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I just listened again. The F5 is flat. M3>M10. But the rest still stands. It's not the right piano to show this stuff on.

Mark, firstly, the problem is this, you are stating your opinion, and maybe some others too with regard to the “superiority” of the 4:2+ octave. That’s fine. I do not have to agree?

The reason I re-posted Ryans quote is to show just this, that there are differing views on the optimal octave size, and I would go further and say that this is probably because of personal preference (like you) and the pianos preference (the piano will not sound good apart from what is dictating)!?

I agree with what Bill Bremmer says but not entirely, as I have stated throughout this thread with regards to what I know and practice. I do not have to agree with everything Bill says either?



Yes, this is what you’re all about and you have said it so well. Please take note of your assertion and claiming that this is your superior 4:2+ octave etc…

This is where the problem begins and ends Mark. I have not harped on this at all. Just stated my difference of opinion and preferance. You, however are harping on this one string and it is just plain obsessive and boring.

Now, Mark the following is your private email to me,



I have not asked you to teach me any "superior tuning techniques" I have not been asking you, you have just been sprouting your version of the story and your preferance and your hobby horse.

In fact, the truth of the matter is, I have actually written about certain aspects of tuning that i have learned and that others have written about (from whom I have learnt).

I think you prove who has the wrong attitude in this whole discussion. Please do not send me any further private mail. I do not appreciate or need them!

Please consider the following for your own edification,



I agree with Ryan entirely and here I stand!

If anybody wonders, this is one of the reasons I have my private email turned off. I prefer to have everything above board.

Mark, I also do kindly request that you start your own thread now, maybe something along the lines of "My superior 4:2+ octaves".

And there's "the rub" whenever techs start these tuning discussions... We tend to come up with "universal approaches" for the "best tuning method", never to admit that they are only universal on really good scales. We go to tuning classes using big pianos. I know I've written before that Virgil Smith was limiting his tuning practice to Steinway grands by the time he was working out his tuning approach....

What does that let us do? Blame any tuning problems due to a specific approach on the "problem scale" of a lesser piano!

So yes, keep up the research - just realize that it may only be the best approach for your ears on certain pianos - which is a very good thing for any tech to discover and share!

Ron Koval

It should be demonstrated. I encourage Mark C. to do so. I think it would be a good thing for all concerned.

But what I don't know is why this happens. It can only happen in the presence of iH. I guess it is either a natural result of the square of the partial/cent-logarithm thing or perhaps some bizarre numbers theory thing. I do not have a science degree. I wonder about the octave size/pure 12th relationship, too. I can demonstrate it but do not know why.

This reminds me of a joke about two contestants on a quiz show. The host could not stump either one, so he invited them to ask each other questions. The first contestant asked the second one about a species of ground hog (the big day is coming...) whose hole has no dirt around it. How does it dig a hole and not leave any dirt? The second contestant replied, that is easy, the groundhog starts from the bottom of the hole and ends at the top. Now my question for you is: How did the little bugger get down there in the first place? The second contestant won.

OK so I crunched the symbols.

First of all let's use the following inharmonicity model.
The offset in cents of the k-th partial is
B*(c[k]-1)
where B is the inharmonicity constant of the note, and c[k]=k*k according to Young's model, but experimentally the following lookup table (taken from the Tunelab manual) is more accurate:

c[1] = 1
c[2] = 4
c[3]=8.45
c[4]=13.18
c[5]=19.72
c[6]=27.27

Now let's tune an octave with inharmonicity constants B1 for the lower note and B2 for the upper note, such that 4:2 and 6:3 are equal beating. The 2:1 octave is now beating at the same speed as the 4:2 and 6:3 if the following formula holds:

B1*(3*c[6]-8*c[4]+5*c[2]) = B2*(3*c[3]-8*c[2]+5).

If we now plug in Young's formula both parenthesized expressions turn out to be exactly zero so 2:1 is always beating at the same speed irrespective of the inharmonicity values B1 and B2. This is just a lucky numerical coincidence.

But if we use the more realistic Tunelab table this is no longer true, and instead we get a condition relating B2 and B1 which turns out to be

B2 = 2.2*B1.

Magically this relation is not too far off on most piano's in the mid-upper range so the equal beating phenomena is still approximately true!

The derivation is a couple of pages of high school algebra which I could post if someone really wants to see it.

Kees

To have a look at the numbers associated with pure 12ths I ran some up. Using a Steinway B inharmonicity curve, and a pure 12th for the ET stretch, the A3/A4 octave came out at:

2:1 0.55 bps wide
4:2 0.30 bps wide
6:3 0.73 bps narrow

I guess this a bit wider than some prefer but can see why it is a reasonable basis for an aural tuning.

Ron, as I am the OP, you lump me into the same group that make claims of a universal approach for the “best tuning method” never to admit that they are only universal on really good scales.

If you really want to, that is ok by me. However, please take note of the following excerpts from some of my posts in this thread.

I hope you can see that I clearly have not done as you have said. BTW, this is the second time that I have brought this to your attention.

Kees

I'd be interested, the back of my envelope soon ran out on this one. PM if you prefer.

Hi Ron,

Thanks for listening and making comments.



As a teacher of a one week basic tuning class, I am constantly trying to develop and explain a universal method that will give good results fast. I have had very good success, so I am trying to pass that on. These techniques, I personally use on all sizes of pianos with differing scales. The only difference is how close to perfect I can get. The P4 window creates an unbelievably accurate and consistent stretch on concert grands.



Well, I was not blaming the piano on my poor tuning, that I blame on myself. I could have muted off one of the F3 bichords and fixed the F5, then it would have sounded awesome.

Did you listen to the recording I posted in a new thread? That was a different piano. Not a pitch raise, but still a small console. Much better results, same technique.

Here is the link to the new recording:

http://youtu.be/ys_2vxtEAnw

It was Kent's article "Every Which Way Temperament which really got me heading in the right direction with regards to striving for accurate tunings.

Some excerpts,

"If one learns nothing else from this paper, one should learn the importance of using fourths and fifths “against ”one another in a refinement procedure to improve a temperament after tuning through a temperament sequence.

The single, distinguishing characteristic of equal temperament is that chromatically ascending and/or descending intervals have smoothly progressing beat rates. The procedure for aurally tuning a piano in equal temperament “lays the bearings” for the tuning within a single octave in the middle of the piano, in this case, F3to F4. The procedure for tuning the temperament octave in equal temperament starts with tuning each note to approximations of its proper beat rates, and then may be followed by a separate refinement procedure to tweak the approximations to achieve the smoothest possible progression of beat rates. The two-step procedure is useful because the exact beat rates necessary to achieve the smoothest possible progression of beat rates of “parallel intervals” will vary a bit from piano to piano due to the variability of inharmonicity. Inharmonicity varies both from piano to piano and through the scale of individual pianos…

There are many “bearing plans” or “temperament sequences” to tune equal temperament. It may be necessary to try many of them to find one that fits your particular aptitudes. There are many temperament sequences because a given tech may be unable to make a given sequence work correctly. The Every-Which-Way plan makes use of many checks early in the sequence. Sequences that use fewer checks may allow the tech to accumulate tuning errors as the sequence progresses. The beauty of the Every-Which-Way plan is that you can use more and more checks as one progresses through the sequence and tune each new note as a “best compromise” with all the previous notes, that is, each new note will not depend only on the last note tuned, so there will be more of a chance that errors will not accumulate in the later notes tuned. The last notes to be tuned in the sequence are tuned from many other previously tuned notes, that is, from “every which way.”…


The piano tech must have general knowledge of the beat rates of intervals relative to the beat rates of other intervals:

Assuming the octaves are stretched, fourths beat faster than fifths in the temperament octave and the beat rates of fourths and fifths can be inversely proportional. That is, if there is a fast fifth then there is likely a slow fourth somewhere or vice versa. This is the basis for an extremely powerful set of checks. If a properly expanded perfect fourth and a properly contracted perfect fifth have a common top or bottom note,and if you change the tuning of the common note, the width of both intervals will be changed; widening the intervals will speed up the beat rate of the fourth and at the same time will slow down the beat rate of the fifth; narrowing the intervals will slow down the beat rate of the fourth and speed up the beat rate of the fifth. This inverse relationship is one of the most powerful checks available in the tuning of equal temperament. The successful piano tuner will have learned to use these checks well. Check the relative beat rates of the fourth and fifth on one side of a note being checked. Example: to check the tuning of D4 within the temperament octave, play A3-D4 and G3-D4. The fourth should beat faster than the fifth. If the fifth is too fast and the fourth too pure perhaps the D4 is flat; if the fourth and fifth beat at the same rate, perhaps the D4 is flat; if the fourth beats too fast and the fifth is too pure, perhaps the D4 is sharp. Do not fail to learn to use 4ths and 5ths in this way...


The interval of the perfect fourth and the interval of the perfect fifth are inverted forms of the same interval.(That is, take the bottom note of a fifth and move it up an octave, and you now have a fourth.) In the mathematical model of equal temperament, perfect fourths and perfect fifths beat at much the same rate. But inthe tuning of real pianos, fourths beat faster. Why? It is because of stretch. There exists the P4-P5 test of the 4:2octave; that is, there is a check of the 4:2 octave that uses as a reference the note that is a perfect 4th above the lower note and the perfect 5th below the upper note. In this check, if the 4th and 5th beat exactly the same then the 4:2 octave is beatless or “just”. But we generally do not tune octaves this way. When tuning octaves up the scale we generally raise the top note and slow the fifth down. As Alan Crane puts it, “Stretch happens.”
If the fourths beat faster than the fifths, then there is sufficient stretch…

“If one must choose between tunings that feel right and tunings that check out right, go with the objective checks every time.”

From my personal experience I know that feeling good about a tuning does not guarantee that the tuning is actually good. Tunings that are a struggle and unsatisfying when they are over may be very good indeed. Emotions are a poor guide. Learn this for yourself by checking many tunings the day after or as soon as you can after the fact when the mood is different.

Pianos are not necessarily in tune because you have performed a tuning procedure on them; they are in tune when you have tuned them AND the tuning checks still work out when you go back to check your work…"

Mark D:

Can we tie together the original subject of this Topic (clean sounding octaves) with temperment sequences? I think this is incredibly important. For instance: fourths and fifths have the inherent ability to test the 4:2 octave, while ladders of contiguous M3s check the 8:4 octave, and ladders of contiguous m3s the 6:3 octave.

Mr. Swafford's method is basically to use all tools available, which is good. But what happens when one check is at complete odds with another? It can be accepted as an "indulgent mystery" and the least-worse compromise made. But if it is understood that some checks are more appropriate for one type of octave than another, a better choice can be made. In particular I am talking about when dealing with a scaling break, whether actually setting a temperment or expanding one.

I believe that if the cleanest sounding octave is chosen the type should be determined and then the co-responding temperment tests and checks should take priority over others. Or a certain octave type can be chosen (if it results in being clean enough) because of the priority of temperment tests and checks that will be used.

Hello Jeff

I want to make an important qualifier, and it is this, fudging/compromising when tuning and knowing when to, why to and how to is a key in tuning.

There are at least three camps of tuners/thinking that I know of, maybe more?

One camp favours RBI's and the other favours SBI's, though they both use either or in tuning. The third camp, seems to use it all. In other words, fudge it all!? Cluster tuning and ETD tuning come to mind

However, in saying that, and from what I understand is, it is that most tuners are striving for the most consonant tuning possible. Then again there are those that will sacrifice the consonance saying that it is the RBI's (some/more dissonance?) which adds/brings the true character out that they and or their clients are looking for.

In saying what I have just said, the whole issue of the amount of stretch comes into play now and so on...

I tend to favour both the SBI and RBI, sometimes tuning for just D8ves and sometimes 4:1+ D8ves and sometimes tempered 12ths and sometimes pure 12ths and so on.

With regards to scaling breaks, I in general use the SBI's to determine/guide. Once I have tuned through I may/will listen to the RBI's and make minor corrections if I think I can and need to.

I have a general understanding of most of the important intervals. I tune for the best possible sounding tuning for the piano that I am tuning, and that may involve much compromise/fudging or hardly any at all.

I hope this answers your question and submission?

Sorry Jeff, to answer, finding tests/checks that are at complete variance with one another in the piano and in the temperament in particular, I cannot think of any.

Can you give me an example or two of such a case so that I am more enlightened and have the opportunity to think it through? Though I may never think it through and may need to ask someone else myself!

Yes I can. I run across this often:

Take a large, old upright with the break around C3. The F3-F4 temperment is tuned and then expanded downward. As each octave is tuned the RBIs such as M3, M6, and M10 (when available) are checked. Everything is hunky dunky until crossing into the bass. Then all these RBIs want to beat faster than they do for the note above the break.

Well, you can make the RBIs more progressive by contracting the octave that spans the break and stretching the octaves above the break. This will make the 4ths and 5ths sound different across the berak, but since they beat slower it won't be so obvious when listening to chromatic checks.

Or you can expand the temperment with good sounding octaves and be assured that the 4ths and 5ths will be at thier best even though the M3s and M10s are not progressive.

However, if the temperment was expanded downward with 6:3 octaves, then you can expect the m3s and M6s to be at thier best even if the M3s P4s and P5s are not. The 6:3 octave test uses m3s and M6s.

Do you follow what I am saying even if you have not experienced this? It happens on shorter, older grands, too. The scaling for a "hockey stick" bridge is the likely culprit.

Ok, I hear you.

I suppose the fudge factor comes in here. 4th, 5th, m3, M3, M6, Octave, D8ve, 10th, 17th. I would try for the best compromise for the best sounding octave and SBI's and then move on. I would not be overly concerned with any particular size of octave and interval here in so much as making it fit into the overall bigger picture and sound as best as is possible to my ears!?

You know, thinking about it, and this is not a boast but just a thought that has come through my mind now as I am writing, I in general, and thankfully so, do not get call backs, so either I am doing something right, or maybe my clients know and realise that pianos are not perfect and what they are hearing is not unpleasant to them or of major concern to them.

Maybe, we should not be overly concerned if our clients are happy with our work.

Mark:

Since tuning is not my livelyhood, more like a paid community service, I have the luxury of considering my own needs in the actually tuning process. I have an inherent need to understand things and find consistent ways of doing things. (This has served me well in my full time careers.)

Anyway, I had been perplexed when reading about tuning CM3s across breaks and not being able to have decent sounding octaves and SBIs when I tried it. After really studying the effects of iH, and learning to objectively listen to the tests and checks in my tunings, I have settled in on something that I understand and is consistent: pure twelfths. It meets my needs.

Even though I have changed how I tune over the past few years, and tuned differently for the same customers, I do not get call backs either. Tuners are usually much more discerning than thier customers. That is as it should be.

I do understand that the needs of other tuners are different. And so they would tune differently.

I guess I agree with Mark, octave size test are useful to learn to hear differnt types of octaves may be, but in the end I totally stopped using them, while I focus on clean sounding octaves as one of the priorities.

there is some room to fudge in most intervals, sticking to an octave type may push the tuner to pass the moment the octave type have to change.
What amaze me is being able to tune by octaves with some even progression of FBI, I have always be instructed that it was not really possible, may be only the habit...

Sure enlarged twelve begin to sound strange, but when going thru the basses the 5ths can enlarge too much also. Any method allowing to have a standard is good, in the end..