TLA CTS-5-CA, 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 
              4 

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)