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Bill Bremmer says the octaves should be equal when tuning a CM3 ladder, but the Baldassin - Sanderson Tuning Temperament says they may need to be somewhat different. I lean toward what S-B says, but in your case, where one ladder is across a change of scaling and the other is not, well...

Why not do one ladder starting on F#3 and the other starting on G#3? Or maybe one starting on F3 and the other on D#3?

Haven't seen anything from Rafael or Mark C. lately, but I don't follow all the Forums and Topics...

Make sure you have two different sizes of octaves! Then, you can prove definitively that CM3's don't work.

Are you saying that Sanderson and Baldassin got it wrong? Why don't you try the challenge and post the results? A video of you actually doing it would be best so we can see just how to do it.

Yes, you are correct. I meant A3-D4. Thanks for pointing this out.

No, I am saying that you got it wrong. Your "challenge" is like asking somebody to eat an apple and then an orange and then admitting that the two have a different taste, so therefore neither is edible.

You always claim that my posts are too ling, therefore you don't actually read them or you would have already known that what you are claiming isn't true at all.

But what is, in fact true and the reality of why so many people fail the tuning exam and tune pianos in Reverse Well for their entire lives is that they try to tune the way you do. 4th & 5th sequences are prone to cumulative error and "backing up" doesn't solve that problem, it only exacerbates it.

I am referring to the Sanderson-Baldassin Aural Tuning from the bottom of page 43 of the SAT-III manual. http://pianotuningtucson.com/wp-content/uploads/2007_SAT_III.pdf (Emphasis added)

"Step 6. Check that the three major tenths formed on the seven notes tuned so far also in the ratio of 4 to 5. Also check the C# and F octaves with both the third-tenth and minor-third-sixth tests. Scale problems will show up at this stage, and it may be necessary to compromise slightly the perfectly rising thirds to get satisfactory octaves and tenths."

But this is really a side point.

No one else is questioning the validity of the challenge. It is not some alternate way to tune, but simply a way to verify that ladders of CM3s are tuned as accurate as they are claimed to be tuned.

I always claim your posts are too long? Hardly! More often than not I simply ignore them with no comment at all.

I think you are just being evasive.

So the solution for irregular scaling would always be to guess at 4ths & 5ths and then back up when they don't work out? If a tuner claims to not be able to hear and adjust RBIs then it follows that Reverse Well would go unrecognized.

No one else is playing the silly game that you are calling a challenge because they know it is nothing but sucker bait. It would prove nothing because that is not how one actually utilizes CM3s in practice.

I suggest that you tell yourself that you proved CM3s don't work the same way you told yourself that Bach wrote the Well Tempered Clavier music for ET. People had better things to do than argue with you about that.

Bill, never mind. I don't have time for your sophomoric arguments that have nothing to do with what I am talking about.

I would like to question the obsession with tuning a "perfect" equal temperament in one pass.
First, there is no perfect temperament on a piano. As Dan Levitan showed in his articles ca. 1995, what we tune is the best imitation of equal temperament that we can discern in a reasonable time. The discernment requires a degree of familiarity with the piano at hand, which will involve some trial and error. (Vide the Entropy tuner process which also proceeds by trial and error.)

In practice, many compromises are necessary to produce a two octave midrange which sounds smooth in all intervals, requiring still more compromises to deal with varying inharmonicities in the octaves and twelfths. These larger intervals are crucial in building a resonant tuning which can make a small piano sound surprisingly big.

So concern with perfection in the first pass is not good practice. It is better to feel easy about getting in a fair first pass, then testing and refining to make it better. The exception to this might be the person who tunes certain models of pianos frequently enough to know what to do on familiar instruments.

Hi Ed:

I didn't see this discussion being about a perfect one pass temperament.

Regardless, what you propose goes against the grain of some people that are kinda perfectionist. Besides, I have "roughed in" temperaments and then tried to make them work. I find more situations where I just can't figure out where the error is or how to improve things than if I am meticulous with a sequence.

Happy Thanksgiving Everyone!

Bob: After thinking about what Ed wrote, I wondered if I was missing something about what you are trying to do with your sequence. I think I am, or at least just confused. You start out by saying:

"Here is a sequence for equal temperament that is short, easy to remember, and gets you close very fast so that final refinements can be made."

Then you go into details about inharmonicity and spreadsheets before describing the sequence that ends with:

"6. You're done, but now, as with all sequences, you will need to progressively refine using all the tests you know."

So I wonder what is the need for spreadsheet accuracy and using the correct formula for iH since the purpose is to quickly rough in a temperament that is then further refined?

I realize now that since these higher mathematical calculations were being used, that I became distracted and thought your purpose was a one pass sequence, as accurate as possible. Thanks Ed, for jarring me out of this mindset.

So now I ponder: Do all temperament sequences just get you close in preparation for further refinement, regardless of the stated intent or our ability to use them? If this is true, then there is no such thing as a "mini-temperament." And also, it is not how I use a temperament sequence, but could I be fooling myself?

I was merely trying to create a sequence that was simple and easy to remember, but that worked out well on most pianos, with the understanding that final refinements are always needed. The spreadsheet I made can be used to check any temperament sequence that uses the notes F3 to F4 and it can easily be expanded to a wider range. You can enter inharmonicity values for any piano and the spreadsheet calculates beat rates for equal temperament.

I can't answer your question about whether all temperament sequences just get you close. I know that that is true for me though. I always have to make refinements. I'm not even to the point where I am certain that my refinements are close enough. I check with Tunelab and find that I'm often more than a cent off on some notes from where Tunelab would like the notes to be. I chalk it up to lack of experience and assume I'll get better with more practice.

I think we are easily fooled by the existential emptiness of ETDs. What I mean by this is that ETDs are fully certain about what is "right," they do not doubt themselves, or search for something better. I find it easy to lapse into trying to tune with the dead on, inflexible and mindless certainty of an ETD. Which is not to say that I never use one. Many times I am grateful for its help. But I must remember not to omit myself from the tuning.

As I understand Dan Levitan's analysis, there is no one, certain equal temperament on pianos, but there are ranges of beautiful "imitation equal temperaments." The same would be true of any other temperaments. And the mid-range, the most harmonically exposed part of the piano, is where the weirdness happens. The lowest plain wire string will have the highest inharmonicity in the middle of the piano, and the highest wound string will have the lowest.

I generally prefer to tune two octaves of contiguous thirds, A2-C#3-F3-A3-C#4-F4-A4, which may take into account some octave irregularities. It might be valuable to go next to a potential problem string (such as those awful short scaled B2 strings, say by tuning all Es, Bs and F#s between the As and C#s. Then you can compare many 4ths, 5ths, octaves and 12ths for resonance. At that point it is fairly straightforward to fill in the rest, and it is nice to have the extra bass notes to test 10ths and 3rds low in the range. (O.K. at this stage it takes real attention to stay playful about it, and not get too perfectionistic at it, just enjoy the sounds, ready to correct and fudge as the ear suggests.)

It takes longer, but you get twice as many notes tuned. Getting past the technical interval checks, I like having two octaves to play real musical sequences. Can I trust my response as a musician? When I tune a piano, must I always do it exactly the same as before? I have many ways to tune, have never found the one-and-only right way. (Currently I'm trying to find a way to fit Stopper's pure 12th into the 2 octave thirds approach.)

Given that 1 cent off a target pitch at A3 is about 0.1 Hz, which is well below the accuracy of the ETD's iH based estimated pitch, you can safely ignore the ETD, or accept that you were right on.

Very few calculated programmes can produce measurement results more accurate than +/- 0.2bps for intervals, and 0.1Hz for frequency. The ETD can, of course, provide relational (strobe-based) pitch accuracy to any arbitrary standard (usually 0.001Hz).

This all reminds me when Conn strob-o-tuners were used to set the temperament, sort of, and then cleaned up. The idea was to save time. I did not attempt it at the time, but I have tried such a thing with Korg tuners, but when there is an obvious error, it is not obvious how to correct it. Like if it takes a 1 cent error in an interval to tell if it is off, which or both notes are wrong if all the others might be between +0.9 and -0.9 cents off? All you can do is go back to the A or C and start fixing stuff from there. But why not tune an aural temperament then?

Anyway, that's how I look at it. Others see it differently.

I was a strict aural tuner for 20 years before I really started experimenting with the ETD. My past experience with ETDs was mostly in relation to administering the PTG tuning exam. Participating in a Master Tuning is a good exercise in the limitations of an ETD.

One of the biggest issues with electronic tuning is interpretation of the display. Piano tone is dynamic and complex and it shows on the display. Often the display will show the note rising and then falling in pitch or going back and forth or stuttering. Without solid aural skills you have to guess at the proper interpretation. However with good aural skills your ear and eye can work together and you can start to make more sense of what is going on with the visual read-out.

This problem is greatly exacerbated when tuning using open unisons, which I believe to be the superior technique, because it is how the piano is actually heard. ETD's are most accurate when listening to a single string. Each additional string makes the ETD readout less reliable.

I really like Ed Sutton's post above. As tuners we are trying to create the best "illusion of equal temperament" that we can (unless our goal is a non ET). As Prout and others have shown, it is not possible to have all the various intervals progress evenly. Thus the goal is to create the best compromise between the slow beating intervals and the fast beating intervals. There is a little "smoke and mirrors" involved to accomplish this.

When refining a temperament, we often find ourselves between a rock and a hard place. We want to speed up a particular 3rd, but if we move either note in the desired direction a 4th or 5th become intolerable. As the temperament becomes more refined it becomes more difficult to solve any problem by moving just one or two notes. When you are tuning with open unisons this means you may have to very slightly adjust 9 strings to make one subtle improvement. This is where the unison "shimming" or "cracking" technique is invaluable.

Every tuner has a mental breaking point where he or she decides that "enough is enough!" and moves on to get the rest of the job done. If your goal is to work in the high end of the market, you have to push the breaking point to near the point of ridiculousness. You split hairs and align pixels. You do it, not because the average piano owner is going to notice all this subtle work, but because we have to constantly practice if we want to refine our skills. That way, when we arrive at a situation where the demands are high, we will be able to succeed.

I often think about how studying tuning is so similar to studying how to play. Both require very subtle control over ear and body. Both require that you "keep your chops up". Both activities can result in discovering greater and greater levels of subtlety and control. I consider tuning a type of Martial Art - or Kung Fu:

From Wikipedia:
"Originally, to practice kung fu did not just mean to practice Chinese martial arts.[6] Instead, it referred to the process of one's training - the strengthening of the body and the mind, the learning and the perfection of one's skills - rather than to what was being trained. It refers to excellence achieved through long practice in any endeavor.[5] This meaning can be traced to classical writings, especially those of Neo-Confucianism, which emphasize the importance of effort in education.[7]"

Ryan, if a temperament is quickly roughed in and then refined to the point you describe where it is hard to tell where the errors are, how can you know if the problem isn't the piano at all, but some underlying quirky twist in the roughing in? The question has been asked about how do temperament sequences get the proper ratio between the beatrates of the 4ths and the beatrates of the 5ths. I have no real answer, just that when the temperment is completed they must be right. Now I am not so sure... This may be just one way that quirky problems occur.

Myself, I do not believe there will be noticeable problems with beatrate progressions unless there is a jump in scaling, or wild partials in wound strings. On a decent piano, I believe that the temperament sequence is the problem, not the piano. Now I will be the first to admit that I do not hear all errors in beatrate progression. But that means that I would not hear my own small errors, yet like others, I come across noticeable errors that I cannot track down on decent pianos. I think it is a cop out to say that pianos cannot be tuned to have progressive intervals because of how they are made. And believing this cop out excuses us to rough-in and refine instead of being more dilligent when setting the temperament.

All these schemes require you to check beat rate progressions (like FA compared to F#A#) but various people have submitted (and even posted as instructional video) what they thought to be progressive M3 sequences which turned out to be not progressive at all.

So there are errors when you set a pitch. Then you continue until you can do a check. This check will also have an error (you may think it's ok when it's not or the other way around). Finally you have the whole temperament interval and you start your checks (whatever they are). You hear something that is not right. Say you do the M3M6 test and it fails. Which one of those 4 notes is wrong?

I think the next improvement on aural tuning sequences will be to add some explicit schemes on when to do a test, and what to do if the test fails.

So an aural tuning scheme will be;

tune X as something to Y.
test some beat rate Z
if Z is too slow, do this, that, and some more
if Z is too fast, do this, that, and some more

rinse and repeat.

To bring theory into this we need to know what humans can detect aurally, so I applaud Mark C for trying to get a handle on this. If we really knew what a tuner can hear we could design an optimal aural sequence with some computer simulation.

Kees

That makes a world of sense, Kees.

From what we have seen when aural tuners posted their best efforts the 6% chromatic RBI beatrate progression is not something we are capable of. A 12% bi-chromatic(?) RBI progression seems to be a practical limit. It may be due to dealing with the pinblock and rendering, but also to just hearing what you expect to hear. I keep wondering if there is some way to "leverage" what we can hear in order to get what we can't hear more perfect. Like if I want a piece of wood 1 inch long +/- 1/1000 inch, but can only measure to 1/100 inch, I can cut 10 blocks and see if they measure 10 inches +/- 1/100 inch. If so, then I know I have my saw set up right even though I can't measure that sort of accuracy.

Another possiblity is we are dealing with too many notes. Like drawing a 12 sided figure with insufficient cross checks. It will tend to be lopsided.

The Sanderson-Baldassin sequence and others are as you suggest and is keeping with Mark C's idea of "windows" where if something is too fast you do one thing, if too slow, another. But if they actually worked as advertised, we wouldn't be having this discussion.

You don't exactly say so, but would the result be getting away from refinement at the end? Have you taken a look at the 8-note mini-temperament I posted in another Topic?

I don't think there is a magic sequence that will solve the temperament puzzle. I sometimes think of it as sculpting, and ponder the Michelangelo quote: "Every block of stone has a statue inside it and it is the task of the sculptor to discover it."

A temperament is discovered not imposed. You have to get to know the harmonic characteristics of the particular piano and then by nudging things around find the most appropriate compromise. It is at the microcosm level of fine tuning where the limitations of the particular instrument and its scale show up. At this level the small discrepancies become apparent - especially (as mentioned earlier) due to the nature of open unisons where every interval is a composite of 6 stings sounding together.

The problem with a sequence is it is always building off previously tuned notes so, even though the intervals tuned early on will be acceptable, the compounding of discrepancies creates a limit to the level of accuracy.