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I have seen many Japanese tuners using a just slightly opened 2:1 octave in mid range. (M10 M17th test)

It is interesting to add 2:1 comparison in regard of the 4:2 6:3 tests. Then you will really finish asking you questions as the 2:1 does not follow a similar logic, it should be enlarged a lot with that 4:2 6:3 octave, it is not

Yes, as I have mentioned before, since the 2:1 partial match is an octave below the 4:2 partial match it will beat at the same speed as the 4:2 when it is twice as wide in cents. This happens when the beat of the narrow 6:3 equals the wide 4:2 and the wider (in cents) 2:1. There is a place where the 2:1, the 4:2 and the 6:3 all beat at the same rate. Whether this is an ideal place for any particular octave is another story.

Hi Mark,

Thanks for your comments. I tried to read your post to find out where you disagree with me, but I couldn't find anything. Maybe you could clarify.




Well, I don't think I ever said I tune as Virgil did. I never got to take a class with him, although I really wanted to, but he passed away before I could get a chance.

I think the confusion lies with my expanded discussion of tuning checks, maybe? I don't know.

Maybe this will help. When I talk of tuning checks, I am speaking as an after-the-fact analysis. I.e. the checks I expound upon are those that have resulted from tuning great sounding 1/2/3 octaves, 12ths, etc, by ear, i.e. confirming that the whole piano sounds in tune, has a tone that is not only pleasing, but at times, scary in-tune. I.e. the intervals sound good because they sound good when listening to the "whole tone", the "complete tone", with open ears. Now, to get that sound, I use the checks, trying to recreate the condition that existed in these checks "after" a high level of quality has been achieved and analysed on previous pianos.



Yes, I speak of partials ringing when octaves are tuned wrong, i.e. 4:2 and 4:2- in the mid range. Others are claiming that these sizes are acceptable, but I have never found a piano where that is the case. The partials that I say beat when tuning a 4:2+ are cancelled out by their "sister partials", for lack of a better term. I.e. for a 4:2+, those would be 2:1 & 8:4, and 4:2 & 6:3.




But, don't you quote Virgil below as saying:


Also, I really like this quote...

because it is the reason I use my "window" technique, which is in effect using "tuning checks [that] are essential for evaluating the accuracy of the tuning." - Virgil Smith
The window technique is
M3<M10<M17<M6
and
m6 below = M17

I am amazed at the times I can find notes within the window that do not fit (not the top, but the others) and have to be retuned. They have drifted or were not set right to begin with. This technique allows me to catch all those imperfections as I go.

Okay, so reading on in your post, I find two completely opposite points of view, but both were said by you. Could you please clarify because I'm sure I am missing something important in your critique.

You say:

and yet quote Virgil as saying, to back up your position:

I look forward to your post. Thanks.

Yes, for preciseness, I will explain the P4 window.

Well, I think we all agree that the check for a P4 is M3 < M6.

Or to be more "Virgilian", when the P4 sounds the best, i.e. is at the size that makes it sound ok while at the same time, producing pleasing "whole" or "full" or "complete" intervals with each and every interval it makes now, or will ever make in the future with any note on the piano, then we find that the M3 < M6.

Now, starting at F3, this test is used at Bb3. (Sorry, I'm a musician and will never get used to seeing F3A#3)
M3 < M6
Db3F3 < Db3Bb3

Okay, now at F4, this window comes into play by tuning F4 so that:
M3 < M10 < M6
Db3F3 < Db3F4 < Db3Bb3

Notice here that
Db3F4 < Db3Bb3 (M10 < M6)
is the test for a P5


In fact, this is a proof that the 4:2 doesn't work because if
M3=M10 (test for a pure 4:2)

then the window looks like this:

M3 = M10 < M6

and by the transitive property

M3 < M6 and M10 < M6 by the same amount

and therefore the fourth and fifth beat at the same speed.

But Reblitz and other texts claim that the fifths beat slower than the fourths in ET! Both can't be true.


Okay, so now the next note to fit into the window is F5, like this:

M3 < M10 < M17 < M6

Db3F3 < Db3F4 < Db3F5 < Db3Bb3

The wide fourth relationship is preserved here:

Db3F3 < Db3F4 < Db3F5 < Db3Bb3

The narrow fifth preserved here:

Db3F3 < Db3F4 < Db3F5 < Db3Bb3

The 2:1+ octave here:

Db3F3 < Db3F4 < Db3F5 < Db3Bb3

The 4:2+ octave here:

Db3F3 < Db3F4 < Db3F5 < Db3Bb3

and the tempered 12th here:

Db3F3 < Db3F4 < Db3F5 < Db3Bb3

Each and every note is checked and re-checked as you progress through the treble and if any drift, you can catch it right away. Very powerful.

The final test is

m6 below = M17 (the test for a pure triple octave)

F3Db4 = Db4F6

So the progression of tests is (starting at F6)

M3 < M10 < M17 < M6 and (m6 below = M17)

Db4F4 < Db4F5 < Db4F6 < Db4Bb4 and F3Db4 = F6

Notice Db4 in all the tests. This makes it very easy to remember. Actually I just noticed that Db4 doesn't need to be in tune, which makes this an even more powerful test because all the other relationships will be preserved only if they relate to each other in the described way.

I know this seems all too mathematical, but you don't have to think about it. I just go through the test quickly and automatically. It is really easy and you don't have to think about it at all. Mindless as Bill Bremmer says.

Hope this is clear. I would be very excited to hear that you tried it out and were pleased.

Monsieur Cerisano: Thank you for explaining so well for all of us. I have the utmost respect for GOOD teachers and yes,schools. Socrates, Plato, Confucius,etc.. The same with Books,PDF files,sheepskins,etc. The knowledge can be transferred verbally,written,in a demonstration in person and so on... NOTHING beats a private one-on-one class with a GOOD teacher. An experience like that is inestimable; but the monetary exchange is not my argument. It is money well spent. IMHO In this field of "Piano care", having a GOOD teacher or a school is heaven-sent. The 'manipulation of the tuning hammer', just to take one aspect, is of course better learned by EXAMPLE. But it is also an ART. One must learn to hear/listen/feel. I went to ART school and learned how to SEE. Same thing. Some people never learn. Some do. Bonne Chance avec votre ecole!! Herr Weiss

For Pete's sake! The texts are talking about when the 4ths and 5ths have a common lower note (and usually non-iH, 2:1 octave, theoretical pitches), not the P4-P5 test for a 4:2 octave where the upper note of the fourth is common with the lower note of the fifth!

Your "P4 window" is nothing new. Another way to look at it is that the algebraic sum difference of beating of the 12th (3:1) and the 15th (4:1) equals the beating of the inferred P4 (4:3) when the 12th and 15th have a common upper note. By placing the upper note in a position where the M6-M17 tests the 12th to be narrow and the M3-M17 tests the 15th to be wide, you are using a stretch scheme that Mr. Bremmer calls "Mindless Octaves" and Mr. Capurso calls "CHAS."

And from a separate post:


Yes, sometimes lower notes have not been set right for a stretch scheme that uses 12ths and/or 15ths. I have mentioned before that depending on the size of the piano, you need different sized octaves in the middle for a specific size of 12ths and/or 15ths. If you want to get the octaves right to begin with, why not start with a specific size 12th and/or 15th and then construct your temperment, including the mid-range octaves, from there?

I have been tuning for 13 years, teaching tuning for 7 and am a mechanical engineer. I think I know what I'm talking about. It appears your constant opposition to my teachings show your lack of openness. How can you go against the largest and most respected piano technology association in the world (PTG) when they state the proper size of the octave in the midrange is 4:2+.

Anyway, no matter which way you cut it, Reblitz lists the highest P5 in the temperament octave as beating faster than the lowest P4, so your critique is way off.

For Pete's sake, the P4 beats (approx.) 1bps while the P5 beats once in 4 seconds, that's 0.25 bps. That's a huge difference, mathematically and aurally. Sorry, your critique doesn't pass the mustard.

Mark:

So your argument is about who is right rather than what is right.

Here is a link to a chart with theoretical beat rates:

http://en.wikipedia.org/wiki/Piano_tuning#Temperament_and_beating

Notice how the beatrate for the C-G fourth is exactly the same as the G-C fifth at 1.18243?

Hi ! that is an interesting suite of checks possibly it fall in place within the CHAS pattern .

I tend to believe that when we compare so many intervals that may have so little difference of beat speed between them, our ear tend to push our evaluation in the direction of "OK" .

Unless you have that progression in your ears as a consonance check (that is possible) I dont believe we can precisely compare as many intervals.

Indeed progression between contiguous intervals is often very slow, but it provide yet a fine control.

All those checks between different styles of intervals I find really tiring for the ears/brain.

Particularly, I find that once on the way during the tuning the tests fall in place when used, so at some point they are almost unnecessary...

Why do you want that an actual real tuning complies with theoretical beat rates ?
I believe this may be the case when "pure x" system is used (while I dont see the real reason why, in the end) , but I say we want consonance, and the beats may fall where they can depending of the piano (within limits of course)

Mark, sorry to say that but A. Reblitz was not a tuner, and at that time the theory was yet obscure.

We need progressiveness or eveness of beats and there are different possible arrangements for that, all fall in the category "ET" while providing very different justness style particularly when compared with an orchestra.

I like the logical part of you check list , any "rule" that allow to check consistency of tuning is good to take.
I am unsure it agree with my actual tuning or listening (probably because my temperament is tweaked in a particular way, so inner relations are not based on a pure theoretical division of a pure octave, but I believe that any method that allow the partials to flow well together on a larger span is good at large for the global enlighting of the tuning, if the piano like that ;
for instance to play classical Jazz on a Yamaha U1, a very close tuning is allowing more roundness and a thicker tone (because the piano sound less "just" in that case, more sour, but warmer in close harmony ), than following the partials to the edge , that can be good to play Ravel or last century classical music...)

All the best for 2013 and thank you for providing your thinking and findings

Why do you want that an actual real tuning complies with theoretical beat rates ?

I did not say I did. I know that they do not. But we must crawl before we walk...

I care about what helps people learn to tune pianos as easily as possible with the best result.

I will take the time to look into your argument with the chart, but on initial inspection, it appears you've confused the intervals; C - G is not a fourth.

Thanks for catching my typo. I meant C-F fourth and F-C fifth.

Mark, 13 years is a modest amount of experience in this field. I've been at it for 20 and am discovering new things about tuning every year. That's part of the fun of this business. I suspect in 5 years you may look back at your old thinking at realize that you didn't have it all figured out. At least that's what should happen to an open minded student of the craft.

I'm not sure what mechanical engineering has to do with teaching tuning. Maybe you can clarify that statement.

I would be careful using the PTG as an authority on tuning. The standard that the PTG promotes and tests for is a minimal standard. A tuner has to work within a 1 cent tolerance relative to the "Master Tuning" in the middle two octaves in both temperament and unisons to get a perfect score. The tolerances increase until they are at 6 cents for the lowest and highest octaves. In fact, in one case I observed an examinee get a very poor score on the temperament, (under 60 percent) yet passed the high treble with very high scores (over 90 percent). He was good at tuning octaves! As he progressed up the scale the tolerances became wide enough to give him better scores.

In PTG literature you will find differing opinions among experts. I do not believe that PTG as an organization has an "official" stand on what the right octave size is.

Hi Ryan,

Your points are well taken. My qualifications should not need to be restated; my arguments should stand on their own.

While I appreciate your input, I wish it were more to the point of the specific question, "How to get clean beatless octaves" rather than a critique of my qualifications.

As for my level of experience, I concur. However, I have always tuned 4:2+ octaves since day one and have never be shown or convinced that what I am doing could or should be done differently in different circumstances. Perhaps I am here to be challenged and convinced. If I can't be convinced, I would hope that others could learn from my perspective.

As for the PTG, the standard, as far as I know, is as I stated; 4:2+ in the midrange as the starting point for the master tuning. This is according to various CTE's I have spoken with. I agree that the tolerances are loose for the examinee, but they shouldn't be for the master tuning, no?

It is really nice to have a new voice in the conversation. Thanks for your post.

I looked at the chart. It appears that there is no stretch in that octave; it is a 2:1 from C - C. According to my tunings, when all the extended intervals are harmonious, the upper fifth (F - C) is beating slower than the lower fourth (C - F). I assume the majority of the stretch is taken up by the fourths.

When you stretch the octave, the 4ths will start beating faster and the fifths will start beating slower (up to the Cordier limit). Is that what you meant?

If at all possible, I'd love to hear you record a 4:2 octave, a 6:3 octave, and then the 4:2+ octave which you tune "perfect".

I think this will be more convincing than theoretical arguments.

Kees

Well, I still think my definition of tuning holds good: "It's part arithmetic and part flower-arranging".

Mark:

Hmmm, you may be missing my point. I did not have a downloadable copy of Reblitz’s beatrate table, which you said showed the highest fifth in the temperment octave beating much slower than the lowest fourth. So, I posted what was available. I have studied my copy of Reblitz, though not lately, and am sure that it will agree with any other theoretical beat table.

You mention that CTEs recommend tuning a 4:2+ octave in the midrange for a master tuning. This will always be on a good sized grand piano. The PTG exam procedure requires it to be. Somehow this is assumed to produce wide 4:1 15ths and narrow 3:1 12ths, and so this stretch scheme would then be appropriate for expanding the temperment. I believe that it will usually produce virtually pure 12ths, and that is the appropriate stretch scheme for expanding the temperment on good sized grands with 4:2+ octaves in the midrange.

Some contributors to this Forum agree with me, others do not. It is not a new subject. You and I, Mark, can simply agree to disagree on this and perhaps still discuss broader issues.

There are two things on my mind. First, (as I have stated before) depending on the size of the piano, a given octave type in the mid-range corresponds to a certain relationship between the 12ths and the 15ths. Perhaps we will have to agree to disagree on this also. I do not believe in a one size fits all mid-range octave.

Second is what to do about the relationship between the mid-range octave and the 12th/15th relationship. Is it better to make a hard choice on the octave, expand it until the type of 12ths and 15ths become apparent and then continue with this happenstance stretch scheme? Or is it better to start with a 12th/15th scheme and find the octave that works for it? Or we could work back and forth between them, which would be time consuming. Or the mid-range could be firmly decided ahead of time and if the 12ths/15ths don’t turn out as expected start moving things around to make any errors less obvious. I understand that mindless octaves are used to expand UTs in this way.

What are your or anyone else's thoughts on this?