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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 f_{2} / f_{1}.
Calculation: Intervals (cents) and Frequency (Hz) as Excel Program (xls)
Cent value-determination of an interval
Instead of the frequencies you can take the fraction numbers − e.g. 4/5 of the interval major third.
written using a log 10 function, available on most scientific calculators via the log button:
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} / 2^{7} = 3^{12} / 2^{19} = 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. |
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 calculation for different octave intervals
Change of pitch with change of temperature
Changing of the frequency about a cent value
Frequency to musical note converter
Find out what note a given frequency is. English system.
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
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 f_{n} = 2^{n/12} × 440 Hz. Conversely, one can obtain n, the number of semitones from A4, from: n = 12 × log_{2 }(f_{n} / 440 Hz). |
To use the calculator, simply enter a value. The calculator works in both directions of the ↔ sign. |
Masterclock calculator (clock rate)
To use the calculator, simply enter a value. The calculator works in both directions of the ↔ sign. |
Calculator with reference frequency
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
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
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 | 1.059463 | 16/15 = 1.066667 | −0.68% | |
Major second | 1.122462 | 9/8 = 1.125000 | −0.23% | |
Minor third | 1.189207 | 6/5 = 1.200000 | −0.91% | |
Major third | 1.259921 | 5/4 = 1.250000 | +0.79% | |
Perfect fourth | 1.334840 | 4/3 = 1.333333 | +0.11% | |
Diminished fifth | 1.414214 | 7/5 = 1.400000 | +1.02% | |
Perfect fifth | 1.498307 | 3/2 = 1.500000 | −0.11% | |
Minor sixth | 1.587401 | 8/5 = 1.600000 | −0.79% | |
Major sixth | 1.681793 | 5/3 = 1.666667 | +0.90% | |
Minor seventh | 1.781797 | 16/9 = 1.777778 | +0.23% | |
Major seventh | 1.887749 | 15/8 = 1.875000 | +0.68% | |
Octave | 2.000000 | 2/1 = 2.000000 | 0.00% |
TET 12 - equal temperament semitone (1/2 tone) has the frequency ratio of ^{12}√2 = 2^{1/12} = 1.0594630943592952645618252949463 TET 24 - equal temperament quarter tone (1/4 tone) has the frequency ratio of ^{24}√2 = 2^{1/24} = 1.0293022366434920287823718007739 TET 48 - equal temperament eighth tone (1/8 tone) has the frequency ratio of ^{48}√2 = 2^{1/48 }= 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" f_{2}/f_{1}. |
Here's a Table of Cents Difference for some frequencies close around 440 Hz:
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 f_{2} / f_{1}. |
Smallest recognizable frequency difference for pure tones at different listening levels
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