How accurate are inharmonicity measurements?

[Jim Coleman, Sr.]

Hi Bob:

I think your study looks pretty good. Getting repeatablility closer than
.2 or .3 cents is pretty rare. We would like to have our CTE examiners
be able to read within .2 to .3 cents reliably.

As far as the difference in computing tunings is concerned, after 
writing my articles on using additional stretch last summer in the 
PTJ, I don't feel that we do a great disservice to the tuning of the 
piano when there is some variation. If there is a .5 cent difference in
the measurements, it can make a small difference in the tuning, 
especially between notes B3 and C4 where the tuning partials change from
the 4th to the 2nd on the SAT.

Jim Coleman, Sr.

PS
I think the biggest difference in readings is caused by the changing
amplitude of the note. A controlled key striker would yield more exact
reading.

On Mon, 3 Nov 1997, Robert Scott wrote:

> To those with visual tuning devices:
> 
>   I would like to confirm some research I have been doing on 
> measurement of inharmonicity for the TuneLab97 program.  A few 
> months ago Jim Coleman, Sr. and I had some exchanges on this list 
> regarding the issue of how voicing might affect inharmonicity.  
> While that particular question may have been left undecided, the 
> more general question that interested me was "How accurately can you 
> measure inharmonicity anyhow?"  A related question is "How 
> accurately do you need to measure inharmonicity in order to use 
> those measurements to construct good tunings?" 
> 
>   Although I have not had personal experience with either the SAT or 
> the RCT, I gather that the operation of these two devices is 
> different regarding the measurement of inharmonicity.  It seems that 
> the SAT relies on the tuner to push buttons to stop the display.  
> The RCT, on the other hand, "listens" for a period of time and then 
> automatically makes calculations of all significant partials.  It 
> seems that each of these methods has its own advantages.  The 
> automatic method is obviously more convenient for the tuner, since
> only one sound sample needs to be taken and the computer calculates 
> all partials from that sample.  But false beats can confuse such 
> algorithms, making the measurement unreliable.  (I have heard that 
> the RCT detects this condition and warns the tuner to take a better 
> sound sample.)  With the more manual method used in the SAT, the 
> tuner has the opportunity to see the irregular movement of the 
> lights caused by false beats and either pick another string or use 
> his judgement about when the lights are the closest to being 
> "stopped".  My question is, which of the two methods is most 
> reliable on the average. 
> 
> I have attempted to implement the automatic method in the next 
> version of the TuneLab97 program and have gotten mixed results.  It 
> seems that when I pick very good and stable strings (no false 
> beats), I get excellent repeatability in the inharmonicity 
> measurements.  My measurements are based on a 3 second sound sample.  
> But when I try to measure strings with a little wobble in them, the 
> inharmonicity measurements are more variable.  The following 
> repeated inharmonicity measurements were made.  The notes and the 
> partials that I selected just happen to correspond to the FAC 
> measurements in order to make it easy to compare my measurements to
> SAT measurements.  The measurements were made on a Kawai 650.
> 
> 
> Note   2nd   3rd   4th   5th   6th   7th   8th  8th-4th
> ---   ----  ----  ----  ----  ----  ----  ----  -------
> F3   -0.42  1.25  2.20  3.20  4.45  5.89  8.01    5.81
> F3   -0.23  1.30  2.06  3.22  4.46  5.86  7.95    5.89
> F3   -0.45  1.29  1.98  3.23  4.44  5.82  7.92    5.94
> F3   -0.38  1.33  2.04  3.32  4.46  5.88  7.94    5.90
> F3   -0.41  1.25  1.99  3.32  4.40  5.86  7.91    5.92
> F3   -0.19  1.33  2.03  3.33  4.44  5.89  7.93    5.90
> F3   -0.19  1.34  2.01  3.33  4.42  5.89  7.95    5.94
> F3   -0.28  1.29  1.89  3.22  4.34  5.79  7.93    6.04
>     ...a different unison:....
> F3    0.64  1.84  2.38  3.72  5.11  6.78  7.97    5.59
> F3    0.63  1.80  2.37  3.70  5.07  6.74  8.65    6.28
> F3    0.63  1.79  2.37  3.69  5.08  6.73  8.02    5.65
> F3    0.64  1.73  2.38  3.67  5.08  6.67  8.61    6.23
> F3    0.65  1.84  2.39  3.73  5.11  6.78  8.02    5.63
> F3    0.56  1.67  2.30  3.61  4.96  6.61  8.55    6.25
> 
> Note   2nd   3rd   4th   4th-2nd
> ---   ----  ----  ----   -------
> A4    1.20  3.27  6.72   5.52
> A4    1.12  3.27  6.74   5.62
> A4    1.11  3.24  6.72   5.61
> A4    1.22  3.36  6.88   5.66
> A4    1.00  3.19  6.73   5.73
> A4    1.34  3.58  7.00   5.66
> A4    1.31  3.69  6.99   5.68
> 
> Note   2nd
> ---   ----
> C6    3.34
> C6    3.23
> C6    2.86
> C6    2.55
> C6    2.26
> C6    2.80
>   ..a different unison:...
> C6    5.95
> C6    6.00
> C6    6.55
> C6    6.15
> C6    5.81
> 
> I would appreciate any confirming or contradicting information on 
> this subject.  In particular, I would like to know how much 
> variation there would be if two or three different tuners measured 
> the FAC numbers on the same piano.  I want to know how much a factor 
> individual judgement plays when strings are less than perfect.
> 
> Bob Scott
> Ann Arbor, Michigan
> (Detroit-Windsor PTG)
> 
> 
>