TLA CTS-5-C, Manual

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3 For all those who wish to learn more about Tuning Set …
3.1 The equal temperament
The Equal Temperament is the most frequently used temperament, it is the basic tuning of
CTS-5. The following example shows its mathematical theory.
Given that standard pitch a' is 440.0 Hertz, then oscillations of the chromatic semi-tone steps
are calculated as follows:
bb' = 440,00 Hz * 12 2 466,16 Hz 12 2 = 1,0594631
b' = 466,16 Hz * 12 2 493,88 Hz etc.
When the standard pitch a' is 442.00 Hertz:
bb' = 442,00 Hz * 12 2 = 468,28 Hz
b' = 468,28 Hz * 12 2 = 496,13 Hz etc.
3.2 The "cent" unit
Cent is a value for proportions of frequencies. A semi- tone is geometrically divided into 100
parts ( = 100 cent). The following example will show how the cent-value is defined
mathematically. The frequency of oscillations is given with 440.0 Hertz and is to be increased by
1 cent:
440.00 Hz * 1200 2 = 440.26 Hz
The frequency of oscillation is given with 440.00 Hertz is to be increased by 5 cent.
440.00 Hz * (1200/5) 2 = 441.27 Hz
The frequency of 440.00 Hertz is to be increased by 100 cent (= 1 semi-tone).
440.00 Hz * (1200/100) 2 = 440.00 Hz * 12 2 = 466.16 Hz
The frequency of 466.16 Hertz is to be lowered by 100 cent (= 1 semi-tone).
466.16 Hz : (1200/100) 2 = 466.16 Hz : 12 2 = 440.00 Hz
3.3 The target frequency genaration of CTS 5-C
Tuning Set CTS-5 contains a microprocessor which generates the nominal frequency (f)
according to the following equation.
n c
o + ---- + -----
k 12 1200
f = --- * 2
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c: "cent" - presetting (+-99.5)
n: number of tone (a=0, bb=1, ... g#=11)
k: standard pitch presetting (380.0 ... 470.0 Hz)
o: octave (1=A2/110Hz, 2=A1/220Hz, ... 6=a4/3520Hz)