Fill out the gray boxes and click at the calculation bar.
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:
|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.
Frequency calculation for different octave intervals
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
f = 440 × 2((n−58)/12)
The original source program has still some faults:
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
|Simply enter the value to the left or the right side.
The calculator works in both directions of the ↔ sign.
Calculator with free 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
Octave division in 12-tone equal temperament TET
|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.
|In the following table are for the most popular pure dyads up to the octave - the frequency ratio is the measure of consonance and the sound sensation of most people.|
|Sensation of sound|
|minor second||16:15||15.49||very dissonant|
|minor third||6:5||5.48||consonant ("minor")|
|major third||5:4||4.47||consonant ("major")|
|fifth||3:2||2.45||very consonant ("neutral")|
|minor sixth||8:5||6.32||consonant ("minor")|
|major sixth||5:3||3.87||consonant ("major")|
|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 = 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.