TLA CTS-5-C, Manual

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14
3.4.3 The adjustment of "cent relation function" and transposer
Use mode 4 "TEMP. HIST" for this. First select a
temperament. The display will be similar to the following:
:
Press keys "S" and "E" briefly and simultaneously. Select the
cent relation tone with the keys "<" or ">" . Then press key "E":
Select with "< >" the transposer as you like.
Press "E".
Select with "< >" mode "TUNE"
After pressing key "E" you can start tuning.
3.5 The "cent"- settings for piano tuning
Striking a string on a piano produces a tone consisting of several harmonics 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 frequencies 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 in theory.
This is known as the "Inharmonicity" of a piano string. It is caused by the stiffness of the string
and can be different from instrument to instrument. This inharmonicity explains why, on a piano,
the bass has to be tuned lower than the theoretical frequency and the descant higher.
The four different stretchings of the octaves have been developed through extensive tests with
various upright and grand pianos. The diagrams of these stretchings may be found on the last
page. See also chapter 3.6 (creating individual piano tunings using the PIANYZER).
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
graphs.
WERCKMEISTER-III
>4< NUMMER 24
CENT REF.: _A_
>4<
TRANSP. A --> A
>4<
>4< TEMP.HIST->
>1< TUNE->
Blinking indicator:
WERCKMEISTER-III
CENT-REF _C_
TRANSP A --> C