Appendix E. Modal Frequency Ratios
Contributed by Scott Lindroth
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.
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.
This ratios can be useful together with opcodes like mode or streson.
Table E.1. Modal Frequency Ratios
| Instrument | Modal Frequency Ratios |
|---|---|
| Dahina tabla | [1, 2.89, 4.95, 6.99, 8.01, 9.02] |
| Bayan tabla | [1, 2.0, 3.01, 4.01, 4.69, 5.63] |
| Red Cedar wood plate | [1, 1.47, 2.09, 2.56] |
| Redwood wood plate | [1, 1.47, 2.11, 2.57] |
| Douglas Fir wood plate | [1, 1.42, 2.11, 2.47] |
| uniform wooden bar | [1, 2.572, 4.644, 6.984, 9.723, 12] |
| uniform aluminum bar | [1, 2.756, 5.423, 8.988, 13.448, 18.680] |
| Xylophone | [1, 3.932, 9.538, 16.688, 24.566, 31.147] |
| Vibraphone 1 | [1, 3.984, 10.668, 17.979, 23.679, 33.642] |
| Vibraphone 2 | [1, 3.997, 9.469, 15.566, 20.863, 29.440] |
| Chalandi plates | ([62, 107, 360, 460, 863] Hz +-2Hz) [1, 1.72581, 5.80645, 7.41935, 13.91935] ratios |
| tibetan bowl (180mm) |
([221, 614, 1145, 1804, 2577, 3456, 4419] Hz) 934g, 180mm [1, 2.77828, 5.18099, 8.16289, 11.66063, 15.63801, 19.99 ratios |
| tibetan bowl (152 mm) |
([314, 836, 1519, 2360, 3341, 4462, 5696] Hz) 563g, 152mm [1, 2.66242, 4.83757, 7.51592, 10.64012, 14.21019, 18.14027] ratios |
| tibetan bowl (140 mm) |
([528, 1460, 2704, 4122, 5694] Hz) 557g, 140m [1, 2.76515, 5.12121, 7.80681, 10.78409] ratios |
| Wine Glass | [1, 2.32, 4.25, 6.63, 9.38] |
| small handbell | ([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) [ 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 |
| spinel sphere with diameter of 3.6675mm |
([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) [ 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 |
| pot lid | [ 1, 3.2, 6.23, 6.27, 9.92, 14.15] ratios |