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II. § 30.] RELATIVE PITCH. 61
tion possessed by individual observers. An experiment which a well-known Cambridge tuner, Mr James Ling, was kind enough to make in my presence showed that in the neighbourhood of middle-C of the pianoforte he was able to distinguish, by listening to them successively, two sounds forming with each other an interval so small that it would take about 250 such intervals to make up a single octave. The difficulty of discriminating pitch increases rapidly with very low or very high sounds; the above instance of what can be achieved by the most highly-trained ears applies, therefore, only to a few octaves in the middle region of the scale. The continuously shading-off gradations presented by the scale of pitch afford no antecedent presumption that particular sets of sounds should be singled out to form the materials of Music. Nevertheless it is found that practically the group of different sounds employed in a musical composition is, relatively to the whole available stock, extraordinarily limited.
30. When one sound has been arbitrarily selected as the starting-point, there are certain other sounds, having fixed relations of pitch to that previously chosen, which are capable of forming, with it and with each other, melodic and harmonic effects especially pleasing to our ears. These are the notes