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Calculation: Intervals (cents) and Frequency (Hz) as Excel Program (xls)
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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:
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| 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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Frequency calculation for different octave intervals
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Changing of the frequency about a cent value
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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: 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
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Masterclock calculator
| Simply enter the value to the left or the right side. The calculator works in both directions of the ↔ sign. |
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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
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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.
| 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. |
| 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 = 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. |

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