Bell Resonance

Discussion in 'Horns' started by Tootsall, Feb 13, 2004.

  1. Tootsall

    Tootsall Fortissimo User

    Oct 25, 2003
    Yee HAW!
    I had posted this under the "Free Blowing" topic, but Larry has asked if we could perhaps start a new thread for a different "take" on the issue: So here it is.

    In my original post under the "Free Blowing" topic, I mentioned what I feel is the mechanism that makes a trumpet "free blowing". In response, several posts were made to the effect that the penultimate sound of a trumpet is more often appreciated by the audience and that you don't want to lose too much of that sound through the vibration of the horn itself. (I may have paraphrased a bit much with that last statement but I think you get my drift).

    While I was writing my post I was thinking about a link that I'd seen on one of the "old" GR mouthpieces website. It had been replaced when their site was redesigned, but thanks to Brian Scriver, I have the link "back again". Personally, I was blown away when I first saw the research that had been done; I'd never thought of the WAY that a trumpet bell vibrates, nor thought through how that energy gets partially reflected back into the air column AS WELL AS radiating off of the outside of the bell. Further, I'd never really considered how it can "color" the sound of a trumpet. Dave's post really "turned on a light" for me when he mentioned the Thomas Moore article and connected "impedence" with "sound out front" rather than "horn design" (which is the more common link).

    Here is the page which shows a trumpet bell being "excited" at different frequencies. Note the pattern of the "nodes" which are moving the greatest distance (and creating the greatest vibrations in the air...hence "sound production"). See how there are more nodes but they are "tighter together" with the higher frequencies and notice how they extend back "down" the bell flare towards the bell tube. Then imagine a horn with different bell material, bell thickness, thickness variance... think about the effect on the vibrating node PATTERN with bracing at a different spot along the bell tube/throat.

    I had written an email to Professor Moore asking him about the apparent "discontinuity" at F=1194 and F=1356; he explained that there actually ARE more nodes at 1356 but that they extend down the bell and towards the rim a greater distance. (As far as I know, this is the same Dr. Moore who wrote the ITG article). The only thing I would absolutely LOVE to see is a video clip of the node pattern as the frequency is continuously increased; I'd like to watch the node pattern move back up the bell towards the bell tube and then "break up" and create a different pattern to support a greater number of vibrating "nodes" (or panels).

    The dark area in between the lighter nodes are areas where the vibration is relatively low. Truly amazing stuff to think of a bell shape vibrating with this pattern...looks like a steel drum!

    Enjoy the link....and thanks, Brian and GR.

  2. Larry Gianni

    Larry Gianni Piano User

    Nov 11, 2003
    Los Angeles
    Great stuff , Tootsall

    Please thank Gary Radtke and Brian Schriver for their help in re-trieving this link

    it's great - a picture, in this case, is definitely worth a thousand words


    Can you calculate what pitches are played and subsequently being photographed as vibration points on the bell. As we all know concert A = .440 Hz ( on a good day ) that being said, in trumpet talk that means our Bb is .440 Hz, right

    So on the chart they start with F = .466 Hz . What pitch, in trumpet terms, would that be ? Maybe someone knows of a chart for this somewhere and could provide the link.

    Thanks and again great stuff,

  3. Tootsall

    Tootsall Fortissimo User

    Oct 25, 2003
    Yee HAW!
    Cribbed from website:

    Calculation for Equal-Tempered tuning [A3 = 440Hz] Hertz
    ..........Octave=0 Octave=1 Octave=2 Octave=3 Octave=4 Octave=5
    0 A 55.000 110.000 220.000 440.000 880.000 1,760.000
    1 A#/Bb 58.270 116.541 233.082 466.164 932.328 1,864.655
    2 B 61.735 123.471 246.942 493.883 987.767 1,975.533
    3 C 65.406 130.813 261.626 523.251 1,046.502 2,093.005
    4 C#/Db 69.296 138.591 277.183 554.365 1,108.731 2,217.461
    5 D 73.416 146.832 293.665 587.330 1,174.659 2,349.318
    6 D#/Eb 77.782 155.563 311.127 622.254 1,244.508 2,489.016
    7 E 82.407 164.814 329.628 659.255 1,318.510 2,637.020
    8 F 87.307 174.614 349.228 698.456 1,396.913 2,793.826
    9 F#/Gb 92.499 184.997 369.994 739.989 1,479.978 2,959.955
    10 G 97.999 195.998 391.995 783.991 1,567.982 3,135.963
    11 G#/Ab 103.826 207.652 415.305 830.609 1,661.219 3,322.438
    12 A 110.000 220.000 440.000 880.000 1,760.000 3,520.000

    So then "Frequency = 466 hz" is Bb ("our" C) and "Frequency = 2736 hz" is ""our high G" (more or less...I'm not in a position to tackle "equal" vs "unequal" temperments and assuming we are still working with the King Silver Flair which is transposing down to concert pitch!)

    Every doubling of the frequency represents a single octave increase.
    Take A=440 as baseline, 880 is one octave up from there and 1,760 is one more octave up (2X880).
  4. dcstep

    dcstep Mezzo Piano User

    Nov 27, 2003
    "Penultimate" means "next to the last." I let it slide earlier, but this thread is taking on more weight, so I thought we'd better get straight what you actually meant to convey with that word. The audience hears the sound last, so maybe you meant the "ulitmate" tone of a trumpet, but I'm not sure. I think you're speaking of the trumpet sound the audience hears, not what the player hears.

    This thread is really broader than "Calicchio", but I'm willing to discuss it wherever it resides.

    I'd like to add that I think that a horn can have an excellent resonance from the player's point of view and still project well and present the audience with a rich palette of focused overtones. One reason I purchased my Selmer Paris is that I love the richness that I hear as a player. Also, it's very dynamic and responsive to the throttle. However, before I bought I got the chance to hear it in a large space played by a great player, finding it very attractive from that perspective also.

    OTOH, I've played horns that sound positively dead from the player's perspective, but they actually sound attractive out front. Yamaha Xenos come to mind. The Yamahas are very sturdy and seem overdamped if you listen only from the player's perspective. For example, after I brought the Selmer home for audition I couldn't stand to play my Yammy Z (I know it's not a Xeno, but the Xenos display even more deadness, IMHO), because it seemed so lifeless in comparison. Yet, I know that the Z sounded good on recording and when I heard others play it.

  5. Tootsall

    Tootsall Fortissimo User

    Oct 25, 2003
    Yee HAW!
    "Irregardless" you knew what I meant! :D

    Just funnin' ya, Dave; I knew it wasn't the word I wanted but couldn't think of the precisely exact one at the moment. (You must watch F1 racing on TV... seems like "penultimate" is the favorite word of the announcers...especially when the cars are bearing down on the white flag!).

    Oh, yes, Dave... I agree with you on the sound. For me, the instrument has to sound "nice and rich" to my ears as well as those of the audience; otherwise how would I ever learn to adjust my sound?... or would I? (Anybody know what Wynton hears when he's playing his M1 Abrahms?... in addition to the cash register?)
  6. dcstep

    dcstep Mezzo Piano User

    Nov 27, 2003
    You think "Shuey" is going to win another championship? I'd love to see Barracello beat him out some way, but it'll never happen.

    Well, I've played some of those heavy horns. I don't understand the attraction. It's probably best left at that. ;-)

  7. Tootsall

    Tootsall Fortissimo User

    Oct 25, 2003
    Yee HAW!
    No doubt the Shoe is going to give it a run for Ferarri's money. The only question I have is "Why did Villeneuve stick with BAR as long as he did?"

    Or... was he either a) laughing all the way to the bank, b) knew he'd never be able to stick with Michael, or c) both?

    On the super-heavy horn thing... having never played one, never touched one, never even seen one in real life.... I can't disagree. Must take one wallop of energy to get those things "moving"!

    While I'm at it... got a little math thing for you. The musical scale and frequencies are based on a logarithmic progression. Since every doubling of frequency represents an octave, and there are 12 steps in an octave, a simple bit of math allows you to figure out how much the frequency changes.

    Let "S" = one step

    one octave = 12 steps

    We'll let "X" be the multiplier from "step to step" but have to calculate what "X" actually is.

    one octave = frequency doubled

    Therefore 2 = X^(12)
    so X = 2^(1/12) (otherwise known as the twelfth root of 2)
    Doing the math, it turns out that X = 1.059463094....

    so take A = 440
    multiply 440 X 1.059.....
    then multiply the result times 1.059......
    when you've done this 11 times (the first multiplication gave you the first TWO steps) you'll see that the frequency is now 880... an evenly tempered scale with all the "white keys and black keys" in place.

    Of course, our western ears perceive the "correct pitch" as something slightly different, depending upon whether it's the 2nd, 3rd, 4th, etc. "step" in the scale so you can then throw all that math junk out the window and just buy a decent trumpet and learn to play it.
  8. Mikey

    Mikey Forte User

    Oct 24, 2003
    On the super-heavy horn thing... having never played one, never touched one, never even seen one in real life.... I can't disagree. Must take one wallop of energy to get those things "moving"![/quote]

    Yes, they are hard on your left elbow, too........... :-)

  9. MPM

    MPM Pianissimo User

    Nov 10, 2003
    Ok ... I'll say it .... UUUGGGG!!!!! :roll:

    Wasn't the original thought / question about the percieved qualities of a "free blowing" trumpet?
  10. Tootsall

    Tootsall Fortissimo User

    Oct 25, 2003
    Yee HAW!
    MPM... Yes, the original question was about free-blowing...
    and that's why this topic got moved out of THAT topic and into it's own. (At least, I think that's why Larry asked if I could move it) Anyway.. it's a cool topic all on it's own I think.

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