We have to make fifty-four such pipes, each of the dimensions proper for the production of its own note, deep in the bass or shrill in the treble.
It is quite clear that we must not work by "rule of thumb," but understand well what we are about from the very first, if we do not wish to cut our wood to waste and cover ourselves with mortification.
Begin thus. Take a sheet of stout paper, and on it, with rule and compasses, draw a scale showing all the requisite measurements.
Here we must be a little arbitrary, and lay down the law without giving lengthy reasons for our ruling. Stopped pipes are half the length of open pipes yielding the same notes. Our CC pipe will therefore be 4 feet long. The four C's of the ascending scale are the halves of each other. Therefore Tenor C will be 2 feet, Middle C 1 foot, Treble C 6 inches, and C in alto 3 inches, in length. The word nearly, or about, must be understood as prefixed in every case to our measurements. Accordingly, the lengths of all the pipes in the stop will be easily obtained by drawing a vertical line 1 foot in length on the paper, and dividing it into twelve equal parts. At the bottom, write Tenor C, 2 feet; at the top, Middle C, 1 foot. Then the length of each of the eleven pipes intervening between these extremes will be at once obtained by easy measurement. By doubling these lengths we shall obtain those of the bass, or 8-feet octave. By halving them, those of the middle octave. By dividing them by four, we get those of the treble octave.
Note well that these rough and approximate lengths are speaking lengths of the wooden tubes, or, in other words, of the column of air within them, measured from the top of the block to the under side of the stopper. Hence, in cutting out the boards, the length of the block—about 3 inches, or less in small pipes—must be added to three of them, and an inch or more allowed to all four of them to give good room for the stopper.
But we are not yet in a position to cut out the boards.
It might be thought that as we get the lengths by the easy arithmetical process described above, so with equal ease shall we get the widths and depths of the blocks. The pipes are not square, but are deeper than they are wide, in the proportion of about 5 to 4. It might be thought that if the block of Tenor C be 2 inches wide and 2½ inches deep, then the block of Middle C will be 1 inch by 1¼ inches; the block of Foot C ½ inch by ⅝, and so on. This is not so. These treble pipes would be quite unreasonably small, and would give weak and thin sounds, while the bass octave, commencing with a block 4 inches by 5 inches, would be needlessly large for a chamber organ. Without wasting words upon a matter which is really very simple, let us say at once that we shall adopt for our Stopped Diapason a scale commencing with a CC block 3¼ inches wide and 4 inches deep, and that the block of Tenor C will be 2⅛ inches wide and 2⅝ deep. Thus the half of the width and depth of the CC block will not be reached until the eighteenth note above it, instead of the thirteenth, and in the higher parts of the scale the diminution in the sizes of the blocks may be yet more gradual.
Fig. 2.