Weiyan, thank you for your interest. "Equal Beating" is actually a method for tuning a temperament. There are many possibilities. Owen Jorgensen wrote a small book called the "Handbook of Equal Beating Temperaments..." In this book, there were many kinds of non-equal temperaments and even one which was close to ET.
What is different about these temperament sequences is that there is never any estimation of beat rates or guessing of any kind. An interval is either tuned pure (no beats) or is tuned so that it beats exactly alike with another. Often, two intervals are temporarily tuned pure then when compared to a common note, a strongly dissonant interval is heard as a result. That note is then moved so it beats equally between the other two, forming an acceptable compromise. One never "counts" the beats. One only listens for the same quality of sound between the two.
When I needed a mild Well Temperament (also known as "Victorian"), I used the ideas in that book to eventually come up with what is today known as the EBVT III. The fact that it was a third adaptation of an idea is a clue to how difficult it was for me to finalize an idea that I had in my mind for a long time. When I finally did arrive at the final solution, it seemed so simple that I wondered why I had not realized it all long before.
Many people helped me including Owen Jorgensen and Ron Koval from this forum. Owen Jorgensen found upon the finalized idea that it was remarkably similar to a concept of a mild Well Temperament that Johann Georg Neidhardt had nearly 300 years before I did. Neidhardt however, had never devised a sequence for executing it.
The idea was for a mild Well Temperament. There are many similar to it and many even milder. Jim Coleman, Sr. and Ron Koval are known for their own ideas and there are others. However, most, if not all of these can only be tuned electronically.
When I first needed to use a mild Well Temperament, however I was strictly an aural tuner and there were no published sequences that did not require a lot of guessing. In other words, I could never know when I had tuned the temperament correctly and I may have had different results each time.
I wanted a sequence that first of all, I could replicate reasonably well each time and if anyone else were interested, that person could get the same results I would get, each time, every time. An Equal Beating method was the solution to that problem.
That being said, what I also found was that there is an effect in Equal Beating which tends to make the piano sound more harmonious or "in tune" with itself. If you read the topic about how "A piano cannot be tuned" (in which I just commented), you will find comments that I made about the problems of inharmonicity.
While there have been others who have made the same kind of discovery, on my own, I discovered ways to make intervals that were slightly tempered (4ths, 5ths and octaves) all have the same amount of tempering. These slight beats have the effect of "masking" each other (as I recall one individual describe it.) In other words, the slightly out of tune sound which cannot be overcome, is somehow hidden.
This effectively causes the piano to have a "cleaner", more in-tune sound when actual music is played upon it. Some years after designing the EBVT, I looked for a way to tune ET by an Equal Beating method. It was named, the "ET via Marpurg". It was an adaptation of one of the temperaments found in Owen Jorgensen's handbook. Using this method, the tuner would not have to guess so much. Again, an interval is tuned either beatless or is caused to beat exactly alike with another. Through the same kind of process as these earlier temperaments, one can arrive at a temperament which for all intents and purposes, is ET.
While the final result is technically a Quasi Equal Temperament ("quasi" means almost) but it is so close to theoretical ET that if the temperament is executed properly, it will pass the PTG Tuning Exam "Temperament" portion with a score of 100%.
Therefore, I began tutoring students who had attempted but failed the tuning exam and students who had previously only tuned electronically to use the idea. They found the sequence idea to actually work for them and therefore many of those people used it to take and pass the tuning exam. Lucas Brookins is one of the many who used it and got a 100% score. He does not even know of any other way to tune ET than what I taught him.
(By the way, I did not try to persuade Lucas Brookins to adopt the sole use of the EBVT III as his usual temperament. He had learned tuning initially on his own by using the free trial version of Tunelab software. He was mildly interested in aural tuning at the time. He asked me which would be easier to learn, EBVT III or ET. I answered, EBVT III, so he went for that.
He got it amazingly quickly! But when it came time to prepare for the PTG Tuning Exam, I offered him two versions: the "Up a 3rd, up a 3rd, down a 5th" idea and the ET via Marpurg. He found the true, theoretically correct version of ET to be "too much information" (as they say) at the time. Too many checks and balances for what he knew and could cope with at the time. The ET via Marpurg offered a simpler solution.
He also found, as the fine pianist that he is, that the EBVT III appealed to him more as a musician than ET did. It was and has been his choice ever since. It made more sense to him than ET does for a practical arrangement of how the piano should be tuned.
The piano is limited in its capabilities of being tuned. That is for sure and completely understood. But for the compromise to be made completely equally as the best and final solution is another question to be pondered and challenged. Should not the Key Signature play a role? That is what the EBVT III, among other characteristics offers: a clear and distinct difference in all 24 Major and minor keys.)
Just as with the EBVT, I found that using the Equal Beating method to tune ET resulted in once again, a more harmonious and "in tune" sounding piano than if I used a theoretically correct method for ET and used other options for stretching the octaves. 4ths, 5ths, octaves and all of their multiples all have the same, slightly tempered sound. It is the only way I ever try to tune ET.
Here is some music captured with a cell phone at a concert where the piano was tuned in the ET via Marpurg. I can clearly hear the effect of the Equally Tempered intervals.
https://www.youtube.com/watch?v=78_uTlOAnUs
