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Hi all.

There has been a lot of discussion on this technique. I thought you might be interested in the likely origin.

The use of the octave-third split was first described by Sabbatini around 1657 as a method whereby the temperament is begun "by splitting the octave into three carefully gauged major thirds, thus setting a limit to the accumulated error over the tuning of successive fourths and fifths."

Also, beat rate tables were published by R. Smith in 1749. This was 168 years before Braid White's book.

All info from di Veroli - "Unequal Temperaments: Theory, History and Practice", pg. 148

While such information and details are truly fascinating... with out a pitch level I believe such formulae become inconsequential. Since I'm aware that pitch varied quite regularly even within a city I'm not sure how anyone can claim that a wide spread use of a particular tuning method.

Hi SMHaley,

What do you mean by pitch level? - pitch as in 415 or 465? That would have no effect on the techniques for tuning. The discussion on the forum has concentrated on the value of using Contiguous Major thirds as the backbone of an ET, rather than depending on narrow fifths and wide fourths.

Please read the book. It would answer so many of your questions and allow you to cite references when making statements. Without those references, the discussion on this forum can become "I believe this, I believe that", which is easily shot down by the next respondent who will say the same thing. It was my hope to provide cited information for those whose are interested. You might be interested that di Veroli provides detailed aural tuning instructiosn for 27 different temperaments including ET, and for most of those temperaments there are also additional "Authentic" and "Original" tuning instructions from the originators of the temperaments.

Edit: I should add that di Veroli's instructions are marked with beat rates that allow tuning in the A=392Hz to A=447Hz range.

Very interesting, it looks like that method has been re-invented many times. Of course this is not affected at all by the absolute pitch standard, as opposed to beat rates, e.g., 7bps at A440 becomes 6.6bps at A415; I assume that's what SMHaley meant.

Kees

Precisely!

Yes, I agree.

Very interesting indeed, considering that it was more or less an astonishing revelation around 1979-1980 or so and that Dr. Sanderson (the maker of the first viable ETD) picked up on it from the former North Bennett Street School of Piano Technology and later Steinway factory education department director, Bill Garlick. Bill Garlick knew something very important!

Where he got it from, nobody knows but it is an example of something that exists will be discovered sooner or later and independently. Oliver C. Faust , who was a contemporary of William Braide-White advocated it but his book was not so much read and studied as Braide-White's book which lead so many technicians down the path of Reverse Well!

Dr. Sanderson proved the theory, citing that the ratio of Contiguous Major Thirds (CM3) in Equal Temperament (ET) is 1:126 (if my memory serves me correctly) and rounded off to 1:125 is the equivalent of 4:5. No aural tuner on earth could ever distinguish between 1:125 and 1:126!

It all amounts to what I have always called a "small difference". It is not the smallest difference there is in ET tuning. That belongs to the difference between chromatic Major and minor thirds.

At the moment, I forget what that ratio is supposed to be but it is so small that recent attempts in this forum to show the definitive ET, either by ear or ETD, have shown that whatever it is, it is not humanly possible to perfect, even with the aid of electronic devices. The electronic device may provide a very precise value but the tuner's hand and ability to tune such a precise pitch is questionable.

So, the "small difference" noted by Dr. Sanderson and called at the time, a "super tuning" is about the best that aural tuners can be expected to achieve. History has shown that in previous centuries, Rapidly Beating Interval (RBI) perception was much lower than it is today. Therefore, it is difficult to imagine that anyone at any time in previous centuries ever did tune what we think of ET as being today. It was all, "kinda, sorta, pretty even" at best.

Today, tuners beat their heads against the wall trying to achieve that elusive perfection of what is nothing more than a theoretical idea and which has no finite end to it. The true art of piano tuning lies elsewhere. Look to Key Signature for the solution!

Funny thing is, I remember the piano tuner we had as a child tuning the CM3s - I kept hearing him playing F3, A3, C#4 and F4 over and over as well as doing P4, P5 and M6 tests. Funny how things stick in your memory. This was in the UK BTW. The tuner was very young, I do remember that - probably early 20s - he's still in business now, but this was all in in the late 1970s.

Paul.

Without a doubt, he was a great tuner then and among the greatest now!

Thanks so much for posting, Paul!

Typo? 5/4=1.25, 2^(4/12)=1.26. Still irrelevantly small of course.

Kees

When starting to tune, full time, in the 70's I, too, noticed what could be done with three stacked M3s within an octave. When using WBW's sequence, if F4 is tuned early, an additional check is available when tuning C#3: A3-C#3 can be compared with C#3-F4. I thought I was really onto something, but within a couple days realised that it wasn't that great. It did nothing for the 4ths and 5ths. You could have great sounding thirds, and lousy sounding 4ths and 5ths! Of course the answer is that ALL intervals need to sound good.

But there is something in the historical record that bothers me. If CM3s have been around a long time, and discovered independently by numerous people, why weren't they popular all along? Why doesn't everyone base their temperment sequence with them? Why do some people feel they need to shove them down other people's throat, and others find it just another useful check in some, but not all, situations?

Of course the whole ET, WT, RW thing will rear it's ugly head, so let me ask one more questions: If RW is so common with 4th and 5th based sequences, why do so few notice or care? I would say for the same reason that CM3s haven't been popular all along: It just doesn't matter.

Good morning Jeff,
With regard to the CM3 sequence not being popular - Probably inertia, in the sense that attempts at tuning ET coexisted with other temperaments. CMs only work in ET, whereas setting the temperament in a Good Temperament usually starts with fifths, and, I am guessing here, tuners just continued to use the technique they had always used.

1.25 vs 1.26 doesn't mean anything unless it is a 12th root of 2 ET without inharmonicity. When you talk about a real piano, the ratio is not constant anyway. M3s less than double each octave. The smaller the piano the more this is so. Even if you did carefully determine this ratio and tuned a set of CM3s with 3 decimal place accuracy there will still be problems, although it might not be noticeable on larger pianos. The ideal CM3 beatrate progression is not purely logarithmic, only approximately so.

I wonder if this is part of the reason CM3s are not universally popular. There are many more small pianos than larger ones.

I think you answered your own question, Jeff. Getting the CM3's right is not easy, so many tuners would rather tune a bunch of 4ths & 5ths and don't really care if the result is Reverse Well. They don't know what Reverse Well is, have never heard of it, so as far as they are concerned, they never tune it nor does anyone else. The book or manual they learned from doesn't teach CM3's, so they don't know how to do that either.

One thing you keep repeating is not true: The scale of the piano does not matter. You can still get the CM3's proportionately correct regardless of it and once you have done that, you can get all of the 4ths & 5ths to fit evenly within it. If, however, you impose an arbitrary beat rate upon F3-A3 and use that as a standard, you will find the dilemma you have always talked about and blamed on the scale.

I repsectfully disagree. But if a tuner does not have an ear for 4ths and 5ths, it may not seem to matter.

As a newer tuner, I think it may be because getting those buggers set can sometimes be frustrating. Some may find that getting fourths and fifths to sound "right" much easier, so why fuss over those thirds. You have to deal with them at some point, but maybe some feel more productive when they can get more notes sounding good, faster.

Just a thought from my perspective.

John

Thanks, John:

So not only is the accuracy of CM3s not as advertised, but the ease of tuning them isn't either. Well, the two together would be a turn off, wouldn't it?

In my experience, if one does not posses a technique with good control to handle tuning 3rds, odds are the unisons are going to be a little on the "catty side"... meeeeeooooowwwww.

Well, I think there is a big difference between hearing meeeeeooooowwwww and wawawawawawawawaw.

Yes, the ratio of difference is a bit higher, however, the relative movement of the string is roughly identical. What changes a M3 but a couple bps also will place it slightly out of unison (if making a correction) and shift the tempered 4th/5th in such a little amount that it is almost undetectable. This is why a 4th/5th temperament procedure has so many pitfalls. The latitude for error before having useable checks is substantially wider.