Mr Bremmer, I find your posts about HT very interesting and inspiring. (As long as they The moment I get more time, I will also try some of the tunings you advised. As it is rather a new field to me I can not contribute much to the discussions. But here you really are behind the times +AD4-If I am not mistaken, or behind the times, most scaling formulas work on a +AD4-theoretical ET frequency value. Of course, when you actually tune the piano, +AD4-you will stretch the octaves to some degree or another. Especially at the +AD4-high and low ends, you will have a difference in frequency from theoretical ET +AD4-which will be far greater than that which you would have in the midrange with +AD4-a typical HT such as a Thomas Young +ACM-1 WT. Perhaps some newer scaling +AD4-programs take octave stretching into account, I don't really know. The German scaling program I use , Mensurix dates from 1989 and gives me the following results in Hertz for the first octave: the overtones are only from the Steinway, The comma and points are a bit mix up but should all be read as points. fundamental fund. fund. overtones tone Theoretical Matz Upright Steinway A 2 3 1 A2 27,500 27,468 27,473 54.961 82.478 2 +ACM-A2 29,135 29,103 29,109 58.233 87.385 3 H2 30,868 30,835 30,842 61.696 92.577 4 C1 32,703 32,669 32,677 65.367 98.082 5 +ACM-C1 34,648 34,612 34,621 69.256 103.920 6 D1 36,708 36,670 36,680 73.376 110.101 7 +ACM-D1 38,891 38,850 38,862 77.739 116.645 8 E1 41,203 41,160 41,173 82.362 123.582 9 F1 43,654 43,608 43,622 87.256 130.910 10 +ACM-F1 46,249 46,202 46,217 92.446 138.699 11 G1 48,999 48,950 48,966 97.943 146.945 12 +ACM-G1 51,913 51,862 51,878 103.769 155.686 13 A1 55,000 54,947 54,963 109.940 164.943 Is this stretch, or isn't it? Certainly all newer software will almost the same results. Mensurix calculates 8 overtones , but 4 is enough for this explanation. Regards, Michiel van Loon mvanloon+AEA-xs4all.nl Meppel Nederland
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