A Small Equation = inharmonicity??

[Don]

Hi Michael,

To make sure we are on the same page a0 is the bottom note of the piano c1
is the first C and a4 is tuned to 440.

First inharmonicity is not my theory. There is a great explanation here:
http://www.afn.org/~afn49304/youngnew.htm
 
Second inharmonicity may cause the type of octave that you are describing
(called a 2:1) to be wide by 1 to 8 cents depending on the scale design of
the piano.

Third most tuners would do a 4:2 or a "wide" 4:2 or a 6:3 in the middle of
a piano, resulting in an even wider octave at 2:1.

Fourth coupling to the soundboard may cause the total inharmonicity in the
system to be a negative number resulting a 2:1 octave that is smaller than
your "pure" 2:1. (i.e. narrow by 1 or 2 cents)

Fifth Reyburn Cyber Tuner calculates a 6:3 from f3 to f4 that is 3.27 cents
wide for a Yamaha C3. I don't have the piano in front of me so I can't
check the 4:2 and 2:1 values at the moment.

Sixth it would not be uncommon for a0 to a1 in a large concert grand to be
tuned as a 12:6 octave. The 2:1 may not even be measureable in such a
situation as it is a very tiny fraction of the total sound output, but if
it does exist would be extremely wide.

One reason I asked what sort of ETD you were using was to know whether it
had a needle type gauge. You answered that it did--without giving the make.
Needle type gauges suffer from parallax error when a user attempts to
"read" them. Some are not very well suited to the task of tuning a piano.
See this web site about parallax error.
http://www.usna.edu/EE/ee331/MAn1.PDF look on page 13.

At 11:05 PM 12/11/2003 -0000, you wrote:
>Hello Don
>Please prove your inharmonicity theory when plotted against that "small
>equation". A pure 8ve. is surely that where the higher note is exactly
>double that of the lower one.....Or is it?
>Over to you with...:-)
>Regards
>Michael G (UK)

Regards,
Don Rose, B.Mus., A.M.U.S., A.MUS., R.P.T.

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