592 PHILOSOPHICAL TRANSACTIONS, [aNNO 1775. 



sounds. Notwithstanding the small extent of this series, yet, by the aid of 

 varying the measure, it is capable of several different melodies, though the 

 general cast of them will be melancholy. 



The specific difference between this system of pipes, and the smaller, 

 described before, will be understood from the following observations. It consists 

 of 10 pipes, joined together in the same manner as those of the smaller system. 

 The first Q pipes exhibit to the eye the same figure as the system before 

 described ; and the 10th pipe is a little longer than N° 4. For in this larger 

 system, N" 8 is 13 inches long ; N° 4 134-, nearly; and N° 10 is 14 inches. 

 The sounds which each pipe exhibits easily, are marked in minims. As the 

 upper minims are 6ths to those next under them, it follows, from the law of 

 harmonic sounds, that the lower minims are 5th to the fundamental sounds 

 of these pipes, which are written in quavers, to show that they are very difficult 

 to be produced. The upper minims of N° 1, 2, 3, 4, 5, and also of 10, are 

 sharp Sds, or rather, major lOths, to the fundamental sound of each pipe. 

 And the upper minims of N° 6, 7) 8, Q, are nearly minor tenths to their 

 fundamentals ; which circumstance seems to agree with what was remarked in 

 the smaller system, as an extraordinary property, touching the minor 3ds. But 

 Mr. S. will not yet assert, that this property is altogether natural, because he 

 found some of the latter pipes were partly obstructed by accidental rubbish, 

 which was drawn out with difficulty : so that he pretends not to decide, whether 

 the cause of their being, not quite, in the same proportion of tune, as he found 

 in the first system, arises from some casual injury, or from original intention, or 

 original inaccuracy. The interval between N° 1 and 2 in these pipes, is only of 

 2 semitones ; whereas that between the N° 1 and 2 of the former system, was 

 of 3 semitones. The series N° 2, 3, 4, 5, and the series N° 6, 7, 8, Q, have 

 similar intervals in both systems. Therefore he imagines these to have been the 

 original extent of the whole modulating series, like the double tetrachord of the 

 Greeks, and that the N° 1 and N° 10 are additional at pleasure ; as, in the 

 smaller system, the interval between N° 1 and 2 was a semitone greater than 

 that between N° 1 and 2 in the larger system ; and N° 10 in the siDaller system 

 was totally omitted, though he had seen 2 others which had it. The sounds in 

 this larger system are 7 tones lower than those of the smaller, which corresponds 

 with the difference of their dimensions ; the pipe N° 4 in this system measuring 

 nearly 1 3-1- inches in length, with diameter seemingly proportional ; whereas the 

 N° 4 in the smaller system measured only 7-1- inches. By increasing the velocity 

 of the blast, these pipes gave sounds still higher, which were 4ths above the 

 upper minims, or octave and 6ths above the fundamentals ; and with a little more 

 force, tritones, or sharp 4ths, above the upper minims, which were octave and 

 flat 7ths above the fundamentals. 



