Here we are interested in displacement antinodes. Piercing the neck precisely on a particular note's displacement antinode will not affect the note's (but only this note's) response. It is even possible to cut the tube here without imparing the note. It thus seems pertinent to use this peculiarity to determine the exact position of this or that note's displacement antinode ( or harmonic).
Place a 2.5 mm hole for the soprano (or a 5 or 6 mm ole for the other saxophones) on the neutral line of the neck curve. It can easily be filled in later.
Play the instrument's second register with the mouthpiece exactly in place. It is possible to play only one note, that being the one whose displacement antinode lies exactly on the hole and which will serve as a reference.
After removing the mouthpiece, measure the distance from the center of the hole to the end of the neck, and add the length of the theoretical pointed cone. This gives the harmonic's wavelength. An example using G with an alto neck, shows:
Length from the center of the hole to the end of the neck=157. Length of the theoretical pointed cone=205.81
Wavelength of the G harmonic (*) 157 + 205.81 = 362.81 [mm]
To find the position of G#, divide this length by the 12th root of 2 (1.05946), deduct this figure from the preceding length and divide by 3. [emphasis added]
For example: 362.81/1.05946 = 342.448, 362.81 - 342.448 = 20.362
20.362/3 = 6.78 mm G# is 6.78 mm from G, etc.
(*) It is in fact a quarter of a wave length (see page 9) since we are actually always working with a quarters (sic) of the total wave length.
