Same Sh*t, Different Day
One day 9,000 years ago, some unknown maker of instruments sat down to work on a crane bone. Music was important to her society, so it was with due reverence that she approached the task of making the flute, which would eventually grace a grave in Jiahu. She had extremely limited equipment. It's true. Not a synthesiser, tuning meter or spreadsheet in sight. She was also able to do a damn fine job of work on the flute, and presumably on many others. She had a couple of advantages: bone is actually easier to drill accurately than PVC if you do it right, and she'd had a lot of practice.
However, apart from the lack of computer gear, she seems to have had a disadvantage: techniques of voicing holes by filing angles don't seem to have been known back then. Voicing an instrument, the technique of making each note sound in tune, is a significant amount of work. I jest. If you make a wooden wind instrument from a kit or from scratch, the old 80:20 rule applies. The first 80% of the work, making it, takes 80% of the time. The last 20%, voicing it, also takes 80% of the time. It's why hand-made wooden recorders are many times more expensive than machine-made ones that are almost as good.
Our mobile phone company, one-2-one, had a series of TV advertisements ,which ran "who would you like to have a one-2-one with". A well-known present-day figure names someone who was famous earlier for the same thing. "I'd like a one-2-one with so-and-so: I'd like to ask..." I'm not famous, and probably neither was our flute-maker, but I'd like to have a one-2-one with her and find out the precise translation of what she said when she discovered the problem with hole 7. Allow me to explain.
Our flute, M282:20, was, like about forty others from the same find, made from the ulnae of the red-crowned crane. It's a vertically held end-blown type and has seven holes. some time prior to 1990 the acoustics were tested: results from eight runs with different embouchure angles were measured. The scale is given in the Nature article as approximating to F#5/G5 A5 B5 C6 D6 E6 F#6 A6. Figures given in earlier sources suggest mean actual values of 784Hz, 888Hz, 963Hz, 1071Hz, 1191Hz 1335Hz 1484Hz and 1718Hz. Reading these, it's easy enough to suggest that Dr Harbottle wanted to hear a Western scale, but I think that's unfair.
All of what follows is supposition, but there's evidence which can be cited to support it, even if it's not the only argument. The paper says, a trifle disparagingly, that "the carefully selected tone scale observed in M282:20 indicates that the Neolithic musician of the seventh millennium BC could play not just single notes, but perhaps even music". This is the academic norm: unless there are actual field recordings, err on the side of safety. I think that both maker and players were rather better than that.
I started by assuming that the hole wasn't a re-voicing, but a deliberate correction for a drift which would occur further up the scale. Many wind instruments have such holes, and I was looking for repeating groups of intervals, which would suggest this would be the case. I played around with the Zhao Feng figues and found a couple of repeats at holes 2-3-4 and holes 5-6-7, but although they make for interesting listening on a wavetable synth, I couldn't find any matches which made sense as a player. (Not all of the figures given in Zhao Feng actually make sense if the maker was seeking to re-voice for an octave, either, though.)
Flute M282:20, scale in cm from the picture. my rather poor re-drafting after a photograph from the paper.
The apparent length of the flute is 23 and a bit cm, a little longer than the dimension given in the Zhao Feng description.
the revoiced hole, no7, is the small dot to the left of the rightmost large hole.
So, I suspect that Juzhong Zhang the co-authors are at least close to the truth. What makes most sense to me, as a player and fledgling maker, is if the tube tone is now about 35Hz sharper than it originally was, giving a scale with two octave pairs in it. Octaves are pretty fundamental things, since they're a physical effect, and my suggestion would be that the pipe isn't meant to overblow holes 1-2 appear to me to be in the wrong place for a straight tube overblow anyway. I suspect the scale was intended to be close to what we would show as F#-A-B-C-D-E, although I don't think the intervals were intended to be quite like that. To be sure, I'd need to look at median figures for each hole with and without 7 and 7a closed, but it doesn't appear to me that Zuzhong Zhang and co. have those, either.So, there are circular markings round the holes which could indicate marking out. That's certainly what I'd do. Drill a small hole with a tiny awl and use a scriber to centre markings on that hole. Then cut, then voice each hole. These holes are not equally spaced, although they look to me as if the main holes were probably counter-drilled with the same tool and then individually adjusted with a tapered reamer. If I'm right, the flute-maker was aiming for hole 2 as an octave of the tube length and hole 7 as an octave of hole 1. Maybe it was a nice day and she returned after morning prayers to pick up from last night. We've all done it: worked that little bit too late and had to... She checked the pitch of hole 7, this morning using the correct embouchure and coming to it with fresh ears. I'd like to know what she said next. This is a significant error which belies the overall craftsmanship.
After a walk by the lake and a refreshing cup of Jasmine, she returned, probably yelled resoundingly at the first person who got in her way, and went back to work. There are many flute fragments and five other almost-complete flutes from the excavation so far, so although this one may have been special, it certainly wasn't impossible to make another.
Nowadays, on a really precious instrument, one would re-drill, plug the hole and start again. I have a Moeck 820 which was repaired in exactly this way but even with modern tools it cost as much as a new one to have the surgery. Someone making an instrument from scratch even today would need a very good reason for doing anything other than discarding it. Sure, if it's your first ever attempt, you do the best you can: once you've made a couple you get blasé, even if it's taken a lot of effort: life's too short.
I can think of several complex reasons why our maker would have kept it. Perhaps it was her first piece, although if so it is superb. Maybe the bone was from a very special or auspicious crane wing. But Occam's Razor suggests that she knew, or could calculate, fairly precisely, the correction needed to make the piece playable. It could be that she knew how big 7a needed to be, but I think it more likely that 7a was drilled with the same awl she used for centring the holes. In that case, she had to get it right first time, and knowing where 7a had to be is even more spectacular. With the pipe as it is, she got within 7Hz, which is rather better than I could manage. If the pipe length was as implied by hole 2, then it's possible that she got within 3Hz, which by my reckoning is nothing short of astounding.
Having given the maker due reverence, I wanted to find out what the flute would do.