It is commonly known that when the mouthpiece is moved on or off the cork that the "short tube" notes are affected more than the "long tube" notes. This is true on both the cylindrical clarinet as well as the conical saxophone.
The attached pdf file gives a chart of the "calculated" pitch difference on an alto saxophone from the shortest open tube note C# (not counting the palm keys) down to low C# just around the bend. These figures are based upon the formula F = C/L where F is frequency, C is the speed of sound (345 m/s), and L is the wavelength in cm.
It is important to note that these "calculations" are based upon the premise that IF the mouthpiece is moved 5mm it adds or subtracts 10mm or 1cm from the note's wavelength. [It becomes 1cm because the wavelength is 2X the physical length of the instrument].
This is a big IF because moving the mouthpiece off 5mm adds approximately 1cc to the effective volume of the mouthpiece that is a substitute for the missing cone. It is still unclear to me what roles adding to the overall length and increasing the mouthpiece effective volume are on the pitch and in what ways, if any, they are interrelated.
That said, the accuracy of the graph is debatable, however it may be useful to show the relative difference in change of pitch as one moves from short tube notes down to long tube notes. It would be interesting to remove the volume added to the mouthpiece by its being pulled out by inserting 1cc of blu-tac or other material to interior of the mouthpiece and comparing the tuning results. Hopefully I can do experiments like this when I get my artificial embouchure up and running.
View attachment Short tube vs long tube tuning study.pdf
The attached pdf file gives a chart of the "calculated" pitch difference on an alto saxophone from the shortest open tube note C# (not counting the palm keys) down to low C# just around the bend. These figures are based upon the formula F = C/L where F is frequency, C is the speed of sound (345 m/s), and L is the wavelength in cm.
It is important to note that these "calculations" are based upon the premise that IF the mouthpiece is moved 5mm it adds or subtracts 10mm or 1cm from the note's wavelength. [It becomes 1cm because the wavelength is 2X the physical length of the instrument].
This is a big IF because moving the mouthpiece off 5mm adds approximately 1cc to the effective volume of the mouthpiece that is a substitute for the missing cone. It is still unclear to me what roles adding to the overall length and increasing the mouthpiece effective volume are on the pitch and in what ways, if any, they are interrelated.
That said, the accuracy of the graph is debatable, however it may be useful to show the relative difference in change of pitch as one moves from short tube notes down to long tube notes. It would be interesting to remove the volume added to the mouthpiece by its being pulled out by inserting 1cc of blu-tac or other material to interior of the mouthpiece and comparing the tuning results. Hopefully I can do experiments like this when I get my artificial embouchure up and running.
View attachment Short tube vs long tube tuning study.pdf
