Warning, long post, got carried away...
This is more a reply to Dave's original post than to the more recent interesting but off topic drift.
An anecdote; a good Irish player was touring this side of the world and she had a button which was up too high and occasionally catching on the action board. She asked me to look and though I seldom do repairs she needed help and I agreed. High buttons can be simple, sometimes the lever needs a tweak and it is done, or a post is coming out. However on a Jeffries it can be a worn pivot hole in the lever and it needs a new lever assembly. So it transpired and I asked her to leave it with me for a day. As an afterthought I asked her if she would like me to tune a low note which I had heard to be out of tune at the concert. She agreed and when she came back I was expecting a lot of satisfaction. Instead all I got was bewilderment. It was like she couldn't get a good rhythm going. This was a note she used a lot in a two note chord and it was the slightly distorted interval that had alerted me to it. The chord was now as sweet as a 4th can be. Trouble is she was using the slight discord as a rhythm marker in her playing, it gave the chord a boost in presence she did not have to strive for with pressure. I reversed the procedure and gave it back. Harmony was restored.
I am on the side of thinking the player is right. Failing direction from them as close to 0 as you can do is best. A difference of 2 is too much for me. When tuning I aim for 0 on the meter but rarely open an instrument to change a + or - 1. If I had opened it already to do a reed nearby I might attempt to shift a 1 to a 0. I would definitely retune if the octave was 1 out the other way. A 2 always gets a tune. Do I hear you say, what about a 1.5? That would get a tune too. I have no issue with Greg's 5 or 6 passes. Because I am predominantly making for the Irish market I presume higher playing pressure and set the reed height and tune accordingly.
I think, though I suppose I would, new reeds have additional problems to reeds only retuned. They shift further according to little understood (by me) patterns. Stress relief in the metal? Could be. Valves changing as well? Could be.
When a tongue is first made I tune it a little sharp, perhaps 15 cents, and then when it is in a frame I like it still a little sharp, at least 5 cents. This because I find higher reeds easier to lower than raise, lower ones are less fussy. This is idealised, some days it does not happen like that. Once in the concertina they will have shifted. I then do a rough tune, (I play the note, put the right hand side of the concertina down, mark the value, pick up the concertina again) aiming for zero, hoping to be within 2 or 3. Any reeds with more than a 5 or 6 cent difference in and out of the concertina get a valve change before a tune. If it is all inside 2 or 3 difference (doesn't happen first time) I play it a lot, sometimes just a bunch of keys held down, in and out, if doing that I will wear earmuffs. There will be differences now and the set will need to be inspected and perhaps adjusted again. I then play the instrument a lot looking for reeds that are missing the last 1% of performance. I have a chart with the concertina and I make markings such as VB, VO (valve beside, valve opposite) S (slow) Q (quiet) and sometimes just ? or F! I play all of the common chords looking for strange sounding intervals. And octaves looking for beating. This procedure is always a challenge and is different every time, sometimes it is quicker, sometimes longer and I am never sure the difference is not me. The rule of thumb is, "it is probably the valve". I replace a few reed tongues in most concertinas, often just to remove the tongue from suspicion. It is a mistake for me to let a concertina go too soon, the tune can change in the first few weeks in a new owners hands and sometimes it will stay that way because people don't realise or have no access to a tuner. It can be a mistake to keep one too long, sometimes I fall in love with a new one and prefer it to my own. Hard to let it go!
I use a vacuum sucker, nothing too fancy, it is a tight clearance duct fan sitting under a plenum chamber. Sorry Terry, I can perceive no difference attributable to this. It gets me 1.6" water column of vacuum on the magnahelic, I would prefer slightly more, one of these days I am going to put a spigot into a bellows and measure typical playing pressures. When measuring tune I try to maintain even pressure on the bellows but I often think this is the reason the tuning process is less precise than I would like. Because I am predominantly making for the Irish market I presume higher playing pressure and set the reed accordingly.
I am very aware of out of tune notes but increasingly lack confidence in my ear as I get older. I did the online test a minute ago that offers two notes with increasingly narrow intervals. I got .9 hertz, mind you that was on the 4th try. I certainly can't do that hearing the notes on the run without the careful comparison, I doubt I could pick 5 cents. I don't like sitting in a nest of flutes (a chord of flutes) as I always blame myself for the out of tune notes. Last night I sat next to a great flute player who didn't play an out of tune note all night but it was disconcerting when he tuned as his low D always sounded very out of tune. He told me once he has to give it more volume to get it in tune while playing and he builds that into the phrasing. Nothing easy about flute playing.
Every time I have delved into the world of temperaments I have backed out again, trying not to knock anything off the shelves, thinking, I'll do this when I have more time.