Scaling

[Michiel van Loon]

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