Books › A descriptive catalogue of the musical instruments recently exhibited at the Royal Military Exhibition, London, 1890 …, 1891 › scan 269
Scan 269
A descriptive catalogue of the musical instruments recently exhibited at the Royal Military Exhibition, London, 1890 …, 1891
174 lines. Read by computer on 1 October 2026. Printed page 249. See the scan on archive.org.
1APPENDIX—AN ESSAY ON MUSICAL PITCH.
3The ratios of the intervals of the equal temperament scale are shown in Table I., and the vibrational value or frequency of any note taken as a pitch note being given, that of any other related note in this temperament can be found by use of the multiplier corresponding to the difference in semitones between the two notes.
5Example: \( c' = 269 \); find \( e' \). \( e' \) being four semitones above \( c' \), multiply 269 by 1.2599,
6\[
7269 \times 1.2599 = 338.91 \text{ value of } e'.
8\]
10EQUAL TEMPERAMENT.
12<table>
13 <tr>
14 <th colspan="3">Table I.</th>
15 <th colspan="3">Table II.</th>
16 </tr>
17 <tr>
18 <th>Difference in semitones.</th>
19 <th>Note.</th>
20 <th>Ratio, or relative frequency.</th>
21 <th>Note.</th>
22 <th>Absolute vibrations.</th>
23 <th>Note.</th>
24 <th>Absolute vibrations.</th>
25 <th>Note.</th>
26 <th>Absolute vibrations.</th>
27 </tr>
28 <tr>
29 <td>12</td>
30 <td>c</td>
31 <td>2.00000</td>
32 <td>g</td>
33 <td>200.00</td>
34 <td>g'</td>
35 <td>400.00</td>
36 <td>g''</td>
37 <td>800.00</td>
38 </tr>
39 <tr>
40 <td>11</td>
41 <td>b</td>
42 <td>1.88775</td>
43 <td>f#</td>
44 <td>188.78</td>
45 <td>f'##</td>
46 <td>377.55</td>
47 <td>f''##</td>
48 <td>755.10</td>
49 </tr>
50 <tr>
51 <td>10</td>
52 <td>a##</td>
53 <td>1.78180</td>
54 <td>f</td>
55 <td>178.18</td>
56 <td>f'</td>
57 <td>356.36</td>
58 <td>f''</td>
59 <td>712.72</td>
60 </tr>
61 <tr>
62 <td>9</td>
63 <td>a</td>
64 <td>1.68179</td>
65 <td>e</td>
66 <td>168.18</td>
67 <td>e'</td>
68 <td>336.36</td>
69 <td>e''</td>
70 <td>672.72</td>
71 </tr>
72 <tr>
73 <td>8</td>
74 <td>g##</td>
75 <td>1.58740</td>
76 <td>d#</td>
77 <td>158.74</td>
78 <td>d'##</td>
79 <td>317.48</td>
80 <td>d''##</td>
81 <td>634.96</td>
82 </tr>
83 <tr>
84 <td>7</td>
85 <td>g</td>
86 <td>1.49831</td>
87 <td>d</td>
88 <td>149.83</td>
89 <td>d'##</td>
90 <td>299.66</td>
91 <td>d''##</td>
92 <td>599.32</td>
93 </tr>
94 <tr>
95 <td>6</td>
96 <td>f##</td>
97 <td>1.41421</td>
98 <td>c#</td>
99 <td>141.42</td>
100 <td>c'##</td>
101 <td>282.84</td>
102 <td>c''##</td>
103 <td>565.68</td>
104 </tr>
105 <tr>
106 <td>5</td>
107 <td>f</td>
108 <td>1.33484</td>
109 <td>c</td>
110 <td>133.48</td>
111 <td>c'##</td>
112 <td>266.97</td>
113 <td>c''##</td>
114 <td>533.94</td>
115 </tr>
116 <tr>
117 <td>4</td>
118 <td>e</td>
119 <td>1.25992</td>
120 <td>B</td>
121 <td>128.49</td>
122 <td>b</td>
123 <td>256.98</td>
124 <td>b'</td>
125 <td>503.97</td>
126 </tr>
127 <tr>
128 <td>3</td>
129 <td>d##</td>
130 <td>1.18921</td>
131 <td>A#</td>
132 <td>118.92</td>
133 <td>a##</td>
134 <td>237.84</td>
135 <td>a'##</td>
136 <td>475.68</td>
137 </tr>
138 <tr>
139 <td>2</td>
140 <td>d</td>
141 <td>1.12246</td>
142 <td>A</td>
143 <td>112.25</td>
144 <td>a</td>
145 <td>224.49</td>
146 <td>a'##</td>
147 <td>448.98</td>
148 </tr>
149 <tr>
150 <td>1</td>
151 <td>c##</td>
152 <td>1.05946</td>
153 <td>G#</td>
154 <td>105.95</td>
155 <td>g##</td>
156 <td>211.89</td>
157 <td>g'##</td>
158 <td>423.78</td>
159 </tr>
160 <tr>
161 <td>0</td>
162 <td>c</td>
163 <td>1.00000</td>
164 <td>G</td>
165 <td>100.00</td>
166 <td>g</td>
167 <td>200.00</td>
168 <td>g'##</td>
169 <td>400.00</td>
170 </tr>
171</table>
173In Table I. \( c \) is taken as the basis, but it is immaterial what note of the scale is represented by unity, so long as the figures given are taken to set forth ratios only and not frequencies. If, however, the
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