e4b\u95f4\u7684\u97f3\u7a0b\u4e0e\u8f83\u4f4e\u97f3\u7684\u4e34\u754c\u5e26\u5bbd\u7684\u6bd4\u503c\uff0c\u8fd9\u91cc\u8981\u4ecb\u7ecd\u4e00\u4e2a\u65b0\u6982\u5ff5\uff1a\u4e34\u754c\u5e26\u5bbd <\/span>(Critical Bandwidth) <\/span>\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4e34\u754c\u5e26\u5bbd\uff0c\u8fd9\u4e2a\u6982\u5ff5\u9996\u5148\u88abHarvey Fletcher\u57281933\u5e74\u63d0\u51fa\uff0c\u8fd9\u4e2a\u6982\u5ff5\u6210\u529f\u89e3\u91ca\u4e86\u8033\u8717\u542c\u89c9\u6ee4\u6ce2\u6548\u5e94\u548c\u63a9\u853d\u6548\u5e94\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4eba\u8033\u5177\u6709\u5341\u5206\u590d\u6742\u7684\u7ed3\u6784\uff0c\u4e34\u754c\u9891\u5e26\u6307\u7684\u662f\u7531\u4e8e\u8033\u8717\u6784\u9020\u4ea7\u751f\u7684\u542c\u89c9\u6ee4\u6ce2\u5668\u7684\u9891\u7387\u5e26\u5bbd\u3002\u4eba\u7684\u542c\u89c9\u7cfb\u7edf\u4e2d\uff0c\u8033\u8717\u8d77\u7740\u9891\u8c31\u5206\u6790\u7684\u4f5c\u7528\uff0c\u8033\u8717\u57fa\u5e95\u819c\u4e0a\u7279\u5b9a\u4f4d\u7f6e\u70b9\u5bf9\u67d0\u4e00\u7279\u5f81\u9891\u7387<\/span>\uff08Characteristic Frequency\uff0cCF\uff09<\/span>\u7684\u54cd\u5e94\u6700\u5927\uff0c\u5f53\u58f0\u6ce2\u504f\u79bbCF\u70b9\u65f6\uff0c\u8be5\u70b9\u7684\u54cd\u5e94\u51cf\u5c11\uff0c\u56e0\u6b64\u57fa\u5e95\u819c\u4e0a\u6bcf\u4e00\u70b9\u53ef\u7b49\u6548\u6210\u5177\u6709\u7279\u5b9a\u9891\u7387<\/span>\uff08CF\uff09<\/span>\u7684\u5e26\u901a\u6ee4\u6ce2\u5668\uff0c\u6574\u4e2a\u542c\u89c9\u7cfb\u7edf\u53ef\u7b49\u6548\u6210\u4e00\u7cfb\u5217\u5177\u6709\u8fde\u7eedCF\u7684\u3001\u76f8\u4e92\u4ea4\u53e0\u7684\u5e26\u901a\u6ee4\u6ce2\u5668\uff0c\u79f0\u4e3a\u201c\u542c\u89c9\u6ee4\u6ce2\u5668\u201d\u3002\u4e34\u754c\u9891\u5e26\u5c31\u662f\u542c\u89c9\u7cfb\u7edf\u5e26\u901a\u6ee4\u6ce2\u529f\u80fd\u7684\u53cd\u6620\uff0c\u542c\u89c9\u6ee4\u6ce2\u5668\u7684\u5e26\u5bbd\u5373\u4e3a\u4e34\u754c\u5e26\u5bbd\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u518d\u56de\u5230\u56fe1-3\uff0c\u6211\u4eec\u53ef\u4ee5\u77e5\u9053\u5f53\u4e24\u4e2a\u97f3\u7684\u97f3\u7a0b\u5904\u4e8e\u4e34\u754c\u5e26\u5bbd\u5185\u7684\u67d0\u4e00\u4e2a\u503c\u65f6\u4f1a\u5b58\u5728\u4e00\u4e2a\u6700\u5927\u7684\u4e0d\u534f\u548c\u7684\u70b9\u3002\u7531\u4e8e\u4f4e\u9891\u533a\u4e0e\u9ad8\u9891\u533a\u4e34\u754c\u9891\u5e26\u4e0d\u540c\uff0c\u8fd9\u4e2a\u4f4d\u7f6e\u4e5f\u4e0d\u4f1a\u76f8\u540c\u3002 <\/span><\/section>\n

<\/span><\/section>\n
\u4f46\u662f\u6211\u4eec\u4e5f\u63d0\u5230\uff0c\u7eaf\u97f3\u5728\u81ea\u7136\u754c\u4e0a\u662f\u4e0d\u5b58\u5728\u7684\u3002\u4e00\u822c\u90fd\u662f\u590d\u97f3\uff0c\u90a3\u4e48\u590d\u97f3\u4e4b\u95f4\u7684\u534f\u548c\u5173\u7cfb\u53c8\u662f\u600e\u6837\u5462\uff0c\u65e9\u671f\u5b66\u8005\u4eec\u5c06\u56fe1\u4e2d\u7684\u7ebf\u6761\u65b9\u7a0b\u5199\u51fa\u6765<\/span>\uff08\u56fe1\u7684\u7ed3\u679c\u662f\u65e0\u6570\u5b9e\u9a8c\u62df\u5408\u51fa\u6765\u7684\uff09<\/span>\u518d\u5c06\u4efb\u610f\u4e24\u4e2a\u590d\u97f3\u505a\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u8ba1\u7b97\u4e24\u4e2a\u97f3\u76f8\u540c\u6b21\u5e8f\u9879\u4e4b\u95f4\u7684\u534f\u548c\u5ea6\uff0c\u6700\u540e\u52a0\u8d77\u6765\u5c31\u5f97\u5230\u4e86\u56fe2\u7684\u7ed3\u679c\u3002\u5e76\u4e14\u8fd9\u4e2a\u7ed3\u679c\u4e5f\u7ecf\u8fc7\u4e86\u5927\u91cf\u7684\u4eba\u8033\u68c0\u9a8c\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/span><\/section>\n
\u56fe1-4. \u4e00\u4e2a\u516b\u5ea6\u5185\u7684\u534f\u548c\u97f3\u7a0b\u5173\u7cfb(\u91c7\u7528\u952f\u9f7f\u97f3\u8272\u8fdb\u884c\u8ba1\u7b97\u5f97\u51fa\u7684\u7ed3\u679c)<\/span><\/section>\n

<\/span><\/section>\n
\u56fe1-4\u4e2d\u63cf\u8ff0\u4e86\u4e00\u4e2a\u516b\u5ea6\u5185\u4e24\u4e2a\u590d\u97f3\u7684\u534f\u548c\u97f3\u7a0b\u5173\u7cfb\uff0c\u8fd9\u4e24\u4e2a\u590d\u97f3\u90fd\u662f\u524d\u6587\u6240\u63d0\u7684\u5177\u67096\u4e2a\u8c10\u6ce2\u53e0\u52a0\u7684\u6cdb\u97f3\u3002\u5176\u4e2d\u4e00\u4e2a\u7684\u57fa\u9891\u4e3a250Hz\uff0c\u5b83\u4e0e\u4efb\u610f\u4e00\u4e2a\u9891\u7387\u5728250Hz\u5230500Hz\u5185\u7684\u97f3\u7684\u534f\u548c\u5173\u7cfb\u5982\u56fe2\u6240\u793a\u3002\u7eb5\u5750\u6807\u8868\u793a\u4e0d\u534f\u548c\u5ea6\uff0c\u6a2a\u5750\u6807\u8868\u793a\u53e6\u4e00\u4e2a\u97f3\u7684\u57fa\u9891\uff0c\u8fd9\u91cc\u7684\u5355\u4f4dcps<\/span> (Cycle per second) <\/span>\u4e0e\u8d6b\u5179\u610f\u4e49\u76f8\u540c\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4ece\u56fe\u4e2d\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u5728\u4e00\u4e2a\u516b\u5ea6\u5185\u534f\u548c\u5ea6\u6700\u9ad8\u7684\u5c31\u662f\u6211\u4eec\u6700\u5f00\u59cb\u63d0\u5230\u76841:1\u4e0e1:2\u7684\u6bd4\u4f8b\u5173\u7cfb\uff0c\u4e5f\u5c31\u662f\u4e24\u4e2a250Hz\u7684\u97f3\uff0c\u6216\u8005\u4e00\u4e2a250Hz\u548c\u4e00\u4e2a500Hz\u7684\u97f3\u3002\u534f\u548c\u5ea6\u6392\u7b2c\u4e8c\u7684\u662f\u5f53\u4e24\u4e2a\u97f3\u9891\u7387\u4e4b\u6bd4\u4e3a2:3\u7684\u65f6\u5019\uff0c\u4e5f\u5c31\u662f250Hz\u4e0e375Hz\uff0c\u8fd9\u4e2a\u6bd4\u4f8b\u4e5f\u5f88\u91cd\u8981\uff0c\u4e0e\u540e\u6587\u8981\u63d0\u5230\u7684\u4e94\u5ea6\u76f8\u751f\u5f8b\u6709\u91cd\u8981\u5173\u7cfb\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u867d\u7136\u8fd9\u4e9b\u4e25\u8c28\u6570\u5b66\u8ba1\u7b97\u5f97\u51fa\u7684\u7ed3\u679c\u572819\u4e16\u7eaa\u624d\u51fa\u73b0\uff0c\u4f46\u5176\u5b9e\u5728\u5f88\u65e9\u7684\u65f6\u5019\uff0c\u4eba\u4eec\u5c31\u53d1\u73b0\u4e86\u4e24\u4e2a\u97f3\u9891\u7387\u4e4b\u6bd4\u4e3a2:3\u7684\u65f6\u5019\uff0c\u8fd9\u6837\u7684\u97f3\u7ec4\u5341\u5206\u534f\u548c\uff0c\u6839\u636e\u8fd9\u6837\u7684\u539f\u5219\uff0c\u4eba\u4eec\u5f00\u59cb\u5236\u5b9a\u97f3\u5f8b\u3002<\/span><\/section>\n

<\/span><\/section>\n

\u4ece\u4e94\u5ea6\u76f8\u751f\u5f8b\u5230\u5341\u4e8c\u5e73\u5747\u5f8b<\/span><\/strong><\/span><\/h2>\n

<\/span><\/strong><\/span><\/section>\n
\u65e9\u5e74\u95f4\uff0c\u4e0d\u4ec5\u6bd5\u8fbe\u54e5\u62c9\u65af\u53d1\u73b0\u4e862:3\u662f\u4e00\u4e2a\u5341\u5206\u534f\u548c\u7684\u9891\u7387\u4e4b\u6bd4\uff0c\u6211\u56fd\u5148\u79e6\u65f6\u671f\u7684\u300a\u7ba1\u5b50\u00b7\u5730\u5458\u7bc7\u300b\u4e5f\u8bb0\u8f7d\u4e86\u6240\u8c13\u201c\u4e09\u5206\u635f\u76ca\u5f8b\u201d\uff0c\u5177\u4f53\u8bf4\u6765\u662f\u53d6\u4e00\u6bb5\u5f26\uff0c\u201c\u4e09\u5206\u635f\u4e00\u201d\uff0c\u5373\u5747\u5206\u5f26\u4e3a\u4e09\u6bb5\uff0c\u820d\u4e00\u7559\u4e8c\uff0c\u4fbf\u5f97\u5230 3\/2F <\/span>(F\u4e3a\u5f26\u7684\u539f\u9891\u7387)<\/span>\u3002\u5982\u679c\u201c\u4e09\u5206\u76ca\u4e00\u201d\uff0c\u5373\u5f26\u5747\u5206\u4e09\u6bb5\u540e\u518d\u52a0\u4e00\u6bb5\uff0c\u4fbf\u5f97\u5230 4\/3F\u3002\u201c\u4e09\u5206\u635f\u76ca\u7387\u201d\u5c31\u662f\u6700\u65e9\u7684\u97f3\u5f8b\u8bbe\u8ba1\u65b9\u6cd5\u3002\u4f46\u662f\u5982\u679c\u52a0\u4e0a\u4e00\u4e2a4\/3F\u7684\u97f3\uff0c\u90a3\u4e48\u4ed6\u4e0e\u524d\u9762\u51e0\u4e2a\u97f3\u7684\u534f\u548c\u7a0b\u5ea6\u5c31\u8fdc\u8fdc\u4e0d\u8db3\u4e86\u3002<\/span>\uff08\u5176\u5b9e\u5728\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u53e4\u4eba\u6700\u65e9\u53d1\u73b0\u7684\u534f\u548c\u9891\u7387\u6bd4\u662f2:3\u548c3:4\u3002\u4ed6\u4eec\u5e76\u6ca1\u6709\u91c7\u7528\u6bd43:4\u66f4\u534f\u548c\u7684\u6bd4\u4f8b3:5\u3002\uff09<\/span>\u6240\u4ee5\u53e4\u4eba\u4e00\u60f3\uff0c\u4e0d\u5982\u627e3\/2F\u76843\/2\u500d\uff0c\u4e5f\u5c31\u662f9\/4 F\uff0c\u4f46\u662f\u8fd9\u4e2a\u6570\u5df2\u7ecf\u6bd42\u8fd8\u5927\u4e86\uff0c\u5e76\u4e0d\u5728\u6211\u4eec\u8981\u7684\u7b2c\u4e00\u4e2a\u516b\u5ea6\u533a\u95f4[F,2F]\u4e2d\u3002\u6211\u4eec\u5fc5\u987b\u627e\u5230\u8fd9\u4e2a\u516b\u5ea6\u91cc\u76849\/4F\uff0c\u4e5f\u5c31\u662f\u75289\/4F\u9664\u4ee5\u79bb\u4ed6\u6700\u8fd1\u7684\u4e00\u4e2a\u6574\u6570\uff0c\u4e5f\u5c31\u662f2\u3002\u8fd9\u6837\u5b83\u5c31\u53d8\u6210\u4e869\/8F\u3002\u6309\u7167\u8fd9\u6837\u7684\u65b9\u5f0f\uff0c\u53e4\u4eba\u5728\u6ca1\u6709\u8ba1\u7b97\u8ba1\u7b97\u673a\u7684\u60c5\u51b5\u4e0b\u4e00\u76f4\u7b97\u5230\u4e86243\/32 F\u3002\u901a\u8fc7\u5982\u4e0a\u7684\u5bf9\u5e94\u5173\u7cfb\uff0c\u5f62\u6210\u4e86\u6700\u65e9\u97f3\u5f8b\uff0c\u6700\u7ec8\u8fd9\u4e9b\u6bd4\u4f8b\u7684\u9891\u7387\u5c06\u4e00\u4e2a\u516b\u5ea6\u97f3\u7a0b\u5206\u6210\u4e86\u4e03\u4efd<\/span>\uff08\u5982\u88681-1\u6240\u793a\uff09<\/span>\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

\u88681-1\uff1a\u4e94\u5ea6\u76f8\u751f\u5f8b\u6f14\u5316\u51fa\u6765\u7684\u516b\u5ea6\u97f3\u9636(\u6ce8\u610f:\u97f3\u540d\u5176\u5b9e\u662f\u4e0e\u56fa\u5b9a\u97f3\u9ad8\u7684\u58f0\u97f3\u4e00\u4e00\u5bf9\u5e94\u7684\uff0c\u6bd4\u5982C4=261Hz\uff0cA4=440Hz)<\/span><\/p>\n


<\/section>\n
\u53ef\u4ee5\u770b\u5230\u6709\u4e24\u79cd\u6bd4\u4f8b\u51fa\u73b0\uff0c\u4e00\u79cd\u662f1.125\uff0c\u53e6\u4e00\u79cd\u662f1.0535\uff0c\u524d\u4e00\u79cd\u97f3\u7a0b\u53eb\u505a\u5168\u97f3\uff0c\u540e\u4e00\u79cd\u53eb\u505a\u534a\u97f3\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u8fd9\u5957\u7406\u8bba\u662f\u901a\u8fc72:3\u7684\u9891\u7387\u6bd4\u5236\u5b9a\u800c\u6210\u7684\uff0c\u5728\u4e50\u7406\u4e2d\u8fd9\u6837\u97f3\u7a0b\u88ab\u79f0\u4e3a\u201c\u7eaf\u4e94\u5ea6\u201d\uff0c\u6240\u4ee5\u8fd9\u5957\u97f3\u5f8b\u88ab\u79f0\u4e3a\u201c\u4e94\u5ea6\u76f8\u751f\u5f8b\u201d\u3002\u4f46\u662f\u8fd9\u5957\u97f3\u5f8b\u81ea\u8bde\u751f\u4e4b\u8d77\u5c31\u9971\u53d7\u8bdf\u75c5\uff0c\u56e0\u4e3a\u5728\u5f26\u4e50\u4e2d\u5f39\u594f1:5\u548c1:6\u7684\u4f4d\u7f6e\u5c31\u5df2\u7ecf\u5f88\u9ebb\u70e6\u4e86\uff0c\u800c\u4e14\u58f0\u97f3\u5f88\u4e0d\u548c\u8c10\uff0c\u73b0\u5728\u5c45\u7136\u8fd8\u8981\u5f39\u594f81:64\u3001243:128\u8fd9\u6837\u7684\u4f4d\u7f6e\uff01<\/span><\/section>\n

<\/span><\/section>\n
\u5bf9\u201c\u4e94\u5ea6\u76f8\u751f\u5f8b\u201d\u7684\u4fee\u6539\u81ea\u5176\u53d1\u660e\u7684\u7b2c\u4e00\u5929\u8d77\u5c31\u6ca1\u6709\u65ad\u8fc7\uff0c\u7ecf\u8fc7\u5bf9\u6bd4\u4f8b\u7b80\u5355\u7684\u8c03\u6574\u540e\uff0c\u7eaf\u5f8b<\/span> (Just intonation) <\/span>\u8bde\u751f\u4e86\u3002\u4f46\u5176\u5b9e\u201c\u7eaf\u5f8b\u201d\u7684\u4fee\u6b63\u4e5f\u5f88\u7b80\u5355\uff0c\u53ea\u662f\u628a\u4e94\u5ea6\u76f8\u751f\u5f8b\u7684\u590d\u6742\u6bd4\u4f8b\u53d8\u7b80\u5355\u4e00\u70b9\u3002\u5373243\/128\u53d8\u4e3a240\/128\u537315\/8\u300127\/16\u53d8\u4e3a25\/15\u53735\/3\u300181\/64\u53d8\u4e3a80\/64\u53735\/4\u3002\u8fd9\u6837\u505a\u7684\u597d\u5904\u5f88\u5bb9\u6613\u7406\u89e3\uff0c\u5c31\u662f\u4e3a\u4e86\u5bb9\u6613\u6f14\u594f\uff0c\u53ef\u662f\u574f\u5904\u540c\u6837\u4e5f\u663e\u800c\u6613\u89c1\uff0c\u5f15\u5165\u4e86\u66f4\u591a\u4e0d\u591f\u534f\u548c\u7684\u9891\u7387\u4e4b\u6bd4\u3002\u4e8b\u5b9e\u4e0a\u8fd9\u6837\u7684\u6539\u52a8\u662f\u5341\u5206\u5931\u8d25\u7684\uff01<\/span><\/section>\n

<\/span><\/section>\n
\u90a3\u65e2\u7136\u4fee\u201c\u6b63\u201d\u4e0d\u884c\uff0c\u90a3\u5c31\u7ee7\u7eed\u7ec6\u5206\u3002\u968f\u7740\u6570\u5b66\u6c34\u5e73\u7684\u4e0a\u5347\uff0c\u5927\u5bb6\u5c31\u5f00\u59cb\u7ee7\u7eed\u7ec6\u5206\u97f3\u8282\uff0c\u770b\u770b\u80fd\u4e0d\u80fd\u5bf9\u7ec6\u5206\u540e\u7684\u97f3\u8282\u8fdb\u884c\u4fee\u201c\u6b63\u201d\u3002\u4e8e\u662f\u8fd9\u6b21\u7531(3\/2)5<\/sup>\u53d8\u6210\u4e86(3\/2)12<\/sup>=129.7\u224827<\/sup>=128\uff0c\u8fd9\u6b21\u5212\u5206\u5341\u5206\u7ec6\u81f4\uff0c\u5df2\u7ecf\u53bb\u5230\u4e86\u7b2c7\u4e2a\u516b\u5ea6\u3002\u5177\u4f53\u7684\u6bd4\u4f8b\u5982\u88681-2\u6240\u793a\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/span><\/section>\n
\u88681-2. \u6700\u65e9\u768412\u58f0\u97f3\u9636<\/span><\/section>\n

<\/span><\/em><\/span><\/section>\n
\u53ef\u4ee5\u770b\u51fa\u968f\u7740\u8ba1\u7b97\u80fd\u529b\u7684\u4e0a\u5347\uff0c\u8fd9\u4e00\u6b21\u7684\u97f3\u9636\u6570\u66f4\u591a\uff0c\u66f4\u52a0\u7ec6\u5316\uff0c\u540c\u65f6\u6709\u66f4\u591a\u7684\u534a\u97f3\u51fa\u73b0\u3002\u201c#\u201d\u8868\u793a\u201c\u5347\u9ad8\u201d\u7684\u610f\u601d\uff0c\u201cb\u201d\u8868\u793a\u201c\u964d\u201d\u7684\u610f\u601d\uff0c\u6240\u4ee5\u9664\u4e86\u539f\u59cb\u7684CDEFGAB\u4ee5\u5916\u53c8\u591a\u4e865\u4e2a\u534a\u97f3\u51fa\u73b0\uff0c\u8fd9\u4f7f\u5f97\u6574\u4e2a\u97f3\u9636\u66f4\u52a0\u5e73\u6ed1\uff0c\u80fd\u591f\u63cf\u8ff0\u66f4\u591a\u66f4\u590d\u6742\u7684\u66f2\u8c03\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u53ef12\u97f3\u9636\u4e5f\u5b58\u5728\u4e00\u4e2a\u95ee\u9898\uff1a\u5728\u8fd912\u4e2a\u97f3\u9636\u5f53\u4e2d\uff0c\u5b58\u5728\u4e24\u79cd\u534a\u97f3\uff0c\u5b83\u4eec\u5206\u522b\u4e3a\uff1a\u81ea\u7136\u534a\u97f3<\/span> (\u6bd4\u4f8b\u4e3a1.0535)<\/span>\u3001\u53d8\u5316\u534a\u97f3<\/span> (\u6bd4\u4f8b\u4e3a1.0676)<\/span>\u3002\u8fd9\u4f1a\u5bfc\u81f4\u4e00\u4e2a\u95ee\u9898\uff1a\u5047\u5982\u6211\u60f3\u5531\u4e00\u9996\u6b4c\uff0c\u4f46\u662f\u6211\u81ea\u5df1\u7684\u97f3\u57df\u8fbe\u4e0d\u5230\u8fd9\u9996\u6b4c\u539f\u8c03\u7684\u8303\u56f4\uff0c\u6211\u53ea\u80fd\u628a\u8fd9\u9996\u6b4c\u964d\u8c03\u6765\u6f14\u5531\uff0c\u4f46\u662f\u5982\u679c\u6bcf\u4e2a\u97f3\u9636\u4e4b\u95f4\u7684\u6bd4\u4f8b\u4e0d\u4e00\u6837\uff0c\u964d\u4e00\u4e2a\u534a\u97f3\u6216\u8005\u4e00\u4e2a\u5168\u97f3\u7684\u65f6\u5019\u65cb\u5f8b\u5c31\u548c\u4ee5\u524d\u4e0d\u4e00\u6837\u4e86\uff0c\u90a3\u600e\u4e48\u529e\uff1f<\/span><\/section>\n

<\/span><\/section>\n
\u540e\u6765\u4eba\u4eec\u53c8\u60f3\u51fa\u4e86\u5404\u79cd\u4fee\u6b63\u7684\u529e\u6cd5\uff0c\u6bd4\u5982\u6784\u9020\u4e00\u4e9b\u7b49\u5dee\u6570\u5217\u6765\u4fee\u6b63\u6bcf\u4e2a\u97f3\u4e0e\u7406\u60f3\u66f2\u7ebf\u7684\u8bef\u5dee\u7b49\u7b49\uff0c\u4f46\u8fd9\u4e9b\u65b9\u6cd5\u65e2\u590d\u6742\u53c8\u4e0d\u80fd\u4ece\u6839\u672c\u4e0a\u89e3\u51b3\u95ee\u9898\u3002\u8fd9\u65f6\u6574\u4e2a\u97f3\u4e50\u754c\u90fd\u5728\u6025\u8feb\u5730\u7b49\u5f85\u65b0\u5f8b\u5236\u7684\u8bde\u751f\u3002\u76f4\u5230\u516c\u514317\u4e16\u7eaa\uff0c\u660e\u671d\u4eba\u6731\u8f7d\u5809\u63d0\u51fa\u5341\u4e8c\u5e73\u5747\u5f8b\uff0c\u867d\u7136\u53ef\u80fd\u6ca1\u6709\u4f20\u5230\u897f\u65b9\uff0c\u4f46\u4ed6\u8fd9\u5374\u662f\u6700\u65e9\u63d0\u51fa\u5341\u4e8c\u5e73\u5747\u5f8b\u7684\u4eba\u300218\u4e16\u7eaa\u7684\u65f6\u5019\uff0c\u5df4\u8d6b\u4e5f\u521b\u9020\u4e86\u5341\u4e8c\u5e73\u5747\u5f8b\uff0c\u4f46\u662f\u4ed6\u7684\u76ee\u7684\u4e0d\u662f\u4e3a\u4e86\u4fee\u5584\u97f3\u5f8b\uff0c\u53ea\u662f\u4e3a\u4e86\u66f4\u597d\u7684\u6559\u81ea\u5df1\u59bb\u5b50\u97f3\u4e50\u800c\u5df2\u3002\u867d\u7136\u5341\u4e8c\u5e73\u5747\u5f8b\u770b\u8d77\u6765\u5f88\u5b8c\u7f8e\uff0c\u4f46\u4e5f\u4e0d\u662f\u5b8c\u5168\u6ca1\u6709\u95ee\u9898\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5341\u4e8c\u5e73\u5747\u5f8b<\/span>\uff08\u88681-3\uff09<\/span>\u7684\u539f\u7406\u5e76\u4e0d\u590d\u6742\uff0c\u65e2\u7136\u662f\u5e73\u5747\uff0c\u90a3\u5c31\u662f\u6bcf\u4e2a\u97f3\u4e4b\u95f4\u7684\u9891\u7387\u4e4b\u6bd4\u662f\u4e00\u6837\u7684\u3002\u56e0\u4e3a\u4e00\u4e2a\u516b\u5ea6\u4e3a[F,2F]\uff0c\u90a3\u4e48\u5c31\u76f4\u63a5\u628a\u8fd9\u4e2a1:2\u7684\u5173\u7cfb\u5206\u6210\u5341\u4e8c\u4efd\uff0c\u6bcf\u4e00\u4efd\u5c31\u662f(2)1\/12<\/sup>=1.059\uff0c\u8fd9\u6837\u867d\u7136\u635f\u5931\u4e86\u4e00\u90e8\u5206\u5b8c\u7f8e\u7684\u534f\u548c\u9891\u7387\u6bd4\uff0c\u4f46\u662f\u8fd9\u5957\u5f8b\u6cd5\u80fd\u591f\u4e3a\u8bb0\u5f55\u548c\u521b\u4f5c\u4e50\u66f2\u63d0\u4f9b\u4e86\u66f4\u591a\u53ef\u80fd\u3002\u4e50\u5668\u4e4b\u738b\u94a2\u7434\u4e0a\u7684\u6bcf\u4e00\u4e2a\u952e\u5bf9\u5e94\u7684\u9891\u7387\u90fd\u53ef\u4ee5\u901a\u8fc7\u5341\u4e8c\u5e73\u5747\u7387\u63a8\u7b97\u51fa\u6765<\/span>\uff08\u56fe4\uff09<\/span>\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/span><\/section>\n
\u88681-3\uff1a\u5341\u4e8c\u5e73\u5747\u5f8b<\/span><\/section>\n

<\/span><\/em><\/span><\/section>\n
<\/span><\/section>\n
\u56fe1-5 \u94a2\u7434\u97f3\u9ad8\u5bf9\u7167\u8868<\/span><\/section>\n

<\/span><\/section>\n
\u81f3\u6b64\uff0c\u8981\u60f3\u9605\u8bfb\u5b8c\u8fd9\u7bc7\u8bba\u6587\u6240\u9700\u8981\u7684\u4e00\u4e9b\u77e5\u8bc6\u5df2\u7ecf\u5168\u90e8\u8bb2\u5b8c\uff0c\u8bba\u6587\u4e2d\u63d0\u5230\u7684\u5176\u4ed6\u4e50\u7406\u540d\u8bcd\uff0c\u7b14\u8005\u4e5f\u4f1a\u5728\u9610\u8ff0\u8bba\u6587\u5185\u5bb9\u65f6\u52a0\u4ee5\u8865\u5145\u3002<\/span><\/section>\n

<\/section>\n

<\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

2. \u7edf\u8ba1\u7269\u7406\u4e0e\u97f3\u5f8b\u7684\u53d1\u5c55<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

<\/section>\n
\u8fd9\u4e00\u90e8\u5206\u6211\u4eec\u5c06\u91cd\u70b9\u8bb2\u89e3Jesse Berezovsky\u7684\u8fd9\u7bc7\u300aThe structure of musical harmony as an ordered phase of sound: A statistical mechanics approach to music theory\u300b\uff0c\u770b\u770b\u5982\u4f55\u4ece\u7269\u7406\u7684\u89d2\u5ea6\u6765\u89e3\u91ca\u5341\u4e8c\u5e73\u5747\u5f8b\u7684\u51fa\u73b0\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/span><\/section>\n


<\/span><\/strong><\/span><\/h2>\n

\u57fa\u672c\u601d\u8def<\/span><\/strong><\/span><\/h2>\n

<\/span><\/section>\n
\u6839\u636e\u4e0a\u4e00\u7ae0\u7684\u4ecb\u7ecd\uff0c\u4eba\u4eec\u6700\u7ec8\u9009\u62e9\u5341\u4e8c\u5e73\u5747\u5f8b\u7684\u539f\u56e0\u662f\uff0c\u5b83\u5728\u4fdd\u8bc1\u4e86\u4e00\u5b9a\u7684\u534f\u548c\u9891\u7387\u6bd4\u7684\u540c\u65f6\u5177\u6709\u201c\u5e73\u5747\u201d\u7684\u7279\u6027\uff0c\u8f6c\u8c03\u64cd\u4f5c\u5341\u5206\u5bb9\u6613\uff0c\u53ef\u4ee5\u9002\u5e94\u66f4\u591a\u7684\u6f14\u594f\u3002\u5047\u5982\u7528\u7269\u7406\u6216\u8005\u6570\u5b66\u6a21\u578b\u6765\u63cf\u8ff0\u67d0\u4e00\u79cd\u201c\u7cfb\u7edf\u201d\u7684\u6f14\u5316\u8fc7\u7a0b\uff0c\u6700\u7ec8\u8fd9\u79cd\u201c\u7cfb\u7edf\u201d\u4e2d\u51fa\u73b0\u4e86\u4eca\u5929\u7684\u201c\u5341\u4e8c\u5e73\u5747\u5f8b\u201d\u3002\u90a3\u4e48\u51fa\u73b0\u201c\u5341\u4e8c\u5e73\u5747\u5f8b\u201d\u7684\u8fd9\u4e2a\u70b9\u5e94\u8be5\u5177\u6709\u4e24\u4e2a\u7279\u5f81\uff1a\u4e00\u3001\u534f\u548c\u7a0b\u5ea6\u5c3d\u53ef\u80fd\u9ad8<\/span>\uff08Minimizes dissonant sounds.\uff09<\/span>\uff1b\u4e8c\u3001\u5b83\u80fd\u5c3d\u53ef\u80fd\u63cf\u7ed8\u8db3\u591f\u591a\u7684\u201c\u97f3\u4e50\u72b6\u6001\u201d<\/span>\uff08Allows sufficient complexity to allow the desired artistic expression.\uff09<\/span>\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u6240\u4ee5\uff0c\u4f5c\u8005\u60f3\u5230\u5982\u679c\u5c06\u4ee5\u4e0a\u4e24\u4e2a\u7279\u5f81\u4ee5\u7269\u7406\u7684\u65b9\u5f0f\u8868\u8ff0\u51fa\u6765\uff0c\u5e76\u770b\u4f5c\u67d0\u4e2a\u7cfb\u7edf\u81ea\u7136\u6f14\u5316\u7684\u65b9\u5411\uff0c\u90a3\u4e48\u201c\u5341\u4e8c\u5e73\u5747\u5f8b\u201d\u4f1a\u4e0d\u4f1a\u5c31\u662f\u8fd9\u4e2a\u7cfb\u7edf\u6f14\u5316\u7684\u5fc5\u7136\u7ed3\u679c\u3002\u4e4b\u524d\u4eba\u4eec\u5bf9\u97f3\u4e50\u590d\u6742\u6027\u7684\u7814\u7a76\u5c31\u5df2\u7ecf\u63d0\u51fa\u4e86\u97f3\u4e50\u7684\u590d\u6742\u6027\u53ef\u4ee5\u7531\u201c\u71b5S\u201d\u6765\u8868\u793a\uff0c\u540c\u65f6\u52a0\u4e0a\u524d\u6587\u6240\u63d0\u5230\u7684\u4e24\u4e2a\u97f3\u4e4b\u95f4\u7684\u975e\u534f\u548c\u7a0b\u5ea6D\u4e5f\u53ef\u4ee5\u5b58\u5728\u5f88\u591a\u7ecf\u9a8c\u516c\u5f0f\u3002\u4f5c\u8005\u901a\u8fc7\u5c06\u7edf\u8ba1\u529b\u5b66\u4e2d\u8457\u540d\u7684\u4ea5\u59c6\u970d\u5179\u81ea\u7531\u80fd\uff08F\uff09\u7684\u8868\u8fbe\u5f0f\uff08\u516c\u5f0f1\uff09\u6539\u5199\u4e3a\uff08\u516c\u5f0f2\uff09\u6765\u63cf\u8ff0\u4e00\u4e2a\u5177\u6709\u5f88\u591a\u4e0d\u540c\u57fa\u9891\u7684\u58f0\u97f3\u4ea7\u751f\u7684\u7cfb\u7edf\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

<\/span><\/section>\n
\u5bf9\u4e8e\u4e00\u4e2a\u5b8f\u89c2\u7cfb\u7edf\u6765\u8bf4\uff0c\u6700\u5c0f\u5316\u81ea\u7531\u80fd\u53d6\u51b3\u4e8e\u5185\u80fdU\u4e0e\u71b5S\u5728\u4e0d\u540c\u6e29\u5ea6\u4e0b\u7684\u6743\u8861\uff0c\u800c\u5bf9\u4e8e\u8fd9\u4e2a\u5404\u79cd\u58f0\u97f3\u7ec4\u6210\u7684\u7cfb\u7edf\uff0c\u8981\u6700\u5c0f\u5316\u5176\u81ea\u7531\u80fd\uff0c\u5c31\u9700\u8981\u964d\u4f4e\u8fd9\u4e9b\u58f0\u97f3\u4e4b\u95f4\u7684\u4e0d\u534f\u548c\u5ea6D\uff0c\u540c\u65f6\u589e\u52a0\u5176\u590d\u6742\u7a0b\u5ea6S\u3002\u8fd9\u6b63\u4e0e\u4ee5\u4e0a\u63d0\u51fa\u7684\u4e24\u4e2a\u65b9\u5411\u543b\u5408\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5f53\u7136\uff0c\u5149\u662f\u5199\u51fa\u8fd9\u4e00\u4e2a\u65b9\u7a0b\u8fd8\u4e0d\u591f\uff0c\u8fd8\u9700\u8981\u786e\u5b9a\u58f0\u97f3\u4e4b\u95f4\u76f8\u4e92\u4f5c\u7528\u7684\u65b9\u5f0f\u3002\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\uff0c\u4efb\u4f55\u4e00\u4e2a\u58f0\u97f3\u90fd\u662f\u7531\u4e00\u7cfb\u5217\u9891\u7387\u7684\u6ce2\u53e0\u52a0\u800c\u6210\u7684\uff0c\u800c\u5176\u4e2d\u632f\u5e45\u6700\u5927\u7684\u90a3\u4e2a\u6ce2\u7684\u9891\u7387\uff0c\u4e5f\u5c31\u662f\u8fd9\u4e2a\u58f0\u97f3\u7684\u57fa\u9891\u3002\u5728\u97f3\u4e50\u7406\u8bba\u4e2d\uff0c\u201c\u57fa\u9891\u201d\u5c31\u662f\u201c\u97f3\u9ad8\u201d\u3002\u800c\u7531\u4e8e\u7ec4\u6210\u6bcf\u4e2a\u58f0\u97f3\u7684\u4e00\u7cfb\u5217\u6ce2\u7684\u632f\u5e45\uff0c\u76f8\u4f4d\u7b49\u5404\u4e0d\u76f8\u540c\uff0c\u6240\u4ee5\u5373\u4f7f\u7528\u4e0d\u540c\u7684\u4e50\u5668\u6f14\u594f\u97f3\u9ad8\u76f8\u540c\u7684\u97f3\u65f6\uff0c\u7ed9\u4eba\u7684\u542c\u611f\u5f80\u5f80\u4e5f\u5927\u4e0d\u76f8\u540c\uff0c\u8fd9\u5c31\u662f\u6211\u4eec\u8bf4\u7684\u201c\u97f3\u8272\u4e0d\u540c\u201d\u3002\u5728\u672c\u6587\u4e2dJesse\u4f7f\u7528\u7684\u5c31\u662f\u952f\u9f7f\u97f3\u8272\uff0c\u4e5f\u5c31\u662f\u201c\u6cdb\u97f3\u201d\uff0c\u8fd9\u7c7b\u97f3\u8272\u4e00\u822c\u53ef\u4ee5\u5728\u5f26\u4e50\u5668\u4e2d\u627e\u5230\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4e3a\u4e86\u7b80\u5316\u8ba1\u7b97\uff0c\u4f5c\u8005\u5c06\u4e24\u4e2a\u97f3\u4e0d\u534f\u548c\u7a0b\u5ea6\u7684\u8ba1\u7b97\u65b9\u5f0f\u8bbe\u5b9a\u4e3a\uff1a\u5148\u5c06\u7ec4\u6210\u6bcf\u4e2a\u97f3\u7684\u6ce2\u6309\u632f\u5e45\u7531\u5927\u5230\u5c0f\u6392\u5217\uff0c\u7136\u540e\u8ba1\u7b97\u5176\u4e2d\u76f8\u540c\u6b21\u5e8f\u7684\u6ce2\u76f8\u4e92\u4f5c\u7528\u5bfc\u81f4\u7684\u975e\u534f\u548c\u5ea6d\uff0c\u6700\u540e\u5c06\u6240\u6709\u7684d\u76f8\u52a0\uff0c\u5f97\u5230\u8fd9\u4e24\u4e2a\u97f3\u7684\u603b\u975e\u534f\u548c\u5ea6D\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5f53\u7136\uff0cJesse\u9996\u5148\u53ea\u8ba1\u7b97\u4e86\u4e00\u4e2a\u516b\u5ea6\u5185\u4e24\u4e2a\u7eaf\u97f3\u4e4b\u95f4\u7684\u975e\u534f\u548c\u7a0b\u5ea6\u4e0e\u7eaf\u97f3\u9891\u7387\u5dee\u8ddd\u7684\u5173\u7cfb<\/span>\uff08\u5982\u56fe2-1\uff09<\/span>\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/span><\/section>\n
\u56fe2-1. \u4e24\u4e2a\u7eaf\u97f3\u7684\u975e\u534f\u548c\u5ea6\u4e0e\u7eaf\u97f3\u9891\u7387\u4e4b\u5dee\u7684\u5173\u7cfb<\/span><\/section>\n

<\/span><\/section>\n
\u5176\u4e2d\uff0c<\/span><\/section>\n
<\/section>\n

<\/span><\/section>\n
\u8868\u793a\u4e24\u4e2a\u97f3\u4e4b\u95f4\u7684\u9891\u7387\u5dee\u8ddd\uff0cfa\u548cfb\u5219\u662f\u4e24\u4e2a\u7eaf\u97f3\u7684\u9891\u7387\uff0c\u4e14fb>fb\uff0c\u5f53\u65f6\uff0c\u4e24\u4e2a\u97f3\u76f8\u5dee\u4e00\u4e2a\u516b\u5ea6\uff0c\u4e5f\u5c31\u662f\u9891\u7387\u6bd4\u4e3a2\u3002\u800c\u5176\u4e2d\u4e0d\u540c\u989c\u8272\u7684\u7ebf\u6761\u4ee3\u8868\u5904\u4e8e\u4e0d\u540c\u9891\u7387\u533a\u57df\u7684\u4e24\u4e2a\u97f3\u7684\u4e0d\u534f\u548c\u5ea6\u3002Wc\u4e3a\u4e0d\u534f\u548c\u5ea6\u6700\u9ad8\u65f6\u7684\u97f3\u7a0b\u3002\u5f53\u8fd9\u4e24\u4e2a\u97f3\u7684\u9891\u7387\u90fd\u5f88\u4f4e\u65f6\uff0c\u5904\u5728\u4f4e\u9891\u7684\u4e00\u4e2a\u516b\u5ea6\u533a\u95f4\u5185\u5f97\u5230\u7684\u6bd4\u8f83\u5927\uff0c\u800c\u9ad8\u9891\u7684\u516b\u5ea6\u533a\u95f4\u5185\u6bd4\u8f83\u5c0f\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u65e2\u7136\u77e5\u9053\u4e86\u7eaf\u97f3\u76f8\u4e92\u4f5c\u7528\u7684\u534f\u548c\u5ea6\u5173\u7cfb\u3002\u90a3\u4e48\u63a5\u4e0b\u6765\u5c31\u53ef\u4ee5\u5bf9\u8fd9\u4e2a\u5145\u6ee1\u5f88\u591a\u4e0d\u540c\u97f3\u9ad8\u58f0\u97f3\u7684\u4f53\u7cfb\u8fdb\u884c\u7f29\u5c0f\u81ea\u7531\u80fd\u7684\u201c\u5b9e\u9a8c\u201d\u4e86\u3002<\/span><\/section>\n

<\/span><\/section>\n

\u5e73\u5747\u573a\u8fd1\u4f3c<\/span><\/strong><\/span><\/h2>\n

<\/section>\n
\u5e73\u5747\u573a\u7406\u8bba<\/span>\uff08Mean Field Theory, MFT\uff09<\/span>\u662f\u5c06\u968f\u673a\u8fc7\u7a0b\u6a21\u578b\u4e2d\u4e00\u4e2a\u5355\u4f53\u53d7\u5230\u7684\u6240\u6709\u5f71\u54cd\u8fd1\u4f3c\u4e3a\u4e00\u4e2a\u5916\u90e8\u573a<\/span>\uff08External field\uff09<\/span>\uff0c\u4ece\u800c\u5c06\u591a\u4f53\u95ee\u9898<\/span>\uff08Many-body problem\uff09<\/span>\u5206\u89e3\u4e3a\u591a\u4e2a\u5355\u4f53\u95ee\u9898<\/span>\uff08One-body problem\uff09<\/span>\u8fdb\u884c\u6c42\u89e3\u7684\u7406\u8bba\u3002\u8fd9\u4e2a\u601d\u60f3\u5df2\u7ecf\u5728\u7269\u7406\u5b66\u4e2d\u88ab\u5e7f\u6cdb\u4f7f\u7528\u4e86\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u97f3\u6765\u8bf4\uff0c\u5b83\u53d7\u5230\u5176\u5b83\u6bcf\u4e00\u4e2a\u97f3\u76f8\u4e92\u4f5c\u7528\u3002\u5728\u4f7f\u7528\u5e73\u5747\u573a\u8fd1\u4f3c\u540e\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u53d8\u6210\u4e86\u4e00\u4e2a\u97f3\u4e0e\u5176\u5b83\u6240\u6709\u97f3\u7ec4\u6210\u7684\u201c\u5e73\u5747\u573a\u201d\u76f8\u4e92\u4f5c\u7528\uff0c\u8fd9\u5c06\u5927\u5927\u51cf\u5c11\u8ba1\u7b97\u91cf\u3002\u6839\u636e\u8fd9\u4e2a\u539f\u7406\uff0c\u5b9a\u4e49\u4ee5\u4e0b\u53c2\u6570\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

<\/section>\n
\u5176\u4e2d\uff0c\u5f0f\uff084\uff09\u4ee3\u8868\u4e00\u4e2a\u97f3\u548c\u5176\u4ed6\u97f3\u4ea7\u751f\u7684\u5e73\u5747\u573a\u4e4b\u95f4\u7684\u9891\u7387\u5dee\u8ddd\u3002\u5f0f\uff085\uff09\u7528\u6765\u8ba1\u7b97\u6574\u4e2a\u7cfb\u7edf\u7684\u4e0d\u534f\u548c\u5ea6\u3002\u4e3a\u97f3\u9ad8\u4e3a\u201cx\u201d\u7684\u97f3\u7684\u6982\u7387\uff0c\u4ee3\u8868\u6240\u6709\u97f3\u4e0e\u97f3\u9ad8\u201cx\u201d\u7684\u97f3\u5f62\u6210\u7684\u4e0d\u534f\u548c\u5ea6\u7684\u603b\u548c\uff0c\u79ef\u5206\u533a\u95f4\u4e3a(0,1]\u662f\u56e0\u4e3a\u8bbe\u5b9a\u4e86\u5468\u671f\u6027\u8fb9\u754c\u6761\u4ef6\uff0c(0,1]\u4ee3\u8868\u4e00\u4e2a\u516b\u5ea6\uff0c\u79ef\u5206\u51fd\u6570\u90fd\u6ee1\u8db3\u8fd9\u4e2a\u5468\u671f\u6027\u7684\u8fb9\u754c\u6761\u4ef6\u3002\u6700\u540e\u5f0f\uff086\uff09\u8868\u793a\u7684\u662f\u8fd9\u4e2a\u7cfb\u7edf\u7684\u71b5\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5176\u4e2d\uff0c\u56e0\u4e3a\u6982\u7387\u662f\u4e00\u4e2a\u5468\u671f\u51fd\u6570\uff0c\u6240\u4ee5\u5f88\u5bb9\u6613\u60f3\u5230\u4f7f\u7528\u5085\u91cc\u53f6\u7ea7\u6570\u4f5c\u4e3a\u4ed6\u7684\u8868\u8fbe\u5f0f\u3002\u53ef\u4ee5\u5c06\u5176\u5199\u6210\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

<\/section>\n
<\/span><\/section>\n

\u56fe2-2.  (A)\u5f53\u65f6\uff0c\u8ba1\u7b97\u7684\u952f\u9f7f\u97f3\u8272\u4e0d\u540c\u9891\u7387\u5dee\u7684\u4e24\u4e2a\u97f3\u7684\u975e\u534f\u548c\u5ea6(\u56fe\u4e2d\u5c55\u793a\u4e86\u4e24\u4e2a\u516b\u5ea6)\u3002\uff08B\uff09\u901a\u8fc7\uff08A\uff09\u56fe\u7684\u975e\u534f\u548c\u5ea6\u8ba1\u7b97\u51fa\u6765\u7684\u516c\u5f0f\uff088\uff09\u7684\u6bcf\u4e00\u9879\u7684\u53c2\u6570dk<\/sub><\/span>\u3002<\/span><\/p>\n


<\/span><\/em><\/span><\/section>\n
\u90a3\u4e48\uff0c\u65e2\u7136\u6240\u6709\u53c2\u6570\u90fd\u8bbe\u7f6e\u597d\u4e86\uff0c\u6211\u4eec\u5c31\u8981\u5f00\u59cb\u6700\u5c0f\u5316\u81ea\u7531\u80fd\u4e86\u3002\u5728\u8fd9\u4e2a\u7cfb\u7edf\u4e2d\uff0c\u9ed8\u8ba4\uff0c\u540c\u65f6\u6e29\u5ea6T\u53ea\u662f\u4e00\u4e2a\u53c2\u6570\uff0c\u5e76\u4e0d\u4ee3\u8868\u771f\u5b9e\u6e29\u5ea6\u3002\u4f46\u662f\u6211\u4eec\u5982\u679c\u4f9d\u7136\u53bb\u6a21\u62df\u4e00\u4e2aT\u4e0d\u65ad\u53d8\u5c0f\u7684\u964d\u6e29\u8fc7\u7a0b\uff0c\u5e76\u4e14\u5728\u6bcf\u4e00\u4e2aT\u4e0b\u90fd\u4f7f\u5f97\u7cfb\u7edf\u7684\u4ea5\u59c6\u970d\u5179\u81ea\u7531\u80fd\u6700\u5c0f\u65f6\uff0c\u8fd9\u4e2a\u7cfb\u7edf\u4e2d\u7684\u97f3\u7684\u9891\u7387\u5206\u5e03\u4f1a\u662f\u600e\u6837\u7684\u5462\uff1f<\/span><\/section>\n

<\/span><\/section>\n
<\/span><\/section>\n
\u56fe2-3. \u968f\u7740\u201c\u6e29\u5ea6\u201d\u4e0b\u964d\uff0c\u4e00\u4e2a\u516b\u5ea6\u5185\u58f0\u97f3\u6982\u7387\u5bc6\u5ea6\u7684\u53d8\u5316<\/span><\/section>\n

<\/span><\/section>\n
\u5982\u56fe2-3\u7eb5\u5750\u6807\u8868\u793a\u97f3\u7684\u6982\u7387\u5bc6\u5ea6\uff0c\u7eb5\u5750\u6807\u8d8a\u5927\u8bf4\u660e\u5728\uff0c\u4e5f\u5c31\u662f\u4e00\u4e2a\u516b\u5ea6\u5185\u5177\u6709\u67d0\u4e2a\u57fa\u9891\u97f3\u7684\u6570\u91cf\u8d8a\u591a\uff0c\u4ee4\u4eba\u60ca\u559c\u7684\u662f\uff0c\u5728T=20.2\u3001T=16.3\u65f6\uff0c\u90fd\u80fd\u770b\u523012\u4e2a\u6982\u7387\u76f8\u540c\u7684\u5c16\u5cf0\u3002\u8fd9\u8bf4\u660e\uff1a\u82e5\u662f\u67d0\u4e00\u4e2a\u97f3\u4e50\u7cfb\u7edf\uff0c\u8981\u5177\u6709\u6700\u5c0f\u7684\u975e\u534f\u548c\u5ea6\uff0c\u540c\u65f6\u8981\u8db3\u591f\u590d\u6742\u65f6\uff0c\u53ea\u9700\u8981\u5728\u4e00\u4e2a\u516b\u5ea6\u5185\u5f62\u6210\u4e00\u4e2a\u6709\u5341\u4e8c\u9879\u7684\u201c\u7b49\u5dee\u201d\u97f3\u9ad8\u5c31\u884c\uff01\u8fd9\u6b63\u597d\u5bf9\u5e94\u7740\u201c\u5341\u4e8c\u5e73\u5747\u5f8b\u201d\u7684\u51fa\u73b0\u3002\u800c\u5728T\u5c0f\u4e8e16.2\u65f6\uff0c\u53ef\u4ee5\u770b\u523012\u4e2a\u4e0d\u540c\u6982\u7387\u7684\u5cf0\u51fa\u73b0\uff0c\u8fd9\u4e5f\u5bf9\u5e94\u7740\u65e9\u671f\u5177\u670912\u58f0\u97f3\u9636\u7684\u7eaf\u5f8b\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/span><\/section>\n
\u56fe2-4.\u7ea6\u5316\u5e8f\u53c2\u91cf\u968f\u6e29\u5ea6\u7684\u53d8\u5316\u60c5\u51b5<\/span><\/section>\n

<\/span><\/em><\/span><\/section>\n
\u540c\u6837\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u7ed8\u5236\u516c\u5f0f\uff087\uff09\u4e2d\u5e8f\u53c2\u91cf\u968f\u6e29\u5ea6\u53d8\u5316\u7684\u89c4\u5f8b\u3002\u6839\u636e\u56fe2-4\uff0c\u4f3c\u4e4e\u53ef\u4ee5\u53d1\u73b0\u6574\u4e2a\u7cfb\u7edf\u7684\u201c\u51b7\u5374\u201d\u8fc7\u7a0b\u5b58\u5728\u4e00\u79cd\u4e8c\u9636\u76f8\u53d8\u3002\u5728\u8fd9\u4e24\u4e2a\u4e34\u754c\u6e29\u5ea6\u4e4b\u95f4\u5b58\u5728\u4e00\u79cd\u5341\u5206\u7a33\u5b9a\u7684\u72b6\u6001\u2014\u2014\u5373\u201c\u5341\u4e8c\u5e73\u5747\u5f8b\u201d\u9636\u6bb5\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/span><\/section>\n
\u56fe2-5. \u4e0d\u540c\u516b\u5ea6\u5185\u7684\u5e8f\u53c2\u6570\u7684\u53d8\u5316<\/span><\/section>\n

<\/span><\/em><\/span><\/section>\n
\u56e0\u4e3a\u4e0a\u4e00\u6b21\u6211\u4eec\u505a\u7684\u5e73\u5747\u573a\u8fd1\u4f3c\u56fa\u5b9a\u4e86\uff0c\u4f46\u662f\u4ece\u56fe2-1<\/span>\u53ef\u77e5\u5728\u4e0d\u540c\u9ad8\u4f4e\u7684\u516b\u5ea6\u533a\u95f4\u5185\u662f\u4e0d\u4e00\u6837\u7684\u3002\u6240\u4ee5\uff0c\u5982\u679c\u4f7f\u7528\u6b63\u786e\u7684\u4f1a\u5f97\u5230\u600e\u6837\u7684\u7ed3\u679c\u5462\uff1f\u5982\u56fe2-5\u6240\u793a\uff0c\u6a2a\u5750\u6807\u4e3a\u6e29\u5ea6\uff0c\u4ece\u53f3\u5230\u5de6\u4e0d\u65ad\u964d\u4f4e\u4ee5\u63cf\u7ed8\u6240\u8ff0\u7684\u964d\u6e29\u8fc7\u7a0b\u3002\u5de6\u8fb9\u7684\u5f69\u8272\u77e9\u5f62\u663e\u793a\u4e86\u4e0d\u540c\u989c\u8272\u5bf9\u5e94\u7684k\u503c\uff0c\u5de6\u8fb9\u7684\u7eb5\u5750\u6807\u4e3a\u503c\uff0c\u5bf9\u5e94\u53f3\u8fb9\u4eceC4\u5230C8\u51714\u4e2a\u516b\u5ea6\u8303\u56f4\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u53ef\u4ee5\u770b\u5230\uff0c\u5728\u9ad8\u9891\u516b\u5ea6\u8303\u56f4\u51fa\u73b0K=12\u7684\u201c\u76f8\u53d8\u533a\u95f4\u201d\u975e\u5e38\u5927\uff0c\u800c\u5728\u5176\u4ed6\u8303\u56f4\u4f1a\u51fa\u73b0\u4e00\u4e9b\u5176\u4ed6\u7684\u97f3\u5f8b\uff0c\u6bd4\u5982\u201c\u4e03\u58f0\u97f3\u9636\u201d\u3001\u201c\u4e94\u58f0\u97f3\u9636\u201d\u7b49\u3002\u4f5c\u8005\u8ba4\u4e3a\u8fd9\u6837\u7684\u73b0\u8c61\u6765\u81ea\u5e73\u5747\u573a\u6a21\u578b\u7684\u9650\u5236\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u539f\u6587\u4f5c\u8005\u63d0\u51fa\u7684\u5e73\u5747\u573a\u6a21\u578b\u8fd1\u4f3c\u8d77\u5230\u4e00\u4e2a\u629b\u7816\u5f15\u7389\u7684\u6548\u679c\uff0c\u56e0\u4e3a\u5e73\u5747\u573a\u8fd1\u4f3c\u5e76\u4e0d\u662f\u7edf\u8ba1\u529b\u5b66\u4e2d\u6700\u51c6\u786e\u7684\u6a21\u578b\uff0c\u4f5c\u8005\u731c\u60f3\u4e5f\u8bb8\u5176\u4ed6\u6a21\u578b\u80fd\u591f\u66f4\u597d\u89e3\u91ca\u97f3\u4e50\u6216\u8005\u97f3\u5f8b\u53d1\u5c55\u7684\u540c\u65f6\uff0c\u751a\u81f3\u53ef\u4ee5\u4ece\u7269\u7406\u51fa\u53d1\u6307\u5bfc\u97f3\u5f8b\u548c\u97f3\u4e50\u7684\u53d1\u5c55\uff01\u5176\u5b9e\u5728\u672c\u6587\u7684\u540e\u534a\u90e8\u5206\uff0c\u4f5c\u8005\u8fd8\u662f\u7528\u4e86XY\u6a21\u578b<\/span> (XY model) <\/span>\u6784\u5efa\u4e86\u4e00\u4e2a\u5c5e\u4e8e\u97f3\u4e50\u7684\u6676\u683c\u7f51\u7edc\uff0c\u201c\u6e29\u5ea6\u201d\u964d\u4f4e\u7684\u8fc7\u7a0b\u4e2d\u53ef\u4ee5\u53d1\u73b0\uff1a\u76f8\u90bb\u7684\u4f4d\u7f6e\u7684\u97f3\u7a0b\u7b26\u5408\u4e00\u5b9a\u7684\u89c4\u5f8b\uff0c\u751a\u81f3\u53ef\u4ee5\u5728\u8fd9\u4e2a\u6676\u683c\u7f51\u7edc\u4e2d\u770b\u5230\u4e3b\u6d41\u97f3\u4e50\u6240\u7528\u7684\u4e09\u548c\u5f26\u3001\u4e94\u548c\u5f26\u3002\u6709\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u4ee5\u67e5\u770b\u539f\u6587\uff0c\u5728\u6b64\u5c31\u4e0d\u8fc7\u591a\u8d58\u8ff0\u4e86\u3002<\/span><\/section>\n

<\/span><\/section>\n

<\/span><\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

3. \u7ed3\u8bed<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

<\/section>\n
\u5728\u672c\u6587\u4e2dJesse Berezovsky\u4f7f\u7528\u5e73\u5747\u573a\u8fd1\u4f3c\u5bf9\u4e00\u4e2a\u97f3\u4e50\u7cfb\u7edf\u8fdb\u884c\u201c\u7f13\u6162\u964d\u6e29\u201d\u8fc7\u7a0b\uff0c\u5728\u6bcf\u4e00\u4e2a\u65f6\u95f4\u6b65\u4e0a\u90fd\u4f7f\u5f97\u7ec4\u6210\u8be5\u7cfb\u7edf\u7684\u97f3\u9ad8\u5c3d\u53ef\u80fd\u534f\u548c\uff0c\u540c\u65f6\u4e0d\u5931\u591a\u6837\u6027\u3002\u7ed3\u679c\u8868\u660e\uff0c\u5728\u67d0\u4e2a\u6e29\u5ea6\u4e0b\u8fd9\u4e2a\u7cfb\u7edf\u7684\u97f3\u9ad8\u7ec4\u6210\u4e0e\u8fd1\u4ee3\u97f3\u5f8b\u7684\u53d1\u5c55\u76f8\u4f3c\u3002\u4f3c\u4e4e\u5728\u51a5\u51a5\u4e4b\u4e2d\u7269\u7406\u548c\u827a\u672f\u5b58\u5728\u7740\u4ea4\u6c47\u70b9\u3002\u8fd9\u4e0d\u7981\u8ba9\u7b14\u8005\u60ca\u559c\u800c\u53c8\u540e\u6015\uff0c\u60ca\u559c\u7684\u662f\u6ca1\u60f3\u5230\u4e25\u8c28\u7684\u7269\u7406\u4e0e\u6570\u5b66\u5c45\u7136\u80fd\u591f\u4e0e\u827a\u672f\u6709\u6240\u7ea0\u845b\uff1b\u540e\u6015\u7684\u662f\u90a3\u4e9b\u827a\u672f\u5bb6\u4eec\u7a77\u6781\u4e00\u751f\u6240\u521b\u9020\u7684\u4f5c\u54c1\uff0c\u5c31\u50cf\u6563\u843d\u5728\u591c\u7a7a\u91cc\u7684\u661f\u661f\u3002\u5728\u6211\u4eec\u5c0f\u7684\u65f6\u5019\u6210\u4e3a\u6211\u4eec\u590f\u65e5\u5e7b\u60f3\uff0c\u800c\u5728\u957f\u5927\u7684\u67d0\u4e00\u5929\u6211\u4eec\u624d\u610f\u8bc6\u5230\u90a3\u6709\u53ef\u80fd\u53ea\u662f\u4e00\u9897\u51b0\u51b7\u7684\u661f\u7403\u4e0d\u77e5\u9053\u53cd\u5c04\u4e86\u8c01\u7684\u5149\u8292\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4e0d\u8fc7\u7b14\u8005\u8ba4\u4e3a\u5373\u4f7f\u662f\u8fd9\u6837\u4eba\u4eec\u4e5f\u4e0d\u5e94\u8be5\u505c\u4e0b\u8ffd\u6c42\u771f\u7406\u7684\u811a\u6b65\uff0c\u56e0\u4e3a\u8fd9\u4e2a\u4e16\u754c\u662f\u5982\u6b64\u590d\u6742\uff0c\u8981\u60f3\u8d70\u5230\u6700\u540e\u53ef\u6ca1\u90a3\u4e48\u5bb9\u6613\uff1b\u800c\u4e14\u65e0\u8bba\u662f\u97f3\u4e50\u3001\u7ed8\u753b\u3001\u751a\u81f3\u662f\u8868\u6f14\u3002\u65e2\u7136\u4ed6\u5982\u6b64\u7f8e\u597d\uff0c\u90a3\u4e48\u6211\u76f8\u4fe1\u5373\u4f7f\u4eba\u7c7b\u6709\u4e00\u5929\u80fd\u591f\u8d70\u5230\u6700\u540e\uff0c\u7ed3\u679c\u4e5f\u5e94\u8be5\u4e0d\u4f1a\u592a\u5dee\u3002<\/span><\/section>\n

<\/span><\/strong><\/span><\/section>\n
\u672c<\/span><\/strong><\/span>\u6587\u53c2\u8003\u8d44\u6599<\/span><\/strong><\/section>\n
[1] Berezovsky J. The structure of musical harmony as an ordered phase of sound: A statistical mechanics approach to music theory[J]. Science Advances, 2019, 5(5): eaav8490.<\/span><\/section>\n
[2] Plomp R, Levelt W J M. Tonal Consonance and Critical Bandwidth[J]. The Journal of the Acoustical Society of America, 1965, 38(4): 548-560.<\/span><\/section>\n
[3] \u970d\u534e\u5fb7, ) D M, \u5b89\u683c\u65af, et al. \u97f3\u4e50\u58f0\u5b66\u4e0e\u5fc3\u7406\u58f0\u5b66[M]. \u97f3\u4e50\u58f0\u5b66\u4e0e\u5fc3\u7406\u58f0\u5b66, 2010.<\/span><\/section>\n
[4] Benson D J. Music : a mathematical offering[M]. Cambridge, UK ;: Cambridge University Press, 2007.<\/span><\/section>\n
[5] \u97f3\u4e50\u4e0e\u6570\u5b66, Simon Fang<\/span><\/section>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n
\n

\u25ba\u25ba\u25ba<\/p>\n<\/section>\n<\/section>\n

\n
\n

\u590d\u6742\u79d1\u5b66\u00d7\u827a\u672f\u7cfb\u5217\u7814\u8ba8\u4f1a\u516c\u5f00\u62a5\u540d\u4e2d<\/span><\/strong><\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

<\/span><\/a><\/section>\n

\u7814\u8ba8\u4f1a\u8be6\u60c5\u4e0e\u6846\u67b6\uff1a<\/span><\/p>\n

Chaos & Muses\uff1a\u590d\u6742\u79d1\u5b66\u00d7\u827a\u672f\u7cfb\u5217\u7814\u8ba8\u4f1a<\/a>
<\/span><\/strong><\/span><\/p>\n


<\/p>\n


<\/p>\n

\n

\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/p>\n