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Originally Posted by Withindale
FYI from Dirk's Manual - http://www.dirksprojects.com/downloads/ManualPianoTuner40_EN.pdf

The maximum accuracy in Hertz and in Cent
The accuracy of the Tuner is better (less) than 0.1 Hertz (waves longer than 10 seconds). The accuracy in Cent gradually changes over the range of the tuner because a Cent is a relative unit. The interval between two successive tones in Hertz increases as the pitch gets higher while the interval in Cent is by definition (always) 100. Some values of the accuracy of the tuner in Cent: C1: 5.2 Cent, C2: 2.6 Cent, C3: 1.4 Cent, C4: 0.6 Cent, C5: 0.4 Cent, C6: 0.16 Cent, C7: 0.08 Cent, C8: 0.04 Cent. So in Cent, the tuner gets therefore more accurate as the pitch gets higher.

Detectable pitch differences
The smallest by human ear detectable pitch difference is approximately 2 Hertz. The accuracy of the tuner of 0.1 Hertz is many times better. This high accuracy is necessary to measure the beatings between two strings. A difference in beating of more than approximately 0.1 Hertz is already detectable by the human ear.


Dirk apparently uses a Discrete Fourier Transform for his iH analysis whose accuracy is limited by the length of the sample - 10 second sample is 1/10seconds= 0.1 Hz or 100 second sample = 0.01Hz and so on. This is OK (adequate) if, when tuning the programme uses the 5th 0r 6th partial and extrapolates the note to be tuned and then uses an accurate beat frequency oscillator to provide the viewer with a target for tuning.

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Originally Posted by prout

Dirk apparently uses a Discrete Fourier Transform for his iH analysis whose accuracy is limited by the length of the sample - 10 second sample is 1/10seconds= 0.1 Hz or 100 second sample = 0.01Hz and so on.

Actually it is possible to do better than that. The Fourier Transform produces a table of amplitudes for frequencies that are spaced as you say (0.1 Hz apart for a 10-second sample time). If you do nothing more than look for the highest amplitude in that list, you would get only 0.1 Hz resolution. But a more advanced approach is to consider the amplitudes associated with the frequencies on either side of the peak (0.1Hz below and 0.1Hz above). These amplitudes give some clues about where the peak really is. This is called pitch estimation by interpolation, and it has a rich literature. The simplest one is called quadratic interpolation. TuneLab uses this to develop an estimate for the pitch that can be 5 to 10 times more accurate than the basic pitch spacing in the Fourier Transform.


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Originally Posted by Robert Scott
Originally Posted by prout

Dirk apparently uses a Discrete Fourier Transform for his iH analysis whose accuracy is limited by the length of the sample - 10 second sample is 1/10seconds= 0.1 Hz or 100 second sample = 0.01Hz and so on.

Actually it is possible to do better than that. The Fourier Transform produces a table of amplitudes for frequencies that are spaced as you say (0.1 Hz apart for a 10-second sample time). If you do nothing more than look for the highest amplitude in that list, you would get only 0.1 Hz resolution. But a more advanced approach is to consider the amplitudes associated with the frequencies on either side of the peak (0.1Hz below and 0.1Hz above). These amplitudes give some clues about where the peak really is. This is called pitch estimation by interpolation, and it has a rich literature. The simplest one is called quadratic interpolation. TuneLab uses this to develop an estimate for the pitch that can be 5 to 10 times more accurate than the basic pitch spacing in the Fourier Transform.


Excellent info. I did not know TuneLab did that. I use several techniques (oversampling and quadratic interpolation) in Java to incorporate the leakage into adjacent bins which allows me to achieve about 0.006Hz on 10 second bass samples.

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Originally Posted by Robert Scott
Originally Posted by prout

Dirk apparently uses a Discrete Fourier Transform for his iH analysis whose accuracy is limited by the length of the sample - 10 second sample is 1/10seconds= 0.1 Hz or 100 second sample = 0.01Hz and so on.

Actually it is possible to do better than that. The Fourier Transform produces a table of amplitudes for frequencies that are spaced as you say (0.1 Hz apart for a 10-second sample time). If you do nothing more than look for the highest amplitude in that list, you would get only 0.1 Hz resolution. But a more advanced approach is to consider the amplitudes associated with the frequencies on either side of the peak (0.1Hz below and 0.1Hz above). These amplitudes give some clues about where the peak really is. This is called pitch estimation by interpolation, and it has a rich literature. The simplest one is called quadratic interpolation. TuneLab uses this to develop an estimate for the pitch that can be 5 to 10 times more accurate than the basic pitch spacing in the Fourier Transform.

You can do even better than that by making use of phase information in the Fourier transform. This allows you to even measure the pitch differences within a slightly detuned tri-chord. The method is described in this paper, section 3.1.

Kees

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Originally Posted by DoelKees
Originally Posted by Robert Scott
Originally Posted by prout

Dirk apparently uses a Discrete Fourier Transform for his iH analysis whose accuracy is limited by the length of the sample - 10 second sample is 1/10seconds= 0.1 Hz or 100 second sample = 0.01Hz and so on.

Actually it is possible to do better than that. The Fourier Transform produces a table of amplitudes for frequencies that are spaced as you say (0.1 Hz apart for a 10-second sample time). If you do nothing more than look for the highest amplitude in that list, you would get only 0.1 Hz resolution. But a more advanced approach is to consider the amplitudes associated with the frequencies on either side of the peak (0.1Hz below and 0.1Hz above). These amplitudes give some clues about where the peak really is. This is called pitch estimation by interpolation, and it has a rich literature. The simplest one is called quadratic interpolation. TuneLab uses this to develop an estimate for the pitch that can be 5 to 10 times more accurate than the basic pitch spacing in the Fourier Transform.

You can do even better than that by making use of phase information in the Fourier transform. This allows you to even measure the pitch differences within a slightly detuned tri-chord. The method is described in this paper, section 3.1.

Kees


Thanks Kees,

I have read a little about using the phase info, but haven't got to the programming stage yet.

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The 0.3 deviations were indeed in cents, not Hz.

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Kees,

I just opened your link and realized I had read your paper on-line some months ago when I was looking for increased accuracy in DFTs. I didn't make the connection. Nice work! - Thank you

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When I first began study in this industry, I asked that same question to a seasoned tuner that was well respected and had been tuning a zillion years. He simply said, "If you can't tune WITHOUT a machine, you can't tune WITH one".


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Originally Posted by Grandpianoman


I forgot to mention the recoding equip...the Tascam 60D, the Rode NT5's with Mike Joly's new add-on capsules...(first time trying those, very pleased with them...Roy P, they are good!


GP. Thanks for the report. I'll probably purchase the add-on capsules eventually. But I've had this Tascam 60D for a few weeks now, and haven't even taken it out of the box yet. I want to try out the stock Rode NT5's first, and see what I get. But the new capsules do sound good. I talked to a pianist today who is willing to be recorded, so that's a start. All in good time.



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Originally Posted by Gary Fowler
"If you can't tune WITHOUT a machine, you can't tune WITH one".
Yes, we heard you the first time.

It's too bad Dirk's tuner doesn't come with a trial version. What he calls a "trial version" is barely more useful to evaluate the software than a screenshot as you can only tune A and E.

I am going to contact him to tell him a "trial version" should allow you to completely tune a piano and judge how it sounds. Please do the same if you feel the same way about it.

Though apparently targeted at DIY tuners, it could still be a good tool for those technicians that have many repeat customers, as the 88 notes have to be measured only once.

Kees

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Mr.Fowler, that is your opinion, that is all it is. I don't need to defend my tunings, they speak for themselves. I can tune a piano very well with just an ETD. I know nothing about tuning a piano by ear, other than unisons. That totally shatters your erroneous and misguided statements that it can't be done.




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Kees, good idea.

I went over the tuning, and made sure the bass was as close to 0.0 as I could get it.....I also slowed down the tempo a bit, so one can hear more of the complex harmonies in the Strauss.

One of the difficult recording issues with these reproducing pianos, is the hum of the motor. It can be lessened with mic placement, but it takes a bit of experimentation, which I did not do this time. This Duo-Art has a LOUD motor. frown

I suppose one could say that Dirk's is one of many ET flavors. smile


"Ramble On" from Der Rosenkavalier Played by Percy Grainger (bass corrections) https://app.box.com/s/y4o2bpx3ej9wkmp7dz2l


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Hi Roy, you're welcome! LOL...I understand about not getting it out of the box....that means you are a busy man!

The stock NT5's are good...these capsules seem to take the sizzle/edginess off the treble end, they also seem to give a bit warmer sound overall.

That's great about your pianist...look forward to hearing the grand you are working on!

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Originally Posted by Withindale
As he is a customer, perhaps Grandpianoman might like to email Dirk with Chris's questions. Even a general answer about the bass would be helpful if Dirk does not want to disclose specific details about his product.

I guess Chris is right when he says "The problem is that in widening the bass with those short strings you may introduce faster beating low-range 10th/17th, which would probably spoil the sonority in my opinion."

GPM agreed I should ask Dirk and draw his attention to this thread.

Dirk says he worked almost full time for over 10 years on his techniques and I am sure everyone will understand why he does not want to reveal too much of his IP.

In agreement with Robert Scott's point, Dirk says he certainly does not need 10 second samples for the bass strings. The tuner software needs to react within a tenth of a second during tuning.

“Normal” Fast Fourier Transformations need very long samples, so Dirk put a lot of work into his own Fast Fourier Transformations to make them as fast as possible. He uses the slope on each side of the peak and the higher harmonics to increase accuracy, but that is only the very beginning of the story.

During his research, Dirk spent a lot of time determining why a tuning sounds good or not. Once he had worked out how to measure a piano's properties by recording all the tones, he knew could walk the reverse path and calculate an optimal sounding tuning.

Dirk points out that it is absolutely necessary to use all the notes for the recording. Every small mechanical deviation in any note, or other part of the piano, contributes to the resulting tuning. The tuner software checks all intervals and calculates the beats in all harmonics in each interval to determine the optimum consonance for the equal temperament.

In other words Chris is right.

PS
GPM posted a terrific recording by Josef Hofmann above. Earlier this morning, I came across Stephen Hough's great Daily Telegraph blog post about him - Why was Josef Hofmann considered the greatest pianist of all?


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I agree with Dirk regarding recording all the notes. His stretch for my piano easily captures the iH changes as the string structure changes in size and composition. it is possible to detect the change in gauge size as well on many of the transitions. The maximum bass stretch for my M&H BB in ET is -29 cents and the treble around +35 cents.
My own recordings of the notes and determination of iH take much longer and are of higher accuracy and clearly show all the string parameter changes, but the increased accuracy hasn't translated into a better stretch curve than Dirk's yet.

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The E-flat still sounds out of tune.
Maybe you might consider tuning the very low bass by ear.

Otherwise your unisons and the middle and treble are very good. The piano is voiced beautifully as well.

Originally Posted by Grandpianoman
Kees, good idea.

I went over the tuning, and made sure the bass was as close to 0.0 as I could get it.....I also slowed down the tempo a bit, so one can hear more of the complex harmonies in the Strauss.

One of the difficult recording issues with these reproducing pianos, is the hum of the motor. It can be lessened with mic placement, but it takes a bit of experimentation, which I did not do this time. This Duo-Art has a LOUD motor. frown

I suppose one could say that Dirk's is one of many ET flavors. smile


"Ramble On" from Der Rosenkavalier Played by Percy Grainger (bass corrections) https://app.box.com/s/y4o2bpx3ej9wkmp7dz2l


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Hakki,

I have just listened to one of your recordings in Warsaw and Seffet playing Chopin on your piano.

In view of the discussion in this thread, have you thought about downloading Dirk's Tuner to see how the curve it comes up for your RX2 compares with the current tuning?

Grandpianoman say Dirk's tuning is comparable with a good aural tuning so the results might be illuminating for you.



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Hakki, thanks for your comments....there has been no voicing done on these hammers..they have been 'played' in so to speak. That's one of the positives of Ari Isaac's hammers.

I don't think it's the software, but rather the bass strings themselves. As I recall, Noam's tuning of his Hamburg Steinway D did not have any issues with bass strings being sharp or flat. If I have the time, will give Dirk's a try on my M&H BB.

Ian, thanks for the explanations. As I mentioned before, this is the best sounding ET for this short piano that I have heard so far, inc a few aural tunings that were done.

Very informative and interesting story about Hofmann, thanks for posting that link.

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Originally Posted by Grandpianoman
I don't think it's the software, but rather the bass strings themselves.


This region of the small belly bass, particularly around Eb2 is, in my experience, the most difficult area of a small piano to get right...if indeed it is possible at all to get it right.

I'm still working the question in my own small bellies. In my experience, its not the strings, though the strings must be designed appropriately down there...but I have changed out strings and changed the string design significantly in experimenting with this annoying region in the small belly 2nd octave.

So I don't think it's the strings, and it ain't the tuning. Its a soundboard restriction which ends up only allowing mid-partials to sound. This means the 10th partial (Maj 10 and octave displaced Maj 10ths) is singled out in the partial structure, and singing annoying loudly...like the tone deaf tenor in the church choir. The resulting sour-ness is an accentuated version of normal Maj 3rd/10th rapid beating.

When the sounding partial structure is in the "normal" range, this RBI is perceived as color, with the lower partials masking this noisy rapid beating. Here, however, the RBI is perceived as fundamental, and as such, it is perceived as noisy and out-of-tune.

In the case of a small belly where this mid-partial is hyper-active, the rapid beating becomes the predominant musically perceptible sound. The resulting sour-ness will not be cured by any tuning whatsoever...at least in my experience and in my own experimentation. It's the board design...not even the aged board condition, but the design.

Jim Ialeggio


Last edited by jim ialeggio; 01/11/14 06:29 PM.

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Originally Posted by Gary Fowler
When I first began study in this industry, I asked that same question to a seasoned tuner that was well respected and had been tuning a zillion years. He simply said, "If you can't tune WITHOUT a machine, you can't tune WITH one".


Sometimes what people say and what they are really saying sound like two different things. What I'm hearing here is someone with all of their eggs of self esteem rapped up in the basket of aural tuning getting a little nervous that there are others' out there that can accomplish the same end result in a different way.

It's OK Gary, none of this takes your talents or abilities away from you.


Tuner-Technician


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