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.

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.
 
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.

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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  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 musical note converter

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

 
Frequency  Hz
 
   
 
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
Hz
     
n = 12*(log (fn/440) / log(2))                                        fn = 2^(n/12)*440

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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

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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.

 
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:
 
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      cents
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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