This is a condensation of an article I wrote for the Piano Technicians Guild. The original article is much more complete with graphs and diagrams. I encourage you to join the PTG so you can receive more informative articles like this one, from other technicians.
Virgil Smith has written that the sound of a tuned trichord is different than that of the single unison string.
Professor Gabriel Weinreich had a study that showed that the pitch of two strings tuned pure was different than the pitch of the single string. (Called the Weinreich Effect)
Some technicians who are aware of this, assume the pitch drops when adding a second string, and some tune the single string slightly sharp. This is a waste of time because it is wrong.
Professor Weinreich is clear: it can drop, or rise, or stay the same.
To prove this, I did some simple tests that any one can do.
Tune a pure unison trichord.
Mute right two, measure left.
Mute outside, measure center.
Mute left two measure right.
Mute right, measure left two as a single pitch.
Mute left, measure right two as a single pitch.
Measure all three as a single pitch.
Conclusions.
The pitch of the final trichord can go up or down or stay the same, relative to the pitches of the single strings, as much as 2 cents!
Even the pitch of the final trichord can go up or down or stay the same relative to the pitches of the double string unisons, as much as 2 cents! (Double string unison means the left two as one pitch or the right two as one pitch. I did not measure the outside two.)
The frequency variation with time, of the final trichord can be different than the single or double unisons, by up to 4 cents. (That is, the variation of the pitch with time can change up to 4 cents. The trichord pitch can change over time even if each single string has a constant pitch!)
Implication.
If you are assuming that the pitch of the single string will not change when you remove your mutes and tune up the trichord, your tuning will suffer, or if you are planning to check everything over again after you remove all your mutes and tune the whole piano, you will be doing extra work you do not have to do.
Recommendation.
Always judge the final trichord before moving on.
I have been able to drastically reduce my tuning time and increase the quality of my tunings using this and other specialized tuning techniques that I have developed. I have had to develop some of these myself because I couldn’t find any resources efficiently describing high level tuning techniques. It seems the big guys keep most of this a secret or aren’t aware or don’t know how or want to explain it.
As for making more money, with a fast and accurate method that uses this and other techniques I have developed, I have been able to tune 9 pianos in one day and make $1350. There was two weeks where I was in high demand where I tuned an average of 7 pianos a day and made $10,500. I can post my schedule if you don’t believe it. (Personally I don’t believe it myself!)
But without these techniques that help me tune high quality tunings fast, I never would have been able to do it.
With these techniques I am able to charge more because I am worth it.
Some technicians are not able to tune these high quality, concert level tunings or would take too much time to do it and choose not to do it for residential customers. Yesterday I did a concert tuning for a residential customer in only 70 minutes.
I encourage people to use an ETD to make these kind of measurements for themselves and really question some of the “common” knowledge that is passed around. I have found that some of it is not explained effectively and some is just plain wrong, passed on from decades of acceptance and not verified.
We now have the technology to measure piano strings and confirm or disprove some of these “truths”.