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.

Thanks Rafael, the problem with the Steinway sequence is essentially the same as with the Braide-White or any similar 4ths & 5ths sequence, as you have seen. It is a problem of cumulative error and/or error canceling out error. When you arrive at an interval to test and find there is an error, you cannot know which previous intervals may have been in error or by how much. It is also possible to arrive at a test interval which seems correct but the previous intervals which lead to it are erroneous but the errors canceled themselves out.

In the latter case, any future intervals tuned from faulty placement will produce cumulative error. That can lead to a long and confusing process of finding and correcting small errors which requires a high degree of skill. Novices rarely have sufficient skill for such a challenge.

Having said that, a Steinway tuner such as one at the factory or who mostly or exclusively tunes Steinway pianos, especially the larger grands, works with only scale design that with practice, becomes familiar. The technician learns how to estimate correctly at each step and is therefore successful. Still, many Steinway tuners produce a slightly irregular temperament but refuse to admit it or recognize it. Their priorities are first with unisons, then octaves, then perceived evenness of 4ths & 5ths. A little irregularity among the rapidly beating intervals is unimportant to them. Franz Mohr actually says that, I have heard him say it on at least 3 occasions, so I know he believes that. I recall one tuning he did for a recital at a PTG convention where the key of Ab was quite pronounced, as if he had done some kind of well or meantone temperament deliberately.

When questioned bout this, he did not seem to have a firm or ready answer. He would only say that among Steinway tuners, they all recognized that each tuned slightly differently. While that could mean differences in the amount of octave stretch, he did seem to recognize that temperament was also one of those differences. He said that Steinway technicians all strive for the same kind of sound because one tuner may often follow another. If each tuning were radically different from another, that would present a problem in itself. That is what they believe and one reason why they strongly maintain ET as the one and only temperament they will ever use.

However, I have also heard Steinway technicians say that when an artist is not completely satisfied, they may call on a tuner known to tune with special "color". They called that tuner, "Rembrandt" (implying artistic "color"). That again can involve octave size but in my view, clearly implies temperament manipulation. The Steinway people could offer no details about what differences there may be.

I can only conclude that there is some degree of contradiction between what Steinway has as a policy and what they really may do in practice. That can be and is probably true for voicing and regulation techniques as well. In the end, they consider piano technology an art which must be practiced and years of experience go a long way towards credibility over written or verbal descriptions of what any technician may do at any given moment.

I found myself very busy this past week and have a full day today and a piano recital to attend tonight. I would like to write a plan for tuning the EBVT and EBVT III by the Direct Interval method. Although it has been said to me that the SAT III is the most useful ETD for tuning with that method, I believe any of the four most popular devices and programs are capable of it.

The advantage is that the ETD can find and capture the exact desired pitch of each note. The tuner will have made the decision in each case, not a calculated program. Once the exact pitches are known, the ETD can be used to really solidify the tuning to the degree which it is capable, 1/10 or 1/100 of a cent from one end of the piano to the other. When each and every full unison (not just a single string) can be verified to hold that exact pitch, the effect of the perfected tuning will be truly stunning. Prepare for a pipe organ effect as you have never experienced it before!

Thanks Bill, we will be wiating for that post!

With the Verituner Pocket PC, which I have, there is no direct interval tuning mode. The Verituner 100, the box, does has a Direct Interval tuning mode.

But the pocket PC version has a feature designed to measure tunings and store the results and that can be used to make direct interval tuning.

It's easy done once you know how to do it, and it becomes faster when you have stored the partial you will use for each note.

For example, to tune F5 as an equal beating 12th-doubleoctave, i.e. F3-F5 double octave beats wide the same as A#3-F5 12th beats narrow, you have to:

1. Set the ETD to measure the first partial of F5.

2. Play F3 and take note, mentally, of the reading in cents. That gives you the offset of the 4th partial of F3.

3. Play A#3 and take note of the reading in cents. That gives you the offset of the 3th partial of A#3.

4. Tune F5 at the mean of the two previous readings.

So for example lets say that in step 2 you measure F3 at 1.3 cents and in step 3 you measure A#3 at 5.5 cents, then you have to tune F5 at (1.3+5.5)/2= 3.4 cents.

And that way you tune an exactly equal beating double octave/octave + fifth interval, i.e. a "mindless octave".

For tuning a given interval in the temperament you proceed exactly the same way. Note that you have to convert beats to cents. For example F3-A3 beating at 6 bps means that

4*A3-5*F3=6 bps so
F3 = (4*A3-6)/5 if A3 = 220 hz then
F3 = (4*220-6)/5 = 874/5 = 174.8 hz and so

M3(F3-A3) = 1200*log2(4*220/5/174.8)= 11.84 cents


Now we can tune F3:

1. Set the ETD to measure the first partial of A5 (which is the coincident partial of F3 and A3)

2. Play A3 and take note of the cents reading, say it is for example 6.3 cents

3. Tune F3 to 6.3-11.8 = -5.5 cents.

And we have the M3 F3-A3 exactly 11.8 cents wide = 6 bps wide.


If I have some free time tomorrow sunday I would make the cents calcul for the entire EBVT temperament and I'll post the results here.

Tooner,

I hope you will be reading this. As you can see with an ETD you can do things that are not possible without it.

I checked. White's figures are all based on A-440. Why did you think otherwise?

Tooner,

In the book of Owen Jorgensen "Tuning", page 689, section 218 called William Braid White's Bearing Plan of 1915, the first step of the sequence says:

Tune C to 517.3 Hz.(International Pitch based on A = 435 Hz)

I don't have the Braid White's book so I trust Mr. Owen Jorgensen.

I have a copy of White's book. It's a reprint of the fifth edition (1946), "revised and enlarged". In this edition, the figures are based on A4=440Hz.

According to my copy, there were 5 editions: 1917, 1927, 1938, 1943, 1946 (and 32 reprints of the last one, at least until 1987). White mentions "the old 435 pitch" in some parts of the book, and offers two plans to "set the bearings": one starting from C, and one from A ("some times convenient to tune to some wind instrument").

I think he used A4=435 in the past (from a C fork), that makes sense historically, and I also think the above mentioned details support this, at least indirectly.

In this case, Mr. Jorgensen's historical overview of tuning seems to deal with the foundation of White's work, in other editions figures were adapted to "the modern standard".

In this edition he mentions using a Conn Chromatic Stroboscope, "with a tolerance of 1 cent" (his assumption of "given the proper source of electric current supply" doesn't make me feel all that comfortable).

He mentions the benefits of using a device... back in freaking 1946! Why not use a modern device today? :p

Erus,

Thanks for enlighting us.

I've once had a copy of White's book in my hands, unfortunately I did not get a copy of it. I don't want to buy the book, I think it has only a historical value and what I have from Mr. Jorgensen covers the Braid White's works on tuning pianos and much more.

When I decided to learn to tune, I went into a piano shop and asked the owner if he could teach me to tune. I paid him the first lesson, the fee of a tuning, and he took out his copy of "Modern Piano Tuning and Allied Arts" and began teaching me temperament setting. It was the only lesson I took with him as he asked me to return when I was able to set the temperament. After that I found the Randy Potter School of Piano Technology and never returned to take the second lesson. I think if I were to teach tuning to someone I will begin with unisons not temperament setting, but I think he started like this because he sees temperament setting as the more important skill in piano tuning.

So Tooner, can you say me what edition of Braid White's book you have?

In a comparative scenario it would be interesting to hear two identical pieces played on a Yamaha Disklavier or Bosendorfer CEUS system with the pianos tuned in the different temperaments. This would give a direct comparison with most of the parameters equalized. I wonder if Bill has access to one of these instruments for this purpose?

White's book is certainly a very important book in the history of piano technology (it is a huge step forward compared to J. Cree fischer's, for example). However, A LOT of the research he quotes has been surpassed (both in physical and in historical matters).

I found it only useful as a historical reference. I got my copy from a set of books I found at ebay (the most interesting and useful book from the set turned out to be one about the harpsichord).

What I've found the most useful book until now is "Tuning" by Owen Jorgensen.

One can experiment tuning all these amazing tunings and temperaments form Pitagoras to CM3s.

I wish I was able to play music from several historic periods to listen to the actual music those systems were designed for.

However one can listen to different temperaments by playing intervals to get an idea of what was achieved in the past.

It is a great excercise on tuning different types of fiths used mainly in the meantone temperaments. Meantone is the most used temperament in human history, more than well temperaments and ET.

It is amazing to listen to Bach's music in a piano tuned as it was in Bach's time.

Unfortunately this book is no more available. I got a used copy at a total of about US $500.00 including shipment and taxes from a bookstore I found in the Internet.

For me it is a very valuable treasure! It is 700 pages long, absolutly rigurous and respectful of the authentic systems of tuning and temprering systems. It is written in a scientific way. Very interesting topics about the evolution of tuning systems.

It has also a very complete appendice on iH and how it affects the piano temperament.

Obviously I have not had enough time to read it completely but I love to read it time to time (when I have nothing more urgent to do).

It was expensif but it is worth every cent I've spend on it.

Thank you for the question Emmery. I don't really have such access but I know the university here has Disklaviers. This has been proposed before. However, I think the logic itself is flawed. When a musician plays a piano in a different temperament, they play the piano differently too. If you had been at the piano recital I was at last night where the piano was tuned in 1/7 comma meantone, you would have seen and heard that first hand.

The 1/7 CMT is a much stronger temperament than either EBVT. Yet, the artist embraced it, playing a set of Brahms, a flashy piece by Liszt and then all of the Rachmaninoff preludes. Much more music was played in the remote keys, those which are supposedly unusable than was played in the mild keys.

The pianist spoke at intermission, saying that he had not planned to do it but felt compelled to say how for the first time in his life, the music that he had learned, practiced and performed so often "spoke" to him in a wondrous way. He said that the piano "told" him the expression to use as he went along.

I'm afraid that if such an experiment were done, it would serve to "prove" only what advocates of ET and ET only wish to prove: that music would sound clumsy and out of tune in anything but ET.

I only wish that you all could have heard and experienced what I did last night. The audience was spell bound. There was certainly no one who got up, muttering about an out of tune piano, saying it made their skin crawl or any other such nonsense. The artist received instantaneous standing ovations after each set. He offered a piece by Scriabin for an encore.

All of this only a very strong indeed, 18th Century historical temperament, complete with the "wolf" key of A-flat. (a 9 cent wide 5th, beating about 4 beats per second). If what the majority of piano technicians, musicians, music educators, etc., believe is to be believed, what did, in fact occur, could not have happened. It would have been thoroughly unacceptable. People would have walked out; there would have been cat calls from the audience. There would be a scathing review in the newspaper today about an out of tune piano and a disgruntled and embarrassed pianist.

What happened instead was a performance of the very highest caliber that the audience had ever experienced.

"Unfortunately this book is no more available. I got a used copy at a total of about US $500.00 including shipment and taxes from a bookstore I found in the Internet."

You were lucky to get it Rafael. I bought my first edition for $75 and had the author autograph it. I knew what the value of it would be at that time but most technicians ignored it. A second printing did go out but most of the copies ended up in half price, "remainders" type bookstores. Then it was junk but now it is one of the most highly sought books on tuning there is.

I have the 1946 edition of Piano Tuning and Allied Arts, the one where Dr. Bill recommends getting a strobe tuner if you can't manage to follow his directions. The only time I look at it is when I want to point out what's missing, obsolete and wrong with it as a tuning manual.

I've heard some "comparisons" rigged in favour of ET: who chooses to play music from the late 18th century, in 1/4 meantone, knowingly using the wolf in what are supposed to be the most consonant harmonies? They could just use a "slendro" scale and take things to the next level (of idiocy).

I've also heard some serious recordings of Scarlatti's sonatas in meantone. They just come to life, and the contrast between sections is amazing. A truly revealing experience. It's amazing how many effects are lost when played in ET. (Some sonatas do sound better in the harpsichord and clavichord, but a lot are just great when played on a piano).

I think it's harder to rig comparisons for milder temperaments, but still possible.

I guess some romantic music with clever modulations would be very nice in EBVT. I've heard Chopin played in romantic temperaments, and key colour can be a really nice thing.

Thanks Erus, I have also heard Chopin, Debussy and Jazz in 1/7 comma meantone at the same venue. The artists eat it up. None of them has complained or even questioned the technician about it. He NEVER tells them though. He just presents the piano he has prepared for them and they play it. He says that if he were to tell them the tuning is MEAN tone, then they would start listening to the way it is tuned rather than performing music.

He always provides a splendid piano. The truly fine pianists accept and expect differences from one piano to the next. Apparently, they are all able to recognize the particular power that the 1/7 CMT has and they take it for a ride.

I mentioned the 1/4 meantone example because those recordings were intentionally rigged, the music was transposed and specifically chosen to make the experience unpleasant.

I've never heard that kind of music with 1/7 meantone. There is certainly a difference between 1/7 and 1/4 comma.

Tuned a Kimball console piano this week using Tunelab and Bill's EBVT 3. This was my first time to tune for this individual. The owner is not one who is known for handing out the compliments. However, I saw her at a restaurant after church today, (She was not at home when I tuned). I asked her if she was pleased with how her piano turned out. She said, "Ryan, that piano has not sounded that good in YEARS!"

Ryan Hassell
Hassell's Piano Tuning
Farmington, MO

Gadzar:

OK, your information on White’s method is hearsay.

You posted: ”So for example lets say that in step 2 you measure F3 at 1.3 cents and in step 3 you measure A#3 at 5.5 cents, then you have to tune F5 at (1.3+5.5)/2= 3.4 cents.”

This would be close, but not quite. If this method was really correct, then two contiguous M3s that were both 400.00 cents wide would beat at the same speed, but of course they don’t. And Alfredo’s algorithm would be much simpler, but it is not.

And let me comment on beats and cents conversions without a long quote. You consistently point out the problem of not including the effects of iH when calculating frequencies and beat rates, and then fail to include iH in your own calculations!

I was thinking on what you said about how I discuss iH and cents without the use of an ETD. Young’s paper came to mind. iH was predicted long before it was measured. Young’s paper is an empirical proof of mathematical theory. I see nothing odd about calculating effects of iH rather than measuring the effects.

Something that I think you (and perhaps Bill…) get confused about is the difference between iH affecting frequencies and iH affecting beat rates. They are two very different things. Something that you may want to try with your ETD is to measure the frequencies of the partials of a well tuned temperament octave and calculate the actual beat rates. Not all the partials would need to be measured, just those necessary for the intervals. Then you could empirically determine if actual beat rates are significantly different from theoretical beat rates due to iH. You could also determine just how equal the temperament is.

I wish I could read Mr. Jorgensen’s section on how iH affects piano tuning. It may be misunderstood and perhaps misquoted….

Bill:

This Topic is a good example of why I no longer choose to have serious discussions with you.

You ask for opinions and when you get one you do not care for, start on a witch hunt that tries to implicate Dr. White into an equal temperament conspiracy theory. Anecdotes (which are really just stories to make a point and cannot be used to prove anything) are sprinkled with the word “fact” to try to lend credence to the idea that the use of Dr. White’s methods will make a tuner into a loser. When deriding Dr. White’s book you do not cite his work, but instead allude to things that he never wrote. Your use of sarcasm shows the desperation in your arguments. Scoffing at mathematics as a tool for understanding tuning theory is directed only at points that you don’t agree with. This shows that you are not interesting in the truth.

I choose to not be involved with your sophomoric debate tactics.

Tooner,



Tooner,

You don't get the point. I am not calculating partials. When I use an ETD, I am measuring partials, I am dealing with actual partials, i.e. inharmonic partials, so iH is already included and taken into account. That's why I said you to use an ETD. By using an ETD you can measure partials instead of having to calculate them.

Furtheremore I am talking about tuning EBVT III via direct interval tuning with Verituner Pocket PC. Mr. Capurso's algorithm has nothing to do here.

I guess you have no idea of what "direct interval tuning" is, because you have no ETD.

You say that what I've said of White's system is hearsay. I have read the statement "Tune C to 517.3 Hz." in Owen Jorgensen's book: Tuning, page 689. That is not "hearsay".

I give up!

I can not make you understand. Your mind is closed. You can not accept facts. If you think I am wrong, you can think so, that doesn't bother me.

I won't talk with you anymore, I will ignore your posts. If you talk to me I won't answer.

Here are some quotes from the 1946 edition of Piano Tuning and Allied Arts: On the use of the Conn Chromatic Stroboscope for measuring the accuracy of Piano Tuning. To tune a piano in ET...is a matter of arranging the scale...on the fundamental ratio for the ET semitone, namely 1:1.0594681. The practical methods have been worked out...but in any case, the margin of error in ordinary practice has often been too wide. It has often been found that, even with what is called a good tuning, a systematic error of more than 2 cents is commonly detected.

This somewhat distressing practical fact, together with others of parallel importance, has now been brought out clearly for the first time...since the monumental edition of Helmholtz. An ingeniously devised apparatus, making use of the optical stroboscopic effect, has been developed by the research engineers of C. G. Conn, Ltd.

The Conn Chromatic Stroboscope (now known as the Stroboconn)is a frequency measurer (sic) of great exactness, giving its readings visually and requiring no use of the ear whatsoever. In this way it is at once possible to tell whether any given tone on a piano is flat or sharp of its proper frequency at the 440 pitch. The control is absolute and takes care of all possible fluctuations of the outside power supply.

The Chromatic Stroboscope may be applied practically to the practical work of piano tuning in the field, given the proper source of electric current supply such is found in all great cities. The apparatus has many other uses too. For example it can be used to calculate and verify the amount of the stretching of Octaves, upwards or downwards, as commonly carried out in high treble and low bass. It can be used to construct a Mean-Tone Temperament or a Pythagorean scale. The Conn Chromatic Stroboscope is a very admirable piece of apparatus, and invaluable addition to the scientific equipment of the piano technician.

*********************************************************

In the next appendix, The Mean-Tone Temperament, the author says this: Now, on the one hand the Mean-Tone Temperament has the virtue of (1) giving smooth Major Thirds and Major Sixths, and (2) within the limits above stated producing an intonation delightfully "sweet". On the other hand (1) the Fifths and Fourths, even within the prescribed limits of tonality, are, to modern ears, unpleasantly distorted, while (2) outside the prescribed limits the howling of certain intervals, as may be seen from the data tabulated above, fully justifies the name of the "wolf" that used to be given to this awkward place in Mean-Tone tuning.

It is easy to see how, with the rapid expansion of musical art during the 17th and 18th centuries, the demand for something more widely useful than a Mean-Tone Temperament soon became irresistible. Sebastian Bach began to tune his clavichords in Equal Temperament so that his pupils might be able to play in all tonalities without frequent retunings (sic). The celebrated Well Tempered Clavier...was the first fruit of this famous experiment in Intonation.

***************************************************************

Do I really have to point out just why this book is obsolete? Even the spelling, punctuation and grammar do not meet today's standards. Obviously, many piano technicians read this material, bought and used strobe tuners in the belief that it would make their tunings scientifically accurate. It took the few people who really knew how to tune to point out to them that it did not.

The paragraph on "Sebastian Bach" reveals what others have written about extensively, The Conspiracy of ET; the deliberate confusion of ET with WT and the suppression of the knowledge of any possibility between ancient forms of tuning, 1/4 Comma Meantone, Pythagorean tuning and the glorious and all powerful ET. In his recent work of fiction, Temperament, Isacoff perpetuates this deliberate misinformation and claims that music as we know it today could not have developed had it not been for ET. Thank you, Owen Jorgensen for revealing the truth and exposing the lies.

Let's go back to the method of tuning an ET. Here are some of the suggestions:

"Of course it is evident that one cannot make use of the beats until one can hear them readily. It is at first a little difficult to hear them in piano strings. The difficulty may be overcome by listening to the beats evoked from the pipes or reeds of an organ. I therefore recommend the student to make use of a pipe organ, a reed organ, or even an accordion, for preliminary practice in detecting the presence of beats. All these instruments are tuned, of course, in ET, and the beatings set forth in Table 3 will be found in them."

It is little wonder why anyone reading this today and actually attempting to follow these suggestions would come to the conclusion that they cannot "hear" beats and have no clue about what ET really is or means.

Octaves: The author provides three different octave tests, one for each of 3 types of octaves of different sizes but suggests they are all equivalent: the 4th/5th test (as described reveals a 2:1 octave), the m3-M6 test (which reveals a 6:3 octave) and M3-M10 test (which reveals a 4:2 octave).

"Estimating Beat Frequencies. This has to be done of course, by ear and from what has already been said, it is easy to see that considerable practice is called for, if one's estimates of beat-frequencies are to be at all nearly accurate". He then provides the well known theoretical beat rates for 5ths, "3 beats in 5 seconds" and 4ths, "1 per second".

He goes on about the rapidly beating intervals: Faster beat rates such as those of Thirds and Sixths are not so readily imitable; but one can usually learn to tap out on a table (using drum sticks) five, six or seven taps per second, against the ticks of an accurate pendulum clock beating seconds".

Doesn't it make sense therefore to use a plan that calls for only one estimate and no "counting" of beats? What about beats which are faster than 7 seconds? How do you count those against a grandfather clock with a drumstick on your kitchen table? What about the beat rates that fall in between whole numbers as are listed on the chart of theoretical beat rates? How do you count them? How do you adjust them for inharmonicity by the very small amount they must be adjusted?

Then, there is the infamous "Bearing Plan": Scheme of "Laying the Bearings in ET between F3 and F4 by 4ths and 5ths with tests".

It goes like this: TUNE (to the fork, no problem). TUNE, TUNE TUNE (which means, estimate, then build another estimate upon that estimate, then build yet another estimate upon the first two estimates). Test. A beat rate of 8.0 beats per second is provided. How do you count that accurately against a grandfather clock with a drumstick on your kitchen table? What do you do if the test is not exactly 8 bps? Do you TUNE TUNE TUNE again backwards? TUNE (estimate). Test, 7 beats per second. TUNE (estimate). Test, 9.0 bps. Test, 10.5 bps. TUNE (estimate). Test, 8.0 bps. Test, 13.0 bps. Test, Major triad, if the chord sounds good, it must be right. But what if that chord sounds a little funny, then what do you do? TUNE (estimate). Test, 10.0 bps. Test, inverted major triad, if it sounds good upside down, it must be right but if it doesn't what do you do? TUNE (estimate), test, test, test, 9.0 bps and more triads. TUNE (estimate) 5.0 bps. Test, test, test, 8.5, 9.5 bps then another chord. TUNE (estimate). Test, test, test, test. 8.5, 10.0, 14.0, then another chord. I sure hope these chords are sounding as good as those on the accordion. TUNE (estimate). Test, test, test, test, test. 7.5, 9.5, 10.5, 12.5 then another chord. This time, compare it to the same chord on your reed organ. Make sure you pump the bellows evenly with your feet (no specification for that, just do your best). TUNE (estimate). Test, test, test, test, test, 11.0, 16.0, 9.5 ,0.0. The last, is the pure octave that you can test three different ways for three different sizes but it should still come out "pure".

Wouldn't a method that involves only one estimate, no counting of beats and no tests but which can and does yield perfect or nearly perfect results each time be just a little more practical? Wouldn't it also be more practical to use tests upon the completion of the sequence and test by comparing intervals rather than counting beats?

***************************************
So, you would like to become a piano technician? You don't need to join any organization or go to any school, I have an old book, the classic method that people learned from during the entire 20th Century and it is still being highly recommended on the internet in places like the Piano World Forums. The instructions for just what to do are all written out in clear and easy to understand terms. It only costs $9.95. The gooseneck tuning lever is only $19.95 and includes a felt strip and two rubber mutes. Such a deal! For an investment of only about $30.00, you can soon be earning $100.00 per hour or more!

(Two weeks later) Oh, you couldn't understand or follow those instructions? You don't have a grandfather clock, a pipe or reed organ or an accordion? I see you do have a drumstick, though. Oh, you would like to by a Stroboconn! Sure thing! You won't have to use your ear at all, just like it says in that book! I have an old used one here in perfect condition, only $50.00. Good luck!

Gadzar:

Read or not and reply or not. Saying so-and-so wrote that so-and-so wrote something is not the same thing as reading it yourself.



The problem with this math is that the fundamental frequency is multiplied by the partial number to determine the frequency of the partial without including the effect of iH. Young’s paper explains how to do this. The odd thing is that although iH definitely affects the frequencies, it makes very little difference to beat rates, especially in the temperament. And that is my point when criticism is made of using theoretical beat rates to tune with. It is impossible to aurally tune by frequencies, so the inaccuracy of theoretical frequencies is not important in itself. What is important is whether the theoretical beat rates are accurate, and oddly enough they are.

No need to believe me, the math will prove it. And there is no reason for me to show the math. If someone can comprehend it, they can perform it themselves, and should do so rather than take my word for it. If they cannot comprehend it, showing the math will do no good. These people can believe what they want. I am not the only one to say that the effect of iH on theoretical beat rates is insignificant, especially in the temperament.

I know that there are members on this Forum that are capable of this and have studied it. I have wondered why they do not join in. It could be to avoid the frustration that I sometimes experience. I guess I am not over being mislead by this myth and having false self-doubts. My ears said one thing, this myth said another. By doing the math, I proved to myself the falsehood of this myth and regained confidence in what I hear. I would like to prevent the same thing from happening to others.

Good post, Bill!

It is worst than I remembered it!

Tooner,

For the sake of exacteness, I will answer this last time, it is worthless I know but even so you can have it:

With actual numbers, as measured on a Knabe Upright I have in my shop for repair:

The actual frequency of the fundamental of A3 does not matter, we measure the actual frequency of the fourth partial of A3.

Offset of fourth partial of A3 = + 1.13 cents

Frequency of fourth partial of A3 = 440*2^((37-49+24+1.13/100)/12) = 880.574575 Hz.

So we must tune the fifth partial of F3 to 874.574575 Hz. (6 hz lower) in order to have 6 bps.

Offset of fifth partial of F3 = 1200*log2(874.574575/(440*2^(33-49+28)/12))) = -10.83653794 cents.

So:

Width of F3-A3 M3 = 1.13 - (-10.83653794) = 11.83653794 cents

After rounding decimals we have:

Width of F3-A3 = 11.84 cents, isn't it?

Sorry, I was interrupted, but i'm back.

For the equal beating 15th-12th we have, in the same Knabe upright, we measure actual partials:

offset of 4th partial of F3 = 0.67 cents

frequency of 4th partial of F3 = 440*2^((33-49+24+0.67/100)/12) = 698.726823 Hz.

offset of 3rd partial of A#3 = 1.69 cents

frequency of 3rd partial of A#3 = 440*2^((38-49+19+1.69/100)/12) = 699.138617 Hz.

So, in order to have equal beating between F3-F5 and A#3-F5 we must tune F5 at the mean frequency:

1st partial of F5 = (698.726823+699.138617)/2 = 698.932720 Hz

and we have:

double octave F3-F5 beat rate = 698.932720 - 698.726823 = 0.20589687 bps

12th A#3-F5 beat rate = 699.138619 - 698.932720 = 0.20589687 bps


Tooner,

So with this system of direct interval tuning you can tune exactly what you want.

Without an ETD you can't do this because you don't have the measured partials involved in the intervals you want to tune.

I hope this time you will give me some credit for my calculations!

This time I will finish my post!

Instead of doing all that frequencies calculations you can go directly with the offsets in cents, the error introduced is negligible, really negligible, as we'll see:

offset of 4th partial of F3 = 0.67 cents
offset of 3rd partial of A#3 = 1.69 cents
mean = (0.67+1.69)/2 = 1.18 cents

Now you tune F5 to +1.18 cents offset, without any further calculations, just as I have said in a previous post.

The error introduced is:

1st partial of F5 = 440*2^((57-49+1.18/100)/12) = 698.932689 hz.

instead of the theoretically correct value of 698.932720 Hz.

error = 698.932689 - 698.932720 = -0.000031 Hz.
error = 1200*log2(698.932689/698.932720) = -0.000077 cents.


The best human tuner can only adjust tenths of a cent so there is no error at all.

You folks have inspired me...

Some time ago, a number of my books and other items were destroyed when I had raw sewage back up into my basement. Of course, my homeowner's insurance refused to cover anything.

My copy of WBW's PT&TAA was destroyed.

Today, I finally went to Amazon and ordered another copy... along with a couple more books:

William Braid White's "Piano Tuning & the Allied Arts"
William Braid White's "Theory & Practice of Piano Construction"
and
Alfred Howe's " Scientific Piano Tuning & Servicing"

I was shocked to see how much my copy of Owen Jorgensen's "Tuning the Historical Temperaments by Ear" is now worth.

For some time I've been thinking about starting a thread (I don't want to hijack this one )regarding modern books that are still in print that deal with modern tuning theory from a mathematical perspective.

Joe,

I don't know if we are talking about the same book of Owen Jorgensen.

What I bought is: (I reproduce all it has in the front cover)

-TUNING-
Containing
The perfection of Eigheenth-Century Temperament
The Lost Art of Nineteenth-Century Temperament
and
The Science of Equal Temperament
(grand piano illustration)
Complete with
Instructions for Aural and Electronic Tuning
OWEN H. JORGENSEN

Edited in 1991, by Michigan State University.

This is a huge red book with letters in gold which has 798 pages.

I think what you have is another book of the same author: "Tuning the Historical Temperaments by Ear".

Hi Rafael,

I'm sure they're different books.

I "think" Tuning the Historical Temperaments by Ear was the first book he published on the subject.

Thanks,
-Joe

You're right, Joe. I looked them up on Amazon and was amazed it was possible at all to buy a used one of either. It is interesting to note that Jorgensen's books command a hefty price of $425.00 or more, Braide White's lastest edition, 1953, $14.00 and Isacoff's work of fiction, $1.66.

The ET via Marpurg method I developed for tuning ET was based upon research from two of Jorgensen's publications: The Equal Beating Temperaments and Tuning...The Science of ET. The latter contains two pages of theoretical beat rate information for ET in a far more readable format than the Braide-White book. So, if I ever need that information, I prefer to use Jorgensen's book. It also contains many other insights into tuning ET which Braide-White's book does not have. It also does not suggest using a pipe or reed organ or an accordion as a true reference for ET the way Braide-White's book does.

Finally, Jorgensen's book tells the truth that has to be told which in my opinion, makes Braide-White's book completely invalid and utterly useless for learning how to tune a piano. "Inharmonicity: the quality whereby the harmonic series deviate from theory by different degrees on various tones of a musical instrument. This in turn causes the intervals to deviate from theory and become distorted...Smaller or cheaper pianos contain more inharmonicity than larger or more expensive ones."

Two factors affect beat rates when tuning in ET: the actual amount of inharmonicity present and the choice of the size of octave within which the temperament is constructed. Braide-White's book offers three different octave tests, each one would produce a different sized octave. So, not only does BW not tell us that these exact beat rates we must use are wrong on one count but also wrong when you consider that he doesn't seem to know anything about octave types.

If you own Braide-White's book, read it for a good laugh, then sell it to some sucker good and cheap. It is thoroughly useless, incomplete, incorrect and obsolete.

I've seen Mr. Jorgensen's book cited in A LOT of serious resources on musical acoustics. I am sure it will be cited and used for a long time, it is a massive piece of research, in a rather obscure field.

An interesting thing: Mr. Jorgensen got into the piano tuning world with Braid White's correspondence course.

Bremmer is being deceitful. I read the first paragraph of his edited quote of Dr. White and see no reason to be mislead any further.

Bremmer quoted:

“The practical methods have been worked out...but in any case, the margin of error in ordinary practice has often been too wide. It has often been found that, even with what is called a good tuning, a systematic error of more than 2 cents is commonly detected.”

Since the emphasis in this Topic has been on methods for setting the temperament it would seem that this edited quote indicates that Dr. White acknowledges that his method is not accurate. But if we read what is substituted between the word “out” and “but” by dots AND WHAT WAS COMPLETELY OMITTED IN OTHER PLACES, Dr. White’s meaning (rather than what Bremmer wishes others to believe his meaning is) can be understood.

From Piano Tuning and Allied Arts by William Braid White, Mus. D. Fifth edition 1946, Appendix III, page 228 (omitted test in bold):

“The practical methods that have been worked out for the purpose of enabling tuners to realize frequencies in accordance with these ratios, can be brought to a high level of accuracy; but in any case, the margin of error in ordinary practice, has often been too wide. By methods now to be described, it has often been found that, even with what is called a good tuning, a systematic error of more than 2 cents throughout five of the seven octaves of the keyboard, is commonly detected.”

Now a reader can make up their own mind what it is that Dr. White means. What it means to me is that his method can be used to create an accurate tuning, and is accurately created in two octaves, but sometimes not in the other five. Which two could be correct and the other five wrong? Obviously, the first two octaves that are tuned, including the temperament.

I will be notifying the Moderator about Bremmer's attempt to deceive.

Let me quote the second paragraph of the preface to the fifth edition so that it will be clear that Dr. White’s method does not include estimates (bold added for emphasis):

”I have taken the opportunity thus presented, to go over the entire test with great care, clarifying obscure passages, simplifying and condensing some of the explanations, correcting errors that had crept in, and above all, expounding in detail various practical checks and tests whereby the accuracy of the tuner’s work may, as he proceeds, be effectively determined, step by step. Most of these tests have been worked out in the course of my own theoretical and practical studies.”

Having preferences for a particular method is understandable. And honest disagreement should be encouraged. But deliberate deceit is outrageous.

In my reading of the complete text as quoted, it could be taken to mean that 2 cents, spread out over 5 octaves is the most error anyone ever makes. That's too much! Buy a Stroboconn! I'll be notifying the moderator of the intent to deceive by William Braide White! From the exams I've scored where people used the BW method, it was more like 2 cents on nearly every pitch!

Where are the practical checks for the estimate, the estimate upon the estimate and the estimate upon the estimate upon the estimate? What do you do when the whole house of cards collapses upon itself?

What about Sebastian Bach inventing ET and tuning his Clavinova with it so his students could play in all keys? I'll be notifying the moderator about that too!

I don't want to read BW's book for a laugh. It is 1000 times more fun to read your posts about using strobocons, pipe organs and accordions to tune pianos or Bach inventing ET to have his students play in all keys.

And I see that I am not the only one to be wondered by this thread.

Hey guys! Have you noted that at this moment this topic has a count of 1,243 views and is only surpassed by another topic on tuning systems? (and of course "O.T. paging Jerry Groot", and "Behavior in this forum")

Congratulations Bill!

Hi Rafael,

I just checked my copy of Tuning...By Ear by Mr. Jorgensen. I have copy number 848 of "A Limited Edition of 2,000" from 1977. I think I bought it in 78. The cover in brown with gold type and it has 435 pages.

Hi Bill,

I understand that tuning theory wasn't as advanced then as it is today. But, what was available to the student in the old days? Dr. White collected the information that was available, expanded upon it, and presented it in books, taught it in his school, apparently developed player piano actions, and on and on. He was a shining light of his time. And, a quick search of "William Braid White" at Google will show that he is still cited today.

I remember reading PT&TAA when I was a student, and yes, tapping out beat rates (with my finger) to try to 'get them into my ear'. It's just what we had to do then. I'm still grateful I had access to his book. Although I do have tremendous respect for your great knowledge of modern methods and theory, and I understand that we need to keep up or be left behind, I hope you'll appreciate that nothing will shake my admiration for William Braid White.

I hope this doesn't cause a problem for someone, but while searching WBW, i came across a web-site that is offering free downloads of PT&TAA in .pdf format:

http://members.shaw.ca/paud122/Miscellaneous.htm

It's that "Behavior in this forum" that needs to go and with an apology for engaging in the very behavior he says he doesn't want. Where is the opportunity to respond to it publicly? Is that opportunity locked out because that person knows that the "complaints" received are from a very few individuals who feel somehow threatened by the strength of organization and solid credentials held by proof of knowledge and skills?

What about the behavior of one individual who constantly tries to deceive unsuspecting people into believing that an obsolete book on tuning, replete with bad grammar and punctuation, which gives information that is incorrect and contradictory is a better way to learn how to tune a piano than the more modern methods? What about a person who consistently claims that a proven method of accuracy is inaccurate? What about a person who consistently claims that inharmonicity has no effect on tuning beat rates? Is that not outright deception, an attempt to show that his way of tuning, in spite of all evidence and records to the contrary, is the best? Is that not self promotion?

What about a person who has no public record or credentials as a professional piano technician who can only claim solid belief in a thoroughly obsolete and disproven system, who spouts mathematics which few if any can comprehend as proof? What about a person who scoffs at and denounces a technique or method, saying that it is imperfect but before he even has time to read all of it, let alone implement it, invents a method of his own which he claims to be perfect but never tells anyone what it is?

What about a person who posts a new thread which is a direct insult to another participant in order to show "errors" but can not and does not yield any at all? What about a person, again with no credentials who advocates a technique never before heard of or even mentioned in any piano tuning publication whatsoever as being the ultimate and most accurate (chromatic minor 6ths). What about a person who says a proven and now commonly used technique(4:5 ratio of CM3s)is crude and inaccurate but instead offers techniques which are far more difficult to verify and effect such as 7:8 and 15:16 ratios and claims that only these are accurate and useful? What about a person who consistently hijacks topics to put forth his own opinion, an opinion found in only one source? Does that not sound something like fanatical fundamentalism? "They spoke in tongues and took up serpents" and therefore everything forward is based upon that and that alone. There are no other truths, there are no other possibilities. They denounced those who did not believe in their ways as infidels and who would be damned.

Shouldn't such a person be permanently banned? Actually, he shouldn't. His views should be seen by others for what they are and measured against the views of others for what they are. He has the right to speak in his tongues which no one understands (meaningless gibberish) and to take up his serpents, be bitten by them and to seek the first aid for the foolish act, outside of his own beliefs but which is common sense to anyone else. He'll only seek to prove once again, all over again that to speak gibberish and to take up the serpent is the one and only one right way.

Hello Joe, yes the Braide-White publication was the standard of its time, even as it edged out the competition from Oliver C. Faust who could well have been seen to have a superior method. Doesn't that sound a bit like VHS vs. Beta and Microsoft vs. Apple? Of course, I am keeping my copy of Piano Tuning and Allied Arts but not so that I can teach the method to anyone. I'm keeping my Helmholtz book too. I have another book from Braide-White's time by Cree Fisher. I also have Let's Tune Up by John Travis and some other books as well. I wouldn't throw any of them away or sell any of them but as a tuning instructor to those who most want to learn what they need to know today as an aural tuner, I would not use any of those methods at all.

Yes, Owen Jorgensen learned first from Braide-White and he included BW's methods among the many flawed methods for attempting ET that there were in the late 19th and early 20th Centuries. Obviously however, Jorgensen grew in his knowledge far beyond what he had first learned. He went back as far as tuning history went, dug up buried and suppressed material and went ahead to embrace modern methodology and is still teaching the most advanced techniques there are today through his writing and communication with actively progressing piano technicians. Anyone would do well to read his latest article in the August 2009 issue of the PTG Journal and to research any previous PTG Journal articles he has published.

Most of us see this particular poster Bill for who he is which is why most of us have stopped most forms of discussion with that person. It is useless. I like the points you make above though. They are good ones.

As you have stated, the Strobe, at that time, was thought to be fantastic. That is, until a tuner with a good ear heard the outcome and said, no way, it sounds bad. Since then, computers and technology have advanced to the point that made the strobe totally and completely obsolete. The same goes for books written with what technology or theory that was available at that time. Since then, books like Owen Jorgensen's have surpassed that comprehension with his own personal studies and practice coming up with various different methods along with perhaps easier ways of tuning with a much better understanding of cause and effect.

Thanks Jer, As someone pointed out to me several months ago, if Braide White were still alive today and issuing new editions, I have little doubt his book would contain the modern ideas we know today such as CM3s, incorporating inharmonicity into tuning, the use and programming of modern ETD's and the correction of the confusion of ET vs. WT terms. Instead of telling us we need to count beat rates of 9.5, 10.5, 13.5, etc. on a table against a grandfather clock with a pair of drumsticks, there would be a more practical method of utilizing interval checks. Certainly, we would not be told to learn to perceive beats by listening first to a reed organ or an accordion!

By now, I'll bet that he would even embrace the concept of non equal temperaments such as John Travis (Let's Tune Up) did before his death. Travis' book had many of the same faults in it as did BW's. Neither seemed to realize just how much inharmonicity there really is in piano strings or how much effect it has on tuning. Travis believed that if you started the temperament on a black key such as C# rather than C, the temperament would end up being "more equal" (sic). Travis actually said in his book that "Bach invented ET and tuned his own piano in it".

These kind of fallacies would have come to light and both would have benefited from editors who could have cleaned up the writing considerably. The charts of theoretical beat rates would still be there and should be but only as a frame of reference the way they are in Jorgensen's book.

The real point about using BW's book today for a novice to study piano tuning is in fact, that it is obsolete. With generations of piano technicians having used it and to a very large percentage, all producing the same kind of identifiable errors from it, it points directly to a serious problem in the method itself. That is why virtually none of the modern methods there are come even close to resembling it. Furthermore, having our fathers, grandfathers and great grandfathers live their whole lives believing such nonsense as "Bach invented ET..." and not even being aware of any other possibility and then having a completely rejectionist attitude about any and all other concepts, all the while producing their own backwards version of what they don't believe in, is reason enough to direct today's novice elsewhere first.

After all, are there any practitioners of psychology or psychiatry who firmly believe in and only practice what Freud taught? Are there medical doctors who treat every ailment with leeches and a shot of brandy? Are there auto mechanics who only refer to the manual for the model T Ford? On the latter, I know that in the past, a good auto mechanic could diagnose a problem just by listening to the engine run. Many may still be able to do that and may have an opinion about what the trouble is but they all now hook up their electronic diagnostic system to the car's internal computer. Physicians can diagnose my sight, smell and touch but they still run blood tests and MRI's. They all use modern technology and have ancient books merely as a point of reference for how far technology today has come.

To start a novice aural tuner today with BW's book is to mislead and misguide them. It is the easiest way to produce a generation of tuners who know nothing at all about tuning but rely solely and exclusively on ETD's.

I am confused. If one cannot use Braid White as a basis for setting the temperament because it is obsolete, why can one use Marpurg, who died a century before Braid White wrote his book?

Braid White describes a method of tuning. I do not feel it is particularly efficient. However, there is no reason one could not set equal temperament correctly using his method. It would just be difficult to do so.

The quasi equal temperament which is commonly called "Marpurg" is one that Marpurg himself wouldn't have recognized. In Owen Jorgensen's second publication, The Handbook for Tuning the Equal Beating Temperaments, there is a temperament scheme with the title, Marpurg-Neidhardt Composite Quasi Equal Temperament. Since the two named people lived at different times, the idea is simply a composite or combination of what both individuals practiced. Marpurg did however have several schemes but all were quasi equal temperaments. None of them would be accepted as ET today. Neidhardt also had some very mild temperaments. Indeed, Owen Jorgensen told me that the EBVT III very closely resembles one of his ideas that can be found in the book by Murry Barbour.

The temperament in Owen's book is between C3 and C4. The contiguous M3s, C3-E3, E3-G#3 and G#3-C4 are truly equal beating rather than at a 4:5 ratio. From C3, E3 and G#3, pure 4ths and 5ths are tuned. The remaining notes, D3, F#3 and A#3 are placed equal beating between 4ths and 5ths that correspond to them. It is relatively easy to tune and replicate very precisely. The hardest part is fitting E3 and G#3 between C3 and C4 so that the three CM3s all beat exactly the same. Then there are six pure 4ths and 5ths (very easy to do and precisely replicate) and the three remaining intervals are tuned so that one interval beats exactly the same as another; no counting, just listening until both intervals have the same, tempered sound.

It is far easier to get the above consistently correct than it is a true ET. There is no guessing except at the very beginning, a little estimating and trial until the three CM3s are exactly right. After that, you don't have to guess whether an interval is pure or not; it either is or it isn't. You can use the checks there are for pure 4ths and 5ths but if you just make a 4th or 5th nice and still, the checks will merely confirm that so they are hardly necessary. You can't be wrong by more than 1/2 cent and no know it. The same goes for the three remaining equal beating intervals; they either beat equally or one is faster than the other. You also can't be wrong by more than 1/2 cent and not know it.

As an aside, that is why I purposefully chose the equal beating path and method for developing a Victorian style well temperament. First, so I, myself could replicate what I want to within a very narrow margin and then secondly, so others could too if they choose. It is still somewhat of a disappointment to me that so many want to use the electronic figures rather than good old aural tuning techniques.

Now, there is another version of the Marpurg-Neidhardt Composite Quasi Equal temperament which is most often practiced and is simply called "Marpurg" for short, even though Marpurg himself certainly never tuned it. The temperament octave is transposed to F3-F4 and it is tuned from an A pitch source rather than C. The CM3s are made to have a 4:5 ratio instead of equal beating. All the rest is analogous. After the CM3s are tuned, the rest is quite easy to effect and very replicable and does not really require any checking although the checks for 4ths and 5ths may certainly be used.

The "Marpurg" temperament is often used as a close but not quite identical cousin to true ET. For those who use it as I occasionally do, it is believed that the pure 4ths and 5ths plus many other equal beating and proportionate beating intervals actually yield a more in tune and pleasing sound than true ET does. The tempered 4ths and 5ths are tempered twice as much as in true ET, so when played alone by someone used to true ET, they sound incorrect. However, when played in a true musical context, those "imperfections" are lost but a more harmonious sound is found. There is no cycle of 5ths "color" in this temperament, however; just a slightly more pleasing consonance to all keys over true ET. This version might most properly be called the Marpurg-Neidhardt-Faust Composite Quasi Equal Temperament because it was Oliver C. Faust, a contemporary of William Braide-White who first utilized the 4:5 CM3s in his book on tuning.

The idea for the "ET via Marpurg" came to me one day when I was tuning the "Marpurg" temperament. I wondered to myself, "What if I resolved the pure 4ths and 5ths there are in the Marpurg the same way that the three notes, G3,B3 and D#4 are resolved, by making then equal beating with corresponding 4ths or 5ths?" Just on a whim, I tried it and to my amazement, the result was an apparently perfect ET!

I immediately wrote to Owen Jorgensen about it and he congratulated me on what he characterized as a "very clever idea". The fly in the ointment, of course is that 4ths and 5ths in true ET are NOT equal beating, not quite. However, when Jorgensen analyzed the idea mathematically, he revealed that there was no single pitch off of true ET by even one cent. The closest to that is D#4 which would be 0.78 cents flat. The F3, A3, C#4 and F4 are exactly the same, of course. A few are about 1/2 cent off and others just a tiny fraction.

While this is somewhat of a disappointment, I still quickly realized the value in the scheme. It could serve to very quickly, without using any checks, bring a very out of tune piano to near perfection. That would be useful in a pitch change and yes, to bring a piano which is de-tuned for a PTG Tuning Exam to a nearly perfect temperament quickly, easily and predictably without any guesswork.

I decided I must give this idea a try with the students I work with who can tune with an ETD but whose aural tuning skills are lacking or even non-existent. I already knew that even these people could hear and tune pure intervals quite well. I also knew they could perceive and tune two intervals so the beat exactly the same without "counting" beats, only working until both intervals beat exactly the same.

I used to use those techniques when teaching ET. Get the 4th or 5th pure first, then temper it and check with another interval to see if it works. It had worked for CM3s too. Get both M3s beating equally, then sharpen the top note slightly and compare again. It works for other combinations such as as M3-M6 where the difference between the two is very slight. When any interval is pure or any two intervals as equal beating, it is not correct in ET but at least one knows where one is and how far one has to go. That was always the strategy and it worked and worked well.

Now, the ET via Marpurg idea has proven to be all the more successful. On the first attempt, all the way through the sequence with only one estimate and no checks whatsoever, the lowest any of my students ever scored was a 90. Others had 93's 95's 98's and one was a perfect score of 100. You can imagine how thrilled these students were to actually do this! Moreover, they all could spot and correct the errors that there were on there own. They had already learned through the process how to identify and correct errors by comparing one interval with others that are related to it. It was apparent that teaching such relationships as a task in itself was not required. They learned it through the process.

It was literally, "Come in knowing nothing, go out knowing how to tune a perfect ET in just 90 minutes". Of course, any who learned the technique will have to practice it an memorize the sequence. You can't be a master of anything by attending one class. However, there is good evidence that the idea can and does build a very firm foundation very quickly.

Bill,

I've often heard that tunings in Well Temperaments last less time than in E.T.

Not that with ET you could get a better stability in setting the tuning pins and rendering the strings, but by the fact that all the intervals in ET are tempered, i.e. already a "little out of tune". And thus a little shifting is less noticeable.

"Au contraire", in WT's there are intervals more harmonious or equal beating, as in EBVT III, which can be destroyed by little shifting.

What do you think about stability in EBVT III, in comparison to E.T.?

Rafael, I have heard that before too. It is only a hypothesis. In my experience, the very opposite is true. Just as imperfection in a WT does not keep it from being a WT, a little drift in stability of a WT is less noticeable than it is in ET. Neither one is a major consideration, however. When the piano goes out of tune, it goes out of tune. The above hypothesis should not be a reason to choose ET over a WT and the reverse is true as well.

Bill,

like I told you once before I came up to the exact "ET via Marpburg" that you did, the only way I could decently get the teperament set.

I saw some web pages of how a harpsicord tuner tetrasected a fifths by first tuning the surrounding 5ths beatless from a given 3rd (which could be of any preferred size that the temperament demamded). Then I borrowed the Potter contagious 3rds and combined those to methods. I thought my method was very "home-made" and you can imagine my surprise when I two months later saw that you had already put it into system, it really gave me a boost of confidence that was highly needed at that point!

Anyways, now im really into your EBVT and mindless octaves. What happens when you have set the temperament, how do you step down until the two octaves / 12ths can take you further? Do you go by octave tuning with some checks, or do you have a different approach? Same for the first notes going up from the temperament. Octave tuning + useful checks? If so, would you mind giving an example?

Regards,
Patrick

Must have been really tired when I wrote the post above A lot of typos, and then some errors, too.

I meant tetrasected a major third.

The interesting web page that got me going was written by Bradley Lehman some years ago, and can be found here:

http://www-personal.umich.edu/~bpl/larips/tetrasect.html

So, to place a tempered fifth exactly in between a major third, you go about it as when making a paper airplane. The same idea as you (Bill) use in your ET via Marpurg, with the slight difference that he doesn´t use equal beating but instead relies on the relationship of 2:3 for the fifths|forths.

I combined this with the Potter temperament that estimates the contiguous 3rds F3-A3-C#3-F4, and started practicing. If you use the relationship of 2:3 you should, theoretically, end up with a perfect ET (please correct me if I'm wrong). And indeed, after months of fighting with "make the fifths sligtly narrow", i could tune ET.

However, I was embarassed using this, as all the other tuners I learned from advocated the temperaments based on estimating 4ths and 5ths. Only months later, I found your "ET via Marpurg" pdf-file, and relaxed considerably

BTW, I wrote a post about this a little over a year ago, it can be viewed here:
http://www.pianoworld.com/forum/ubbthrea...html#Post626956

Regards,
Patrick

Patrick:

You seem to be a critical thinker, so I think you will understand what I am about to say without being offended.

It bothers me that there is a double standard in regards to tuning with CM3s verses with 4ths and 5ths. The fact that iH changes the frequencies of partials is used as an argument that beat rates are different than theoretical, but is ignored when considering beat rate ratios. Is the beat rate of 4ths to fifths really 3:2? And is the ratio of CM3s really fixed?

Jeff: No offense taken

This is my humble empiric analyze:

1) on some pianos the 3:2 works really well. read: on bigger grands.

2) the smaller the piano, the bigger the inconsistency in what beat ratios between the 4ths and 5ths allow you come out with at least something resembling ET

3) this is why, lately, I´ve tried to intersect the 4th/5th pair where it sounds balanced, not by counting. This has given me a better result, and is also why I stated the 3:2 as a theoretically ideal relationship above - hunting for that might not necessarily be the best practical choice in all situations.

Jeff, you reasoning sounds logical. If the CM3 beat rates are affected by iH, so are the ratios. They are part of the same plain math.

This has been a fascinating thread. Bill, I am on my way to Madison this Friday to play a show and then to Minneapolis on Saturday for another. I wish I had time to take a lesson from you. I hope to do so in the near future. Thank you for making your teachings so readily available.

To say that inharmonicity does not affect the beats is missing the point. They may or may not affect the beats (I think it depends on what interval and what frequency the inharmonicity of that particular set of intervals happens to be... it can certainly confuse matters). But they definitely affect how the piano and the temperament sounds.

And for a relative newbie like myself, that can lead to confusion and lack of confidence. "Well, I'm pretty sure I'm counting 6.9 beats (or whatever), but man this temperament sounds like crap!" Why doesn't it work? What am I doing wrong?

I've been enjoying the EVBT profile in Tune-Lab. It has helped my ear immensely.