Books › A descriptive catalogue of the musical instruments recently exhibited at the Royal Military Exhibition, London, 1890 …, 1891 › scan 258
Scan 258
A descriptive catalogue of the musical instruments recently exhibited at the Royal Military Exhibition, London, 1890 …, 1891
13 lines. Read by computer on 1 October 2026. Printed page 238. See the scan on archive.org.
1length of time. In the reed-tonometer, constructed by Herr Appunn, with which Mr. Ellis made his first series of measurements, there were, unfortunately, no means of maintaining equality of pressure; the pressure was not constant even while one reed was sounding, and when two reeds were speaking instead of one, further change of pressure ensued, hence Mr. Ellis's first results obtained by this apparatus were vitiated, but with proper precautions a reed-tonometer can be made a very valuable instrument, deserving more attention than it has hitherto received.
3DIVISION OF THE OCTAVE OR SCALE SYSTEMS.—As all instruments are not tuned from the same pitch-note—a' and c'' being those chiefly used—it is necessary, when accurate comparisons are required, to know the scale system to which any instrument whose pitch is noted conforms. The major diatonic scale in just intonation, that is, when its different notes as used in harmony are the most satisfying to the ear, has its intervals in the following order:—
5c d e f g a b c
68 major tone 9 minor tone 10 semi-tone 10 2/3 major tone 12 minor tone 13 1/3 major tone 15 semi-tone 16
74 major third 5 minor third 6 – perfect fourth – 8
83 – perfect fourth 4 – – perfect fifth – – 6
92 – – perfect fifth – – 3 – perfect fourth – 4
101 – – – – octave – – – 2
12In this scale system it will be noticed that a perfect fifth, as from c to g, comprises a major and a minor third, or two major tones, a minor tone, and a semi-tone. The fifth, from d to a, however, comprises two minor tones, a major tone, and a semi-tone; the difference between the two forms of fifths is, therefore, that between a major and a minor tone, or the comma of Didymus, ratio, 80:81. In other words, the a, which is correct in either the scale of c or that of f, is too flat for the scale of d. Other similar difficulties arise in passing from scale to scale, the root of them all being simply the arithmetical fact that the fraction 1/2 (the ratio of the octave), raised to the seventh power (1/2)^7, is not identical with the fraction 2/3 (the ratio of the fifth) raised to the twelfth power (2/3)^12. The first of these values represents an interval of seven octaves, the second an
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