Scan 51
Musical instruments in the Great Industrial Exhibition of 1851, 1851
65 lines. Read by computer on 29 September 2026. No printed page number was found. See the scan on archive.org.
1lumn of air),—or, vice versâ, halving the length makes it speak an octave higher. It is found, by experiment, that an open pipe, about eight feet long, will speak the C forming the lowest note of the violoncello, or the note produced by about 128 vibrations per second; and hence we have the following scale:—
3<table>
4 <tr>
5 <th>No. of Vibrations per Second.</th>
6 <th>Note.</th>
7 <th>Length of Open Pipe.</th>
8 </tr>
9 <tr>
10 <td>2048</td>
11 <td>C in alt.</td>
12 <td>½ foot</td>
13 </tr>
14 <tr>
15 <td>1024</td>
16 <td>The C on the 3rd space in the treble clef</td>
17 <td>1 ,,</td>
18 </tr>
19 <tr>
20 <td>512</td>
21 <td>The C called middle C; the note of the C clef</td>
22 <td>2 feet</td>
23 </tr>
24 <tr>
25 <td>256</td>
26 <td>{ The C called tenor C; the lowest note of the viola }</td>
27 <td>4 ,,</td>
28 </tr>
29 <tr>
30 <td>128</td>
31 <td>The lowest note of the violoncello</td>
32 <td>8 ,,</td>
33 </tr>
34 <tr>
35 <td>64</td>
36 <td>The lowest C of a grand piano-forte</td>
37 <td>16 ,,</td>
38 </tr>
39 <tr>
40 <td>32</td>
41 <td>The C below</td>
42 <td>32 ,,</td>
43 </tr>
44</table>
46It is useful to bear this scale in mind, as it affords a key to the arrangement and nomenclature of the various stops, as will be hereafter explained. Moreover, it is now very customary to express the notes by the lengths of pipes corresponding to them: for example, the lowest C of a grand piano-forte is often called 16-feet C; middle C is called 2-feet C; and so on.*
48* Some explanation is necessary, to prevent misunderstanding, in reference to this scale.
50In the first place, the number of vibrations is approximately that of the old church pitch; the modern orchestral pitch is considerably higher.
52In the case of a string, the numbers in the table refer to single vibrations, not to complete or double ones. The latter are used by some writers on harmonics, and the difference, if not explained, would create confusion. The former are evidently the most correct, as indicating the number of distinct impulses given to the air, and corresponding with the oscillations of a pendulum.—See Chladni's elaborate work, "Die Akustik," Leipzig, 1830.
54The number of vibrations corresponding to any given note is indicated by a very ingenious instrument, invented by Baron Cagniard de la Tour, and called the sirène. It may also be calculated as follows:—Stretch a wire (a piano-forte wire, for example) over two rests, and tighten it by a weight till it sounds the given note. Let l represent the length in inches, and w the weight in lbs., of the vibrating part of the wire; also, let T represent the tension, or stretching weight, in lbs., and V the number of single vibrations per second. Then,
56\[
57V^2 = 386.156 \frac{T}{lw}
58\]
60The relation between the sound of any note and the corresponding length of pipe is as follows:—Let L represent the length of the tube part of the pipe, above the mouth, in feet, and V the number of vibrations per second corresponding to the given note. Then, approximately,
62\[
63V = \frac{1024}{L} \text{ or } L = \frac{1024}{V}.
64\]
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