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#2322986 - 09/02/14 06:47 AM Re: An aural and visual demonstration of the Skeleton. [Re: Chris Leslie]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1318
Loc: Montreal, Quebec, Canada
Originally Posted By: Chris Leslie
Kees, so a larger error of F3 causes a smaller error in C#4


Isn't that the opposite of what Kees said in the first graph?
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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#2323000 - 09/02/14 07:27 AM Re: An aural and visual demonstration of the Skeleton. [Re: Mark Cerisano, RPT]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 653
Loc: Canberra, ACT, Australia
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: Chris Leslie
Kees, so a larger error of F3 causes a smaller error in C#4


Isn't that the opposite of what Kees said in the first graph?

No. It is what I see in the second graph where a large change in F3A3 bps corresponds to a smaller change in A3C#3 bps. It is also what I believe you demonstrated in your video with the paper markings lining up the way they do.
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

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#2323004 - 09/02/14 07:46 AM Re: An aural and visual demonstration of the Skeleton. [Re: Mark Cerisano, RPT]
Mark R. Online   content
2000 Post Club Member

Registered: 07/31/09
Posts: 2024
Loc: Pretoria, South Africa
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: Chris Leslie
Kees, so a larger error of F3 causes a smaller error in C#4


Isn't that the opposite of what Kees said in the first graph?


No. Look at the scales of the axes. F3A3 can vary all the way from 4 bps to 10 bps, and still, C#4 will be off (flat) by no more than 1 cent. The point is: if F3, A3, F4 and A4 are placed with any modicum of accuracy, then C#4 will be very accurate.

Regarding maintaining ratios, and the degree of accuracy in doing so, we've had this discussion before. Doel commented that one of his problems is not to recognize increasing beat speeds, but to get the differences / ratios the same. I did some quick sums.

Assuming that the M3 beatrate doubles from F3A3 to F4A4, then each subsequent beatrate should increase by the third root of two, which is about 1.26 (classically called "5/4"). Looking at the numbers, using 7 bps for simplicity's sake, a geometric progression would be (rounded to one decimal point):
7
8.8
11.1
14
While an arithmetic progression would be:
7
9.3
11.7
14

Is the difference between the two really significant?

At A3C#4, the two methods give a 0.5 bps difference at the common partial, which is C#6, i.e. 1109Hz. In that range, 1Hz is less than2 cents, i.e. the 0.5 bps difference is an error of less than 1 cent.

Similarly, at C#4F4, the two methods give a 0.6 bps difference at the common partial, which is F6, i.e. 1397Hz. In that range, 1 Hz is not much more than 1 cent, i.e. the 0.6 bps difference is once again an error of less than 1 cent.

So, I submit that the question of geometric (correct) vs. arithmetic (technically wrong) is somewhat academic. "Evenly" progressive, whether geometric or arithmetic, appears to be good enough.

My problem is, much like Kees's, that I can't readily distinguish the above two progressions from, for example,
7
10
12.5
14
This sequence would have errors larger than 1 cent.

Hope this makes sense...
_________________________
Autodidact interested in piano technology.

1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

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#2323152 - 09/02/14 02:08 PM Re: An aural and visual demonstration of the Skeleton. [Re: Mark R.]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1738
Loc: Vancouver, Canada
[quote=Mark R.]
So, I submit that the question of geometric (correct) vs. arithmetic (technically wrong) is somewhat academic. "Evenly" progressive, whether geometric or arithmetic, appears to be good enough.[/quote]
Yes, the difference is too small to be of any practical significance; a small enough segment of an exponential (or log) will be almost a straight line segment.

Funny thing I thought of: In theory (probably not in practice) you could find the correct F3 using [b]only[/b] the upper skeleton (i.e., without using F4A4) by finding the F3 that allows the sharpest C#4 within a progressive F3A3C#4F4 set.

Kees

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#2323170 - 09/02/14 02:36 PM Re: An aural and visual demonstration of the Skeleton. [Re: Mark Cerisano, RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1738
Loc: Vancouver, Canada
[quote=Mark Cerisano, RPT][quote=DoelKees]Mark, geometric progression means that the beat rate ratio of A3C#4 and F3A3 is the same as the beat rate ratio of C#4F4 and A3C#4 and the same as the beat rate ratio of F4A4 and C#4F4.
Zero error when F3A3=6.9, look closer.

Kees [/quote]

So maintaining ratios is not accurate. I will create a skeleton, making the speed differences equal as far as my ear can tell, and measure them in Audacity. We will see what it is. What is the correct ratio? Log? What base? Are you considering iH? [/quote]

Sorry Mark, but I mostly have no idea what you are trying to say/ask (also "Maintaining ratios?" comment).

I calculated with no IH, but the results for the sensitivity of C#4 to F3 should not depend on it in any significant way.

Kees

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#2323361 - 09/02/14 09:35 PM Re: An aural and visual demonstration of the Skeleton. [Re: Chris Leslie]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1318
Loc: Montreal, Quebec, Canada
Originally Posted By: Chris Leslie
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: Chris Leslie
Kees, so a larger error of F3 causes a smaller error in C#4


Isn't that the opposite of what Kees said in the first graph?

No. It is what I see in the second graph where a large change in F3A3 bps corresponds to a smaller change in A3C#3 bps. It is also what I believe you demonstrated in your video with the paper markings lining up the way they do.





Ok. I read (past tense) it as "when the F3 error is big, the C#4 errors decreases". Right. I see. When the F3 error increases, the C#4 error increases less.
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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#2323382 - 09/02/14 10:04 PM Re: An aural and visual demonstration of the Skeleton. [Re: Mark Cerisano, RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1738
Loc: Vancouver, Canada
BTW interesting interaction of theory and practice.

Mark posts a video claiming you can set C#4 even if F3 is off, purely based on experience (I assume).

Rafael gets upset and claims "wrong if F3A3 is at 11bps you get more than 1 cent error in C#4".

Theory confirms both are right, but it is a fact that the error in C#4, when set from an erroneous F3 is much less than the error in F3.

Chris then points out the the upper skeleton can use the same method to set F4 more accurately using the same principle (C#4 if off by a little, but applying the same method to the upper skeleton results in the error of F4 to be much less than the error in C#4).

If only we could really tell if a beat rate progression was evenly geometrically progressing we could all tune a perfect ET.

As a digression note that if F3A3 beats at around 8.5bps it is possible to make the 3 M3's F3A3C#4F4 all equal beating, which results in a peculiar unequal (pseudo reverse well) temperament with C#major the best, A major next, and F major the worst key.

Kees

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#2323419 - 09/02/14 11:33 PM Re: An aural and visual demonstration of the Skeleton. [Re: DoelKees]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1318
Loc: Montreal, Quebec, Canada
Originally Posted By: DoelKees
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: DoelKees
Mark, geometric progression means that the beat rate ratio of A3C#4 and F3A3 is the same as the beat rate ratio of C#4F4 and A3C#4 and the same as the beat rate ratio of F4A4 and C#4F4.
Zero error when F3A3=6.9, look closer.

Kees


So maintaining ratios is not accurate. I will create a skeleton, making the speed differences equal as far as my ear can tell, and measure them in Audacity. We will see what it is. What is the correct ratio? Log? What base? Are you considering iH?


Sorry Mark, but I mostly have no idea what you are trying to say/ask (also "Maintaining ratios?" comment).

I calculated with no IH, but the results for the sensitivity of C#4 to F3 should not depend on it in any significant way.

Kees


When calculating the error, what did you use as the reference? A log ratio? Or something else?

When I tune and measure my skeleton, I want to calculate the error. I was thinking of using Tunelab and measuring the skeleton notes and creating the stretch curve with that.
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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#2323422 - 09/02/14 11:41 PM Re: An aural and visual demonstration of the Skeleton. [Re: DoelKees]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1318
Loc: Montreal, Quebec, Canada
Originally Posted By: DoelKees

If only we could really tell if a beat rate progression was evenly geometrically progressing we could all tune a perfect ET.



We can try.

First, use RBI as much as possible. Not just setting them approximately, but bisecting windows with the idea that you need to fit three more M3 into the CM3 window, for example, so there needs to be daylight in each CM3. This will serve to train the ear and improve beat speed difference recognition.

And of course, we always have Audacity and spectrograms!
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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#2323440 - 09/03/14 12:33 AM Re: An aural and visual demonstration of the Skeleton. [Re: Mark Cerisano, RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1738
Loc: Vancouver, Canada
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: DoelKees
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: DoelKees
Mark, geometric progression means that the beat rate ratio of A3C#4 and F3A3 is the same as the beat rate ratio of C#4F4 and A3C#4 and the same as the beat rate ratio of F4A4 and C#4F4.
Zero error when F3A3=6.9, look closer.

Kees


So maintaining ratios is not accurate. I will create a skeleton, making the speed differences equal as far as my ear can tell, and measure them in Audacity. We will see what it is. What is the correct ratio? Log? What base? Are you considering iH?


Sorry Mark, but I mostly have no idea what you are trying to say/ask (also "Maintaining ratios?" comment).

I calculated with no IH, but the results for the sensitivity of C#4 to F3 should not depend on it in any significant way.

Kees


When calculating the error, what did you use as the reference? A log ratio? Or something else?

Very simple. Without IH the correct C#4 is 220*2^(1/3). I report error wrt that in cents.

Kees


Edited by DoelKees (09/03/14 12:34 AM)

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#2323495 - 09/03/14 04:14 AM Re: An aural and visual demonstration of the Skeleton. [Re: DoelKees]
Mark R. Online   content
2000 Post Club Member

Registered: 07/31/09
Posts: 2024
Loc: Pretoria, South Africa
Originally Posted By: DoelKees
If only we could really tell if a beat rate progression was evenly geometrically progressing we could all tune a perfect ET.


My vote for aphorism of the year!
_________________________
Autodidact interested in piano technology.

1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

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#2323555 - 09/03/14 08:26 AM Re: An aural and visual demonstration of the Skeleton. [Re: DoelKees]
Chris Storch Online   content
Full Member

Registered: 08/13/09
Posts: 203
Loc: Massachusetts
Originally Posted By: DoelKees

As a digression note that if F3A3 beats at around 8.5bps it is possible to make the 3 M3's F3A3C#4F4 all equal beating...
Kees


Interesting digression...

Kees, I'd be curious to know what the beat speed would be if one tuned C#3/F3 - F3/A3 - A3/C#4 to all be equal beating contiguous major thirds, bracketed into a ~6:3 C#3/C#4 octave. (Because I believe that's one of the starting points of the Jack Stebbins method).
_________________________
Chris Storch
Acoustician / Piano Technician

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#2323681 - 09/03/14 01:08 PM Re: An aural and visual demonstration of the Skeleton. [Re: Chris Storch]
Hakki Offline
2000 Post Club Member

Registered: 05/26/01
Posts: 2612
Originally Posted By: Chris Storch
Originally Posted By: DoelKees

As a digression note that if F3A3 beats at around 8.5bps it is possible to make the 3 M3's F3A3C#4F4 all equal beating...
Kees


Interesting digression...

Kees, I'd be curious to know what the beat speed would be if one tuned C#3/F3 - F3/A3 - A3/C#4 to all be equal beating contiguous major thirds, bracketed into a ~6:3 C#3/C#4 octave. (Because I believe that's one of the starting points of the Jack Stebbins method).


Chris, I think that would depend on the IH of the specific piano. So without knowing the scale and IH of the specific piano it would be meaningless to answer your question.
_________________________
Put in one of IMO, I think, to me, for me... or similar to all sentences I post

http://www.youtube.com/user/hakkithepianist

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#2323787 - 09/03/14 05:59 PM Re: An aural and visual demonstration of the Skeleton. [Re: DoelKees]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 653
Loc: Canberra, ACT, Australia
Originally Posted By: DoelKees

As a digression note that if F3A3 beats at around 8.5bps it is possible to make the 3 M3's F3A3C#4F4 all equal beating, which results in a peculiar unequal (pseudo reverse well) temperament with C#major the best, A major next, and F major the worst key.

Kees

I disagree. If the rules are to have equal beating 3 M3's F3A3C#4F4, and all other M3rds in the octave equal beating, then there is an infinite number of varying results.


Edited by Chris Leslie (09/03/14 06:02 PM)
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

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#2323814 - 09/03/14 08:04 PM Re: An aural and visual demonstration of the Skeleton. [Re: Chris Storch]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1738
Loc: Vancouver, Canada
Originally Posted By: Chris Storch
Originally Posted By: DoelKees

As a digression note that if F3A3 beats at around 8.5bps it is possible to make the 3 M3's F3A3C#4F4 all equal beating...
Kees


Interesting digression...

Kees, I'd be curious to know what the beat speed would be if one tuned C#3/F3 - F3/A3 - A3/C#4 to all be equal beating contiguous major thirds, bracketed into a ~6:3 C#3/C#4 octave. (Because I believe that's one of the starting points of the Jack Stebbins method).

All beat speeds would be multiplied with 2^(-1/3).

Kees

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#2323818 - 09/03/14 08:07 PM Re: An aural and visual demonstration of the Skeleton. [Re: Chris Leslie]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1738
Loc: Vancouver, Canada
Originally Posted By: Chris Leslie
Originally Posted By: DoelKees

As a digression note that if F3A3 beats at around 8.5bps it is possible to make the 3 M3's F3A3C#4F4 all equal beating, which results in a peculiar unequal (pseudo reverse well) temperament with C#major the best, A major next, and F major the worst key.

Kees

I disagree. If the rules are to have equal beating 3 M3's F3A3C#4F4, and all other M3rds in the octave equal beating, then there is an infinite number of varying results.

Well I was thinking of filling up the M3's with equal P5/4's but you are right you can do infinitely many other things.

Kees

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#2325198 - 09/07/14 11:09 PM Re: An aural and visual demonstration of the Skeleton. [Re: Mark Cerisano, RPT]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1318
Loc: Montreal, Quebec, Canada
Kees, Is there only one possible result if we have a fixed octave size?
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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#2325220 - 09/08/14 12:58 AM Re: An aural and visual demonstration of the Skeleton. [Re: Mark Cerisano, RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1738
Loc: Vancouver, Canada
Originally Posted By: Mark Cerisano, RPT
Kees, Is there only one possible result if we have a fixed octave size?

No. 3 notes don't determine a temperament of course as CHris pointed out.

Kees

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