I suggest another tuning after the next change of season is well established. I say that the next tuning will last better, but this one will make the biggest difference.
I do between two and three passes, depending on the part of the scale. I'm not allergic to work the first time I see a piano. It gets the relationship off to an excellent start, which promotes trust and cordiality from then on. It's also a chance to deal with any little problems the piano is having, and to answer questions and deal with concerns the owner may have.
One thing about being 75 and semi-retired: I never need to rush to another job.
Terry and all,When calculating a pitch correction, this is what CyberTuner does. First it calculates a tuning for the piano, based on sampling the 5 A's A1 - A5 on that piano. We start our tuning at A0 and move chromatically up to C8, unisons as you go. It measures the pitch of each note before tuning it and calculates a target pitch based on a unique overpull percentage for each note. Not just 25%, but rather 22% for a note and 28% for the next note. As you move up the scale having tuned the prior notes lowers the pitch of the coming notes, called pre-drop. CyberTuner uses this information. In addition to having a percentage overpull chart for each note, we use 4 different overpull charts, based on the size of the piano. This leads to a very refined first tuning.Like most of you, I learned to do a quick first pass and then a careful fine tuning. I now do a careful first tuning and a quick 5-10 minute second touch up tuning. CyberTuner is amazingly accurate after just one tuning.We treat every tuning as a pitch correction, whether it is 5¢ or 25¢.. For corrections of less than 20¢ only one pass is necessary followed by optimizing the unisons. I can do a very solid 20¢ pitch raise in an hour or so.I tuned aurally for years and have tried other ETDs. Good technicians develop a feel for pitch raises and make their own small adjustments based on experience. Good as that is, it is not as accurate as modern computing techniques.
RCT has preprogrammed overpull percentages for different sections of the piano. The overpull for each note is based on the trailing average so if you have an outlier it doesn't necessarily follow a strict note by note calculation.
i agree with Carl that RCT has the most sophisticated and reliable pitch raise function and will do a one pass tuning very well within a certain range. I think 20c is pushing it unless it's a piano that doesn't require a really precise tuning. But even there the tuning will often be acceptable.
Where the pitch range function is less reliable is if the piano is out of tune in various directions, some notes sharp some flat. That's not typical, most pianos responding to humidity or time move in one direction or the other. But on a large pitch correction where you are roughing it into place quickly you might miss on both sides of the target pitch. In that case I often set the RCT on fine tune mode for the second pass where overpull is removed from the equation.
As far as charging for pitch raises, I charge by time. My basic "tuning only" rate is based on a one hour appointment. If pitch correction, or voicing or regulation pushes it to 90 minutes or two hours I charge for the time required. Most modest pitch corrections can be accomplished with a one pass tuning and unison check, easily done within an hour. Two full passes pushes that time up a bit but usually if the piano has not been serviced recently enough to avoid that kind of pitch correction it will need other work as well and I'm scheduling a full service appointment anyway which ranges from 2-4 hours, sometimes more. If I schedule a two hour or four hour appointment they are paying me for the time I spend, I don't charge by each menu item.
Choose a pitch. Tune all the A's to that Pitch+10%. Then tune all the C#'s and F's to that pitch. Next tune all the G#'s to that pitch+8%. Next tune all the C's and E's to that Pitch. (you're half-way there!) Now tune all the G's to that pitch + 6% followed by all the B's and D#'s. Finally tune all the F#'s to that Pitch+4% followed by all the A#'s and D's. That's it. Chromatically the instrument should be merely out of tune, but roughly at the chosen Pitch - and there shouldn't be any string breakage. Now simply fine-tune the whole thing to your chosen Pitch and Temperament.