TLA Tuning-Set CTS-32-C, Руководство пользователя

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Original table of the Kirnberger-III temperament:
a b h c c# d d# e f f# g g#
0 +6,5 -1,5 +10,5 +0,5 +3,5 +4,5 -3,5 +8,5 +0,5 +7,0 +2,5
First the table is transposed by 3 semitone steps to the right:
a b h c c# d d# e f f# g g#
0,5 +7,0 +2,5 0 +6,5 -1,5 +10,5 +0,5 +3,5 +4,5 -3,5 +8,5
It is then recalculated to match the cent reference = “a” (-0,5 cent):
a b h c c# d d# e f f# g g#
0 +6,5 +2,0 -0,5 +6,0 -2,0 +10,0 0 +3,0 +4,0 -4,0 +8,0
4.5 Stretchings
Striking a string on a piano produces a tone consisting of several harmonics (partials), which are
not in tune with their fundamentals.
For example, the tone produced by a piano string for tone a' can consist of a 440 Hz fundamental,
with a second harmonic at 881 Hz and a fourth harmonic at 1768 Hz. If the partials had a harmonic
proportion of frequency to each other, the second harmonic would have a value of 880 Hertz and
the fourth harmonic 1760 Hertz. However, in our example the second harmonic is one Hertz and
the fourth harmonic 8 Hertz higher than demanded by theory.
This is known as the "inharmonicity" of a piano string. It is caused by the flexural strength of the
string and can be different from instrument to instrument. This inharmonicity explains why, on an
upright piano or on a grand piano, the bass has to be tuned lower and the discant must be tuned
higher.
The three different stretchings of the octaves pre-programmed in the Tuning Set were achieved
through extensive test with various upright and grand pianos. The diagrams of these stretchings
(PIANO_STRETCH_1 thru 3) are found on the last page.
In the lowest octave (A 2 to G#) the Tuning Set responds to the fourth harmonic, and in the octave
(A 1 to g#) to the second harmonic. This is the reason for the two discontinuities in the beginning
of the graphs.
You can combine the stretchings with temperaments as you please. If you select a temperament
and a stretching at the same time, in the tuning mode, the Tuning-Set will add the temperament
cents to those of the stretching.
For users who want to deal with intense piano tunings, we recommend the chapters 2.3.5 and
2.3.6. “Pianyzer” and “Piano Editor”.
4.6 Correction of organ pipe length automatically
The tuning of an organ pipe will be measured, and the variation in dimension to reach the correct
tuning, will be calculated automatically by the tuning-set.
For this reason a “reverence length” is introduced as a parameter of the instrument programs.
This value refers to the pitch a’. The default value of the reverence length is 390.1 mm (half wave
length of air at 440 Hz and 20 °C). See also chapter 2.3.3.10
First the theoretical pipe length (lp) will be calculculatet by the tuning set with the formula:
lp = (f_pitch / f_target) * reference length