The idea of actually being able to tune and/or measure pitch on any piano to within one tenth of a cent accuracy is very wishful thinking.
And the idea that the piano ‘system’ is capable of a stability within one tenth of a cent is also very wishful thinking.
To put all this into perspective, Dr. Al Sanderson said that in order for us to hear the difference in the beating of a Major 3rd, the interval’s width needs to be changed by .3 cents.
Please keep that in mind when reading these posts. And especially keep it in mind when trying some of these mapping procedures, measuring the widths of the prime 5ths, balancing the prime 5ths, and using those prime 5th widths to determine the width of the prime octave.
If you try to tune and measure everything to an accuracy of .1 c., you will make yourself crazy and give up.
But even at that, you will learn a few things. First, you will learn just how unstable the system in general really is, and, you will learn just how fine the SAT’s measurements are and how hard it is to really ‘stop the lights’ and use our tuning hammers to that degree of accuracy.
Whenever you read a guideline here for a particular interval’s suggested or measured width, please don’t take the numbers as absolute truths.
Using these guidelines will get us very very close. If I say the prime 5ths @ -1.5 c. are the best, getting one of them to -1.4 c. and the other -1.6 c., is also going to be very close. Easily close enough for the pair of (almost) balanced prime 5ths to sound pretty even.
As these skills become more comfortable, you will begin to hear the difference in what a couple tenths of a cent sound like here and there.
When I suggest starting A1 as a 3.0 c. wide 6:3 from A2, that’s just a starting point for the location of A1. If that’s the right width for that A1/A2 6:3 octave for that piano, it is going to sound pretty good. But tuning and measuring exactly exactly 3.0 c. wide of a 6:3 from A2 may not be exactly exact. The placement for A1 may be +/- .2 c. and it will still sound pretty good there. In fact, moving it a little one way or the other may be a better location for A1?
“The BIG disclaimer” is that even though I really do attempt to do exactly what I’m saying, I know I’m not getting them exactly exact every time. I don’t think it’s possible on every string on every piano. It’s easier on some pianos than on others, but even on the lesser pianos, we can still get them to within .2 c. or .3 c. and sounding pretty good, considering the situation.
But for writing these posts to describe procedures and routines I’m must use cents settings.
It’s hard enough trying to write about this stuff without having to say every time, +/- .2 c., +/- .2 c. , +/- .2.c.. So I will say it here and try to link to this BIG Disclaimer on each post.
If we were to use Dr. Sanderson’s comment that it takes a .3 c. change in the width of a Major 3rd for a change in the beat rate to be heard, I like to think that we should be able to tune and make most of our measurements within a .2 c. degree of accuracy.
As always, it all depends on the piano. The better the piano, the easier it is. In fact, some pianos are quite capable of coming really close to the .1 c. accuracy.
But others, as we all know, not so much. It’s the lighter scales that are the most challenging, and require the most educated compromises.
Striving for .1 c. accuracy while ending up with .2 c. accuracy will still sound pretty darn good.
So when you read here about tuning the prime 5ths to a width of -1.5 c., generally speaking, read that as being to within one tenth of a grain of salt.