My first flute was almost a success.
Like, it was a success. I spent time and energy and concentration and now I have an out of tune PVC whistle that I can get a couple of different tones from.
But I'm going to start over and change a bunch of things. Not going to bother to finishing this first one by tuning it properly because I'm not happy with it; it's just misaligned with my expectations.
But it was useful because now that I know its first-hand performance attributes, I can connect the felt-sense to the numbers, and so now I can knowingly choose the numbers to pull felt-sense things in the desired direction.
Figuring out how to make this thing was frustrating.
There's like, this one random French guy on YouTube who gives a tutorial. Super clear trilingual directions, very simple tutorial, zero amounts of bullshit (beyond the obligatory preamble of "hey check out this cool weird instrument! Listen to me play some neat little tunes on it to prove it's a musical instrument!"), and his measurements are all in millimetres. Lovely. Wonderful. Literally the single best outcome you could possibly hope for from a video tutorial.
But he doesn't talk about the accoustic physics, or about how it feels to play.
Just "use these material and cut to this length, and then make these other cuts."
And also did not explain how to measure the other cuts (which fortunately doesn't seem to actually matter, because any high-precision acquired from fine measurement would be obliterated entirely by my extremely low precision implementation method: random rusty woodworking tools I found in the garage.)
So, okay, fair enough one guy isn't the repository of all human knowledge. I'll just look up "DIY PVC overtone flutes" elsewhere.
👨🏻🏫 couple of other random YouTube guys, being all "wow, that French guy made a cool thing! What a fun little project that will be for me to try. Here's my own little video about how I followed his tutorial and made my own copy. That was pretty fun, but it was annoying when he used millimetres because I'm American." And then they digress into talking about how they adopted the first guy's project specs into their native gobbledygook measurements.
👨🏻🏫 one or two blog posts that were the same thing, basically
👨🏻🏫 couple of amateur websites about Native American Flutes (and COMPREHENSIVELY so). Awesome!
- while NAFs *function as* overtone flutes, they have some added design elements to add functionality and improve their performance as musical instruments
- all their measurements in fractional inches
So for me to parse guidance from those resources I have to figure out how to unpack their formulas to get at exclusively what's relevant to my simplified design, convert their fractional measurements into decimal measurements, and then convert from imperial measurements into metric measurements.
Goddamn pain in the ass when I'm trying to work on a project in the evening and I'm crashing off all my meds and all this bloody runaround isn't impossible merely very difficult and very very very frustrating.
👨🏻🏫 a random post on a forum for people who make flutes and et cetera.
- guy being like, "hey I'm trying to make an overtone flute, and I'm using pvc pipe to simplify things for myself, and I started my numbers off using this science paper about didgeridoos (because the physics is the same; vibrating columns of air with one end closed) but something's awry with it can you give me some pointers please?"
- other guys being like "yeah man, of course. Okay, see, to get nice overtones whatcha want is for the dimensions of your column of air to have super high diameter-to-length ratios. Like, 1:35 is bare minimum, 1:40 is better, 1:50 would be amazing."
❌ That French guy who made the really awesome YouTube tutorial, his ratio in that tutorial is more like 1:20, lol
So while his flute does function and is super simple to create, it's janky as fuck.
❌ And because he doesn't explain ANY of the relationships between his measurements, the accoustic properties of his flute, how it feels to play, and how that relates to the range of tones it can play; it's impossible to know which measurements you should tinker with to redistribute the project's jankiness in order to emphasise a different prioritisation in the pursuit of high ratios.
❌ As an additional fun layer of obfuscation, the numbers used in the French guy's tutorial are the length and width of the plastic pipe, and not the length and width of the vibrating air column held within it (which is what the ratio is about), so that makes it even harder to connect the dots there.
The lengths being different is easier to catch, since those are measurements you've made yourself and there's a clear and separate starting point for each of the two measurements.
and then it's also a difference that doesn't even matter in the end anyway, because you end up adjusting the length of the pipe by shaving tiny increments of the end to get your flute into tune.
So you can't target a fixed ratio by measuring to an arbitrary length, because the lengths aren't arbitrary. Best you can do is have a desired target range of ratios, to hit a ballpark length for your desired tone.
But the widths being different is harder to catch. Because "20mm" is a designation of a type of pipe, and not necessarily a measurement of the air column that we imagine inside of the tube when doing calculations about it. 🙃
Good luck even noticing that without a set of callipers! And have fun getting your calculations all sorted out when you're trying to work out the ballpark lengths of pipe required to get your flute in tune!
(Because starting with a wrong width measurement leads to everything that follows being "imprecisely correct" at best)
What does the comprehensive NAF website have to say about it?
They have a simplified version, which, in its examples, uses fractional inches as assumed input figures, and then simplifies the equations with those figures in them,
so when I want to plug in my own numbers into the formula they provided, I can't do that, because I don't know which numbers are part of their assumed inputs and which numbers are part of the function which relates input to output. Grr.
And then they also have an extremely in-depth version, where they treat it like a physics homework problem and get deep into the nitty gritty of accoustic physics,
which is equally as useless, because that gives an unachievable precision of measurement, which simply can't be implemented with the tools, skills, and materials at hand. Best you can do is that french guy's way, of getting it close enough to where you want and then gradually shaving the length down to get it into tune.)
High ratios = overtone flute.
Low ratios but it doesn't sound horrible and it isn't horrible to play = different kind of flute.
Different kind of flute that doesn't sound far worse than an equivalent overtone flute of similar materials and construction methods = far beyond the scope of this project
Therefore overtone flute is inherently janky, jankiness which can not be removed, only reallocated.
The kind of flute I could make the best using what I have at hand is an overtone flute, so I'm going to embrace the jankiness as a design feature and work on building the best overtone flute I can, even though an overtone flute isn't the best kind of flute that I could try to make (flutes without jank is a solved problem; the technology of overtone flutes was superceded in the stone age)
- to make nice music with overtone flutes, you need to be able to close off the open end of the flute with your hand while playing, which gives you more tones to be able to use.
- therefore the length of your air-column is restricted by the physical length of your arms
(Because one end of the tube goes to your mouth, where you blow in air to get the tone, and the other end of the tube has to go somewhere within reach of your hands)
- and so if you want to pursue a high ratio, you have to make your flute higher and higher pitched by shrinking the diameter of your air column instead of its length
(- also, thinner pipes can be longer than wider ones, because you only need a finger to close the far end and not the palm of your hand, which improves their ratio even more.)
To get higher overtones you have to blow harder which makes them louder.
The limits of my lung capacity and of my eardrums are thankfully closely paired, which is a limitation on the number of overtones you can have for a given pipe.
More overtones by way of high ratio, by way of shrinking the air column's diameter makes the flute's tones more and more high-pitched. This steadily increases the whistle's irritation factor but eventually becomes inaudible.
Same at the low end; once you get long enough the fundamental frequency requires you to blow air so slowly that the tone is inaudible. Any tones you can hear, then, are some higher overtone or another, and so you lose the bottom part of your theoretical maximum range too.
A nominally 15mm pipe needs 525mm of length for a 1:35 ratio, 600mm for 1:40, and 750mm for 1:50.
Which note the fundamental frequencies are for those lengths idk.
The didgeridoo paper that the guy mentioned in his post on the flute-making forum, that was supposed to have a table of lengths to frequencies, wasn't it? Let's go have a look!
1. Dead link, but oh well never mind that,
2. Found the paper, and it's an undergraduate homework project rather than a publication from professional academia, and not that that matters, but oh well never mind that
3. All their measurements are in fractional inches because of course they fucking are (🤮), but oh well never mind that,
4. Didgeridoos aren't flutes, so they're occupying a very different zone of the frequency scale, so this paper's table of lengths to frequencies stops before it gets up to the numbers I need. Drat.
So! Where I'm at is that I have a long whistle I'm not super happy with, which is good because now I've got a spare metre or so of 20mm PVC which I can entirely sacrifice to practicing and refining my PVC-cutting skills, and testing which of my cutting tools are best suited to the job.
And then there are two possible directions to go in for the next attempts:
- loooong whistle with a wider bore, with a deep voice like a fujara
- looong whistle with a narrower bore, with a high piping voice like a penny whistle, to try to push that width:length ratio as high as I can get it just to see what that's like
