How accurate are inharmonicity measurements?+

[pianoman]

WOW!
James Grebe
R.P.T. from St. Louis
pianoman@inlink.com
"Only my best is good enough"

----------
> From: Robert Scott <rscott@wwnet.com>
> To: pianotech@ptg.org
> Subject: How accurate are inharmonicity measurements?
> Date: Monday, November 03, 1997 11:53 AM
> 
> 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)
> 
>