All the holes are oval in shape. The divisions of the four holed pipe are from top hole to fourth 10-5/8 in., to the second 1-3/8 in., to the third 1-3/8 in., to the fourth 1-1/4 in., to the end 3 in.; these together making 17-5/8 in. The division of the three holed pipe are from the top to the first hole 13-1/2 in., to the second hole 1-3/8 in., to the third hole 1-3/8 in., to the end 1-1/2 in.; making 17-6/8 in. The stalk knots of the reed are in each pipe at 6-5/8 in. distant from the upper end, and a knot is again found at the the extreme lower end of the four holed pipe, causing the opening to be partially occluded. This contraction would have a flattening effect and consequently the three holed (which is free from such a knot) is the longer of the two, evidently cut with the view to coincide in pitch with the other. Obviously also each hole from the top is larger than the one previous; this arises from the fact that, as stated, the pipes are not truly cylindrical, but narrow toward the bottom, and so they may require the holes to be enlarged to sharpen the notes; equivalent this to cutting the holes higher. To the musician investigating these matters it is of interest to observe that the two upper holes of the three-holed pipe coincide in their position with the two lowest holes of the four-holed pipe and consequently do not extend the compass of the notes, they merely pair the other pipe, yet if the reed of either differs, then, in flatness or sharpness the interval would show variation, and such an effect might be a designed one, giving a choice to the player. The lowest hole of the three-holed pipe extends the sounds that limit the tetrachord by one tone, and this method by extension reappears in aftertime in the Greek systems as an added tone also. It is doubtful whether we are to consider that the open extreme end of a pipe is intended to produce a sound which is to be taken into the musical scale, even the least civilised people seeming to regard the note given as outside the designed series and not to be used; but it is easy to conceive how a pentatonic scale might have been developed by bringing it into use. Another point to be noticed as affecting the pitch is that the distance between the fourth and the third holes is an eighth less than exists between other holes, and it may be that it was so intended to compensate for flatness, or to make a slight difference of interval.