Cents to Hertz Conversion Instructions and Revised Chart

[Kent Swafford]

ROGERIO CUNHA wrote:

>I thanks to all that send  answer to me but I would like to know more about
>the formulas provided by Steve Fairchild.
>It's true that there are 120 cents in one semitone?
>ROGERIO CUNHA IC MEMBER OF THE GUILD

100 cents to a half-step and 1200 cents to an octave in the mathematical 
model of 12-tone to the octave equal temperament.

Steve Fairchild, practical teacher that he is, does not assume that every 
piano tech who might want to figure some cents deviations knows enough 
math to do so. Good assumption. Steve provided button-by-button 
directions about how to use a scientific calculator to do cents/Hertz 
conversions. These are cumbersome in ASCII, but I'll give it a try.

To figure the number of cents between any two frequencies (such as 440 
and 442):

Enter the larger number in the window.
Press "division" button.
Enter the smaller number in the window.
Press "equals" button.
Press "LOG" button.
Press "division" button.
Enter the number "2" in the window.
Press "LOG" button.
Press "multiplication" button.
Enter the number "1200" in the window.
Press the "equals" button.


To figure what frequency is a given number of cents higher than a 
beginning frequency:

Enter the number "2" in the window.
Press the "y to the x" button.
Press the ( left parentheses button.
Insert the variable, that is, enter the number of cents into the window.
Press "division" button.
Enter the number "1200" in the window.
Press the ) right parentheses button.
Press the "equals" button.
Press "multiplication" button.
Enter the original frequency into the window.
Press the "equals" button.


To figure what frequency is a given number of cents lower than a 
beginning frequency:

Enter the number "2" in the window.
Press the "y to the x" button.
Press the ( left parenthesis button.
Insert the variable, that is, enter the number of cents into the window.
Press "division" button.
Enter the number "1200" in the window.
Press the ) right parenthesis button.
Press the "equals" button.
Write down the number in the window or press a "Memory Store" button.
Enter the original frequency into the window.
Press "division" button.
Enter the number that you just wrote down or press the "Memory Recall" 
button.
Press the "equals" button.


Better to just carry a chart of the common conversions needed.
I have added 420 and 425 to the following chart.

Kent Swafford


                        CENTS/HZ  CONVERSION CHART

               Frequency(Hz) to Cents Deviation (Offset)
                          A4 = 415Hz =   -101.3 cents
                          A4 = 420Hz =    -80.5 cents
                          A4 = 425Hz =    -60.0 cents
                          A4 = 428Hz =    -47.9 cents
                          A4 = 430Hz =    -39.8 cents
                          A4 = 435Hz =    -19.8 cents
                          A4 = 440Hz =      0.0 cents
                          A4 = 441Hz =      3.9 cents
                          A4 = 442Hz =      7.9 cents
                          A4 = 443Hz =     11.8 cents
                          A4 = 444Hz =     15.7 cents

                    Cents Deviation to Frequency(Hz)
                         A4 =  -50.0 cents = 427.5Hz
                         A4 =  -25.0 cents = 433.7Hz
                         A4 =  -15.0 cents = 436.2Hz
                         A4 =  -10.0 cents = 437.5Hz
                         A4 =   -5.0 cents = 438.7Hz
                         A4 =    0.0 cents = 440.0Hz
                         A4 =    5.0 cents = 441.3Hz
                         A4 =   10.0 cents = 442.5Hz
                         A4 =   15.0 cents = 443.8Hz