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This post is to discuss specific information contained in "The Saxophone Is My Voice" by Ernest Ferron. Although the book contains several errors and some dated information nevertheless it is an excellent entry level text to learn more about saxophone acoustics.

On page 104 Ferron writes:

The basic question is why did Ferron divide by 3? What is his rationale for doing so once the distance to the antinode of the note a half step away is found by dividing (or multiplying) by 1.05946. The ramifications of this question are important since Ferron represents the "sensitive harmonic sites" in an alto neck in the illustration below copied from his book on p. 19.

A Mark VI alto neck including the tenon measures 195 mm. Going from the antinode length of G which is 362.81 mm according to Ferron's figures and the antinode of G an octave higher 362.81 / 2 = 181.405 would indicate that the difference of 181.405 would encompass nearly the entire 195 mm length of the neck. This would indicate that there are not 3 octaves of antinode positions, but only one.

My thinking is that the illustrations of "the sensitive harmonic sites" in alto and tenor necks in Ferron's book that have been widely distributed on the internet are incorrect because of the division by 3 which does not make any sense to me. Am I missing something here? Opposing thoughts and opinions are welcome.

On page 104 Ferron writes:

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 mmG# 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.

The basic question is why did Ferron divide by 3? What is his rationale for doing so once the distance to the antinode of the note a half step away is found by dividing (or multiplying) by 1.05946. The ramifications of this question are important since Ferron represents the "sensitive harmonic sites" in an alto neck in the illustration below copied from his book on p. 19.

*Note that he shows 3 octaves.*A Mark VI alto neck including the tenon measures 195 mm. Going from the antinode length of G which is 362.81 mm according to Ferron's figures and the antinode of G an octave higher 362.81 / 2 = 181.405 would indicate that the difference of 181.405 would encompass nearly the entire 195 mm length of the neck. This would indicate that there are not 3 octaves of antinode positions, but only one.

My thinking is that the illustrations of "the sensitive harmonic sites" in alto and tenor necks in Ferron's book that have been widely distributed on the internet are incorrect because of the division by 3 which does not make any sense to me. Am I missing something here? Opposing thoughts and opinions are welcome.