So my reference instrument right now plays around 593hz at some breath pressure right before the jump, based on your guess in “All whistles play out of tune”.
By that definition it’s slightly sharp, but it’s what I get both with Freeman’s fipple and a 3d print of this fipple.
Using Ernoult-Fabre rectangular bend equation with edge angle effect (e.q. 10 + 16 + 23) I get 577.3hz @ 20C which is definitely a reachable frequency with my reference whistle (barely), and it’s 16 cents off what I measured.
Then I read your comment about CO2 Temperature and Humidity, and started investigating my air properties.
I’m using Lefebvre’s air properties right now, which I’m guessing are dry air (I don’t have access to Keefe 1984). So I ran a similar bore in WWIDesigner and humidity going from 0-100% sharpens it by frequency 3hz, but increasing CO2 to 40kppm decreases it by 6hz. So a net -3hz isn’t what I’m missing, but it did make me consider the temperature I was using:
For fun, I blew on a thermometer and got 32C, at this temperature the equation predicts 588.8hz. It’s really easy to hit this frequency with a slightly softer blowing pressure, so it feels like a pretty good prediction to me.
So here are the factors I’m aware are not accounted for:
- Humidity and CO2. I see three relevant references in the WWIDesigner bibliography I’ll check out.
- A correct balance between breath and ambient air properties
- My breath pressure and measuring error. This settles it, I need to build a blowing machine.
- Inaccuracy of the model itself
- Differences between recorders and whistle mouthpieces.
Am I missing anything? I’ll start working on toneholes now