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#1999016 - 12/13/12 03:31 PM Using the Spectral Centroid to Study Pianos
PaintedPostDave Offline
500 Post Club Member

Registered: 06/09/10
Posts: 522
Loc: Upstate New York
In the first video, the spectral centroid is introduced and used to help decide whether American pianos have different characteristics than European pianos. You might perhaps remember a previous video which had the same goal but used the cumulative line spectrum map as a metric.

http://www.youtube.com/watch?v=gjpqNRmnl5Q

The second video uses the spectral centroid to study the effect of different piano key strikes.

http://www.youtube.com/watch?v=QFveZhKQJQY






Edited by PaintedPostDave (12/13/12 05:20 PM)
_________________________
Dave Koenig
Yamaha M1A console
1927 Knabe 7' 8" grand
https://sites.google.com/site/analysisofsoundsandvibrations/

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#1999019 - 12/13/12 03:34 PM Re: Using the Spectral Centroid to Study Pianos [Re: PaintedPostDave]
Phil D Offline
500 Post Club Member

Registered: 01/15/10
Posts: 551
Loc: London, England
Deciding whether American pianos have different characteristics than European pianos is a Holy Grail? Really??

I could answer that question for you: Do American pianos have different characteristics than European pianos? Yes, they do.
_________________________
Phil Dickson
The Cycling Piano Tuner

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#1999023 - 12/13/12 03:40 PM Re: Using the Spectral Centroid to Study Pianos [Re: PaintedPostDave]
BDB Offline
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21285
Loc: Oakland
Yes, American pianos are made in America. European pianos are made in Europe. Except those that are made in Asia, of course!

Just kidding, of course. I appreciate your studies, Dave, even though I often think that the results do not show anything which leads to general conclusions.
_________________________
Semipro Tech

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#1999029 - 12/13/12 04:01 PM Re: Using the Spectral Centroid to Study Pianos [Re: BDB]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 555
Loc: Canberra, ACT, Australia
That each study leads to a general conclusion is not so important. More important is the inspiration and linkage it provides towards further studies and our understanding of the bigger picture.
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

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#1999070 - 12/13/12 05:12 PM Re: Using the Spectral Centroid to Study Pianos [Re: PaintedPostDave]
Minnesota Marty Offline

Platinum Supporter until October 5 2014


Registered: 05/15/12
Posts: 7239
Loc: Rochester MN
Isn't the Holy McPhail contained within the Ark of the Cunninghams? grin
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Marty in Minnesota

It's much easier to bash a Steinway than it is to play one.

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#1999294 - 12/14/12 07:38 AM Re: Using the Spectral Centroid to Study Pianos [Re: Minnesota Marty]
Emmery Offline
2000 Post Club Member

Registered: 04/02/08
Posts: 2356
Loc: Niagara Region, On. Canada
Since the spectral centroid is just an single snapshot within the long duration of a pianos attack>decay period, how was the location of that point determined? Isn't this analysis the same as taking a single frame from a movie reel and trying to determine the entire films plot from it?
_________________________
Piano Technician
George Brown College /85
Niagara Region

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#1999347 - 12/14/12 10:09 AM Re: Using the Spectral Centroid to Study Pianos [Re: PaintedPostDave]
rxd Offline
1000 Post Club Member

Registered: 03/11/09
Posts: 1703
Loc: London, England
Some of the graphs look amazingly like some graphs that I saw in a book about piano tone published in 1950's. "Pianos pianists and sonics" by G. A. Briggs, the man who made the famous Wharfdale speakers.
_________________________
Concert & Recording tuner-tech, London, England.
"in theory, practice and theory are the same thing. In practice, they're not." - Lawrence P. 'Yogi' Berra.

Eschew obfuscation.



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#2002361 - 12/20/12 08:19 PM Re: Using the Spectral Centroid to Study Pianos [Re: rxd]
PaintedPostDave Offline
500 Post Club Member

Registered: 06/09/10
Posts: 522
Loc: Upstate New York
As this post sinks into the higher numbered pages of PW, I fill it is time to obtain closure on the reply posts. Several of them had the usual PW snarkiness but some grabbed my attention.

First,
"Deciding whether American pianos have different characteristics than European pianos is a Holy Grail? Really?? I could answer that question for you: Do American pianos have different characteristics than European pianos? Yes, they do."

Then there was:
"Isn't the Holy McPhail contained within the Ark of the Cunninghams?"

I think these two are supposed to be funny but...

Then there is this one:
"Since the spectral centroid is just an single snapshot within the long duration of a pianos attack>decay period, how was the location of that point determined? Isn't this analysis the same as taking a single frame from a movie reel and trying to determine the entire films plot from it?"

I do not think this was meant to be funny but it struck me as being hilarious.

The next reply really piqued my interest:
"Some of the graphs look amazingly like some graphs that I saw in a book about piano tone published in 1950's. "Pianos pianists and sonics" by G. A. Briggs, the man who made the famous Wharfdale speakers."

There is the hint of plagiarism here so I went immediately to Amazon and ordered the book from a second hand dealer. It arrived today. This is an incredibly delightful little book. Since it was published in 1951 I was pretty sure that the spectral centroid did not play a part. On reading it I see many analog time domain traces and several analog spectra based on oscilloscopes/stroboscopes but since this was before digital computers became accessible to anyone other than an atom bomb scientist there are no spectral centroids or cumulative line spectra, etc.

Mr. Briggs compares time domain traces for strikes with different force. I did not do this for the original post but I have gone back and reviewed the time traces and may make some modifications. I suppose Mr. Briggs has moved on to his reward by now but his book certainly has earned a treasured place in my library.
smile
_________________________
Dave Koenig
Yamaha M1A console
1927 Knabe 7' 8" grand
https://sites.google.com/site/analysisofsoundsandvibrations/

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#2002401 - 12/20/12 10:27 PM Re: Using the Spectral Centroid to Study Pianos [Re: PaintedPostDave]
Emmery Offline
2000 Post Club Member

Registered: 04/02/08
Posts: 2356
Loc: Niagara Region, On. Canada
Originally Posted By: PaintedPostDave

...Then there is this one:
"Since the spectral centroid is just an single snapshot within the long duration of a pianos attack>decay period, how was the location of that point determined? Isn't this analysis the same as taking a single frame from a movie reel and trying to determine the entire films plot from it?"

I do not think this was meant to be funny but it struck me as being hilarious.


PaintedPostDave, with 2 question marks in my statement, what it should have done is simply struck you as an inquiry. (It was not meant to be funny) Instead you ridicule it for no explainable reason. I don't see any time or phase referance on the charts so I'm assuming analysis is a specific snapshot....thus my questions stand valid. BTW, to respond in kind to your ridicule, I thought the video was hilarious myself...hard to find scientific credibility on a statement such as 2:03 of the first video "2. F4# to A5# Bosendorfer emphasizes fundamental more than Bosendorfer".

Not proof reading an assertation = Fail
Publically posting it on Youtube in this condition = Double Fail
_________________________
Piano Technician
George Brown College /85
Niagara Region

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#2002420 - 12/20/12 11:58 PM Re: Using the Spectral Centroid to Study Pianos [Re: Emmery]
PaintedPostDave Offline
500 Post Club Member

Registered: 06/09/10
Posts: 522
Loc: Upstate New York
Emmery, you apparently have no understanding of what a cum sum does or what a spectral centroid is and nothing I can write here is going to solve that problem - in fact it isn't a problem. If you don't understand what I am talking about you are among many.

It was probably a mistake to post in this forum but I only do it because occasionally it get an insightful response like the one about Brigg's book. One has to separate the chaff from the wheat. No problem. smile
_________________________
Dave Koenig
Yamaha M1A console
1927 Knabe 7' 8" grand
https://sites.google.com/site/analysisofsoundsandvibrations/

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#2002512 - 12/21/12 08:15 AM Re: Using the Spectral Centroid to Study Pianos [Re: PaintedPostDave]
David Jenson Offline
2000 Post Club Member

Registered: 10/22/06
Posts: 2038
Loc: Maine
Oh goody. Can I get in on the "snarky" list. I can't think of anything sassy to say, but I do like that list. (Hmmm. that comment looks snarky. Yay, I made the list ... I hope.)

Seriously, any application to the real world of slippery roads, poor cell phone reception, and worn out old pianos escapes me.
_________________________
David L. Jenson
Tuning - Repairs - Refurbishing
Jenson's Piano Service
-----

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#2002530 - 12/21/12 09:00 AM Re: Using the Spectral Centroid to Study Pianos [Re: PaintedPostDave]
Emmery Offline
2000 Post Club Member

Registered: 04/02/08
Posts: 2356
Loc: Niagara Region, On. Canada
PPD....Unfortunately, we had used up all our tinfoil to wrap the turkey here so I must admit, my head is a little bare to absorb all this. my apologies.
_________________________
Piano Technician
George Brown College /85
Niagara Region

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#2002574 - 12/21/12 10:15 AM Re: Using the Spectral Centroid to Study Pianos [Re: PaintedPostDave]
Chris Storch Offline
Full Member

Registered: 08/13/09
Posts: 189
Loc: Massachusetts
PaintedPostDave,

It's fascinating. Keep going.

I understand what you're doing. I don't know when the information will come in handy, but it's good to know that the information is there. (Reminds me of my spoon bender tool.)

Chris S.
_________________________
Chris Storch
Acoustician / Piano Technician

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#2002623 - 12/21/12 11:40 AM Re: Using the Spectral Centroid to Study Pianos [Re: Chris Storch]
PaintedPostDave Offline
500 Post Club Member

Registered: 06/09/10
Posts: 522
Loc: Upstate New York
Thank you, Chris.

Spoon bending may become the new craze. Check out the following on Amazon:

Mental Magic: Spoon bending, mind reading, clairvoyance by Max Mindbender

(somehow I think Max's last name is probably not Mindbender).

Emmery, I am not sure how to take any of your comments...but I am going to apologize for being too thin skinned. At the risk of adding insult to apology I am taking you off the list.

David Jansen, I have no real world application in mind with anything I post on PW. However, I have found that if I keep the spectral centroid near the middle of the right hand lane I can deal with slippery conditions quite nicely. There is a patent application in the pipeline but I am not holding my breath.

In any case, you have not made the list. Your comment is just not snarky enough. Give it some thought and try again. Alternatively, you can chime in on my forthcoming post concerning the use of the Lipschitz condition to estimate the vibrato of C8#.
_________________________
Dave Koenig
Yamaha M1A console
1927 Knabe 7' 8" grand
https://sites.google.com/site/analysisofsoundsandvibrations/

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#2002687 - 12/21/12 01:50 PM Re: Using the Spectral Centroid to Study Pianos [Re: PaintedPostDave]
Emmery Offline
2000 Post Club Member

Registered: 04/02/08
Posts: 2356
Loc: Niagara Region, On. Canada
PPD, a spectral centroid measurement can be taken over various lengths of duration on a tone, its entire attack decay cycle, or on a specific snapshot of narrow time frame, or any duration in between. As tuners we recognize that various partials (or fundamental even) will decay at their own rates and not necessarily hand in hand with the rest of the spectrum. As a cumulative sum, even if taken over the entire attack/decay cycle, there is no indication of the subltle distinctiveness of the tone due to this effect. Eg. It starts off bright with low fundamental amplitude, and ends with a relatively prominant fundamental and little or no upper partials (or vice versa). Is this not the same as scraping the entire painted surfaces off of oil paintings, grinding and mixing it back together as a sum, and then commenting on the differences between the brown colors you end up with.

BTW, I was not being comedic or snarky or anything other than curious about whats being done, so there is no need for the Robert Di Santo attitude.
_________________________
Piano Technician
George Brown College /85
Niagara Region

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#2002706 - 12/21/12 02:22 PM Re: Using the Spectral Centroid to Study Pianos [Re: PaintedPostDave]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1921
Loc: Suffolk, England
Dave

How is spectral strength measured?

In your mathematical model what are the reasons for equating the contributions of say the second partial at a certain spectral strength and the fourth partial at half that strength?
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2002718 - 12/21/12 02:53 PM Re: Using the Spectral Centroid to Study Pianos [Re: Emmery]
PaintedPostDave Offline
500 Post Club Member

Registered: 06/09/10
Posts: 522
Loc: Upstate New York
The cum sum is applied to the difference between the spectral centroids for all 88 keys for two pianos.

For all of the samples of striking the keys I gathered data starting just before the strike and lasting until the sound had died away. I did this for all 88 keys for several pianos and I sampled at 44KHz.

For each piano and each key the line spectrum was constructed. For each key's line spectrum the weighted average of the frequencies, i.e., the spectral centroid, was computed with the weight being the strength at the frequency. The sum was carried out over all frequencies from the fundamental to the Nyquist frequency (22050 Hz) for each key stroke. So, for each piano there were 88 spectral centroids.

The strengths at frequencies above 10 KHz are basically negligible and contributes essentially nothing to the sum.

For each piano I plotted the 88 spectral centroids against the key numbers 1 through 88. On the same graph I plotted the theoretical fundamental frequencies against key numbers 1 thru 88.

If the fundamental is by far the dominant component for a given key then the spectral centroid plot point for that key will lie on top of the fundamental frequency plot point. For the low frequency notes there is relatively little strength at the fundamental. Therefore for the deep bass notes the spectral centroid plot-point would lie above the fundamental frequency plot-point. At the treble end of the keyboard most of the strength lies at the fundamental so the spectral centroid plot-point would lie on top of the fundamental frequency plot-point.

Let S(k,p) for k=1,...,88, be the 88 spectral centroids for the 88 keys of the p th piano. For two pianos, say the p th piano and the q th piano I computed the difference, as in,

dpq(k)=S(p,k)-S(q,k) for k=1,...,88.

The p th piano might be the Knabe grand. The q th piano might be the Bosendorfer. So, for a pair of pianos there were 88 differences, one for each key.

Plots of the differences between two pianos, i.e., the dpq, were not particularly insightful but I presented them anyway.

To address the differences with more insight I used the cum sum of the differences, as in,

Cs(K)=sum over k from 1 to K of dpq(k) for K=1,...,88

In words...
The cumsum for the first key A0, namely, Cs(1), would equal
Cs(1) = dpq(1) where dpq(1) = S(p,k) - S(q,k)

The cumsum for the 2nd key A0#, Cs(2), would be
Cs(2)=Cs(1)+dpq(2) or Cs(2)=dpq(1)+dpq(2)

The cumsum for the third key B0, Cs(3), would be
Cs(3)=Cs(2)+dpq(3)

Therefore we are accumulating the growing sums of the differences.

This goes on until the cumsum for the last key C8, Cs(88), which is
Cs(88)=Cs(87)+dpq(88);

So, there are 88 cumsums for each pair of pianos. For a particular pair the Cs can be plotted against the key numbers 1 to 88.

Statisticians have used cumsums for years to detect changes in noisy data. I searched the web for a simple explanation of cumsums and did not find anything worth mentioning here.

These plots are, at least in my humble opinion, insightful because they show where offsets occur between the two pianos. They also tell the sign of the offset, how long the offset persists and, by the slope of the cumsum, how great the difference is. For the Knabe and the Bosendorfer there seemed to be two sections of the key board where the keys had a spectral centroid consistently above or below the other. That would suggest, at least to me, that in those sections one piano emphasized the fundamental more than the other.

When comparing the Bosendorfer and the Schimmel the cumsum seemed a lot less varying indicating, at least to me, that the two pianos were relatively similar with regards to the spectral centroid.

The data that I looked at, for what it is worth, suggests that the two European pianos were relatively similar, that the two American pianos were relatively similar and that the European pianos were different from the American pianos. I make no other suggestions.

I posted the results simply because I thought they were interesting. I still do.
_________________________
Dave Koenig
Yamaha M1A console
1927 Knabe 7' 8" grand
https://sites.google.com/site/analysisofsoundsandvibrations/

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#2002795 - 12/21/12 06:06 PM Re: Using the Spectral Centroid to Study Pianos [Re: PaintedPostDave]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1921
Loc: Suffolk, England
Dave

Thanks for your comprehensive, lucid explanation. I'd like to suggest an extension of your analysis.

Looking at the spectral centroid curves for Knabe and Bosendorfer, what strikes me is the relative smoothness of the Bosendorfer curve and some rather wild excursions in the Knabe.

The main difference seems to be that Bosendorfer is quite flat up to #50 and then follows the fundamental up to #88, whereas the Knabe jumps around from about #47 to #66. The Bosendorfer also appears to have rather more powerful overtones in the bass and tenor up to around #36 (as you have highlighted with you cusums).

Some say the Bosendorfer does nothing for them very possibly due to the evenness of reponse so clearly shown by your curve. In comparison I imagine the Knabe might appear to have more character. On the other hand that curve would be characteristic of the ranges of tone and colour for which Bosendorfer is so well known.

What would be really interesting is to explore the fundamental and its harmonics versus other overtones and resonances the piano produces.

Would you be able to sum your Anfn terms separately for these two sets?

This would give you two spectral centroid curves for each piano which might shine a spotlight on other differences lurking in your hard won data.
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2002867 - 12/21/12 09:52 PM Re: Using the Spectral Centroid to Study Pianos [Re: Withindale]
PaintedPostDave Offline
500 Post Club Member

Registered: 06/09/10
Posts: 522
Loc: Upstate New York
Thanks for you comments and suggestions, Ian. Your suggestion is interesting and I will have to pursue it.
_________________________
Dave Koenig
Yamaha M1A console
1927 Knabe 7' 8" grand
https://sites.google.com/site/analysisofsoundsandvibrations/

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#2002968 - 12/22/12 06:22 AM Re: Using the Spectral Centroid to Study Pianos [Re: PaintedPostDave]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1921
Loc: Suffolk, England
That would be good. Spectrum analyses show how a piano's sound depends not only on the vibrations of its strings but also on its resonances.

In the piano forum recently a pianist who had owned one of the smaller Shigerus was looking at a M&H BB. He found it had everything he wanted - dynamic range, richness of tone and so on - except tonal range. Then he put in his musician's earplugs and found the tonal range he had been looking for had been there all along.

His Etymotic ER-15 earplugs start to roll off gently above 6 kHz and steeply above 8 kHz. The implication is that the M&H BB must have been producing enough other higher frequency sounds to drown out the effect of the higher harmonics of the fundamental.

Suppressing the higher harmonics (up to 10 kHz as you observed) has a dramatic effect on the tone of a piano. This happened to my upright where something was affecting all the strings at the pressure bar. I am sure Herr Schiedmayer was not responsible for doing that due to some urge to emphasize his fundamentals in 1925!

I'd say the higher harmonics are just as important as the fundamental in any piano and we need to isolate other tones to explain the distinctions between a European and an American brand.


Edited by Withindale (12/22/12 08:50 AM)
Edit Reason: added two paragraphs
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2003051 - 12/22/12 11:24 AM Re: Using the Spectral Centroid to Study Pianos [Re: Withindale]
PaintedPostDave Offline
500 Post Club Member

Registered: 06/09/10
Posts: 522
Loc: Upstate New York
Very Interesting. thumb
_________________________
Dave Koenig
Yamaha M1A console
1927 Knabe 7' 8" grand
https://sites.google.com/site/analysisofsoundsandvibrations/

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