[CAUT] Re. Link to Young Paper

[Fred Sturm]

On Jan 17, 2007, at 10:35 AM, James Ellis wrote:

> The Conn stroboscope that I believe Robert Young used for his  
> measurements
> was pleaty good for showing the inharmonicity trends that he  
> discusses,
> despite the fact that we can make more accurate measurements now.
Yes, accurate enough for laying a foundation. But it was limited to  
+- 1 cent resolution, and B7 top pitch. It would be interesting to  
see if the top end is as predicted, or if things change, for  
instance, especially with the shortest strings.
>
> There is the fact that a string in a real piano is subject to the
> characteristics of the piano's acoustical system being reflected  
> back into it.
Yes, precisely. There seems to be a wide variance from the predicted  
in real pianos, due to all sorts of effects. For example, I find that  
measured inharmonicity fairly consistently becomes lower after a  
piano is tuned, setting aside pitch. Ie., if a piano is basically at  
pitch but out of tune with itself, it will measure higher  
inharmonicity than after a fine tuning. I wonder whether different  
stretches might also affect measured inharmonicity.
>
> Regarding bass strings:  Fred mentions anomalies in inharmonic  
> ladders that
> Dean Reyburn has discussed.  I have not seen Dean's work, but I can  
> say
> those anomalies are very real.  They are NOT from faulty measurements.
> They come form the fact that it is IMPOSSIBLE to wind a PERFECT bass
> string.  The very slightest irregularity of ANY kind in the winding  
> or core
> wire will cause it.  I have been measuring and plotting inharmonicity
> curves of bass strings for nearly two years now, using a monichoord I
> designed just for that purpose, and some state-of-the-art analysis  
> programs.
I don't think Dean has ever documented or published results. I think  
he has just observed the phenomena in the process of developing his  
software, which relies heavily on partial ladders. In order to obtain  
good calculated tunings, he had to find a way to account for  
irregularities (I don't know what he came up with, but presumably  
some kind of averaging).
	I don't think they occur only on bass strings. Plain wires can also  
have anomalies, as I discovered when I first started tuning with an  
SAT a little over ten years ago. I found that results were "odd"  
often enough that I looked into it a bit. SAT relies on the  
discrepancy between two partials to predict a virtual partial ladder.  
I found that I could get a better calculated FAC tuning if I measured  
the distance between the A4 and A6 partials of A4, and between C6 and  
C8 partials of C6 (as opposed to A5 and A6 partial of A4, C6 and C7  
partial of C6), and extrapolated a result. The distance between 1st  
and 4th partial seemed to "average out" the anomalies in the  
measurement between 2nd and 4th, 1st and 2nd, and yield a result that  
calculated better tuning spreadsheets.
	I have had similar "strange" experiences with RCT on a few pianos,  
where I have got wide variances in calculated tunings on measurements  
made the same day. (I look particularly on the values for G#4 and C8  
in comparing, as they are good benchmarks). Unfortunately, the  
partial ladders that RCT automatically measures are hidden from view,  
so I can't come to any useful conclusion other than to keep my eyes  
and ears open for anomalistic numbers and patterns (looking at the  
charts in the Custom EQ window helps a lot). Where do the anomalies  
come from? Perhaps the biggest factor is termination, though that is  
just an educated guess. There can certainly be a wide differences is  
termination from piano to piano and from string to string.

Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu






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