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PostPosted: Mon Jul 22, 2019 2:32 pm 
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It may just be because I'm not very good, but I find the standard metal tube whistle to be more expressive and it feels like it's because of the thinner walls. Pitch bends just seem more emphatic and easier to pull of in a musical way. The Ellis "essential flute" I have is handles half holing much better than my Delrin M&E. But I would not trust my own opinion since I'm still a beginner


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PostPosted: Thu Aug 22, 2019 11:21 pm 
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Dang! I totally missed this thread. I wrote an essay on practical flute acoustics this spring, that you may be interested in: it addresses both wall thickness and undercutting in detail and in summary (summary toward the end of the essay). It is available on my website at https://www.aldglen.org/acoustics

In proper forum etiquette, rather than merely directing yall away from this page, I will supply some of the text here. (It feels weird because I dont want to flaunt my essay, but also I wrote it to be a resource for exactly questions like this.)

"The wall thickness, at the location of a tonehole or the embouchure hole, affects the volume (space) of the tonehole when closed, and also affects the acoustic admittance of the hole when open and thus the frequency. "

"The same holds true for the embouchure hole’s end-correction. So, a thicker wall at the embouchure hole means a flattening of the entire flute, while a thickening of the wall at any given tonehole means a flattening of the frequency at that tonehole. Furthermore, for closed tone holes, an increase in wall thickness and volume acts as an increase in the perturbation to the bore at that point-- usually flattening the frequencies of toneholes downstream, but also having various effects depending on the location of the standing waves in reference to that perturbation."

"In general, undercutting a tonehole at all will raise its frequency. [...] However, it is clear that undercutting acts as a widening of the perturbation of the bore at that point, which, as we will discuss later, would raise the frequency of the tonehole (see ‘Bore Perturbations in General’). In practice it is obvious that any undercutting will generally sharpen the frequencies associated with that tonehole."

"Undercutting in a particular direction, either downstream or upstream, will raise the frequencies of both the fundamental and the upper registers, but will raise them at different rates, ‘shrinking or widening the octave.’ "

Something important to understand is how these aspects all affect one another. What happens at the site of one tonehole will affect other toneholes in various ways due to various dynamics.

Thinning the wall at a middle tonehole will sharpen that toneholes frequency by increasing the admittance at that tonehole-- but it also decreases the volume of the perturbation of the bore at that point when the tonehole is closed, which, for totally different reasons, may sharpen or even flatten the frequencies of toneholes lower down the flute, depending on how the standing waves line up with that middle tonehole.

Maybe im being redundant at this point. Sidenote, does anyone else frequently typo "tonehole" as "tonehoke"?

I like to make my flutes as thick as possible, mainky for durability, strength-- but I am limited by the intersection of two constraints: there is an optimal thickness for the wall at the embouchure hole, and i want the flute to have a moreorless cylindrical exterior, despite the taper of the bore. So this determines the wall thickness for me.

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PostPosted: Fri Sep 20, 2019 12:47 pm 
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For a given tonehole diameter, a thick wall (tall tonehole) will give a lower note. Thinning the wall makes the note sharp.
A thick wall will give rise to more harmonics, and more tonal headroom (the faculty of manipulating the tone for artistic effect). In contrast, a thin wall gives a "thin sound;" some people describe the pennywhistle as a musical straw.
Undercutting a tonehole raises its respective pitch. Undercutting below (down the bore) tends to stretch the octave. Undercutting above compresses it. Undercutting all the toneholes adds volume to the whole instrument, lowering its overall pitch.
The walls should not be parallel, but bulging toward the inner space (= rounded where they meet the bore, and rounded where they meet the outside of the body = undercut and overcut, per Benade). Naturally, a thicker wall makes undercutting possible. On fancy metal flutes, undercutting means a rounded sweep up-the-bore and down-the-bore. These cuts improve tonal headroom, playability, legato notes, etc.. The undercutting option requires soldered-on toneholes (as opposed to drawn toneholes). Undercutting and overcutting would be possible. Of course, hydraulic forming would do the job.
If you take a good flute and apply your own undercutting to the holes, the musical scale will be disturbed. Undercutting must be considered as part of the original design, evaluation and construction.
There's an extreme form of undercutting called "bassooning". Imagine a rather large tonehole covered with a disc, and the disc has a smallish hole in it (I mean they're cut this way in the body of the instrument with a fraise). Holes that are radically wider at the bottom will tend to compress the octave. I think they're noisy. Wm Callender of Boston fraised his toneholes.
High toneholes create extra volume in the bore. This extra volume compounds at the top of the physical scale (top of the left hand) where the toneholes get closer together. The extra volume will raise the pitch of those notes. This effect is what make the tapered bore necessary. Boehm minimized the height of the chimneys, thereby minimizing these pesky effects.
On a note like low F#, hole #5 is near a flow antinode, and its companion pressure antinode is an inch or so above the C# hole (when sounding the fundamental). As you go down the scale to D, the pressure antinode falls into the C# hole at the top of the left hand. Suddenly, this antinode meets a section of bore that has a greater cross-section. According to Rayleigh's Rules, this octave will be wider than the notes around it: flat foot explained in a nutshell.
Rudolph Cornelius Wiedoeft was a saxophone virtuoso during the 1910s. For a time, Holton made a Wiedoeft model saxophone with high toneholes.
Generally, I make the wall 25% of bore diameter at that point: ID x 1.5 = OD.
Large toneholes tend to stretch the octave.
The octave will stretch with proximity to an open tonehole below (sub-semitone venting). G is complicated because it's only a half step above F#, an open hole. The other chromatics have a normally-closed key; when playing the chromatics, there are now 2 open toneholes in a row. Such a flute is now diatonic: one set of harmonics for the "natural D-scale," another when using the keys. Nicholson liked to play in the key of Eb (the player must open these levers: D#, E#, G#, A# and B#).


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