<?xml version="1.0" encoding="UTF-8" standalone="no"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> <title>Appendix E. Modal Frequency Ratios</title> <link rel="stylesheet" type="text/css" href="csound.css" /> <meta name="generator" content="DocBook XSL Stylesheets V1.76.1" /> <link rel="home" href="index.html" title="The Canonical Csound Reference Manual" /> <link rel="up" href="index.html" title="The Canonical Csound Reference Manual" /> <link rel="prev" href="MiscFormants.html" title="Appendix D. Formant Values" /> <link rel="next" href="MiscWindows.html" title="Appendix F. Window Functions" /> </head> <body> <div class="navheader"> <table width="100%" summary="Navigation header"> <tr> <th colspan="3" align="center">Appendix E. Modal Frequency Ratios</th> </tr> <tr> <td width="20%" align="left"><a accesskey="p" href="MiscFormants.html">Prev</a> </td> <th width="60%" align="center"> </th> <td width="20%" align="right"> <a accesskey="n" href="MiscWindows.html">Next</a></td> </tr> </table> <hr /> </div> <div class="appendix" title="Appendix E. Modal Frequency Ratios"> <div class="titlepage"> <div> <div> <h2 class="title"><a id="MiscModalFreq"></a>Appendix E. Modal Frequency Ratios</h2> </div> </div> </div> <h2><a id="idp88118680"></a>Contributed by Scott Lindroth</h2> <p> John Bower, a student of Scott Lindroth, compiled this list of modal frequencies for various objects and materials. Some modes work better than others, and most need to be in a particular frequency range to sound plausible. Caveat emptor. </p> <p> In general, wooden objects will not sound "wooden" unless a stochastic component is present in the sound (try banded waveguides). Nonetheless, some of the wooden objects make wonderful metallic instruments as well. </p> <p> This ratios can be useful together with opcodes like <a class="link" href="mode.html" title="mode"><em class="citetitle">mode</em></a> or <a class="link" href="streson.html" title="streson"><em class="citetitle">streson</em></a>. </p> <div class="table"> <a id="idp88084480"></a> <p class="title"> <strong>Table E.1. Modal Frequency Ratios</strong> </p> <div class="table-contents"> <table summary="Modal Frequency Ratios" border="1"> <colgroup> <col /> <col /> </colgroup> <thead> <tr> <th>Instrument</th> <th>Modal Frequency Ratios</th> </tr> </thead> <tbody> <tr> <td>Dahina tabla</td> <td>[1, 2.89, 4.95, 6.99, 8.01, 9.02]</td> </tr> <tr> <td>Bayan tabla</td> <td>[1, 2.0, 3.01, 4.01, 4.69, 5.63]</td> </tr> <tr> <td>Red Cedar wood plate</td> <td>[1, 1.47, 2.09, 2.56]</td> </tr> <tr> <td>Redwood wood plate</td> <td>[1, 1.47, 2.11, 2.57]</td> </tr> <tr> <td>Douglas Fir wood plate</td> <td>[1, 1.42, 2.11, 2.47]</td> </tr> <tr> <td>uniform wooden bar</td> <td>[1, 2.572, 4.644, 6.984, 9.723, 12]</td> </tr> <tr> <td>uniform aluminum bar</td> <td>[1, 2.756, 5.423, 8.988, 13.448, 18.680]</td> </tr> <tr> <td>Xylophone</td> <td>[1, 3.932, 9.538, 16.688, 24.566, 31.147]</td> </tr> <tr> <td>Vibraphone 1</td> <td>[1, 3.984, 10.668, 17.979, 23.679, 33.642]</td> </tr> <tr> <td>Vibraphone 2</td> <td>[1, 3.997, 9.469, 15.566, 20.863, 29.440]</td> </tr> <tr> <td>Chalandi plates</td> <td><p>([62, 107, 360, 460, 863] Hz +-2Hz)</p> <p>[1, 1.72581, 5.80645, 7.41935, 13.91935] ratios</p></td> </tr> <tr> <td>tibetan bowl (180mm)</td> <td><p>( [221, 614, 1145, 1804, 2577, 3456, 4419] Hz) 934g, 180mm</p> <p>[1, 2.77828, 5.18099, 8.16289, 11.66063, 15.63801, 19.99 ratios</p></td> </tr> <tr> <td>tibetan bowl (152 mm)</td> <td><p>([314, 836, 1519, 2360, 3341, 4462, 5696] Hz) 563g, 152mm</p> <p>[1, 2.66242, 4.83757, 7.51592, 10.64012, 14.21019, 18.14027] ratios</p></td> </tr> <tr> <td>tibetan bowl (140 mm)</td> <td><p>([528, 1460, 2704, 4122, 5694] Hz) 557g, 140mm</p> <p>[1, 2.76515, 5.12121, 7.80681, 10.78409] ratios</p></td> </tr> <tr> <td>Wine Glass</td> <td>[1, 2.32, 4.25, 6.63, 9.38]</td> </tr> <tr> <td>small handbell</td> <td><p>([1312.0, 1314.5, 2353.3, 2362.9, 3306.5, 3309.4, 3923.8, 3928.2, 4966.6, 4993.7, 5994.4, 6003.0, 6598.9, 6619.7, 7971.7, 7753.2, 8413.1, 8453.3, 9292.4, 9305.2, 9602.3, 9912.4] Hz)</p> <p>[ 1, 1.0019054878049, 1.7936737804878, 1.8009908536585, 2.5201981707317, 2.5224085365854, 2.9907012195122, 2.9940548780488, 3.7855182926829, 3.8061737804878, 4.5689024390244, 4.5754573170732, 5.0296493902439, 5.0455030487805, 6.0759908536585, 5.9094512195122, 6.4124237804878, 6.4430640243902, 7.0826219512195, 7.0923780487805, 7.3188262195122, 7.5551829268293 ] ratios</p></td> </tr> <tr> <td>spinel sphere with diameter of 3.6675mm</td> <td><p>([977.25, 1003.16, 1390.13, 1414.93, 1432.84, 1465.34, 1748.48, 1834.20, 1919.90, 1933.64, 1987.20, 2096.48, 2107.10, 2202.08, 2238.40, 2280.10, 0 /*2290.53 calculated*/, 2400.88, 2435.85, 2507.80, 2546.30, 2608.55, 2652.35, 2691.70, 2708.00] Hz)</p> <p>[ 1, 1.026513174725, 1.4224916858532, 1.4478690202098, 1.4661959580455, 1.499452545408, 1.7891839345101, 1.8768994627782, 1.9645945254541, 1.9786543873113, 2.0334612432847, 2.1452852391916, 2.1561524686621, 2.2533435661294, 2.2905090816065, 2.3331798413917, 0, 2.4567715528268, 2.4925556408289, 2.5661806088514, 2.6055768738808, 2.6692760296751, 2.7140956766436, 2.7543617293425, 2.7710411870043 ] ratios</p></td> </tr> <tr> <td>pot lid</td> <td> <p>[ 1, 3.2, 6.23, 6.27, 9.92, 14.15] ratios</p> </td> </tr> </tbody> </table> </div> </div> <br class="table-break" /> </div> <div class="navfooter"> <hr /> <table width="100%" summary="Navigation footer"> <tr> <td width="40%" align="left"><a accesskey="p" href="MiscFormants.html">Prev</a> </td> <td width="20%" align="center"> </td> <td width="40%" align="right"> <a accesskey="n" href="MiscWindows.html">Next</a></td> </tr> <tr> <td width="40%" align="left" valign="top">Appendix D. 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