Understanding flute tuning

Understanding flute tuning

Postby Adam Beaudoin » Wed Oct 09, 2019 4:27 pm

I'm new to making wind instruments, and have started with simple bamboo whistles. I'm running into some trouble understanding the process of tuning.

So, while the math is beyond me, I basically understand the existence of end corrections & acoustic length vs physical bore length. What I don't quite get is how the placement of tone holes is correlated with their pitches. I pretty much anticipated the placement being similar to dividing a string by ratios (I'm assuming a just intonation relative to the fundamental), but offset in one direction – I think away from the mouthpiece? – to account for the acoustic length of the air column. But that doesn't seem to match with the results I'm getting from a flutomat style calculator (https://whistlemaker.com/calculator). For example, when plugging in my values (.5" bore diameter, .15625" wall thickness, .07sq" area of flue opening, fundamental at – really just flat of – E329.63Hz) and using their default 6-hole scale, the sixth hole (D#622.26Hz) is calculated at 10.47" (presumably from the end of the physical bore length, as there's no reference to the acoustic length or the amount of end correction). This seems wrong to me, as the entire length of this flute is under 11".

So, is there something about the nature of cylinders that supercedes the usual ratios of a divided string? Am I making an error in filling out the calculator? Is that calculator wrong? I'd imagine that the disconnect comes from some mis- or incomplete understanding on my end, but I can't see what.
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Re: Understanding flute tuning

Postby Jim McConkey » Wed Oct 09, 2019 10:03 pm

Before I even get started, in my experience none of these flute calculators is very exact. They should get you in the ballpark, but you always have to fine tune.

First, I suspect the bell frequency you are using is way too low. My D flute (~293 Hz) is roughly 22" long. Your 11" E flute should be just over an octave higher, nominally 659 Hz. Second, I believe the hole measurements returned by the calculator are given from the END of the flute, not the end you blow across. Try the new base pitch and see if the numbers agree with your flute better from the end of the flute.

The pitch of a blown column of air is proportional to the length of the air column. Shorten the column and the pitch goes up. If you halve the length, the pitch goes up by an octave, same as with a string. An open hole effectively ends the air column. Don't forget in a flute that the embouchure is NOT at the end of the air column. The end is typically a couple inches up inside the head. As you said, any holes in a thick tube will also effectively add to the length, even if they are closed. There can be some tradeoff between hole position and diameter. Moving a hole closer to the embouchure will require a smaller hole, and moving a hole closer to the end will require a larger hole from the calculated suggestions (though there are obviously practical limits to this).

All math aside, use the calculator to find the approximate positions of the holes, then adjust them up or down slightly so your fingers lay on the holes comfortably. Drill undersized holes (small than what the calculator says) at your preferred locations. With all holes closed, trim the end until the base pitch is correct. Open only the lowest hole. The pitch of this note will initially be too low. Gradually enlarge the lowest hole until the pitch comes up to its correct value. Then open the lowest two holes and gradually enlarge the 2nd hold from the bottom until the pitch is correct. Repeat for all holes. You may have to go back and repeat, because fingering a larger hole effectively lengthens the pipe just a little. The only caveat to this type of tuning is that cross-fingerings may not work as intended.
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Re: Understanding flute tuning

Postby Adam Beaudoin » Thu Oct 10, 2019 12:57 pm

Thanks, Jim. I have read up a bit on the procedures for tuning the finger holes, so I do anticipate somewhat low precision for the calculators. But it would be good to have a general road-map, or know how to make one, in order to experiment with scales & tunings while keeping the finger-holes around the same size.

Okay, I'm going to bet that the problem was entering in the wrong octave! I'm not overblowing or anything, I just wasn't comparing the generated pitch to the flute, and counted on remembering accurately later which of the two is the sound my flute was making.

Thanks for the breakdown of the fine-tuning procedure, very clear and direct. I'll be sure to bookmark the thread for quick reference. One clarification - you're saying to drill the undersized holes before tuning the fundamental? I assume that's because the holes change the shape of the air cavity, but in that case wouldn't I want to wait until the holes were all perfectly tuned before setting/tuning the fundamental and octave? Or is it a process of back and forth tweaking adjusting for the effects of each other?

Good to know it follows the length-ratio pattern I'm familiar with. Once I get a better grip on the math for the end corrections, at least, that should allow me to lay these out without the calculator. Mark in the just ratios, size holes to approximate pitch, and then temper as/if desired.
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Re: Understanding flute tuning

Postby Jim McConkey » Fri Oct 11, 2019 9:44 pm

You are technically correct that the final end tuning might have to be done at the end. You need to start with undersized holes because you can make a small hole bigger, but not visa versa. The larger holes will effectively lengthen the instrument, so the total length my have to be corrected at the end. But you have to start somewhere, so start by getting the the pipe and minimal covered holes to the correct pitch, then adjust from there.

The hole placement is a tradeoff between playability and a reasonable hole size. As I mentioned before, cross-fingerings make it even more complicated, but you should master the procedure without them before going down that hole.
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Re: Understanding flute tuning

Postby Adam Beaudoin » Sat Oct 12, 2019 12:14 am

Jim McConkey wrote:The larger holes will effectively lengthen the instrument


Amazing!
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