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Search for the missing cone

Discussion in 'Books, Literature, and Websites' started by jbtsax, Mar 7, 2010.

  1. jbtsax

    jbtsax Distinguished Member Distinguished Member

    I read this as saying you know more than Benade on this topic. Given a choice, I think I will go with Benade's interpretation in his published works, if you don't mind. You are of course welcome to your theories built upon your misinterpretation of his use of the term "constriction". I can think of much better uses of my time than to continue a pointless debate on the fine points of your theory about what Benade should have actually said had he not been so vague.
  2. What I can say, without the slightest doubt, is that the example of the one-piece, straight sided soprano, every bit as much a true saxophone as any other, is the clearest demonstration of what a saxophone is, what it's essential mechanical and acoustical parts are, and how Benade's sometimes generalized statements apply. I think anyone can see that.

    Once one understands why the mouthpiece/constriction, the substitution, the surrogate missing cone, ...whatever you want to call it.... has it's own resonant frequency, when ON the saxophone body under normal playing conditions, and the influence it has on the other resonances of the complete air column, one can understand Benade's substitution frs requirement, and the insistence, for primarily convenience and mechanical reasons (you can't separate the neck opening from the neck tube) upon the mouthpiece + neck as the testing unit. Testing the frs of the mouthpiece + entire neck is a mere approximation of whether the actual and very real, occurring in the horn under playing conditions, mouthpiece + constriction resonance is the same as it's theoretical, measured from the apex to that point, equivalent. To borrow your original terminology - that is the "True" frs requirement.

    All of the post-Benade studies substantiate this, except for yours.
  3. Now I have a question about the Mouthpiece Equivalent Volume Study, which you posted this link to above:


    It appears to me, that here you made tests with the tube/cork inserted 10mm into the mouthpiece shank exclusively, from which you calculated the actual equivalent volume (reed compliance) added 28% more volume to the hard-walled, mouthpiece chamber, actually used. I think these results are accurate, however, I question your conclusion, that based upon these results at 10mm insertion, you claim that increasing or decreasing the amount of insertion, and therefore mouthpiece volume actually used, that the same 28% increase would apply in every case.

    If you made tests with the tube at different insertion lengths, with the same results, then of course, you must be correct. You don't mention any however, and as such, your conclusion would seem scientifically, a bit premature.

    I'm inclined to think that, though changing the mouthpiece volume used would have some effect, that to a substantial degree, the reed compliance is fixed, determined by the reed, the lay of the mouthpiece, and the players vocal tract, and independent of the mouthpiece chamber volume.

    Let's say we substituted a clarinet tenon-style coupling for the mouthpiece and the tube, and the mouthpiece had the same inner diameter as the tube. What would the added volume be then? It would be 28% of what then, the entire tube volume?

    I think this requires more testing before any such absolute conclusion (add 28% in every case - as per your Missing Cone Volume Study) can be made.
  4. jbtsax

    jbtsax Distinguished Member Distinguished Member

    The more I read the more confused I get. If you don't mind, here are a few questions to provide an opportunity to put down your thoughts and ideas more clearly.

    What exactly does this mean?

    Exactly what are you referring to as the mouthpiece/constriction? Is it the mouthpiece plus the constriction that has no length that you keep referring to? What is the "substitution"? Is it just the mouthpiece, or is it the mouthpiece and the neck?

    Once you have answered that, please share your understanding of why that has its own resonant frequency when on the saxophone body under normal playing conditions. Also what would that resonant frequency be on an alto saxophone, for example when the note being played is a low C.

    This quite confusing. I think I know what Benade's "substitution frs requirement is", but what exactly is the influence the Frs of the "whatever" on the other resonances of the complete air column?

    Again, this statement makes no sense to me. Exactly what point are you trying to get across?

    Exactly what is the true Frs requirement you are referring to?

    All of the post-Benade studies substantiate what exactly? Which study of mine are you making reference to. I have done several and put them on my website. Can you make a numbered list of all of the information in said study that you believe is in error?
  5. jbtsax

    jbtsax Distinguished Member Distinguished Member

    Your point is well taken. In that particular study the mouthpiece effective volume was found to be 2.78 ml greater than the physical volume of the mouthpiece used which was an increase of 28%. This was with the mouthpiece only 10 mm on to the cork.

    In the comparative missing cone volume study, the mouthpiece was placed 28.2 mm on to the neck. Without doing another mouthpiece effective volume study I had the choice of using the 28% increase or the 2.78 ml increase and I chose the former.

    I plan to do another mouthpiece effective volume measurement with the mouthpiece on the cork 28.2 mm and then put that result into the missing cone study. I am also going to use my beaded string device to check the neck length and the graduated cylinder measurement for the mouthpiece volume as well in the interest of accuracy. I will announce when the study with these revisions is posted.
  6. John,

    Thanks. I'll be interested in your results.

    I got very accurate mouthpiece volume results using a 30 unit (3/10cc) srynge. I only had to fill it 42 times to get my Bari Richie Cole mouthpiece volume.

    Measuring the shortest inside neck length (bottom) and the longest (top, with a slotted rubber insert pressing the solder against the top of the tube it's entire length), the averaged length was 3mm longer than the best center-line measurement I could do by hand.

    The correct volume unit for these tests is the cubic centimeter, or cc = 1000mm3. The centi-liter, or cl, is actually 10,000mm3.
  7. I think you must empty your cup first.
  8. jbtsax

    jbtsax Distinguished Member Distinguished Member

    [From Wikipedia] One cubic centimeter corresponds to a volume of 1⁄1,000,000 of a cubic meter, or 1⁄1000 of a litre, or one milliliter; thus, 1 cm3 ≡ 1 mL.

    In many scientific fields, the use of cubic centimeters has been replaced by the milliliter.
  9. jbtsax

    jbtsax Distinguished Member Distinguished Member

  10. Just from a quick glance, I see that you calculate the frequency of your neck section using the formula for a perfect, straight sided cone, yet in your last neck study, you showed us that your neck was far from anything straight sided, having, according to your measurements, 6 different conical tapers. I see no reference in this latest study to your previous neck measurements, nor any reference to how you treat the 21mm of cylindrical tenon, so clearly diagrammed, which are considered neck length and volume.

    In that light, I'm not sure how to interpret the results of this study compared to those previous . There seems to be conflicting information.
  11. jbtsax

    jbtsax Distinguished Member Distinguished Member

    Please try to understand my response to your questions so we don't get into another circular argument like before.

    1. The natural resonant frequency of the fundamental is based upon the length of a cone x 2 or the length of a cylinder x 4. The taper of the cone or its irregularity only affects the modes above the fundamental. F = c/2L applies whether the cone is perfectly straight sided or not.

    2. The 21 mm tenon of the neck is a part of the neck's length that determines the length of the soundwave and therefore the frequency.

    3. There is no conflicting information if one understands the principles underlying the calculations used in each study.
  12. John,

    Thanks. I was unaware that the formula for the frequency of a perfect cone also applied to non-cone shapes. Following your method, I measured my unaltered Martin tenor neck (211.41mm), center-line, tip to tip, and calculated it's theoretical frequency (818.29Hz). Then I stopped the tenon end (flat across the open end) and tested it's actual frequency by both popping and blowing across the small end. The neck produced a perfectly in-tune concert Ab (830.64Hz). That's a difference of 25 cents. That is certainly not good enough for musical intonation. Is that close enough for frs tuning? It would appear that those missing ca. 3 ml do make a difference.

  13. Sorry, I made a mistake. No transposition necessary, so the actual pitch generated by my tenor neck was a perfectly in-tune concert Bb (932.32Hz) and that's a difference of 226 cents ( 2 semi-tones and 26 cents).
  14. John,

    I just tested my Martin alto neck (tenon removed) via your method.

    Length: 169.86mm
    Played Frequency (stopped and popped/blown): 1480hz
    Calculated (by length F = 346m/169.86mm*2: 1018.47Hz

  15. jbtsax

    jbtsax Distinguished Member Distinguished Member

    This is great Lance! You always force me to go do some more research. Here is the answer to the conundrum you have presented from Wikipedia at this link:



    An open conical tube, that is, one in the shape of a frustum of a cone with both ends open, will have resonant frequencies approximately equal to those of an open cylindrical pipe of the same length. Open cylindrical tubes resonate at the approximate frequencies

    f = v/2L v=speed of sound

    The resonant frequencies of a stopped conical tube — a complete cone or frustum with one end closed — satisfy a more complicated condition:

    kL = nπ − tan − 1kx where the wavenumber k is k = 2πf / v

    What is happening then is that you are creating a closed cone by the manner you are generating the sound. When the mouthpiece is on the cork and played on the neck, the neck is an open frustum which behaves much like an open cylinder as far as resonant frequency is concerned. I have been trying to find a way to get a stable resonant frequency from my alto neck with both ends open with little or no success. I was able to get the calculated frequency one time, but have been unable to recreate striking it in exactly the same manner to repeat the result. If you find a way, please let me know.

  16. John,

    No problem. The open tube is the same as a flute or recorder, so just blow across the small end, and you will hear the pitch. It doesn't form a strong regime. Actually, it's very weak, but you can hear a definite pitch. It's the same, blowing on the large end, though even softer. Don't forget to plug the register hole.

    The played pitch of my alto neck was 932Hz. The calculated pitch was 1018Hz. That's a difference of 153 cents, or, a half step + quarter tone.

  17. jbtsax

    jbtsax Distinguished Member Distinguished Member

    I'm curious as to how your are measuring the Frequency of your played note so exactly.

    Also how is it you are getting the same blown pitch with both ends open as before with one end closed. That does not correlate with the information in the link I provided.

    A truncated cone open on both ends behaves much like an open cylinder. A closed cone has a much different formula to find its pitch. I believe it is safe to assume that pitch is not the same as a cone open on both ends. Yet your "blowing" test both open and closed revealed the exact same pitch. What's up with that, as Jerry Seinfeld would say? :)
  18. pete

    pete Brassica Oleracea Staff Member Administrator

    No soup for you!
  19. I have 2 methods.

    1. Blowing the neck while simultaneously playing a digital keyboard. Remarkably, in these cases, the played pitch has been either a perfect unison or within a few slow beats of a perfect unison. Changing blowing angle does not influence the pitch appreciably.

    2. A digital tuner with digital and analog read-out.

    What's up with that is, it pays to read the information slowly and carefully. You are confused. So what would Jerry say then?

    The alto neck was first play tested as a closed frustum (1480Hz) and calculated using the open cone formula, as having a calculated frequency, by length F = 346m/169.86mm*2, of 1018.47Hz. As you pointed out, the neck should be play tested as an open cone.

    The second play test of the same alto neck, as an open cone, and tested from each open end, resulted in a frequency of 932Hz. Again, the same neck calculations using the open cone formula, as having a calculated frequency, by length F = 346m/169.86mm*2, of 1018.47Hz.

    There are no errors in the second test. The difference between the tested and calculated, open cone frequencies was 153 cents, or, a half step + quarter tone.

    Do not confuse the tenor neck test results with those of the alto neck. If you doubt the integrity of my numbers, I suggest you play test your own neck as an open cone. It's quite simple. Just put your lips together and blow.
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