Pianotech

Please forgive me if this is not the right group for this post. I am looking for people to help me with a study by taking an online aural test.

I recently wrote an article for the PTG journal entitled "The Skeleton" alongside a reprint of Jack Stebbins "Jack's Stack"
A reader took me to task concerning my omission of the 4:5 ratio technique.  
It is my belief, as well as Jack's which you can read in next month's letter to the editor, that 4:5 is not accurate nor precise.
But it is only a belief.
So, to answer the question of whether 4:5 is precise or not, meaning are we able to hear and set a 4:5 ratio every time, I created a simple quiz to test this hypothesis.
The quiz plays an F3-A3 at 7 bps.
Then there are six different A3-C#4's, ranging from 6.4 bps (10% slower) to 9.5 bps (35% faster).
The correct answer is 8.8 bps (25% faster)
The next two closest answers are 8.3 bps (17% faster) and 9.5 bps (35% faster)
I need as many people as possible to take this test so I can have a better sample size.

The test can be found at https://internationalpianotechniciansschool.com/courses/ear-training-tests/
It requires you to register for a free account so I can see your answers.

William, you have brought up some good points.

1) 4:5 ratio three times does not equal 2 because 4:5 is not the mathematical ratio needed. It is 25.99%

2) But the study is not about accuracy. It is about precision. I.e. even if 25% were accurate, could we do it? Take the test and see for yourself. It doesn't just ask if you can tune 25%, it asks if you can tune between 17% and 35%. That's a huge range and it's a range that people can't do. So far only one person got it right 2 times out of 5. That is not precise. Precise is 5 times out of 5.

3) You are right. Progressive beat rates are not the only requirement, we also need fourths and fifths that do not stand out. But if we use a technique that isn't precise or accurate, what's the point? Well, the point is to get close, right? But what if there was a better way, one that was not only more precise, but more accurate and efficient as well? That's what people like me are trying to find.

4) We teach that once we get into the treble and bass and are tuning what we call the "Stretch Interval Set" (Pure 4:2/6:3/P11/12/19/2 and P@8:6, see my journal article on stretch) and we find intervals that are not pure, we will look to progressive beat rates to get permission to tweak intervals so they are pure, but if we think maybe we have destroyed some progressive beat rates, we won't be too upset about. Why? (This is one of the pillars of the method we teach)

"Progressive beat rates are not musical. Pure intervals are. We will always choose musical criteria over non-musical ones."