| Description | Hipkins writes: 'The string observed was a steel pianoforte wire, gauge number 19½, diameter 1.17 mm. = 0.07 inch, of exactly 45 inches vibrating length, stretched by a tension of 71 kilogrammes = 156.63 lbs., and forming the note C of 135.2 vibrations, in the second space of the bass staff, in one of Broadwood’s concert grand pianofortes accurately adjusted to be struck by the hammer at one-eighth the length of the string from the wrestplank end, or 39.375 inches from the belly-bridge. Actually three such strings, forming the usual trichord of a grand pianoforte accurately tuned in unison, were used to augment the volume of tone. The positions of all the nodes less than 39.4 inches from the belly-bridge for the first 20 harmonics, were previously calculated. All three strings were stopped at the same distance from the belly-bridge with the edge of a piece of felt glued to a piece of wood by Mr. Hartan, the foreman of the tuners, while I struck the note. A considerable weight and steadiness of blow was necessary to excite the harmonic. The sound at first was dull and unmusical, but immediately afterwards the harmonic corresponding to the node touched, sang out, always clearly enough to be unmistakably recognised, and sometimes, especially where the node corresponded to several harmonics, with a long clear ring, that was made brighter and longer by removing the stopper from the string, which then vibrated in the small loops conditioned by the node touched. The following are the first 20 harmonics of this C determined theoretically. Against each is placed its number of vibrations, and the name of the nearest note on the equally tempered scale, which was that of the piano used, with the theoretical number of hundredths of an equal semitone which had to be added to, or subtracted from, the pianoforte note, in order to give the true pitch of the harmonic. This list enabled the note heard to be immediately identified, by touching the corresponding notes on the pianoforte. Finally in the last column is given the number of inches from the belly-bridge at which one or more of the nodes of the harmonic would lie theoretically, for all the harmonics actually observed and brought out on the 29th July, 1884.'
Annotations in pencil and ink.
Subject: Music / Physics
Received 8 October 1884. Read 20 November 1884. Communicated by Alexander James Ellis.
A version of this paper was published in volume 37 of the Proceedings of the Royal Society as 'Observations on the harmonics of a string struck at one-eighth of its length'. |