In an effort to figure out why some whistles are flat in the upper register while others are not, I have determined that an understanding of the physics behind sound in a tube will solve the dilemma.
My first question is why does overblowing cause the whistle to be one octave higher? The obvious answer is that the sound is vibrating exactly twice as much as on the lower register. But is that correct and how does it happen?
As I get closer to the answer, I’ll be sure to keep everyone posted. Those who care and those who don’t.
Your surmise about the frequency doubling is correct. It doubles because overblowing increases the velocity of the air impinging on the blade across the window. At certain specific velocity ranges, the air column will vibrate at one of the higher resonant frequencies of the tube. I haven’t directly measured the laminar speeds for this, but I would guess that doubling the speed of the laminar flow, for example, would cause a one-octave incease in pitch.
Cheers!
serpent
well considering that an octave is a doubling in frequency, then this would seem feasible. you could also cut the length of your tube in half and it should do the same thing, heh
With that said, it stands to reason when a whistle is flat on the second octave or gets progressively flatter the higher you go, something is preventing the soundwaves from reaching that doubling of wavelength.
I experimented last night with some of my more difficult whistles and discovered that I suffer from a fear of high notes (A2 and above). In an effort to be more quiet I don’t blow as hard. This certainly causes a flat sound. OK fine. However some of my other whistles are still flat on D2 and above (I say “D” but it could be any note for a particular key whistle, e.g. A2 on an A).
My next step is to figure out what that something is if it’s not my breathing.
Although a whistle is supposed to play one octave higher in the second register it does go a little flat. The reason deals with the effect of high frequency and high pressure.
First, higher pressure obtained by overblowing produces a wider windsheet coming out of the windway travel across the window to the blade. This causes a whistle to behave differently in the second octave and up.
Also, higher pressure in the bore travels closer to the bore surface than low pressure does, toneholes appear a miniscule fraction larger with higher pressure but this a small insignificant effect.
Higher pressure also can allow the air column to travel into the atmosphere a little more.
Second, high frequency. High Frequency sees things in the bore that low frequency doesn’t see. The Taper in the Boehm flute doesn’t do much at low frequency but at high frequency (second octave) there are two air columns forming in the bore instead of one, it just so happens that the first air column closer to the fipple gets a slight size distortion due to the reduced area where the taper is located. If effect, the instrument tunes better between octaves.
BTW - Higher frequencies in wood instruments will be affected by porousity in the wood grain more than the low frequencies.
Now during the ‘sound’ unit we recently finished in my Advanced Placement Physics class I’m taking, we studied this type of stuff, and the lightbulb clicked when I realized it’s relevance to whistles.
It all has to do with the Open Tube equation.
First of all, you have your V=F(greek landa) equation for speed of sound. V - velocity of sound through the medium (in this case air- 343m/s)
F- frequency (D at 294 Hz)
Landa- wavelength
That said, the open tube emitts a base frequency which is 1/2 Landa.
So your equation for the D note would be:
V=F(1/2 Landa)
Or:
343m/s=294Hz(1/2)
or: a wavelength of 2.33 (with all holes closed)
To spare you the Physics of it all, point blank, the upper octave would be slightly under the natural (base) frequency. Therefore, we need to compensate for that mathematical imperfection. ie. blowing slightly harder than normal, or tuning to the upper octave, then blowing under so the lower notes are in tune.
Did that make sense? Really, it’s all about playing with the frequencies and knowing what to do in an order to keep the pitch in tune. Some instruments in particular are tempermental, and you, as musicians, have to learn what to do to “fix” it. (My saxophone is perpetually sharp on it’s C, and I always have to under blow or drop my jaw to keep it in tune, then re-adjust for the rest of the notes.)
wouldn’t that be lamda, the greek L? i only insist because i’m jealous that i can’t understand the physics. at the risk of boring one and all, my new sweetheart pro D is in fantastically good tune: northern birch laminated with a phenolic resin, slightly conical bore. maybe somebody can tell me something about the physical properties of that! it should behave a lot like a polymer/plastic/whatever. ralph sweet says the effect of humidity/moisture should be minimal to no effect at all.
I can prove why there are only certain notes produced by an open pipe, but it involves the use of partial differential equations, so it’s inappropriate to post it here. Basically the air pressure inside a tube producing a musical tone satisfies a certain system of equations. These equations can be solved to show that the only frequencies which can be produced by the pipe are integer multiples of a certain fundamental frequency. These integer multiples are called harmonics. On a D whistle (with all holes closed), the fundamental frequency is the first octave D, the second harmonic is twice that frequency, which is the second octave D. The third harmonic would be second octave G (but G is only played this way on a tabor pipe). The fourth harmonic is 3rd octave D, etc.
Isilwen’s post contains the quantitative information about the fundamental frequency and wavelength for the low D whistle.
Ridseard, in fact playing harmonics with the holes closed is a good exercise for lip control on the flute.
For anyone who isn’t sure what the “harmonic” notes are just think of the first four notes of “Thus Spake Zarathustra” (2001 Space Odyssey).
Last night I was working with my Susato A and discovered I can get A2 and B2 with a little better breath control but the D and up is still real flat.
Then I started lifting my finger just a tiny bit of the D hole and of course it played in tune.
Therefore I have decided that I am going to attempt a surgical procedure on the c# hole. I am slowly going to widen it. I must be very careful since I don’t want to sharpen the lower too much.
If it fails then I’ll be forced to buy a new low A.
Do you want to buy my Susato low A? I never play it, and have no idea if it would be in tune by your book or not. I also don’t know if it would be any different from the Susato A you have now. But let me know if you are interested.
While I agree with most of you on this topic, I would like to say that overblowing modes(octaves is imprecise)produces an elongated false bore air column at the bore end as well as extended false bore at any open tonehole and the voicing hole.
In whistles or Duct Flutes with deep toneholes the air column is forced up into the deep toneholes by internal pressure in what Benade calls “The Tonehole Lattice Effect”,increasing total cubic volume of the air column in the upper harmonic modes for flatter tone.
Another reason for flatness in the overblown modes is due to unused cubic area in the top of the cylindrical bore headjoint . In the first mode/octave the low pressure air column only uses a parabolic area with a vertex at the fipple face and when overblown,this space is “filled in” by the pressurized air column because of increased (used) cubic volume. If the headjoint were a parabolic eflector,this flattening effect would be lessened. The Boehm flute achieves this in part with its’ conoid shaped headjoint.
In Recorders, the flattening effect is reduced by using a decreasing conical bore to match the first and second modes/octaves at the expense of the practical use of the 3rd and 4th modes/octaves that are available(though imperfect)to the cylindrical Tin whistle.
note: If you wish better control of pitch in the upper modes of a cylindrical whistle, I suggest adding a dorsal(thumb) “speaker hole” between the 1st and 2nd toneholes for “pinching” like a Recorder. When a Recorder player pinches open this hole he/she disrupts the fundamental frequency mode allowing the next dominant mode to take over(the second mode in cylindrical acoustics) and this hole can double as a pitch bending device.
at the risk of boring one and all, my new sweetheart pro D is in fantastically good tune: northern birch laminated with a phenolic resin, slightly conical bore. maybe somebody can tell me something about the physical properties of that! it should behave a lot like a polymer/plastic/whatever. ralph sweet says the effect of humidity/moisture should be minimal to no effect at all.
Yes, I guess it would be Lamda… with an m…