Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Does a "Let the piano tell you" ET 5ths/4ths sequence exist?

Now that you have posted your sequence (thank you), I can illustrate what I mean directly on it.



How do you check G-A#?
You have no other inerval to compare it with!
If you listen 11 bps, or 10.5, or 10 or whatever you hear, how do you know if it is correct or not?

Gadzar:

I know G-A# is very, very close because I know what tempered fourths and fifths sound like. Then "the piano tells me" what the beat speed of G-A# is for how those fourths and fifths are tempered. Later this will be confirmed or not.

The G-A# is very, very close because of the interrelationships between the Fs, C, A# and G. In a way the resulting intervals are self checking much like a set of CM3s. If, for example, F-C is not tempered enough, C-F will not be tempered enough either unless F-F is too wide. And the relationship between F-A# and A#-F is also the P4-P5 test. The G-C is tempered similar to the other fourths and F-C is compared to A#-F. I think it requires that the tempering be perceived directly, not just the beat rates being compared.

Very, very close is all that can be expected from the first few notes that are tuned, even from CM3s.

I was reviewing BW yesterday. There is, of course, the table of theoretical beat rates. But when the sequence is explained the beat rates are rounded to the nearest whole number and are used to make sure that an SBI was not tempered wide when it should have been narrow, or used to assure a general progression of beat rates.

Contrary to what some may believe (and caused me to think along false lines), the idea is not to tune an RBI and then make fine corrections to the SBIs that formed it. The idea is that the tuner knows what a tempered SBI sounds like and then the progression of the RBIs are used as proof of ET not the absolute beat rates, even though they may have been believed to be always correct. (Which I have doubts about. The variance from theoretical beat rates may have been omitted because there was no explanation for it, and the precise beats rates really don't matter, especially for intervals that are used as checks.)

I do not know Mr. Mohr’s sequence, but perhaps you can see why I chose the order of my sequence to take advantage of which note completes the first augmented chord (CM3s) and the first diminished chord (Cm3s). There may be things about Mr. Mohr’s sequence that are not obvious from looking at just the order of notes. In any case, it worked for him.

I don't understand you.



That is a "Tuner knows how" approach, not a "The piano tells you"

In short: you check with an interval, G-A#3, which beat rate is not relevant because you know how to temper fifths?

So what are you checking with G-A#3?

a minor third - but whatever works ....the sequence is certainly useable but give no real size of the octave (seem to me )

I have worked with dozens upon dozens of students who have tried and tried to use a 4ths & 5th sequence. They all knew 4ths & 5ths should be tempered but that is about all they knew. They never could even get close to using the fine checks which are necessary to make a 4ths & 5ths sequence work. Using CM3s just seemed to work better for them and many have gone on to pass the exam.

Here is an e-mail I received just today. It is now the 5th person who says they now plan to take the tuning exam using the ET via Marpurg at the PTG convention next summer. He is already a fine and professional technician who learned to tune using an ETD but is also determined to pass the exam and become an RPT. Yes, it is an anecdote but I feel it is a timely anecdote to this topic.

"Hello Bill,

I don't know if you will remember me but I have taken two tuning tutors from you during the last two PTG conventions. Last year was a special one you did for me right before my tuning exam. [I took him outside of my already full schedule without compensation of any kind for it].

As you may remember I failed part one by 4 points because I didn't pay close enough attention to the very edges of my midsection. C3 and B4. I did get a 90 on my temperament sequence. [He had used the "CM3s, then Up a third, down a 5th" sequence which was written and published in 2003].

I am writing you this note to tell you how excited I am by the new articles on Marpurg. I have been trying the sequence and it is a perfect fit for me. I am getting outstanding results using it. I do make a few fine tunings once the sequence is complete but I am sure with my next take of the tuning exam part 1 I will score very near 100 percent on the temperament. The speed with which I can tune my temperament will also allow me more time for the extended mid range.

I am also teaching it to my young apprentice and hope that he will be able to incorporate your ideas into his own temperament journey. [This is very encouraging to me because it is my hope that other technicians will teach the idea too].

Thank you for all your hard work and the articles you are doing in the journal. Please keep me in mind because I intend to take you for that beer we were going to drink at last years convention this next year.

With my warmest regards,

Steven [last name omitted for privacy]
[a city in Texas, omitted again for privacy]"

What I have read from the comments here seems to agree with Rafael's observations: using a 4ths and 5ths temperament successfully requires a high degree of skill. The piano does not tell, the tuner what is right, the tuner tells the piano what is right. If there is an irregular scale, what the tuner tells the piano doesn't work and the conclusion is that the piano cannot be tuned. In turn, that leads to the proclamation that only certain brands and sizes of pianos are worth tuning and all others are beneath the dignity of the technician to to even accept.

That is the case of Franz Mohr, or course, surely one of the finest technicians there ever was. But where does that leave all other technicians who can't be Steinway & Sons chief technician? Where does that leave all the other technicians who tried to take the tuning exam but failed it? What does it say about how close to clinical ET all of the RPTs who passed the exam but only barely within tolerance? What does it say about those who passed with a score of 90 which is considered superior? They still had 4 significant errors between 1.0 and 1.9 cents.

How could all of these possibilities still all be the perfect ET that so many technicians not only aspire to but assume is performed every day, by virtually every piano technician all over the world and always has been? Isn't it possible that at least some of these temperaments which aren't really a perfect ET exhibit the characteristics of reverse well?

Isn't it also possible that the temperaments tuned by those who can't manage to tune a clinically perfect ET actually quite consistently exhibit the characteristics of reverse well? Isn't it possible that this has been done for an entire century or more and that all recipients of it accepted it as a "piano tuning" (presumed to be and accepted as ET)?

If so, what is the reason why a 4ths & 5ths temperament has not worked for so many people? If CM3s are also just guessing, why is it that so many more technicians pass successfully when they use them? Why do their temperaments, even those with errors typically not exhibit the characteristics of reverse well?

I know he's checking a m3, that's obvious. But what is less obvious is how he's checking it. He says only that this m3 is the fastest interval in the sequence at 11 bps approximately.

When we make a test we always compare two intervals to see if they are equal beating or if one beats a little faster than the other. But here we are comparing G3-A#3 m3 to nothing but an arbitrary figure of 11 bps which may change dependig on the iH of the piano.

So what can we conclude by listening to this m3? It won't tell us if the fifths previously tuned are correctly tempered.

Thanks Bill.

My English is so poor that I have a lot of pain to express my ideas clearly. But you seem to understand well what I am trying to say.


When learning the CM3 setting, I had a bad time to tune F3. Nobody was able to explain me how to accurately tune F3, until I read your article on tuning the midrange and discovered how the sequence is self-correcting.

The same thing is happening now to me with the correct tempering of fifths/fourths.

Each time I pose the question I receive the same vague inaccurate answer: experience and a lot of practice.

That is why I ask here if there isn't a sequence "experience free" in which the piano tells us how much tempering is correct for a fifth in ET.

All the posters that have participated in this thread say that an experienced tuner can tune correct fifths, but none of them can explain how it is done! And that’s what makes me doubt if they do indeed tune right tempered fifths.

I believe they really don’t. Not at least directly. They have to do a little guessing and then use some other resources to refine them. That’s why they can’t explain beyond “experience and a lot of practice“.


I like the way you, Bill, have putted it: "the tuner tells the piano" vs "the piano tells the tuner".

You give me some light when you say that there are bad scaled pianos for which what "the tuner says" doesn't work. These are the pianos I usually tune (mostly Wurlitzer spinets). I seldom tune fine pianos, so I need a sequence which will work right, even for bad scaled pianos.

I think that's one of the reasons why I prefer now WT over ET. In particular Moore and EBVT III which play well in all keys and sound fine even in small spinets.

I am not saying I can not tune ET in those little beasts, only that I can not do it using a fifths/fourths based sequence. I used to successfully tune ET for almost two years using CM3 based sequences in which the piano tells me what it needs.

I’ve heard Franz Möhr have tuned only Steinway & Sons pianos for many years, no other brand. I believe he even only tuned Ds and Bs, no small pianos. I wonder if he would use the same approach, same sequence and same tests to tune a Betsy Lester spinet.

I use the same techniques to tune a Betsy Ross spinet as I use on Steinway D. Tuning is tuning, it is the art of making the intervals sound the way they are supposed to sound.

Oh yeah!

It's the same thing: a D and an Estey spinet! The intervals sound the same in both, just the way they are supposed to sound. Particularly in the bass!

Well, it is easier on the D. But that is why people like what I do on the difficult pianos.

BTW BDB,

You have not said what you do on the difficult (and easyer) pianos.

Do you use a fifths/fourths based sequence?

On the more difficult pianos, I tune contiguous thirds, fourths and fifths between one major third, and contiguous thirds to fill in the rest of the fourths and fifths, with the addition of tests from the Travis method. The all-important final step is to check everything afterwards. Note that I say I use tests that are based on Travis' method, rather than using his method exactly. Also note that I do not say what note I start with. Once you develop the method and understand the method, none of that stuff matters. You can start anywhere and do things in different orders. The final result is what matters, and that is a result of the final check.

On the easier pianos, I tune contiguous thirds, fourths and fifths between one major third, and contiguous thirds to fill in the rest of the fourths and fifths, with the addition of tests from the Travis method. The all-important final step is to check everything afterwards. Note that I say I use tests that are based on Travis' method, rather than using his method exactly. Also note that I do not say what note I start with. Once you develop the method and understand the method, none of that stuff matters. You can start anywhere and do things in different orders. The final result is what matters, and that is a result of the final check.

For those who are not familiar with the Travis method, he tuned contiguous thirds, and then a fourth, and contiguous thirds from that, comparing with his original thirds. I feel it is better to fill a third with fourths and fifths, and once you have done this, you can compare the rest of the fourths and fifths with the thirds that you have tuned initially.

Lots and lots of checks, not just in the initial temperament octave, but everywhere you tune, makes for a very well-tuned piano.

So there is another CM3s tuner.

I am afraid there is no "let the piano tell you" sequence based on fifths/fourths tempering.

All:

I can only say what I do and why I do it. I cannot say what others do what they do or why they get the results they do.

If the very first time you tried to set a temperment the sequence worked, most any one would favor that sequence. That is the case with me and BW. I have made just the modification of including F4 and A#3 at the beginning of the sequence.

The sequences that include CM3s all sound wonderful, but do not work as well for me.

To me, setting an octave to start with without listening to its effects on the sound of the fourths and fifths is the tuner telling the piano, not the piano telling the tuner. And setting the octave is always done before tuning fourths and fifths in CM3 sequences.

I cannot explain what properly tempered fourths and fifths sounds like. If you don’t know, it would be best not to try to tune with them.

Gadzar:

It seems again that you had already decided that what you are asking for does not exist in fourth and fifth tuning. Of course “the piano tells you” for any sequence if a true ET is the result. What else could tell you? The question is: in what part of the sequence is the piano telling you?

Perhaps your thinking is locked into the glib statement of “let the piano tell you” meaning what it was meant to convey in whatever article it came from. Which seems to be that fourth and fifth tuning is about arbitrarily choosing beat rates for intervals which are then used to adjust the fourths and fifths. If you look at fourth and fifth tuning as distributing the comma so that all RBIs are progressive you may see that “the piano tells you” if you are tempering correctly.

In a fourth and fifth tuning (and perhaps all sequences), the ninth note is what proves if things have gone correctly. As I said in an earlier post, “I know G-A# is very, very close because I know what tempered fourths and fifths sound like. Then "the piano tells me" what the beat speed of G-A# is for how those fourths and fifths are tempered. Later this will be confirmed or not.” Comparing F#-A# to F-A and G-B is how “the piano tells me” if the fourths and fifths are correct. And when the fourths and fifths are correct. then the intervals that they create are correct. It is about beat progression, not beat rates. And, yes, it takes nine notes or eight fourths or fifths to get to that point. That requires great accuracy, but I think you have to be able hear the tempering of fourths and fifths, not just their beats.

Let me add some comments so you can understand the value of G-A# in the sequence. A m3 is made from 2 fourths and 1 fifth. A M3 is made from 2 fourths and 2 fifths. A M6 is made from 1 fourth and 2 fifths. If there is a tendency to tune the fifths insufficiently tempered it will show up more in comparing a m3 to a M3 than it will comparing a M6 to an M3. And by checking the one fifth that is used to form the m3 with an octave and a fourth, the m3 can be consider to be tuned with 3 fourths and an octave - the octave that “the piano tells you” is correct because of how the fourths and fifths sound. So now there is a limit for how fast the M3s can beat and will point out any tendency for the fifths to not be tempered enough. This is especially valuable when tuning E. If C-E is not slower than G-A#, then the place to look is in the fifths that form C-E: G-D and A-E. Notice that these are not involved in the tuning of G-A# and, of course, C can be depended upon as it is the starting note. After E is verified by having made sure C-E beats slower than G-A#, the next 2 intervals are fourths and brings us to the ninth note without tuning any more fifths.

I don’t think you will benefit from this post; I can only hope other readers might. I continue to think that the purpose of this Topic is to bash, not understand, fourth and fifth tuning.

How can I understand what the "piano is telling me" when tuning a fifth, if even an experienced fifth's tuner like you can not explain how it should sound like?

What you say about a m3 being two fourths and 1 fifth; and a M3 being 2 fourths and 2 fifths sounds interesting however and much less arbitrary than tuning 0.5 bps narrow fifths and 1 bps wide fourths.

If you prefer to tune the octave by tuning the 4th + 5th and 5th + 4th, (instead of tuning it directly by testing 6:3 and 4:2 types), I have no objection: yes, you are tuning a good sounding octave, taking into account partials 2, 3, 4 and 6 of the notes involved.

But the the question is still blowing in the wind: how do we tune fourths and fifths?




Yes, if they are correct, but what happens if they happen to not be correct?

You say it takes 10 notes to have an answer, and that is too much to know how to correct them. There are too many intervals to tweak to have a right progression of FBI's.

If I may interject, I believe what Rafael means when he says "let the piano tell you," is something specific, and that is a sequence by which the following occurs:

• Octave width in the temperament area is chosen ahead of time.
• Two octaves are tuned, with one or two overlapping M3rds, one of which is initially estimated.
• The note between the remaining two M3rds is adjusted such that the beat rate of the middle of the three contiguous M3rds is "in-between" the two outer ones.
• Once the middle M3rd beat rate is discovered, the piano has "told you" how wide it should be, for the given octave widths, and for the iH of the piano in that range.
• Given the fixed octave widths, the rest of the M3rd beat rates "fall out" naturally when tuned for smoothly increasing beat rates, as do the beat rates of the 4/5ths.

So the question about whether a similar sequence exists for 4/5ths tuners is one of strategy. In the steps I describe above, the octave widths are chosen ahead of time with the assumption that you can make a wise choice (how that happens is another topic), and given that assumption, the rest of the sequence can be performed mechanically, and produce good results.

My impression is that with 4/5ths tuning, the high level strategy is different, that one does not choose octave widths as a high level guide, and therefore such a sequence may not exist, hence Rafael's query.

Has anyone looked at Virgil Smith's temperment? I'm not sure if it's a 4ths/5ths method, per se, but you work with the A3-A4 octave, guess F3, use 4/5 for the D octave, and then use a fourth for the speed of the a major third. I know it's complicated, but I'm not sure if I'd be breaking any rules by copying a copyrighted work on a public domain. His book is only $7 or something.

I don't personally use this, but I thought it does bridge a few gaps.

Regards.

Gadzar:

I can no more tell you what properly tempered 4ths and 5ths sound like than I could tell you what the color blue looks like. But I could point to the sky and tell you that is the color blue. And if you are not color blind, you will know what I mean. And you can listen to a well tuned piano to see what properly tempered 4ths and 5ths sound like. But if you do not recognize the tempering (which is really best discerned while tuning) and only hear beats, then you will not know what I mean.

Jim:

If what you described is what Gadzar is really asking about, then he would recognize that a 4ths and 5ths sequence does the same thing as a CM3 sequence, but in more steps (which adds accuracy). This is why I do not believe that is the purpose of this Topic. And when starting out there is no reason that a 4ths and 5ths sequence cannot be used with a predetermined octave or a predetermined 12th or a predetermined 17th.

Tdowel:

I know that Virgil Smith’s sequence is on the internet already. I believe I saw it on this Forum. If I remember right, it starts with a specific beat rate, or color, for an initial 5th. I think there may be more to this that I thought at first. With a shorter piano this will produce a narrower octave than on a larger piano which is exactly what you want! It was posted recently about a master tuning committee having difficulty in discerning the difference between the 4:2 and 6:3 octave on a particular piano because of low iH. Perhaps a wider than 6:3 would have been best on this piano and could have been obtained through using a predetermined 5th instead of a predetermined octave. Thanks for putting this thought in my head!

[Edit:] Maybe that is just what I am doing but didn't realise it....

Yes, I have his book, but have not studied his sequence in much detail (was more interested in his approach and philosophy).

I do not get the impression it is a 4/5th's temperament per-se. More that he uses all the interval checks he thinks appropriate to get the balances he wants. For example, in the part you referenced, his actual text is:


I'm sure I'll get around to trying the sequence out, but I'm still working on my ET and EBVT aurally, and that's enough for me to wrestle with for now