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V. § 62.] PITCH AND LENGTH OF PIPE. 127
An open pipe, to produce the same note, would therefore have to be two feet in length.
It has been just shown that the vibration-number of the lowest tone producible, either from a stopped or an open pipe, varies inversely as the length of the pipe. The length of the pipe therefore varies inversely as the vibration-number. Hence the relations established in § 55 for strings hold also for columns of air contained in pipes. The case of the pipe-sounds is, however, somewhat simpler than that of the string-sounds, since the pitch of the latter depends on the tension of the strings as well as on their lengths, whereas, in the former, pitch depends, under given atmospheric conditions, on length alone. Hence we may define a note of assigned pitch by merely stating the length of the stopped, or open, pipe whose fundamental tone it is. The open pipe is commonly preferred for this purpose, and accordingly organ builders call middle C '2-foot tone ;' the Octave below it '4-foot tone,' and so on. The lowest C on modern pianofortes is '16-foot tone;' that one Octave lower, which is found only on the very largest organs, '32-foot tone.' The highest note of the pianoforte, usually A, would be about '2-inch tone.'