I’ve been putting some energy into improving half-holing.
I’ve got the Bb, half-holing it enables me to bend the note
which helps playing blues. The G sharp is now only a little
less easy than using a key. F natural is tougher
but improving, and I seem to now actually be able
to do Eb pretty regularly.
I wonder how others are doing? Is anybody trying
this as a serious alternative to keys?
I’m waiting for a keyed Olwell and it occurs
to me that perhaps this is a remedy.
Bb..ok, G#..ok, Fnat…varies flute to flute, Eb…tell me more !
Yes, Jack, you can get an Eb on a simple-system, 6-hole flute if the 6th finger hole is large enough, although, by no means, is the half-holing technique a substitue for keys, in my opinion. Jemtheflute gives a demonstration of a two-octave chromatic scale being played on my low D flute on a YouTube video at my channel (link below). The video is the last one in the group of videos.
I’m putting down R3 straight and slantwise, so that it’s just barely creasing
the edge of the hole, if that. Down it goes decisively in that position.
Seems to be working OK. Rather unexpected success.
I’m beginning to prefer it to the key, because I find
my pinky on the key a bit unstable.
The idea is attractive that perhaps one can escape
the tyranny of keys, paying for them, waiting for them,
and so on.
I discovered I could cross-finger G#. It may not be a perfect G#, but I’m very happy. I can play in A Ionian now.
My idea is that we could use both approaches. If you want to slide a note you can’t by using a key. And also is some particular passages it might be tricky to use the key, while it could be easier to get the note by half holing.
Don’t limit your thinking that keys are just for achieving accidentals, keywork is very useful for venting in the third octave. I am not sure if you could get a fully chromatic third octave without them.
I find that G# and Fnat can be half holed pretty easily, Bb has a decent cross-fingering something like XOXXOX (individual results may vary) you can mess around with it a bit to see what works best on your Flute. I just don’t have the money to get keys. I would like a keyed Flute, to be able to play tunes in odd keys and to play the same tunes in different keys. I find that it is very hard (not impossible) to cleanly half hole notes in a faster tune, keys would make things a bit easier, but still have their own down falls as you guys know.
Oh, half-holing!
On the one hand, it’s a real temptation to extend the range of a keyless flute, by means of half-holing.
However, because I have so frequently been dismayed with the results, I have more often reached for a flute with keys.
The frugality in me continues to work at half-holing, but I admit to frequent defeat.
Thinking about it, I realize that I half-hole notes that I’m bending, and in fact it’s more like rolling my finger off or onto the hole than half holing.
To play an accidental that isn’t supposed to bend or slide, I use a forked fingering.
For Bb, I put the center of the ball of L2 on the downward
edge of the hole. I aim for that edge instead of
the hole. This works very well, virtually
as well as a key, and by rocking L2 into the hole
I can shade the note.
I like the as many options approach.
Cross fingering, half holing, keywork.
I practice half holing on my C# bell note bansuri
and not on my small tone holed Irish flute.
Bansuri is the diatonic flute par excellence for half holing
and a tradition of it that goes back a long, long time.
Firstly, it has large tone holes in relation to the tube width which is similar to the ratio found in most tin whistles which are also, IMO, the fipple flutes par excellence for half holing (cf recorders!). Large tone holes provide a greater canvas for half holing (often to the detriment of cross fingering).
Secondly, it is bamboo and therefore the lightest of the flutes. This means that providing you have a right technique for the “grip” (really a balance) you will have a lot of scope for full attention to the pivotting control required for sensitive half holing. (NB, the bamboo for bansuri is a lighter type than used in Chinese and Japanese instruments which tend to have thicked walls).
Thirdly, it is a thin walled instrument. The thinnest walled flute about. That means subtle techniques with your fingers will have a more pronounced effect. (forget flutes for a minute. do this. get two whistles in the same key with large tone holes, one with wooden body, the other with thin walled metal body. half hole them and compare.)
Fourthly, there are traditions of bansuri half holing that go back thousands of years. Good bansuri players are not only able to get a chromatic range (in the western 12 semitone sense) but are expected to obtain microtonal shadings and actually do so in performance. So there is ample scope for tuition in a well embedded trad. (A lot of high quality bansuri teachers are native American or now reside in the US so someone like you would have little problem finding one.)
Fifthly, aren’t you all so glad I don’t have any further points (as yet) otherwise you would have had to suffer the sloppiness of words like tenthly and even the possibilty of twelfthly, nineteenthly and the like! 
I’m a macrotonal guy in a microtonal world ; )