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Originally Posted by Jim Ialeggio
I suspect its mathematical, as the program does not seem to "measure" before thinking. Although. on the other hand, I do find, when using the program, that it will seem to "change its mind" sometimes. As I bring a note in aurally, sometimes if I look at the display it will be well off of target. Then as I bring note to the display's target, I hear it disagreeing aurally. Then I mess around with the note and find it both on target and agreeing aurally. Somewhat mystifying.


That's interesting, Jim. I'd love to get into the code of that machine. The patents for all the other tuning machines are available and free to access online. Not this one.

Originally Posted by Jim Ialeggio
Meaning what? like the sweet spot of a unison where there is no beat...stillness...and the tone also blooms?


My understanding of this is that when the amplitude and sustain duration of the interval is maximized, the highest alignment of all the beneficial partials concerned create this quality.

What I hear first is a stillness, then within that alignment, there is a fine point that really glows.

I assume Bernhard hears a similar thing.


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Originally Posted by Tunewerk
Originally Posted by Jim Ialeggio
I suspect its mathematical, as the program does not seem to "measure" before thinking. Although. on the other hand, I do find, when using the program, that it will seem to "change its mind" sometimes. As I bring a note in aurally, sometimes if I look at the display it will be well off of target. Then as I bring note to the display's target, I hear it disagreeing aurally. Then I mess around with the note and find it both on target and agreeing aurally. Somewhat mystifying.


That's interesting, Jim. I'd love to get into the code of that machine. The patents for all the other tuning machines are available and free to access online. Not this one.

Originally Posted by Jim Ialeggio
Meaning what? like the sweet spot of a unison where there is no beat...stillness...and the tone also blooms?


My understanding of this is that when the amplitude and sustain duration of the interval is maximized, the highest alignment of all the beneficial partials concerned create this quality.

What I hear first is a stillness, then within that alignment, there is a fine point that really ly glows.

I assume Bernhard hears a similar thing.



That mean the machine detect a peak of consonance, as for Chas tuning. Something aural tuners can hear, after some training.

What puzzle me is that it sound way larger than the 12-15 based Chas tuning, which is yet stretched enough.

May be, as the resonant spot is large, the way it is attained allows the tone to stabilize differently in both cases.

I would be ready to accept the Stopper tuning as nice and singing, if it where the case. But it sound forced and not very natural when the piano is played.

One more dead end. It have at last the advantage to have some tuners listening differently, if it is an advantage.

At that point I see enthusiastic tuners, but they may miss comparative points.

Beat canceling only quite the minor chord, at the expense of major ones. So the dose is not easy to decide.

About "resonant spot" they are audible since the 5th octave to the top at the unison, or individual note level.

within the octave, the 12th, the 15 , and even farther, and the eveness of tone coloration at the individual note level may signal an interval mistake 2 octaves away.
No necessity to play all the tones.
SO I understand a software can do it, probably.

The tuner can "temper" that and use an adequate equilibrium spot. For me it means that slow beating intervals must be retained as they warm the tone of the piano.


Last edited by Olek; 10/06/13 04:24 AM.

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I had an interesting experience with this program and my ear while fine tuning a small Knabe grand I recently redesigned/remanufactured. All of my designs are high sustain...its what I and obviously my clients are wanting.

So...fine tuning the two octaves above the temperament...

When tuning the octaves, only a 2 note interval being played, the reference note and its single octave (rather than the beat cancelling triad)...clearest in the high 5th and 6th octaves where this piano has excellent bullet proof treble sustain with no impact noise...as I brought the octave interval into place, first it became still, then as I continued to seek the sweet spot, with unmistakable clarity, a musically audible, clear 2nd partial of the tuned note appeared. In consulting the Onlypure screen,I saw that the placement, approached not as a triad, but as an interval, absolutely zeroed the display.

This was tuning to a 3 string open reference note, and single string octave.

I thought, wow! I found something here, and it is so easy to hear, as it is a musically perceptible tone rather than an isolated partial. But taking this show on the road, to other pianos, I can't reproduce the effect. In writing this I'm wondering why. Is the impact noise, which is endemic in this "killer octave" area, to almost all pianos either masking or destroying this appearance of the octave's 2nd partial? Or is it the sustain level, which is also lacking in the vast vast majority of pianos? This appearance of the 2nd partial by the way, is a similar, if not the same effect Isaac has referred to in tuning unisons.

I don't know if the lack of impact noise or presence of the impact noise either enables or disables this alignment, and looking to understand what caused this phenomenon...obviously in a desire to reproduce it on other pianos other than my own.

The impact noise in the 5th 6th octave is quite obvious in Isaac's Sokolv youtube from the Menhuin festival, though not present at all in the Onlypure youtube. The treble in this area displayed by these two samples echo the experience I am relating here regarding the pianos I service and whole, where the impact noise is always a defining part of the sound and my own pianos where it is not. I find the tonal implications of this noise as well as the tuning implications of this noise, a defining aspect of the experience of listening to these particular clips.

Jim Ialeggio


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I am not sure I understand you Jim, it is normal to hear partials lining.

What is "less" is to perceive them when tuning one note only.

As if the damped notes react (only if well tuned of course)

What I like is have them jump off the tone, that is where crispness is.



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Originally Posted by rxd
.....

The elephant in this room ain't got no clothes.


I have finally found something worthy to have tattooed on my person.


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Originally Posted by Tunewerk
First, I'd like to thank Jim Ialeggio for sending me his original information from Kansas City. It's here now to openly enjoy and interpret, with my explanation below.

Second, Mark, it would be great if you would share what you have learned from Mr. Stopper himself and we can add to this discussion even further.

Originally Posted by Mark R.
I would encourage anyone who is seriously interested in the actual "mechanics" behind Bernhard Stopper's one-page handout to contact Mr Stopper. That's what I did, and I'm still discovering things as I try to put his responses to my questions into practice.


I started looking at Stopper's work 5 years ago or so. I was working on tuning alignments in the 3:1 region and was doing some simulations when I ran across his website and all the work he has done since 1988.

At one point in time, he had a summary of the mathematics behind the exact alignment of his tuning. Now, all he has posted is this:

http://www.stopper-scale.com/1.html

Originally Posted by Bernhard Stopper
A pure twelfth (an interval with a range of an octave and a fifth, and a frequency ratio of 3/1) is divided into 19 equal steps. (nineteenth root of three) The scale results in a slightly stretched octave (+ 1,25 cent) slightly narrow fifths (-1,25 cent).


I thought this was interesting to post, because he literally says here that his stretch point bisects the difference between the 5th and the 8ve.

There are 1901.955c in a 12th: the same amount of extra width that's in a 5th (+1.955c). This means that in a pure duodecimal 8ve, there would be (+1.955c * 12/19) = +1.235c, and in its 5th, there would be (+1.955c * 7/19) = +0.720c. The width of a pure 5th is +1.955c, so (+1.955c - 0.720c) = 1.235c narrow. (Not quite 1.25, but not a big deal.)

So, according to his website:

Stopper's 8ve: 1.235c wide
Stopper's 5th: 1.235c narrow

We all know from translating cents to beats that they have funny, sometimes inverted relationships.

So, translating here (no iH):

.....


Sorry, when I read "So, translating here (no iH)":
I skipped to the next post. Been there done that. With no iH, we aren't talking about a piano.


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Originally Posted by UnrightTooner
Originally Posted by rxd
.....

The elephant in this room ain't got no clothes.


I have finally found something worthy to have tattooed on my person.


You can thank Mick for that, it's his ...m....me....met..... analogy.


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Originally Posted by Jim Ialeggio
...as I brought the octave interval into place, first it became still, then as I continued to seek the sweet spot, with unmistakable clarity, a musically audible, clear 2nd partial of the tuned note appeared. In consulting the Onlypure screen, I saw that the placement, approached not as a triad, but as an interval, absolutely zeroed the display.


This is interesting, Jim. Are you talking about the 2nd partial of the top note? And how did you know you were hearing this?

So this would mean you began tuning a 4:2 octave in that upper region, without the need for other reference notes, and that OnlyPure agreed with that amount of stretch?

It seems to me you've created an instrument with remarkable sensitivity, so the spectrum it creates is different. Pianos without this design may not have a 2nd partial here with as much amplitude.

As you wrote this, I reflected on and aligned my own experience listening. When I do fine tunings, I do rely on a 2nd and 3rd partial in the 5th - 6th octave. What truly defines great pianos to me is where I begin to hear the 2nd and 3rd partials here. They are very delicate. Sometimes it lasts only 5/6 notes, but on a great piano it can last an octave and a half.

Last edited by Tunewerk; 10/07/13 11:10 AM.

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Originally Posted by Tunewerk
This is interesting, Jim. Are you talking about the 2nd partial of the top note? And how did you know you were hearing this?

Yes the top note. However, the only thing I can really say about what I heard, is that I'm trying to understand what I heard. I thought it was the 2nd partial of the top note, but obviously, I need to hear it more often, and together with someone else with ears to understand and challenge what might be going on.

In playing with this over the weekend, not in the fray and time constraints of a site tuning, but quietly at home, I have the feeling that the sound I was hearing (which I think is the top note's 2nd partial, musically audible as opposed to audible only through beats) was the sound I heard way back, when I attempted, for ear training reasons, to tune a shop piano with no dampers. This is an impossible task if you try to listen to beating partials, but I was able to pull off some beautiful 8ve's by listing for something similar to what I'm relating here.

As well, if you read in the last PTG journal, the personal essay by Donna Byrd about how she got into tuning, and why she tunes, one of the the motivating experiences she has had is hearing something, I would say, similar to what I'm describing, on occasion, in a really fine tuning. She refers to it poetically as a descant.

Originally Posted by Tunewerk
So this would mean you began tuning a 4:2 octave in that upper region, without the need for other reference notes, and that OnlyPure agreed with that amount of stretch?

This is tricky, because we are talking about a whole un-muted tone with many partials contributing to the sound. I find the 4:2, 6:3, etc, etc single partial beat comparisons to be a highly unmusical experience, and do not lead me to do my best tunings.

Originally Posted by Tunewerk
It seems to me you've created an instrument with remarkable sensitivity, so the spectrum it creates is different. Pianos without this design may not have a 2nd partial here with as much amplitude.
As you wrote this, I reflected on and aligned my own experience listening. When I do fine tunings, I do rely on a 2nd and 3rd partial in the 5th - 6th octave. What truly defines great pianos to me is where I begin to hear the 2nd and 3rd partials here. They are very delicate. Sometimes it lasts only 5/6 notes, but on a great piano it can last an octave and a half.

Though opening up the dampers in a open string tuning might get you there as well. Definitely keep the two notes of the 8ve open with the sostenuto if you decide to mess with this.

Jim Ialeggio

Last edited by jim ialeggio; 10/07/13 04:54 PM.

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I was trying to quantify what you were saying here, but I see that you're tuning to the whole tone. You're wise to be careful about the language around it.

Your 2nd partial was then matched to maybe a group of partials, or in-between several, not necessarily the 4th from the octave below.

I too have experimented with this, and I know what you mean. The interesting thing, is this could be quantified if you were to set up the same situation again, with that experience and OnlyPure agreeing - and take an FFT of the frequencies within +/-10Hz of 1f, 2f and 3f of the top note frequency with the dampers open.

The noise could be seen along with the aligning energy in a very information rich format. I'd be very curious of the results.


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I am puzzled with such expressions as whole tone.

Does it mean that some tuners do not judge the justness of the note listening in its totality ?

When w train to locate beats at a certain level, it is just for the theory, not really useful later.



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Last edited by bkw58; 10/11/13 09:02 AM. Reason: withdrawn

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Originally Posted by Tunewerk
Second, Mark, it would be great if you would share what you have learned from Mr. Stopper himself and we can add to this discussion even further.

Originally Posted by Mark R.
I would encourage anyone who is seriously interested in the actual "mechanics" behind Bernhard Stopper's one-page handout to contact Mr Stopper. That's what I did, and I'm still discovering things as I try to put his responses to my questions into practice.


Tunewerk, I must apologise for having missed this post. I certainly didn't intend to ignore it. Only when I came back to this thread, to look for some other information, did I see this.

Your most recent contributions to this thread have really added more than I ever could. The only thing I could add, was that Mr Stopper advised me, when playing the triads, to approach the note (or interval(s)) from the over-tempered side, and stop as soon as the beat-cancelling effect sets in. And, like Mr Stopper added, this method requires an advanced hammer technique. I haven't achieved this yet...


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Mark, I subsequently missed your post and this thread got buried in the elapsed time!

What you added here is a huge contribution (for me) and it connects with thoughts I had when analyzing and tuning the Stopper method.

Originally Posted by Mark R.
The only thing I could add, was that Mr. Stopper advised me, when playing the triads, to approach the note (or interval(s)) from the over-tempered side, and stop as soon as the beat-cancelling effect sets in. And, like Mr. Stopper added, this method requires an advanced hammer technique.


In my initial post, I was too quick to assume I understood the sequence based on typical patterns I'd seen before. I made a mistake that I'd like to correct.

This method is not as simple as it seems. It uses three note patterns and the beat masking effect from two intervals at a time to tune an equal temperament. Central to its accuracy is the beat masking effect. Without that, it would be a quasi-equal temperament of little value.

What Stopper said here is another important piece to the puzzle. When tuning 3 notes to mask a beat, you must start from the over-tempered side in the right direction. Otherwise, you can never be sure with changes that fine, that you are on the right side of the interval by the necessary amount. Overshooting can cause several other points that sound 'good', so nailing the first point is critical. That is the beat masking point.

In physics, it is known that phase relationships must be right to achieve beat masking, or wave cancelling. However, in physics, most relationships can be limited in terms of variables and in isolation, precise results can be obtained. In theory, or using generated sine waves, perfect cancellation can occur.

In the real world piano, there is a huge amount of noise and complex wave energy. Not a single beat is clean. However, I can say from experience that a beat masking effect can be produced in the piano when there is no definite phase alignment. The beat masking is not perfect, but it can be described as a phenomenon.

So this general effect can in fact be used to tune, by matching one beat rate with another to achieve a kind of nullification through chaos. Not a perfect nullification, but a type.

In looking deeper at the temperament, I noticed there are exactly 4 weak zones in the structure: in steps 7, 10, 16 and 19. In these steps, two contiguous 5ths are tuned with no parent octave relationship to use the beat masking effect against. To secure placement, the tuned note has to be checked with the steps before and after to ensure accuracy. A M6th formed in the prior step, can also be used each time to roughly match the M6th formed by the note without the beat masking reference.

In all other steps, there is a 5th/8ve relationship of some sort that allows the tuned note to be adjusted to an exact amount of tempering because of being able to transfer it through beat masking. One might call this method of transferring tempering, 'cloning the interval'. It only works because of the relative consistency of 5th beat rates in the temperament region; and only on a good piano.

Cumulative error can be a problem in this temperament scheme if hammer technique is not extremely advanced. Stopper looks like he reverses the form at D4 in order to check this. At the very end of the tuning, the final note forms a check 5th with the last note of the first part of the sequence (G#3-D#4).

Exact quality on this 5th acts as proof of excellence or error.


Addition: Initial work in tuning this temperament yielded small errors in the final 5th when following Stopper's directions explicitly without any checks. To solve this, I produced an edited version using the exact same beat masking patterns, but resulting in near zero error in the final 5th.

The Stopper method is an advanced technique, but particularly interesting because it is the first legitimate method for high accuracy, open-string tuning that I've seen. Also interesting is that this method allows one to see the discrepancies between partial locations in the piano. M3rds turn out slightly quasi-equal according to variations in the 2nd and 3rd partial fields.

A duodecima spanner is helpful in setting the temperament, but not completely necessary. The sostenuto pedal can be used, although it makes things more difficult and prone to error.

If any technicians would like the aural tuning instructions on how to achieve the Stopper temperament with near zero error in the final 5th, feel free to contact me.

Last edited by Tunewerk; 05/02/14 09:00 PM.

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Reviving this old thread; if I understand correctly the goal of "Stopper tuning" is to have the purest sounding 12ths across the keyboard.
For the upper range (however you want to define it) this is 3:1 12ths, as the beats due to the higher partials (6:2, 9:3, ...) are not audible.

Going down to the lower notes it becomes less obvious, as the 6:2, 9:3,... beats start to play a role.

Aurally it is simple; just tune the 12ths to "sound best".

However Stopper tuning can also be tuned with an ETD, the celebrated (I've never seen any complaints about its results ) OnlyPure software.

So I am very curious how the aurally optimal balance between 3:1, 6:2, 9:3, ... is implemented in that software.

If it's a trade secret , I understand. If not I'm interested to know.

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If it were me, I would use a weighted average of 3:1, 6:2, 9:3 based upon relative intensity of the partials. I think that is how I unconsciously hear it when aurally finding the sweetest spot....... if I were tuning that way.
Edit: for each note which may end up different for different ranges.

Last edited by Chris Leslie; 10/06/17 05:06 AM.

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Originally Posted by DoelKees

If it's a trade secret , I understand. If not I'm interested to know.

Kees


It is...
What i can say, it is not something calculated by partials, although partials influence the outcome and some FFT is used somewhere in the processing core for note detecting. Rather think of some weighted(??) autocorrelation.

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Originally Posted by Bernhard Stopper
Originally Posted by DoelKees

If it's a trade secret , I understand. If not I'm interested to know.

Kees


It is...
What i can say, it is not something calculated by partials, although partials influence the outcome and some FFT is used somewhere in the processing core for note detecting. Rather think of some weighted(??) autocorrelation.

Perfect, that's enough of a hint get the idea, without being able to copy it. Thanks.

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Bernhard,

This is mainly to put this thread back at the top.

I will post for you tomorrow.
.

Last edited by alfredo capurso; 10/06/17 05:52 PM.

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Originally Posted by DoelKees
Originally Posted by Bernhard Stopper
Originally Posted by DoelKees

If it's a trade secret , I understand. If not I'm interested to know.
Kees
It is...
What i can say, it is not something calculated by partials, although partials influence the outcome and some FFT is used somewhere in the processing core for note detecting. Rather think of some weighted(??) autocorrelation.
Perfect, that's enough of a hint get the idea, without being able to copy it. Thanks.

I did some experiments with synthesized tones with inharmonicity, seeing what the autocorrelation does at various time intervals, weighted averaging ad hoc etc. and indeed got some peaks in the average which give "in-between" sizes of optimal 12ths. I can see the path to making this work, though I do not intend or am able to walk it (you already did).

This is indeed a great step forward from just measuring partials and aligning them according to some fixed (though user adjustable) heuristics. I now understand in principle how your software can tune optimal unisons using similar ideas, even with imperfections in the strings (which no other ETD can do).

I hope I live to see the details get published at some point.

Kees

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