Cents to frequency ratios conversion and convert frequency ratio to cent interval pitch audio change fraction tuning TET calculator ¢ convert hertz to semitones equation half tone - sengpielaudio Checker
 
Deutsche Version UK-flag s/w - sengpielaudio D-flag - sengpielaudio
 
Conversion  of  Intervals  −  ¢ = cent

Frequency ratio to cents and cents to frequency  ratio

cents    |    Frequency ratio 
      |      
        |        
      |      
 Frequency ratio    |   cents 

Fill out the gray boxes and click at the calculation bar.

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Calculate the cent value of an interval

 Frequency 1  Hz
 Frequency 2  Hz
   
      
   
Interval  cent 

Instead of the frequencies you can take the fraction numbers e.g. 4/5 of the interval major third.

Formula for converting the interval frequency ratio f2 / f1 to cents (c or ¢).
¢ or c = 1200 × log2 (f2 / f1)
log 2 = 0.301029995
This formula employs a log 2, or logarithm base 2, function. This formula can also be
written using a log10 function, available on most scientific calculators via the log button:
c = 1200 × 3.322038403 log10 (f2 / f1)
1/log 2 = 1/0.301029995 = 3.322038403
The formula expressed using log 10, rather than log 2.
3.322038403 is a conversion factor that converts base 2 logarithms to base 10 logarithms.

The Pythagorean comma is the frequency ratio (3 / 2)12 / 27 = 312 / 219 =
531441 / 524288 = 1.0136432647705078125. The resulting is converted to
23.460010384649013 cent. Twelve perfect fifths (3 / 2) reveales 8423.46 cents
seven octaves, however, reveales only 8400 cents.

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Frequency calculation for different octave intervals

Initial tone  Hz 
Step  of  steps
   
      
   
 Frequency  Hz

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Changing of the frequency about a cent value

Initial Frequency  Hz 
Pitch change  cents
   
      
   
 Resulting frequency  Hz

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Frequency to note calculation

Find out what note a given frequency is. English system.

Frequency  Hz
   
            
   
Note 
 Offset  cents
Thanks to Christopher J. Struck for his kind help to correct this program.
The original got still some faults:
http://www.birdsoft.demon.co.uk/music/notecalc.htm
The frequency of 440 Hz is the concert pitch note A4.
If someone tells you different, this person is in error. See also:

Table: Frequencies of equal temperament and Note names

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Masterclock calculator

To use the calculator, simply enter a value.
Calculator works in both directions of the sign.

 
 Reference wordclock 48.0 kHz
 Piano tuning f:
Hz
 
 ↔ 
 Reference frequency 440 Hz
 Studio wordclock fs:
kHz
 

 
 Reference wordclock 44.1 kHz
 Piano tuning f:
Hz
 
 ↔ 
 Reference frequency 440 Hz
 Studio wordclock fs:
kHz
 

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Calculator with free reference frequency

 Reference wordclock kHz              
Reference frequency Hz
Piano tuning f Hz
     
     
Studio wordclock fs kHz
Interval deviation cent

For downward tuning the reference frequency and piano tuning can be changed.

Note names: English and German System by comparison

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Octave division in 12-tone equal temperament TET

Interval Frequency ratio Cents
Unison 1.000000 : 1      0
Semitone or minor second 1.059463 : 1    100
Whole tone or major second 1.122462 : 1    200
Minor third 1.189207 : 1    300
Major third 1.259921 : 1    400
Perfect fourth 1.334840 : 1    500
Augmented fourth/Diminished fifth 1.414214 : 1    600
Perfect fifth 1.498307 : 1    700
Minor sixth 1.587401 : 1    800
Major sixth 1.681793 : 1    900
Minor seventh 1.781797 : 1  1000
Major seventh 1.887749 : 1  1100
Octave 2.000000 : 1  1200

Some like to tell us that calling a tempered fifth "perfect"
is a misnomer and perfect intervals are only proper fractions.

Temperierte Frequenzen - sengpielaudio

Name Exact value in 12-TET Decimal value Just intonation interval Percent difference
 Unison   1 1.000000 1 = 1.000000 0.00%
 Minor second \sqrt[12]{2^1} = \sqrt[12]{2} 1.059463 16/15 = 1.066667 −0.68%
 Major second \sqrt[12]{2^2} = \sqrt[6]{2} 1.122462 9/8 = 1.125000 −0.23%
 Minor third \sqrt[12]{2^3} = \sqrt[12]{8} 1.189207 6/5 = 1.200000 −0.91%
 Major third \sqrt[12]{2^4} = \sqrt[3]{2} 1.259921 5/4 = 1.250000 +0.79%
 Perfect fourth \sqrt[12]{2^5} = \sqrt[12]{32} 1.334840 4/3 = 1.333333 +0.11%
 Diminished fifth \sqrt[12]{2^6} = \sqrt{2} 1.414214 7/5 = 1.400000 +1.02%
 Perfect fifth \sqrt[12]{2^7} = \sqrt[12]{128} 1.498307 3/2 = 1.500000 −0.11%
 Minor sixth \sqrt[12]{2^8} = \sqrt[3]{4} 1.587401 8/5 = 1.600000 −0.79%
 Major sixth \sqrt[12]{2^9} = \sqrt[4]{8} 1.681793 5/3 = 1.666667 +0.90%
 Minor seventh \sqrt[12]{2^{10}} = \sqrt[6]{32} 1.781797 16/9 = 1.777778 +0.23%
 Major seventh \sqrt[12]{2^{11}} = \sqrt[12]{2048} 1.887749 15/8 = 1.875000 +0.68%
 Octave \sqrt[12]{2^{12}} = {2} 2.000000 2/1 = 2.000000 0.00%

TET 12 - equal temperament   semitone    (1/2 tone) has the frequency ratio of 12√2 = 21/12 = 1.0594630943592952645618252949463
TET 24 - equal temperament quarter tone (1/4 tone) has the frequency ratio of 24√2 = 21/24 = 1.0293022366434920287823718007739
TET 48 - equal temperament eighth tone   (1/8 tone) has the frequency ratio of 48√2 = 21/48 = 1.0145453349375236414538678576629


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