To those who have been interested in hearing just how the EBVT III sounds when played on a piano, my webmaster has posted some files that I have for listening. I do not consider any of these examples to be ideal, only what I have that I can legally post.

Many of the performances I tune for are not recorded or if they are, I do not have permission to use. These examples will show however that the EBVT III can be used for all types of music. Most people will not be able to easily recognize the difference between the EBVT III and ET. That is expected and it should alleviate the trepidation that many have to trying this very mild Victorian style temperament.

The fact is that there is a distinction between all 24 Major an minor keys but it is a very small distinction. Other non-equal temperaments present a much larger difference and that makes them ultimately unacceptable for general use.

The EBVT III is in fact the way I tune most pianos today and if you you listen carefully to these selections, you will hear that it not only works for modern music but it still does offer the distinction from one key to another which was a fundamental part of music history.

I will accept an appreciate all comments.

Here is a direct link to the page where these sound files can be found: http://www.billbremmer.com/ebvt/

Well, I will bite.

I listened to the samples, first on my computer speakers, and then I hooked it through my sound system.

It is a little difficult to evaluate. None of the pieces modulate much, so I could not really evaluate the differences between keys, which I would think would be the main purpose of using a non-equal temperament. I think that most of the music stays in keys which have thirds which are purer than equal temperament. However, I have to say that I have never cared much for pure thirds. They make the music sound dull to me. I guess equal tempered thirds is just something that I have learned to like.

PS, I know about the problems of finding legal sound files. There must be a few hundred of archival recordings of shows I have tuned for, and I cannot listen to any of them!

Thanks for your response, BDB. The EBVT and EBVT III have no pure M3s, far from it. If they did, you would have clearly heard that and probably not liked it at all. The range in size of the M3s is from about half that of ET up to about 17 cents for the EBVT III and 19 cents for the EBVT (without looking it up). The graphs on the same page as the sound files show all interval sizes.

One of the acoustical tricks that equal beating plays, however is that equal beating M3s and M6s tend to cancel each other out, thus the harmony often sounds "purer" than it really is.

I would remind everyone that I virtually never tune a piano for anyone in ET for any reason and I haven't now for 20 years. If my clients consistently had a problem with that, I would have reverted to ET tuning long ago. Both versions of the EBVT are specifically designed not to shock the ear but only to provide very subtle distinctions in key color, nothing more.

So, the comment I most often hear, even from technicians is, "I can't tell the difference". They often add that the piano sounds good but then wonder what the point really is.

That raises some interesting questions. There are people who want to try either mine or some other well temperament but have so much trepidation, as if they are afraid of being absolutely horrified but then are disappointed when they are not. I have run into that on any number of occasions. For instance, when I went to the Chicago Fazioli dealer a few years ago, he seemed quite disappointed. It was not that he didn't like the sound, he thought the piano sounded great. It was because he couldn't really tell what the difference was!

To me, the reactions or lack thereof have always been an interesting subject in itself. Neither EVBT would "pass" the PTG tuning exam for temperament. They are distinctly enough different that each would "score" in the low 70's or high 60's. When the electronic scoring shows an "error" and the note in question is verified aurally as it would be at an exam, it is clearly "wrong" with respect to ET. Simply playing all the intervals as one would to test for equality as one would with ET reveals several minor "errors" but enough so that the temperament seems rough or crude, apprentice level at best from the viewpoint and we have for ET today.

When I designed both versions, I kept in mind the fact that many technicians aural skills can do no better than that yet they still tune pianos for a living and apparently have satisfied customers. I worked long and hard for many years to perfect my skills, so I can execute a temperament any way I want and have it be what I intend. So, I took certain parameters, those which apparently lie within the range of tolerance that most people would have. I took those parameters and designed a distinctly different temperament, one based upon the principles of well-temperament. There are others who have done so too.

The only way, as I see it that pianists and technicians alike will ever be able to pick up on the differences between any mild well temperament and ET would be to have two pianos, as identical as possible, one tuned in ET, the other in a WT. Music of various styles and periods, played by the same pianist would be performed on each.

It would be a good idea to make such a recording and for anyone to be able to access it. So far, no one has been willing to put up with the cost of equipment and production of such an experiment, not even PTG. It would seem to me that some university somewhere would be interested in such a project, just for the value that comes from experimentation.

Most university faculty however, have it in their minds already that there would be one "normal" piano and one "freak" piano. They wouldn't want to even expose their ears to it or waste a minute of time with it, much less any money. That's really a disappointment because I truly do believe that most pianists would find that a piano tuned in a certain, focused way other than strictly ET has a warmth and character to it which they definitely prefer. Music would come to life for them in a way which it never had before.

These kinds of advanced tuning techniques of course, need to be combined with all of the other advanced techniques there are to make pianos sound better and play more responsively. There really is no finite solution to better quality music from the modern piano.

Hi Bill Bremmer,

I think those selections sound great! I would have to hear the same selections played with ET then EBVT III to tell the diff. I like what I hear. Sound's great with the other instruments too with no dischord that I could hear.

The downloadable .pdf file showing the temperment helped.

If it sounds good ... Use it!

Thanks Bill

Bill:

Thanks so much for making these recordings available. I had read many things about UTs, but the only recording I had been able to find on the internet was Valotti on a harpsichord. It made me cringe.

I finally got to listen to the recordings on a computer that was capable of it last night. I now know that ET and only ET is for me. Thanks again.

I did not need a computer to listen to EBVT III.

Fortunately, I am able to tune it by ear in my piano and in some clients´s pianos, following the instructions given in the file available at Bremmer's site. No need to listen recordings. I prefer the real thing.

I was also able to tune it with my Verituner, but I must say that it was inferior to the aural tuning. I guess because my ETD also stretches the fifths that are suposed to be pure, as stated by Bill Bremmer in one of his posts. And also to the fact that this same stretching can tweak the equal beating intended in this temperament.

And it is a wonderfull thing to hear the pipe organ effect! Which is not heard in ET.

What pity for those who are not able to tune it. They can not appreciate the pipe organ effect on those recordings.

Interesting sound clips...and again, thanks for posting them.

It listened to all, and I found the jazz music perhaps the most "opened up" by the tuning. There is a definite sense that the piano is "on a pleasant edge"...that's how I'd describe it...it reminds me of what some folks like about analog gear i.e. tubes and compressors, in recording. The imperfections (in analog, extra noise, hiss, etc) actually give a certain warmth...I found the EBVT pleasant in that same way...

But I think it would be most useful for lyrical jazz...Bill Evans kind of stuff...(but that's on my first listen, admittedly)

RPD

Thank you again, Rafael and RPD.. I very much appreciate the fact that you can tune it by ear. Although I do think there are some advantages to the other ETD programs over the ETD I have, the SAT III, I have not yet been convinced that any of them, including the SAT III can really do what I want and need them to do. Therefore, I continue to use the SAT III in the Direct Interval mode which does suit my purposes. In other words, I tell the ETD what to do, it does not tell me.

I have long had those recordings but have resisted posting them because I know they do not reveal all of the magic there is to be appreciated from the EBVT III. It is like looking at a work of art through a dirty window pane at a mere glance. Years of satisfied customers and customers who repeatedly ask for me and only me from the dealer I work for confirm that the way I tune their pianos is the way they like it. They have tried the others, those who tune a perfect ET but they still prefer the special magic that an equal beating mild well temperament provides.

The theory of ET is easy to understand but difficult to apply. Let's cut through all of the varieties and create one single idea that everyone will accept. What's more, let's force them to accept it. Let's suppress and destroy all of the documentation about how keyboards were tuned in the past and leave only one for comparison: MEAN tone. That is what the book by William Braide-White did. That is what the modern work of fiction, "Temperament" (Isacoff) also did. It deliberately mixed true research with outright lies to try to prove a point.

If you keep telling the same lie over and over, eventually people will believe it. I have heard that somewhere before. Isacoff actually said that ET was the “final solution”. I also heard that somewhere else before too. Since the beginning of the 20th Century, thanks mostly to Braide-White, there is only ONE way to tune. As far as most people know, including piano technicians, there is only one way, there never was any other way and there never will be any other way. It doesn’t sound “right” any other way.

Unfortunately, Braide-White’s solution was better suited to the very kind of tuning he abhorred. It follows the cycle of 5ths the same as all of the temperaments he desired to quash. He succeeded in removing all other ideas but he never did explain how to perfect the idea he wished to force on the world. He only provided a list of irrational numbers. So, the most common result of attempts to do what Braide-White wanted was and still is a backwards version of what he didn’t want. Piano owners from amateur to professional have learned music most often nurtured themselves not on harmony bereft of distinctions from one key to another but a confused, distorted and backwards arrangement of what it should be. It took the perfection of ETD’s and techniques beyond what Braide-White offered for piano technicians to finally be able to really tune ET near the end of the 20th Century.

Isacoff claimed that the music of today could not exist had it not been for ET. How could that be when the ET he imagines hardly ever existed? People learned to actually ignore what was really coming from their pianos and only imagine they were hearing the sound that should have been there. Thanks almost entirely to Professor Owen Jorgensen, RPT, we are now able to restore to the piano the kind of sound there always should have been.

Bill Bremmer deliberately misrepresents the Braid White Method and its results. Read the book "Piano Tuning and Allied Arts" if you want to know what the method really is.

I now tune using only the EBVT 3. I debated whether or not to even tell my customers. Some I do, some I don't. I tuned a piano today and explained to the owner about the EBVT 3. She loved it, and said, "finally, sharp keys sound like they are supposed to." I always offer to put it back to ET for free if the customer is not satisfied. EVERYONE has loved it!

I think there is some apprehension to try the EBVT because many tuners do not play and do not have a way to really hear the differences. I do play, and was able to try songs in several different keys. That's where the magic happens. If you only run a few chords, you will not get a full picture.

Using this tuning has set me apart as a tuner and customers are telling me that they prefer my tunings over others. I would HIGHLY encourage those of you thinking about trying this temperament to go for it.

Ryan Hassell
Hassell's Piano Tuning
Farmington, MO

It is a good idea to offer to retune ET for free if client is not satisfied.

I've heard of some tuner that used to do that (I don't remember well but I think it was Bill Bremmer), once he had a client who asked him to re-tune the piano in ET, so he did. Then the client tried the piano and ask him to re-re-tune it in EBVT III, this last time for pay! So the tuner collected his fee twice!

Bill, do you have the figures for EBVT III to input into the Reyburn CT? I know it may not be perfect, but would like to try it. Thanks.

Here are the offsets in cents:

http://billbremmer.com/ebvt/summary_ebvt_sequences.pdf

Thanks for posting that Erus. I was going to look at Bill's website for that information, not the offset in cents but the rest of it but now I don't have to try and find it.

Thanks Erus.

I've read the Braid White Book and I can not tune ET following the instructions given there.

There is no way to tune a fifth that beats 0.59 times in a second or the other figures stated in this method.

To get an accurate ET one must tweak each and every one of the fifths and fourths already tuned, making checks that use fast beating intervals as they become available. Even if the fifths and fourths sounded good at first, it is until checked with fast beating intervals that one discovers they are off and can correct them.

Furtheremore, the figures given by White are for a C 517.3 Hz fork, it corresponds to A 435 Hz. So you can not tune to the present standard of A 440 Hz. I know of sequences "a la Braid White" starting with A 440 Hz. and using m3-M3 tests, but then it is no more the Braid White Method, these and other modern tests were not used by White and the figures must be re-calculated for this new reference frequence of 440 Hz.

In fact the figures are useless due to iH, which puts out all of the theoretical beat rates mainly for the 5ths and 4ths intervals.

The fast beating intervals, M3s and M6s are less affected by iH and the real rates, as tuned in a real piano, are closer to the theoretical values and thus can be used as an aproximate reference and are more suitable to set a temperament than 5ths and 4ths.

So why use the Braid White method if one must tweak it in order to achieve a real ET?

The method of the honorable William Braid White, acoustical engineer educated at Cambridge University, founder of the American Guild of Piano Tuners, which eventually evolved into the present Piano Technicians Guild, thus the "Father of the PTG": is now outdated.

It was published in 1917 and became the standard of tuning and the most used, even the only method taught to the tuners in great part of the 20th century. But now, it was surpassed by new procedures, more efficient and accurate.

Modern ETDs are the result of the evolution of the tuning technology, which is becoming a science, no more an art.

The recently discovered effects of the inharmonicity of piano strings have changed the way we now see the piano tuning.

We can not stay tuned to the old years usage, we must evolve.

Bill,

I have a question concerning EBVT and iH.

How does iH affect the beat rates you tune in EBVT, if it does at all?

In EBVT III you tune F3-A3 M3, C4-E4 M3, G3-E4 M6 and G3-B3 M3 to beat at 6 BPS. Do you use another value depending on the size of the piano or do you use always 6 BPS?

In ET there is a change depending on the iH. For example, when tuning ET in a concert grand F3-A3 M3 beats at near 7 BPS, but for a small spinet this same M3 beats only at 6 BPS aproximately. Is there such a change in EBVT III?

Gadzar:

I will check and let you know if there is a difference in Mr. White’s compared to Mr. Reblitz’s beat rate tables. I don’t think there is. I am very sure that Mr. White's method starts with a 523.3 C fork. But even if a piano is tuned 20 cents low, the beat rates change very little, because all of the notes are lowered by the same pitch.

I have read many times that iH changes the beat rates in the temperament section. Many agree that the change is insignificant. This is the first that I have seen that the M3s change less than others. Do you have some math to back this up?

And just because you cannot tune a temperament by using Mr. White’s method, does not mean that it is in error or cannot be done. I know different.

[Edit:] But also, over and over again, I read about the accuracy of CM3s. I have asked on this Forum and on the Pianotech List about how accurate they really are. This seems to be unknown. But tuning M3s that are 4 semitones apart and expecting to have a progression accurate enough so that chromatic M3s (and M6s) will also be progressive is expecting an awful lot. Until someone shows that the accuracy of setting a set of CM3s equals or exceeds the accuracy required to have progressive M3s and M6s (we can leave P4s and P5s and the M6-M3 test out of the picture for now…) we cannot say if they are accurate enough to tune ET, without later refinement (which is the major criticism of White’s method.)

Oh sure, there are people who use the BW method successfully, about 1 in 100, I would venture to say. I was one of them back in 1983 when I passed my tuning exam with a perfect temperament score. Then, I and others in my chapter began to notice the alarming regularity of people who used the same sequence and got reverse well instead.

Gadzar already showed you with the math quite some time ago why and how CM3s work and did so better than I could have. His post on why the BW system doesn't work for most people was also more through and complete than I would have cared to try to put together for you again for the umpteenth time. Thank you for doing that, Rafael.

Rafael, to answer your question regarding the EBVT, the fact that you don't really need to get any WT as precisely accurate as you do ET for ET to be ET and for any WT to still be a WT is part of the reality and beauty of using a WT.

The instructions for the EBVT tell you to tune the F#-A3 M3 at 6 beats per second. Now, that is an easier beat rate to estimate than 7 beats per second and it is possible to make that interval beat at whatever rate you desire. So, it does not really matter whether the rate is 6.0 beats per second or not. If it is even one beat per second faster or slower, that is fairly easily perceived although it does require some experience and skill. So, the instruction may be taken as "approximately 6 beats per second" although for figuring the cents deviation for electronic tuning, it is taken as exactly 6.00 beats per second.

You can use an ETD to set that beat rate without a calculated program. If you have A3 set at 0.0 and reading on the 4th partial (octave 5) and then set F3 also reading on the 4th partial at 1.0, the rate will almost always be correct. Set the two notes as such and then listen to the beat and time it against a watch or metronome and you will almost always find it to be right on. The most different I have ever found it to be such as on a poorly scaled piano would be F3 at 1.5.

If you tune A4 from A3 set at 0.0 as a 6:3 octave, and A4 reads on the second partial (also octave 5), it will usually read between 1.0 and 1.5 but sometimes as much as 2.0 and will also confirm itself to be exactly at or very marginally off of standard pitch by less than 1/2 cent. If perfection of pitch is desired, then A4 can be corrected and A3 and F3 moved by the same amount.

Once you have set the F3-A3 M3 at 6 betas per second, there are three more rapidly beating intervals to tune at the same rate. The ear can easily hear when two rapidly beating intervals beat exactly the same. A skilled aural tuner could hardly make more than a 1/2 cent error. So, it doesn't matter what the inharmonicity profile of the piano is, you set these 4 intervals to beat exactly the same as each other. Inharmonicity will affect the resulting pitch, yes but you can still tune them as equal beating regardless of the effect of inharmonicity. Then, subsequent intervals are set as either beatless or equal beating. Inharmonicity does determine the exact pitch for these intervals.

The problem with trying to tune ET according to precise beat rates is that if you could determine these exact rates which is not really humanly possible but if you could, you might get a few of them exactly right but when you reach a point where there are interval checks available, you would find that the checks don't work. Then you have to adjust everything you've done so far. Most aural tuners simply don't have the skill to do that, so the result of trying to tune ET according to that scheme is an unequal temperament and much more often than not, reverse well rather than well.

Inharmonicity certainly does affect the exact pitches for each note in ET or any other temperament, that is what calculated programs from ETDs attempt to provide: the deviation from theoretical. If inharmonicity did not affect tuning, we would not need these calculated deviations; we could tune each pitch to 0.0. That is what strobe tuners did and we all know that the results using a strobe tuner were flawed.

To quote Owen Jorgensen again for the umpteenth time, "The value of using the CM3s is that they serve to precisely and unequivocally divide the octave into three equal parts." There is a new article in the PTG Journal by Owen Jorgensen this month where he talks about the value of using minor thirds in perfecting ET on poorly scaled pianos. I found it ironic that he says the very opposite of what Tooner says he believes and does. Owen says what I told Tooner but Tooner always seems to know better than anyone else about these matters.

Tooner claims he believes only in ET and tunes only ET but readily admits that he alters the temperament routinely in the only kind of pianos he ever gets to tune. So, those temperaments are not, in fact ET but something else by his own description of what he does. I'm not out to put anyone down but there is an obvious contradiction in what has been claimed in writing on this forum. It has been written and defended many times.

It is not going to serve any purpose to go back to square one with "I still don't believe that CM3s can be accurate" and to put a bunch of math and complex tuning checks on here to try to prove that the BW system consistently yields more accurate results than any more contemporary system which uses CM3s. They all do and people get better results when they use any one of those systems than they did when they try the old way of temperament construction. Anyone can tune any way they feel comfortable. I don't try to teach people who already know how to tune successfully, I teach people who want and need to learn.

So, if you are satisfied with the way you tune, then that is fine. You don't have to join any organization or take any tests if you don't want to. You can read any book or not read any material you choose. You can write an article about your way of tuning if you want. You can write a book about it too if you want. No one is telling you what to do or what not to do. There are many opinions and each may have its own validity and each person has the right to believe what they want and practice what they believe to be the best way to tune.

Everyone has to find which methods and technique work best for themselves. If someone writes something like, "I tried that once and it made my skin crawl", that is their experience and they have the right to say it but it shouldn't be then expected to be the truth that applies to all. Each person perceives the piano and its tuning and voicing differently. The best and most successful technicians know how to adapt and satisfy their customers desires.

What I am still waiting for is a proof that the accuracy of an initial set of CM3s is sufficient to construct a true ET. Something like: “The above math shows that it is necessary to have all pitches within x cents of ideal values in order to guarantee that both M3s and M6s beat progressively (again, we can leave P4s, P5s and the M6-M3 test for another time…). If a note in an initial set of CM3s has an error of this x cents, the progression will be such and such. If a tuner can hear this such and such difference, then an initial set of CM3s can be tuned that a true ET can be constructed from.”

And I would also like to see a proof that the theoretical beat rates are in significant error while equally proportional CM3s are not. Something like: “Such and such a piano has the following iH values. The ideal frequencies are such and such. This produces the following ideal beat rates. The difference in cents between the theoretical beat rates and the ideal beat rates are such and such. And the difference in cents between the beat rate of the equally proportional CM3s and the ideal CM3s is such and such.”

Tooner,

What you say in your last post about Mr. Reblitz reveals that you have the first edition of his book, which recommends the Braid method.

In the second edition of the Reblitz’s book he doesn't use the Braid White method anymore. Instead he explain two procedures to set the temperament, here is an extract of the second edition:



Here I give the bearing plan of these two methods. I omitted the details, tests and checks of these procedures because I don’t have a permission to post them here.

The Defebaugh sequence is:

Tune:
1. A4 from fork
2. A3 from A4 an octave below.
3. F3 from A3 a third below.
4. D4 from A3 a sixth above.
5. A#3 from D4 a third below.
6. C#4 from A3 a third above.
7. G#3 from C#4 a fourth below (This is the only fourth tuned in the hole temperament setting).
8. C4 from G#3 a third above.
9. F#3 from A#3 a third below.
10. D#4 from F#3 a sixth above
11. B3 from D#4 a third below.
12. G3 from B3 a third below.
13. E4 from G3 a sixth above.
14. F4 from G#3 a sixth above.

The Potter sequence is:

Tune:
1. A4-fork
2. A3-A4 octave down
3. F3-A3 third down
4. F4-F3 octave up
5. C#4-A3 third up
6. D4-F3 sixth up
7. A#3-D4 third down
8. F#3-A#3 third down
9. D#4-F#3 sixth up
10. B3-D#4 third down
11. G3-B3 third down
12. E4-G3 sixth up
13. C4-E4 third down
14. G#3-C4 third down
15. F#4-A3 sixth up
16. G4-A#3 sixth up
17. G#4-B3 sixth up


As you see the Potter temperament uses the CM3s system, which is referred in this book as the "Pivotal Tones Set", i.e. Contiguous Major Thirds F3-A3-C#4-F4-A4

For your convenience I reproduce here what Reblitz comments about the CM3s:



More than 40 years have elapsed from the first edition of the Reblitz’s book. The second edition was published in 1993, that is 16 years ago. As you can see, Mr. Reblitz has switched from Braid White to a better procedure also.

There are people like Mr. Capurso and Mr. Stopper and many others, which are in search of the new age in tuning. New concepts and new procedures that go beyond what is known today. And you are still using and defending Mr. Braid’s centenary system! And worst of all, you are questioning and rejecting the modern methods! Please open your mind!

Tooner,


Why do you love to be locked to outdated books and systems?


BTW, I DO can tune ET using Braid’s method. But it is so difficult, time consuming and cumbersome that I prefer not to use this system. At last it is the run of thirds which tells me when the temperament is right, so why not beginning with thirds in the first place?

How many tuners are needed to convince Tooner that CM3s are the present and Braid White was the past?

None! He will never accept it!

Sorry,

One! Tooner, himself!

Tooner,

Do you really need a mathematical proof?

Buy an ETD and measure yourself!

You are always talking about cents and maths and you not even have an ETD, so how do you work with cents and do the maths?

The fact is that you work on beats, because that is all you have. And from beats you pretend to calculate cents and do a lot of maths. Please buy an ETD and measure your tunings, check you accuracy in tuning ET. Then you would give CM3s a try and measure its accuraty.

Please leave your shell. There is a hole world out there to get wondered by.

Tunelab Pro is not so expensif, you can make an effort to buy it, and then you will see, you will measure, you will know what your ears are not aparently telling you!

Tooner,

How iH affects beat rates in ET tuning?

With CM3s systems you don't bother. The figures are useless. What is important is the ratios, the relatif progression of intervals, the actual values of the rates are not minded.

In the other systems, 5ths and 4ths a la Braid White, it happens the same! The actual beat rates are meaningless, what bothers is the progression, the smoothness, the uniformity. That is ET.

Braid White sequence imposes you arbitrary figures you must tune. And, as Bill Bremmer says, you can get it until certain point where it is not more possible and you have to tweak all the system. Why? Because iH is not integrated in the procedure. You are forced to tune arbitrary beat rates in the first fifths and fourths you tune and when trying to close the circle it doesn't fit! Even before that, when you have the first third available and you check it, you have no reference to check with. And then you must go back your steps and re-adjust what you've done to this point.

As I've said before, it is cumbersome, difficult and anoying!

Gadzar:

My edition of Reblitz does not have the BW method, however it does have a table of theoretical beat rates. I will compare this to the BW tables to see if there is a difference like you mentioned. I don’t think there is. What edition of White do you have? You do have one, I hope, and not just going on hearsay.

Glad to hear that you can tune the BW sequence after all. I thought you said it was impossible… But, if you are waiting until the end to correct problems with unprogressive M3s, you are wasting time. I now think it is better to not proceed a single additional step until each check is correct. Then the last notes just drop into place.

I do not need an ETD to do the mathematical proofs. That takes a calculator. Actually, I already know the answer to the proofs that I have asked for. The reason I did them is because modern tuning theory and my ear did not agree. That is why I bothered looking into the theory deeper. But it is really up to those, like you, that say an old method has certain problems and that a new one does not, to prove it.

Just saying that iH affects the frequencies, although true, is not enough to show that there is a significant difference in beat rates, which there generally is not. Let alone that the progression in beat rates is not also affected in those situations when the beat rates are significantly affected. Remember that equal octave types create ever increasing octave ratios. Consider what this does to the beat speed ratio of CM3s.

Now all this is not to say any method is “better” than another. Only the tuner and customer can make decide that. I can only surmise that some tuners can use SBIs better than others.

Rafael, I am continually amazed at how you are better able to explain what you have learned in a language foreign to you than I am able to explain in my own language!

Tooner, I cannot "prove" how well CM3s work or don't work according to the description you are looking for and I doubt that anyone else can either. The process of dividing the octave into three equal parts is self correcting. By its very nature, it could be considered an endless procedure; one where the ultimate and absolute perfection can never really be found. But if you want to look at it that way, using the CM3s as a short cut to establishing reliable pivot points is profoundly easier and more reliable than masking several estimates upon estimates and then trying to straighten out the mess.

Think of the perfection of ET as we would like it to be as a target at which we would shoot an arrow or throw a dart. The exact center point of the bull's eye is a point with no dimension at all. Even the point of the arrow or the dart is massively larger in diameter than the center point which has no dimension. No one could ever hope to fit that arrow or dart point perfectly centered of the exact center point of the bull's eye and no one ever needs to. Anywhere within the bull's eye is considered a perfect hit.

So, when you tunes a series of CM3s and you hear what it is you are looking for, you have it right and you move on. No one ever said they are "set in stone", those are your words. Getting an acceptable ET is a matter of technique and the use of CM3s is an obviously useful technique. Of course, it takes skill and practice to learn to do that too. For those set in their ways, it may seem an odd, even cumbersome technique. But for those who are new at trying to learn aural tuning, it is something that very apparently has a far better success rate that the older methods.

I see far to many claims of "I tried that one time and it didn't work or I hated the results". That applies to just about every aspect of piano technology. Just how many times have you really tried to use CM3s and did you ever really follow the directions or did you make up your own just to prove they can't work? It does not mean estimating a third, then estimating another third, then estimating another on top of it. That is the, "I can't tune all those thirds" defense. For someone who claims to be able to tune as accurately as you do, it simply does not make any sense that you could not make CM3s work as accurately as virtually any beginner can with a little practice.

There are only two editions of "PIANO SERVICING, TUNING, AND REBUILDING, FOR THE PROFESSIONAL, THE STUDENT ADN THE HOBBYST, BY ARTHUR A. REBLITZ: The first, which was published in the 1970´s, and the second which was published in 1993.

In the first, as I depicted in my post, he uses a fifths and fourths system a la Braid White.



I did not mention a difference! I say that these figures are theoretical values that can not and in fact are not tuned in a real piano tuning.



Of course I have not only one but two books of Reblitz. One I bought before taking the Randy Potter's course and a second which came within the text books of the course. And of course, I have the second edition. I don't have the first edition.



I was forced to tune a fifths and fourths sequence as part of my training in the Randy Potter's Course.

In the Tuning section there is a chapter on temperament tuning where one must learn to tune different temperamnet settings as follows:

1. First we learn to tune the Defebaugh F-F Temperament.

2. Then Coleman A-A Temperament, which is basesed on CM3s followed by 4ths and 5ths.

3. Then Potter's I Temperament, also based on CM3's followed by the tuning of a m3rd and then M3s and M6ths.

4. Then the Potter's II Temperament, which uses the CM3s and then the scheme: up a sixth, down a third, down a third, which is described in Reblitz's second edition.

5. And last, the European A Temperament, as taught by Franz Möhr, (Vladimir Horowitz's tech) at Steinway Hall in the Concert and Artists Training Program, which follows the sequence up a 5th, down a 4th: A4, A3, E4, B3, F#4, C#4, G#4, D#4, A#3, F4, C4, G4, D4.

As you can see this sequence is the same up a fifth down a fourth of Braid White System, the only difference is that we start at A4 (440 Hz.) instead of C4.

and I don't wait to close the circle to start correcting the fifths. I correct them as soon as I can.



Let me ask you somethig, pulled out of your own words: Why must we correct what we just tuned? Why do we find problems with unprogressive M3s, when we are tuning fifths and fourths? Isn't it because nobody can tune them right in the first place, i.e. because nobody can tune correct fifths and fourths with enough accuracy and we need fast beating intervals to get them right?



That's why you need an ETD, to solve the conflict between the modern theory and what your hear, your ear may be fooling you, an ETD doesn't.



You don't want to accept the proofs. I gave you the calculated accuracy of CM3s and you answered you were no going to post anymore on this thread out of respect to the topic poster (Bill Bremmer). (?) What respect? You had no more answers!



Fifths don't progress as predicted by theory. The theoretical beat rate of C3-G3 is 0.44 bps. If fifths have to progress theoretically then C4-G4 would beat at 0.88 bps, which sounds reasonable, but C5-G5 had to beat as fast as 1.76 bps narrow. And C6-G6 at 3.52 and that is clearly wrong. In fact the fifths become purer as we advance to the top of the scale. And some tuners tune them inverted (i.e. Mr. Capurso and Bill Bremmer, which says fifths become wider than pure at some point in the treble). So, iH affects drastically the progression of the beat rates of the fifths! The figures of the Braid White system are theoretical numbers that not correspond to what is really tuned by technicians in E.T.



No, definitely there are bad systems and good systems, and some systems are better than others. It is not a subjective issue. As I've said before: tuning is becoming a science, which as all scientific procedure is not subjective.

E.T. is E.T. The customer has nothing to say about it.

If you tune a temperament which is accepted and appreciated by your customers: good for you! But that doesn't mean you are tuning E.T.

"5. And last, the European A Temperament, as taught by Franz Möhr, (Vladimir Horowitz's tech) at Steinway Hall in the Concert and Artists Training Program, which follows the sequence up a 5th, down a 4th: A4, A3, E4, B3, F#4, C#4, G#4, D#4, A#3, F4, C4, G4, D4."

This last sequence which I do not recommend may be good for Steinway techs with Steinway training on Steinway pianos but will not transfer well to other pianos, especially small, spinet type pianos or any others with irregular scaling. Owen Jorgensen has interesting remarks about this in the latest issue of the PTG Journal. Basically, it won't work as intended. An often made mistake is to believe that what would work for a Steinway concert grand would work for lesser pianos.

I reserve my judgement about anything to do with tuning until I have had a chance to hear it. To do otherwise is mere speculation.

Bill,

It is interesting to know that some procedures work fine for certain pianos better than for other brands of pianos.

My experience is not that vast, I seldom tune a Steinway D, in fact I regularly tune only 2 of them. Though I have noticed that in a concert grand all I ever try will work better than in smaller pianos. The better the piano the easyer the tuning.

I tune ET using the Sanderson-Baldassin sequence based on CM3s, that works wonderfully even in spinets and what I did with the Franz Möhr/Steinway sequence was part of my training process when I was learning to set ET. I don't use it in my day to day work.

All I can say is that this sequence involves a try and error process which makes you go back and forth until you finally find the correct tempering for the fifths and fourths and can successfully close the circle of fifths. The problem here is that you have to tune many notes before having a test available to check what you've done so far.



BDB,

You can give it a try by tuning one piano using this sequence and hear the results you get from it in that particular brand and type of pianos. This sequence has no much testings. If you are interested I can PM you the details.