Dear List, Because so many people have asked me both in public and private mail, I will try to explain the meaning of this term thoroughly. If it comes up again in the future, this post should be easy to locate in the archives. First of all, I think it can be considered jargon. I don't think the term can be found in any published book but may be found in articles and yes, I have used it extensively in this List. To me, it is self explanatory. It describes a backwards version of a typical Well-Tempered Tuning (WT) [often called Well-Temperament]. I did not invent the term but it may have been just something I heard another member of my Chapter say to describe the kinds of errors we were noticing that other tuners were making with a disturbing, consistent and uncomfortable frequency. The term began to be repeated and since I have used it a lot, others have used it too both on this List and elsewhere. It has for me until recently always been meant to identify a very commonly made error in tuning. I recall Skip Becker RPT who writes essays about Historical Temperaments (HT) mentioning something about DeMorgan and Reverse Well but I had never read section 128 in Professor Owen Jorgen's book, "Tuning" which describes this temperament. To my surprise, it describes a mildly unequal temperament that is exactly backwards of most other 19th Century temperaments which usually adhere to historical precedents. To understand what Reverse Well is, you have to know and understand Andreas Werkmeister's Rules for Well Tempered Tuning. In these rules, it states that the major 3rds must progress in their beat speeds not chromatically as they do in Equal Temperament (ET) but in an alignment with the Cycle of 5ths. Thus, 3rds of a typical WT would sound uneven but in a specific way. A Reverse Well Temperament would be one in which this pattern of unevenness is more or less the opposite. In the instructions for tuning my Equal Beating Victorian Temperament (EBVT), I include the following description of the difference between the two. <<The following is the way the 3rds played chromatically will sound from F3-F4. Just imagine all values inverted and you have Reverse Well. F3-A3: slow F#3-A#3: fast G3-B3: slow Ab3-C4: quite fast A3-C#4: moderate, about the same as ET Bb-D4: moderate B3-D#4: very fast C4-E4: slow, half the speed of ET C#4-F4: very fast>> When trying to create your own WT, you need to be aware of what are called "imbalances". That is, you cannot have a 3rd from the top of the Cycle of 5ths beat faster than a 3rd from the bottom or vice-versa. That would break the rules and as such, is considered improper and contrary to the whole logic of the very reason to tune this way. When trying to understand why so many tuners who believe only in tuning ET actually have as a result a backwards version of a WT, I have always thought it had to do with two things: the order in which notes are tuned and a tendency that the late John Travis RPT had noted in his book, "Let's Tune Up", the "tendency to err towards the just 5th". Mr. Travis believed that most tuners would try to tune the 5ths a little too close to pure rather than leaving them tempered by the right amount to have a true ET. Most WT's have a pattern that starts with C, then to F, Bb, Eb, Ab and Db, all as pure or nearly pure 5ths. Then, the rest of the 5ths, mostly among the white keys would have to be tempered more than for ET in order for the temperament to work out. When an aural tuner uses a pattern that starts with either A or C and makes the error of tuning the first half of the 4ths and 5ths too purely, those among the white keys, then the rest of them, those among the black keys must be tempered a little more than would be proper for ET. This would result in an uneven pattern of beating for the 3rds which is exactly opposite of the way they should be for a WT, hence Reverse Well. Here is what Jean Jousse said in 1832 about what I and other members of my Chapter had also noted: <<ET...has the following disadvantages: ... it cannot be obtained in the strict sense as may be proved, not only mathematically, but also by daily experience; therefore the best equally tempered instruments are still unequally tempered, and, what is worse, oftentimes in [the] wrong places.>> (see "Tuning", page 417). Since 1980 or so, the PTG Standardized Tuning Exam has made a Quantum leap in many tuner's ability to tune a true ET. Dr. Sanderson not only invented the first Electronic Tuning Device (ETD) that could really compensate for Inharmonicity to produce a true ET on the modern piano but he also identified the 4:5 Ratio of Contiguous 3rds to the aural tuning profession. Since the time this Standardized Exam was implemented, more and more aural tuners have been able to produce a true ET because more of them know all of the interval checks, the 4:5 ratio being the most important of all. Still, many tuners have not yet taken this Exam and have not learned these advanced techniques. An aural tuner who relies mostly on 4ths & 5ths and does not distinguish the fine gradations in the beating of 3rds & 6ths can easily produce a Reverse Well temperament and not even be aware of that fact. This may be particularly true if the error that John Travis identified is also made. I have heard many tuners express that "temperament doesn't matter", that good unisons and octaves are more important. This may be true to a certain extent but what can happen if there is an *accumulation* of errors, that is, one error compounding another and subsequently, the end result of the temperament can be a very significant effect that was not intended and not recognized for what it is but which does have an effect on the music and the way a person might play the piano. This effect might well be opposite of the kind of effect expected when tuning a true WT. Imagine the skewed perception of music a person might have who spent a whole career of study on a piano consistently tuned in Reverse Well. There have also been other instances of Reverse Well, done erroneously that I cannot explain. It can even happen when using an ETD. I have done it myself. It takes very little error to produce an audible inequality in ET. Any accumulation of errors will result in some kind of deviant pattern. It is unfortunate that when errors are made, they so often are made in opposition to what might be considered a beneficial alternative. There have been a few people who have timidly confirmed that they have also witnessed Reverse Well tunings. Many of these people would only dare to say it in private mail. I have found it virtually everywhere I have looked, from New York to Los Angeles, from Montreal to Mexico City and everywhere in between. I have always known and witnessed that the very discussion of temperament tends to bring out strongly held beliefs and emotions. Technicians should not take the mindset however that "everything I always believed in is now invalid". There is simply more to the entire story, that's all. How else could there be such a blatant contradiction as that of the DeMorgan Temperament? I have long contended that the study of HT's is important for all tuners, even those who wish to only tune ET. It is so that the tuner can really recognize errors and their effects and so the Reverse Well error can be avoided. Bill Bremmer RPT Madison, Wisconsin
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