The method I use, which is similar to that which Paul Coats uses, I got for free from Arthur Benade. It is printed right there in his published papers from the 1970's, and since I first started reading him 4 years ago, I have heard the key phrases tossed back and forth on the various saxophone forums and seen them quoted in many a doctoral thesis, absent of any apparent comprehension as to what they actually mean in their practical application. I'll paraphrase:
1. Saxophone players should be as meticulous in matching their mouthpieces to their horns as oboist/bassoonists are in fiddling with their reeds. That sounds nice. We know about volume and frs/frequency, but did anyone ever bother to go see just what it is that oboists/bassoonists actually do? There must be something there we can learn from. I don't see any orchestras tuning up to the soprano saxophone's concert A.
2. That meticulousness includes tweaking the volume/frs to get the optimal results. That means that once we got into the ballpark using the numbers, we abandon them to score.
Benade's oboe reed balancing routine boils down to this when related to the saxophone:
We are well aware from previous discussions of the volume induced tendencies of the conical air column - how at a 1/1 mouthpiece volume/missing cone volume ratio and lower, they induce sharpness in the upper registers, and a bit lower than 1/1, those tendencies lessen and then become inverted. We are also aware that a large chambered mouthpiece increases those tendencies in the upper registers compared to a small chambered mouthpiece - the frs of the two are different.
To eliminate the conical air column effects for the played instrument we must abandon the A=440 pitch center for a moment, and anchor the mouthpiece volume (i.e. where it is placed on the cork) so that the low end of our overblown tube (D1/D2) has optimal resonance alignment - it must produce a perfect octave. Easy. Pull out (or push in) until D1/D2 is a perfect octave - and here is where "meticulous" comes into play. Tune the octave using a tuner so that the center of your unavoidable pitch variations on D2 is at 0 cents deviation from where the D1 is (not necessarily 0 on the meter). One uses a steady, normal embouchure making absolutely no adjustments. No adjustments. No adjustments. We are halfway there.
Now, unless we had a perfect mouthpiece to start with, our pitch center is off, as is the resonance alignment of the short end of the overblown tube (C#2/C#3). Whatever we do to fix this, we must maintain the initial, optimal mouthpiece volume alignment (Not the place on the cork, but the perfect D1/D2 octave). Realize that the initial "pulling out/pushing in" adjustment changed two aspects of the mouthpiece, the volume AND the length, for a pretty gross change in the stretching of the scale. We now make gradual adjustments to the length alone, or frs - the pitch tendency of the chamber type in the upper registers, using the shortest overblown tube as our reference. Making the chamber fatter while maintaining volume, raises the overall played pitch of the mouthpiece, affecting the upper register more than the lower. Making the chamber narrower while maintaining volume lowers it.
Between repeated steps of checking the D1/D2 octave for perfection and then making the appropriate chamber geometry adjustment, raising or lowering the pitch to improve the C#2/C#3 octave, the short tube will come into perfect alignment (same 0 cent deviation at center of pitch wobble) . With both ends of the basic tube perfectly aligned, the ends (bell tones/palm keys) and in-between (middle register) take care of themselves. The entire scale is within 5 cents of flat (on my horn, verified by 3rd party), perfectly situated in the A=440 pitch center.
One experiences a new playing and listening sensation - one voice - no perception of register changes. The sound gets a silvery "sheen" to it as the horn resonates more perfectly with the cosmos - really. Now, after you experience this, from both the playing and listening standpoint, it becomes addictive. You immediately notice the conical air column effect qualities that you left behind, to varied degrees, in the playing of others - everywhere (almost - some got lucky or were smart with their setup). It sticks out like wrong notes in Mozart. You can even start listening to the silvery sheen evenness more than the notes they are playing, as you realize that hearing the conical air column effects is tiring, even annoying.
There is in fact a fairly narrow range of mouthpiece designs which can be successfully optimized - extremely high baffles being the main design problem.
1. Saxophone players should be as meticulous in matching their mouthpieces to their horns as oboist/bassoonists are in fiddling with their reeds. That sounds nice. We know about volume and frs/frequency, but did anyone ever bother to go see just what it is that oboists/bassoonists actually do? There must be something there we can learn from. I don't see any orchestras tuning up to the soprano saxophone's concert A.
2. That meticulousness includes tweaking the volume/frs to get the optimal results. That means that once we got into the ballpark using the numbers, we abandon them to score.
Benade's oboe reed balancing routine boils down to this when related to the saxophone:
We are well aware from previous discussions of the volume induced tendencies of the conical air column - how at a 1/1 mouthpiece volume/missing cone volume ratio and lower, they induce sharpness in the upper registers, and a bit lower than 1/1, those tendencies lessen and then become inverted. We are also aware that a large chambered mouthpiece increases those tendencies in the upper registers compared to a small chambered mouthpiece - the frs of the two are different.
To eliminate the conical air column effects for the played instrument we must abandon the A=440 pitch center for a moment, and anchor the mouthpiece volume (i.e. where it is placed on the cork) so that the low end of our overblown tube (D1/D2) has optimal resonance alignment - it must produce a perfect octave. Easy. Pull out (or push in) until D1/D2 is a perfect octave - and here is where "meticulous" comes into play. Tune the octave using a tuner so that the center of your unavoidable pitch variations on D2 is at 0 cents deviation from where the D1 is (not necessarily 0 on the meter). One uses a steady, normal embouchure making absolutely no adjustments. No adjustments. No adjustments. We are halfway there.
Now, unless we had a perfect mouthpiece to start with, our pitch center is off, as is the resonance alignment of the short end of the overblown tube (C#2/C#3). Whatever we do to fix this, we must maintain the initial, optimal mouthpiece volume alignment (Not the place on the cork, but the perfect D1/D2 octave). Realize that the initial "pulling out/pushing in" adjustment changed two aspects of the mouthpiece, the volume AND the length, for a pretty gross change in the stretching of the scale. We now make gradual adjustments to the length alone, or frs - the pitch tendency of the chamber type in the upper registers, using the shortest overblown tube as our reference. Making the chamber fatter while maintaining volume, raises the overall played pitch of the mouthpiece, affecting the upper register more than the lower. Making the chamber narrower while maintaining volume lowers it.
Between repeated steps of checking the D1/D2 octave for perfection and then making the appropriate chamber geometry adjustment, raising or lowering the pitch to improve the C#2/C#3 octave, the short tube will come into perfect alignment (same 0 cent deviation at center of pitch wobble) . With both ends of the basic tube perfectly aligned, the ends (bell tones/palm keys) and in-between (middle register) take care of themselves. The entire scale is within 5 cents of flat (on my horn, verified by 3rd party), perfectly situated in the A=440 pitch center.
One experiences a new playing and listening sensation - one voice - no perception of register changes. The sound gets a silvery "sheen" to it as the horn resonates more perfectly with the cosmos - really. Now, after you experience this, from both the playing and listening standpoint, it becomes addictive. You immediately notice the conical air column effect qualities that you left behind, to varied degrees, in the playing of others - everywhere (almost - some got lucky or were smart with their setup). It sticks out like wrong notes in Mozart. You can even start listening to the silvery sheen evenness more than the notes they are playing, as you realize that hearing the conical air column effects is tiring, even annoying.
There is in fact a fairly narrow range of mouthpiece designs which can be successfully optimized - extremely high baffles being the main design problem.
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