Hi Frank,
I was sick with the flu for a week and had plenty of time to think and study what the best tuners actually listen for when tuning. I came to the conclusion that the most important thing is to listen to major thirds and sixths. Then I also discovered certain patterns in tuning this way, including the expression of interference beats in these intervals.
When tuning a piano using only this method (I’m no longer capable of doing it myself, but my colleague is truly an outstanding tuner), the fifths, fourths, octaves, and tenths come out exactly as they should. However, there is a significant difference in the thirds and sixths compared to all tuning software. The only one that supposedly comes somewhat close is Reyburn Cybertuner. This is not just my own idea—my colleague and I discuss this issue a lot.
The problem with all tuners is that they make the thirds and sixths too fast, which results in a very harsh tuning. I’m attaching a table of interference beats as well.
With Pianoscope, I still have an issue—even in the Beta version—starting from G#3 downward (in most cases, Pianoscope places these tones too high; when I tune this area by ear using major 3rds and 6ths, I place the notes a bit lower) and from A#4 upward. Going towards the bass, the lower register ends up lower overall compared to Pianoscope, and the same applies to the treble.
Do you think it would be very problematic to create a new tuning style based on this principle? I don’t know to what extent Pianoscope accounts for this, but it seems to me that it doesn’t much. Maybe it’s just my impression. In temperament, we are fairly close, but in the areas I mentioned, not at all. The result of this tuning is that the whole instrument sounds more harmonious and pure.
I mean that Pianoscope would first calculate the exact frequencies of each note starting from a reference pitch, such as A4, based on precise interference beat rates. Then, for each note, it would display whether the number of beats is too low or too high—just like it currently shows whether you’re flat or sharp.


Explanation:
Number of Beats is determined by the frequency difference between two tones.
This difference (in Hz) is perceived as the interference beats, which are changes in amplitude that the human ear detects as a rhythm or pulsation.
Number of Beats therefore represents how fast the tones are oscillating in a way that creates a perceptible "beat" to the ear.
Then perhaps it wouldn’t even be necessary to record each instrument to determine inharmonicity—it’s just a hypothesis, because all the intervals would essentially "fall into place" on their own.
Don’t take this the wrong way—you’re doing a great job, and I’m very happy with Pianoscope. I’m just looking for ways to improve it.