Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum I just can't get my head around temperament!

A lot of them have had a few too many fifths.

I wonder what temperament this is......it certainly is a different way of interpreting this music...;)

http://www.npr.org/blogs/deceptivecadence/2014/04/17/304152235/classical-quartet-gets-all-twisted

Just noticed.
It's no wonder her ET tuning keeps getting a wolf in that last fifth. The piano is backwards.

[Laugh!]

Excellent!

Ya just wonder what would happen if they met up with the Piano Guys.

Piano Guys....now that would be something!!

Piano sounds 'out of tune' ...."must be ET 'cause WT/UT don't sound like that" ..... Analogous to: "Must be jelly, 'cause jam don't shake like that."

The last song was good. When the audience starts clapping in time, ya know ya got a real song!

Sometimes, I think I should just give up! I should just let the ET only crowd have their way. Bach invented ET, it has been universally accepted ever since and it provided the foundation for all music that followed.

Almost everyone wants to believe that. It sounds "logical" to divide the scale equally so that there would be "complete freedom of modulation", etc. The recent video posted said at the end that a certain piece could not have existed without ET but there was nothing at all about it that involved tempering of any kind!

It is all deception! It is all a myth, none of it ever happened but most people, including piano technicians who really ought to know better, just accept it all as factual!

That has been going on for as long as I have been aware of it but another, far more insidious problem of which I have long been aware has mostly been rejected as a complete fabrication (which is what that video is and Stuart Isacoff's book as well) and that is the very pervasive presence of Reverse Well!

Every time I mention it, I get virtual stones thrown at me! It doesn't happen, it couldn't happen, it is unknown except for the singular writings of one person, ME! Yet, I have always maintained and I still very strongly do and shall always that the reason it exists and is more pervasive than any of us would ever want to believe, is precisely because of the BIG LIE that has been told over and over, is being told in that video, In Stuart Isacoff's book called, Temperament, in any number of books on piano tuning and probably is also in the text that has been referred to me but which I have yet to have a chance to read, that tuning took a quantum leap from Meantone and/or Pythagorean to ET with the discovery of ET by J.S. Bach and the writing of the Music for the Well Tempered Clavier.

That is simply NOT the truth!

But because it has been accepted and believed to be the truth by so many, including music educators and piano technicians alike, virtually ANY rendering of temperament on a piano today is accepted and believed to be ET!

I have long been plagued by that and tried to tell whoever would listen about it and mostly been scoffed at for it. I would be just as willing to retreat from it for a while and let others confirm that what I am saying is true but just today, I was approached by a high school student who wanted to learn something about piano tuning. The pianos at his school just did not sound "right" to him!

Upon further investigation, I found out what the reason was. Not only was the "temperament" not ET but it dug back to J.S. Bach's time before he allegedly discovered or "invented" ET and was a backwards version of what Bach himself tried to rectify! I had encountered it before numerous times! Unbelievable but people had actually paid for it! Reverse Meantone!

The week before, the house technician at the concert hall I serve in that same area asked me to comment on a piano in another area of the building. Same thing, Reverse Meantone! Pure thirds and wolf fifth, all in the wrong places! Exactly backwards of what was typically done in the early 18th Century! I had heard it at a party I attended in that area a few years ago and encountered the same thing a few other times.

No excuses or explanations about how those tunings could have somehow morphed from ET into that will due, I am sorry! But there is one very plausible explanation, the same plausible explanation that there is for why so many compositions had the correct key signature! That tuners tuned in 4ths & 5ths and inevitably put in Well-Tempered key color!

I have seen any and all kinds of explanations of why they did what they did except for the most obvious one!

In this case, however, the "tuner" not knowing of any of that specifically because any and all of that knowledge had been denied him, he dutifully made every interval sound "good" as he tuned them but gave up at some point around the circle of 5ths and ended up with a backwards Meantone temperament! And, he does that on every piano he tunes!

He gets paid for that and obviously believes that what he does is ET! His customers believe it is ET because virtually everyone believes in the complete myth that ET became the standard tuning ever since J. S. Bach first used it.

I might surmise that this is an isolated case except that there was another tuner in the area who is now deceased who practiced the very same, completely backwards kind of temperament from what Bach himself tried to rise above. That tuner was very well respected because he was also a piano teacher. He had a loyal clientele. Only very occasionally were there people who thought that what he did just did not sound "right".

So, in my mind, anybody can go on believing whatever they want but I know what the truth really is: J. S. Bach did NOT write his two books of "Well Tempered Clavier Music" for ET, did not play them in ET and ET never had anything whatsoever to do with any music either composed or performed thereafter!

The efforts that there have been to distort and disguise the truth about temperament history have really only served to turn temperament into a backwards version of that which was being attempted to suppress! And hardly anyone has ever been aware of that! But to me, it has often been quite painfully obvious!

Heard and acknowledged. Everything you say here is true. I'm glad to finally read a clear definition of 'Reverse Well'.

Temperament path is critical to the quality of the tuning. Accumulated error (and how the error accumulates) matters. All pathways to equal temperament are not equal.

What we have here is a clash between two vastly different mathematical approaches to music.

One is the ratio of small integers, which arises naturally from the way things such as piano strings and air columns vibrate. They produce overtones by dividing into halves (octave higher), thirds (octave and a fifth), quarters (two octaves), etc. Given the octave and the fifth, now you can invert and get the fourth, and off you go around the famous circle.

The circle almost sort of closes when you have twelve tones in your octave. Temperament is all about what to do about the almost sort of closing.

The second mathematical approach looks at the first and says "OK, thanks for the twelve tones. Too bad they're not evenly spaced." What would it mean to have our tones evenly spaced? The whole mess works by multiplication, so we want a number which when we multiply it by itself twelve times, gives us an octave. That's the twelfth root of two. To go up a semitone, you multiply by the twelfth root of two.

The funny thing is how that mashes up with the integer ratios. The perfect fifth is a 3:2 ratio, or exactly 1.500.... It's also seven semitones, so in the equal temperament world, it's the seventh power of the twelfth root of two. IIRC, that works out to something like 1.498, really close.

That bit of luck is what makes equal temperament work to the extent that it does. It's close enough and very convenient for most purposes, but also different enough from perfection that people get fascinated with the alternative solutions.

That's as close as I can come to putting the problem in a nutshell. The solutions don't fit in nutshells, they drive you nuts.... ;-)

Thanks for your, umm, concern, but I have a very good life - and that includes perusing this forum without having to bad-mouth it, or any of its "bickering" techs.

Right backatcha, "dude".

Bill,

I have never read that Bach invented ET. Where do you get that from? He wrote a book called the well tempered clavier, not the equal tempered clavier.

You even bashed me, saying I said Bach invented ET in one if my video lessons. Where did you get that from? I certainly don't know who invented it. Who does?What I do know is that he wrote 24 etudes, 12 major, 12 minor, that were meant to be played in a well temperament, in order to show the different colours of well temperament.

Please stop saying we are all saying Bach invented ET.

Correction - The WTC is a collection of 48 Preludes & Fugues issued to two volumes.

It is a common misconception, even among some early music performance practitioners, that Bach invented ET. I was at a Bach concert the other day conducted by a Dutch early music specialist who told me he always keeps his harpsichords in ET because Bach invented ET and used ET.

Go figure.

Unfortunately, it is a very common misconception.

To the best of our knowledge, Bach didn't invent well-temperament either. There is no doubt that he was convinced of its value, however.

That 2nd sentence is incorrect. There is no historical record of Bach's opinion on equal temperament. (There is on other temperaments like 1/6' meantone.) There are plenty of records of current-day doubts on the subject of Bach and ET by scholars and musicians.

Kees

Kees,

Do you not consider the WTC as proof enough?

I referenced well-temperament, not ET, and the fact that they are not the same. I have never found any absolute definition of the exact temperament to which Bach referred to as "wohl." It could also be translated at "good."

There is no indication that Bach invented either "equal" or "well" temperaments. Germany, at that time period, was rife with experimentation of temperaments. However, he was impressed enough with the 'pleasantly usable' temperament that he wrote 48 Preludes & Fugues to celebrate its existence.

Thank you, Marty, for that. I don't think Kees and you disagree on much at all.

I often write that "Bach invented ET" because that is what I have heard so many people actually say! (or I have seen it written, even in books!)

One does not "invent" a natural phenomenon that exists to be discovered. For example, Isaac Newton did not "invent" gravity nor did Benjamin Franklin "invent" electricity. One does invent, however a tool or device such as Thomas Edison invented the incandescent light and phonograph or Alexander Graham Bell invented the telephone.

What really gets me is how so many publications seem to want to confuse Well Temperament with ET, essentially calling them synonymous when, in fact, the two are mutually exclusive.

It may well be that J. S. Bach's acceptance of a tuning system which permitted access to all 24 major and minor keys through the new idea at the time, Well Tempered Tuning (as I still prefer to call it), was a turning point in music history.

Sadly, however, so many books, even recent ones such as Stuart Isacoff's Temperament seem to deliberately choose to truncate the facts to make it appear as though keyboard tuning took a quantum leap after Bach's creation from 1/4 Meantone, directly to ET! It is simply NOT the truth!

Then, to take an untruth ever so much further, a video such as the one displayed on here, seeks to tell the general audience that all music after the WTC event was made possible and due entirely to ET!

I rehearsed with the Jacques Offenbach cast where the piece that was identified in that video called, "Barcarolle", a part of the opera called, "The Tales of Hoffman" on a piano that was tuned in the Victorian Style Well Temperament I most often use was on the piano. If that music had actually required ET, the way I tuned the piano would not have worked!

I have also sung the same song, either as a duet or modified to be a solo, in the original key, accompanied by a piano in the same Well-Temperament, countless numbers of times!

So, now, I quote what an opera sponsor asked me at one point, "Wouldn't an unequal temperament (with the gripping fear of howling wolves and blood curdling dissonances that would make you very skin crawl) tend to throw the singers off? The answer to that question was, "No, it would be far more likely to keep the singers on!"

That beautiful Offenbach melody had absolutely nothing to do with ET! Any singers who ever sing it do not sing in ET! Nobody ever does! The orchestra that plays in that video is not playing in ET! The accordions that play in that video have their unisons de-tuned so much that no one could ever really discern how much or little the tempering is equalized or not but the video narrator claims that they are in ET!

The very notion that everything ever written since Bach's time was always in ET is not only untrue, it is patently ridiculous!

Sorry Marty. For some reason I read "equal" when you wrote "well". Please disregard my nonsensical comment, and accept stupidity as an excuse.

Kees

Well you see I didn't know what I didn't know. Now that I know what I didn't know, I know it. Thanks

Actually Kees, that points out the problem precisely. When "Well" is read or heard, the mind immediately responds/understands "Equal." The problem is as pervasive as Bill points out.