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Tuning for Math Geeks

jbtsax

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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.
 

Attachments

  • Short tube vs long tube tuning study.pdf
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JTHANK

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this makes me think if I should use the open C# for tuning when I adjust the position of the mpc, since it is most affected by the slightest change in the mpc position...
 

Nick Wyver

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Except open C# in often a flat note on saxes. It's also the note most affected by embouchure, so, unless you're sure your embouchure is solid, it's better to go for G or below.
 
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jbtsax

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I have always advocated tuning to an F# on saxophone, A concert on alto and bari and E concert on soprano and tenor. It seems that this note is very near the center of the range on the chart which makes perfect sense. If the octaves were between C and low C, the F# being the tritone is at the exact center between the two pitches.
 

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