Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Better Equal Temperament Sequence?

¿And what are these other options?

Independently of the tuning sequence used to tune, I've tried many of them, I've never been able to set a correct temperament without refining it. So I am curious to know if and how you can do it.

If the iH curve is smooth, it is possible to calculate progressive M3s and M6s. The P4s and P5s, while close, do not always flow progressively, due to octave sizes forced on the tuner.

To answer your questions - 1)in the small range of a temperament octave, it may be possible to achieve a subset of progressive intervals -2)neither the ear nor the machine (it seems) can accurately measure the minute changes in beat rates required of both the SBIs and RBIs to create a progressive set of all intervals.

I agree with your idea of M3/M6 as a practical, though not necessarily a desirable, goal for 12TET.

Edit: If a particular piano, as a whole, in all keys, sounds better without the benefit of progressive M3s/M6s, whatever, why not just let it be?

In the video I posted above, she sets a very good temperament in one single pass but as Prout measured the M3s do not progress evenly. I think she could do better if she had refined it. In particular she has imposed the size of the initial octave A3A4 with the M3M10 test, but then she tuned F3A3 at 6 bps ans F4A4 to 12 bps with a narrow F3F4 4:2 octave, wich I suspect was the right size for this piano. In that sense she had to discover the right size for the octaves in this piano and the right tempering of the M3s to build up this octave size, there is no way IMO to know all that in advance but roughing a tuning in and refining it then.

Rafael:

Perhaps it is really the attitude.

One can decide that no matter what, I can only get so close, so let's be pragmatic. I can tune a passable ET fairly quickly and then polish up until nobody can say how it could be improved.

Or one can decide that with determination and practice the limiting factors (hammer technique, beatrate acuity, scaling) will be dealt with to the best of my ability. I will make the RBIs as progressive as possible by knowing which limiting factors are causing which problems.

No, I cannot tune chromatically progressive RBIs. I think I have tuned bi-chromatically ones, though. Almost always I experience hammer technique as a limiting factor. There seems to always be some notes I want tuned in a certain place, but just can't get them there. And also I get to the point that I am not sure if some beatrates are progressive or not. Then I come across minor errors that are multi-note problems and I can't decide what to do, and so leave them. I suppose understanding the sequence is another limiting factor.

The 8-note sequence has helped quite a bit.

But let me ask a question back. Have you ever "been able to set a correct temperament" even WITH refining it? By correct temperament I mean progressive RBIs. If so, let's hear a recording. (Please forgive the playful dig. )

If a particular piano, as a whole, in all keys, sounds excellent, without the benefit of progressive M3s/M6s, or whatever, why not just let it be?

All of these attempts to set a progressive ET is a wonderful validation of the human desire for challenges, but does not necessarily improve the listener's enjoyment of the music being performed.

We think of the 'concert tuning, whatever that means, as the 'nec plus ultra' of piano tuning. I would love to do an analysis of such a tuning, or several different such tunings that we here all agree are just about perfect. I seriously doubt that any of them are, nor should they necessarily be, made of progressive intervals.

I would hope that the tuning makes the piano sound fabulous.

Prout, would you say that a tuning where the RBIs are progressive sounds bad? If not, what's the problem? Do tuners striving for progressive RBIs cause you physical pain or something?

But consider where the "listener's enjoyment of the music being performed" might lead: https://www.youtube.com/watch?v=GcsFcQJeycM

I, for one, am not going to try to second guess what the listeners will enjoy. I am going to tune the piano the best that I can. And that means RBIs as progressive as possible.

I only argue that, on some pianos, progressive RBI's might not lead to the best possible sound for that piano, given the variations in iH, including the affects of bridge rocking and longitudinal modes, which affect all possible intervals on the piano. It is possible that some other combination of sequential M3s and M6s might be better suited to that piano.

OK, is there an objective way to tell when this is the case? Otherwise, it would more likely be a skewed opinion based on something not related to the piano at all. Something like "Oh, the M6's aren't all that progressive, but you know, I think I like it that way after all! How nice I 'discovered' this tuning hiding within the piano."

If you think a piano sounds better if it is equally tempered, you want the intervals to be progressive. Otherwise it will sound worse. If you think it sounds better if the intervals are not progressive, then you do not want it to sound like it is equally tempered. It is as simple as that. The problem comes with the word "better," not with the tuning.

Jeff, I think you missed the point of the cartoon video. It is based on the idea of 'consensus', which is a subjective, empirically derived measure of a large sample of people. His point was that most people prefer the first two iterations of Jingle Bells, and therefore found Lucy's preference of the third amusing.

BDB. No, it is not as simple as that. Very few people, including tuners (and tuners, in general, have the most acute sense of beat rates), can tell if an ET tuning has progressive intervals or not. they can accept the tuning as ET as long as the consensus is that it sounds good.

Very few people care whether a piano is equally tempered or not. They are more interested in whether any notes or intervals sound bad, not whether they sound good. That is why so many digital pianos get a pass even though they are not nearly as well tuned as I can tune a piano.

The point of the cartoon is about narcissism, not consensus. That is MY point, too.

I am amused that you think Schroeder looks amused:

My use of 'his' was misleading. I meant it to refer to Schulz. Sorry. I did not mean that Schroeder was amused. I meant that most people seeing the cartoon are amused, and not by the narcissism, which was limited to just a few words from Lucy.

Well, it was the best example I could find of what I meant.

Exactly. Some of those bad sounding intervals may just be the result of a well structured ET instead of a good tuning as you do.

And my point is that there are so many factors at play in making the intervals sound bad. It is just possible that, if the perfect ET were achieved on a real piano, it might sound worse, because of those factors, than a more holistic tuning.

I liked it.

I wish there was some way to quantify a 'best tuning' for a given piano just so I could see why the artistry of the aural tuner works so well. Alas, it is not likely to come to pass.

I do not know what you mean by "a well structured ET." For that matter, I do not know what you mean by "the perfect ET." The digitals are not tuned to the aural standards that I use. Which bad sounding intervals are you talking about?

I can tell you what I mean by a bad sounding interval, but the definition is vague: it is an interval that beats badly enough that it is grating to the ear.

How can anything be said about what you wrote, except that nothing can be said: ... many factors at play ... just possible ... might sound worse ... more holistic tuning.

There is nothing objective to respond to.

Good points. We need a consensus on definitions, obviuosly, but here are mine.

Perfect 12TET: all 87 chromatic semitones 100 cents apart and all other intervals beating at their theoretical values derived from zero iH. This is clearly not possible on an acoustic piano.

Near Perfect 12TET: all 87 chromatic semitones adjusted so that all M3s, m3s, M6s, m6s, P4s, P5s and their extensions (10ths , for example), are progressive. This is not probable on an acoustic piano.

Well Structured ET: chosen temperament range (usually F3-A4) adjusted so that all M3s, m3s, M6s, m6s, P4s, P5s are progressive.

Good ET: when heard, the consensus is that there are no objectionable intervals anywhere on the piano, whether or not an analysis reveals that they are, or are not, progressive.

It is my opinion that a Good ET is the most desirable tuning of the above four types, since the tuner considers the whole piano and it is possible to achieve.

But that is my whole point. You are trying to create an 'objective' basis for tuning any piano, and I am saying that the result can only be assessed 'subjectively'.