The discussion about piano tuning and how it relates to intonation of woodwinds, brass, and strings, has been really interesting. Horace Greeley had a lot to say about the discussion based on his immense knowledge and experience with these instruments and their use in ensembles.
One point I would like to clarify is how inharmonicity affects these other instruments. It has been my understanding that these "driven instruments" (as opposed to a freely vibrating string) do not have significant inharmonicity due to the effect of mode-locking which forces the partials to align very closely with their theoretically correct frequencies. I have measured inharmonicity on church organs and found that there was virtually no inharmonicity. My ETD clearly showed that C5 was at 523 hz, C6 was at 1046, C7 2092, and C8 was at 4184. On a piano with minimal stretch C8 will be somewhere in the neighborhood of 4263hz, a differenece of 79hz.
A "roughly scientific" experiment on my own trumpet gave the following results.
A#4 read 464.75 hz. I used Tunelab to assist me in trying to keep the display as steady as possible (with my limited abilities).
I recorded the tone and then played it back and measured partials two and three. I found that the partials came very close to their theoretical frequencies:
Partial 1: 464.75
Partial 2: 929.14 (464.75 x 2 = 929.5)
Partial 3: 1393.52 (464.75 x3 = 1394.25)
I did the same experiment with my wife's flute and the results were identical. Basically the partials do not exhibit significant inharmonicity.
If I understand Horace correctly, what he was really getting at was this: how do actual professionals play in their upper ranges? If a flute, horn, or violin player is in tune at A4, where are they actually landing when playing A5, A6, or C7 in relationship to an average piano tuning?
I spent some time on Youtube looking for examples of high note playing on various instruments and found that their intonation is very inconsistent. One thing I'm looking forward to is talking to more symphony musicians about this topic. I just received a call this afternoon from a retired conductor who is willing to spend some time talking with me on this subject and I'm looking forward to hearing his input. It would also be interesting to get together with some of the first chairs from the local symphony and measure the frequency of their notes in various octaves to see how consistent they are able to be and what their tendencies are.
Lastly - Here is an interesting link to a text on orchestra intonation that I found interesting:
http://faculty.gvsu.edu/duitmanh/home/321links_files/Long%20Intonation.PDF------------------------------
Ryan Sowers
Olympia WA
360-705-4160
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