I'm trying to make my own bamboo flute or perhaps "saxophone" of sorts, and before wasting any material I want to have the right construction plans.
I've seen some examples of simple types of bamboo flutes, but they usually seem to be built for one key only, and if you want to play at other keys (or basically playing chromatic notes) you have to either half-hole or use cross-fingering (or both even).
Now, as I've been trying to study the physics behind the sound production of the woodwinds, what I understood is that playing chromatic notes using cross-fingering (=tone holes being closed below the first open tone hole, rather than keeping a continuous series of open tone holes) isn't perfect in terms of intonation, so the chromatic notes are off from what's expected (to my understanding, flat) and thus you can't modulate accurately to all keys differing from the instrument's base key.
To my understanding, the issue for a long time of these instruments' histories is the physiological limitation of the number of fingers humans have, such that we can't place a finger to control each dedicated tone hole in a truly chromatic tone hole-configuration. So I then understood that the mechanical key systems developed for these instruments in their later stages involved enabling each finger the control more than one tone hole in some convoluted interconnected way, and thus I figured there now should be a dedicated tone hole for each chromatic note.
But when I read about the concert flute, I can't figure how many tone holes are actually being controlled. Different places cite different numbers, but on Wikipedia the concert flute is said to usually have 16 tone holes, while the range is 3 octaves. I know it overblows to an octave, so 16+12 (overblow in semitones) is only 28, not 36. Does that mean in the modern concert flute still not all chromatic notes are played without actual (I disregard how the fingers look when pressing the key mechanism) cross-fingering? Does that mean some notes within a flute of a specific keys are known to have somewhat impaired intonation or tone?
And how does the saxophone have it, on the other hand?
The layout I imagined would "only" involve 12 tone holes each a semitone apart (so opening all 12 plays the octave of the bass note), so with the overblow you'll have a range of 2 fully-chromatic octaves with no cross-fingering patterns. I'm still trying to figure out the possible mechanism for operating that.
Thanks in advance.