cents to frequency ratios conversion convert frequency ratio to cent interval Hz piano tuning calculator pitch audio change fraction TET cents to hertz (herz) ¢ minor third major calculator ¢ convert hertz to semitones equation keyboard - sengpielaudio
 
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Conversion  of  Intervals  −  ¢ = cent
 
Frequency ratio to cents and cents to frequency  ratio
 
Change of pitch with change of temperature
 
1 hertz = 1 Hz = cps = cycles per second
The unit most commonly used to measure intervals is called cent, from Latin centum,
meaning "one hundred". It stands for one hundredth of an equal-tempered semitone.
In other words, one octave consists of 1200 cents.

 
cents   |   Frequency ratio f2 / f1 
   |   
       |        
   |   
 Frequency ratio f2 / f1   |         cents 
 

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

How many cents are in a hertz?
There is no conversion from Hz to cents and vice versa.

Scroll down to the bottom: "Table of Cent Difference".

Statement: Cent is a logarithmic unit of measure of an interval, and that is a dimensionless "frequency ratio" of f2 / f1.

Calculation: Intervals (cents) and Frequency (Hz) as Excel Program (xls)

Different Thirds
 
Thirds

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Cent value-determination of an interval

 
 Frequency f1   Hz (hertz) 
 Frequency f2   Hz (hertz) 
 
              
 
Interval   cents 
Ratio f2 / f1   
 

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 log 10 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 log10 rather than log 2.
3.322038403 is a conversion factor that converts base 2 logarithms to base 10 logarithms.
1 Cent = 2(1/1200) = 1.0005777895065548592967925757932
One cent is thus the number that multiplied by itself 1200 times results in the number 2.
The cent is an interval which is calculated from the interval frequency ratio as follows:
(In of the interval frequency ratio / ln 2)×1200 = cents value of the interval.
An interval of a halftone is equivalent to: 2(1/12) = 1,0594630943592952645618252949463.
That is: [ln (2(1/12)) / ln (2)]×1200 cent = 100 cent.
 
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) reveals 8423.46 cents and
seven octaves, however, reveals only 8400 cents.

Note line

Conversions of Semitone Intervals
An interval is the difference between two pitches or the
distance between two frequencies in terms of semitones
.

Enter any two known values and press "calculate" to solve for the other. Please, enter only two values.

 
 Frequency f1  Hz 
 Frequency f2  Hz 
 Number of semitones   
 
 

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Frequency calculation for different octave intervals

 
Initial tone f  Hz 
Step  of  steps 
 
            
 
 New frequency f  Hz 
 

 
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Change of pitch with change of temperature†

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Changing of the frequency about a cent value

 
Initial tone f  Hz 
 Change of pitch J  cents 
 
        
 
 New frequency f  Hz 
 

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Frequency to musical note converter

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

 
 Frequency f  Hz 
 
   
 
 Musical note 
 Offset  cents 
 
Formulas: f = 440 × 2(−58/12) × (2(1/12))n and f = 440 × 2((n−58)/12)
 
The original source program of Iain W. Bird is still faulty:
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
 
Change of pitch with change of temperature

sengpielaudio

The frequency as semitone distance from A4 = 440 Hz

For a note that lies n semitones higher (or −n semitones lower) from A4, the frequency is fn = 2n/12 × 440 Hz.
Conversely, one can obtain n, the number of semitones from A4, from:
n = 12 × log2 (fn / 440 Hz).
 
To use the calculator, simply enter a value.
The calculator works in both directions of the
sign.

 
Semitone n as distance from A4
Semitones
 ↔  Frequency fn - Reference: 440 Hz 
Hz
     
n = 12*(log (fn/440) / log(2))                                        fn = 2^(n/12)*440

Rainbow Line

Masterclock calculator (clock rate)

To use the calculator, simply enter a value.
The 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 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.
 
100 cent is equivalent to a semitone (halftone).

Note names: English and German System by comparison
 
Calculations of Harmonics from Fundamental Frequency
 
Change of pitch with change of temperature

Rainbow Line

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.

 
Keyboard

Temperierte Frequenzen
 
In the following table are for the most popular pure dyads up to the octave - the frequency ratio is themeasure of consonance and the sound sensation of most people.
 
Dyads Frequency
ratio
Consonance
value
Sensation of sound
minor second   16:15 15.49 very dissonant
major second   9:8   8.49 dissonant
minor third   6:5   5.48 consonant ("minor")
major third   5:4   4.47 consonant ("major")
forth   4:3   3.46 consonant
tritonus   45:32 37.95 very dissonant
fifth   3:2   2.45 very consonant ("neutral")
minor sixth   8:5   6.32 consonant ("minor")
major sixth   5:3   3.87 consonant ("major")
minor seventh 16:9 12.00 dissonant
major seventh 15:8 10.95 dissonant
octave   2:1   1.41 very consonant ("neutral")
 
Name Exact value in 12-TET Decimal value Just intonation interval Percent difference
 Unison    1 1.000000    1 = 1.000000   0.00%
 Minor second Formula minor second 1.059463 16/15 = 1.066667    −0.68%
 Major second Formula major second 1.122462 9/8 = 1.125000 −0.23%
 Minor third Formula minor third 1.189207 6/5 = 1.200000 −0.91%
 Major third Formula major third 1.259921 5/4 = 1.250000 +0.79%
 Perfect fourth Formula perfect fourth 1.334840 4/3 = 1.333333 +0.11%
 Diminished fifth Formula diminished fifth 1.414214 7/5 = 1.400000 +1.02%
 Perfect fifth Formula perfect fifth 1.498307 3/2 = 1.500000 −0.11%
 Minor sixth Formula minor sixth 1.587401 8/5 = 1.600000 −0.79%
 Major sixth Formula major sixth 1.681793 5/3 = 1.666667 +0.90%
 Minor seventh Formula minor seventh 1.781797 16/9 = 1.777778  +0.23%
 Major seventh Formula major seventh 1.887749 15/8 = 1.875000  +0.68%
 Octave Formula octave 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
 
Question: How can I convert cents to Hz?
Answer: You cannot convert cents to hertz, because cents are not a frequency.
cents are the measurement between intervals, that is a "frequency ratio"
f2/f1.

Here's a Table of Cents Difference for some frequencies close around 440 Hz:
 
Frequency Difference
435 Hz −19.78 cents
436 Hz −15.81 cents
437 Hz −11.84 cents
438 Hz   −7.89 cents
439 Hz   −3.94 cents
440 Hz   ±0 cent
441 Hz   +3.93 cents
442 Hz   +7.85 cents
443 Hz +11.76 cents
444 Hz +15.67 cents
445 Hz +19.56 cents
 
So, the conversion factor 4 cents / Hz is valid for the purposes of tuning as an exception only very close around 440 Hz.

There is no conversion from Hz to cents and vice versa.
Statement: Cent is a logarithmic unit of measure of an interval, and that is a dimensionless "frequency ratio" of f2 / f1.

Smallest recognizable frequency difference for pure tones at different listening levels
 
Smallest recognizable frequency difference for pure tones

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