Interval conversions - sengpielaudio
interval intervals American English international units conversion conversions converter convert calculator calculation calculations calculate computer compute table tables chart charts measure measures unit units octave division in 12-tone equal temperament TET unison second third forth fifth sixth seventh octave semitone cent frequency ratio to cents standard pitch a middle C interval intervals major minor perfect augmented diminished sengpielaudio Sengpiel Berlin
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Interval  conversions

Frequency ratio to cents and cents to frequency  ratio

cents:        Frequency ratio:   
↓        ↓     
Frequency ratio    cents 

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

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Cent value of an interval

Frequency 1:  Hz     Frequency 2:  Hz
    ↓           
  Interval   cents

Instead of the frequencies you can take the fraction numbers e.g. 4/5 of the interval major third.

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Frequency calculation for different octave intervals

Initial tone:  Hz
Step:  of  steps
Hz

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Changing of the frequency about a cent value

Frequency:  Hz
Pitch change:  cents
Hz

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Frequency to note calculation
Find out what note a given frequency is. English system.

Frequency:  Hz
Note: 
Offset in cents:   

E.g. at the entry of 261 Hz the pitch is shown one octave too low. Other
values within the octave (C4 to G#4) do not work as well; see the original:

http://www.birdsoft.demon.co.uk/music/notecalc.htm - Who can help me?

Note names of the English and German System

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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 1,000
Major seventh 1.887749 : 1 1,100
Octave 2.000000 : 1 1,200

Some like to tell us that calling a tempered fifth "perfect"
is a misnomer and perfect intervals are only proper fractions.

Temperierte Frequenzen - sengpielaudio

name Exact value in 12-TET Decimal value Just intonation interval Percent difference
 Unison   1 1.000000 1 = 1.000000 0.00%
 Minor second \sqrt[12]{2^1} = \sqrt[12]{2} 1.059463 16/15 = 1.066667 -0.68%
 Major second \sqrt[12]{2^2} = \sqrt[6]{2} 1.122462 9/8 = 1.125000 -0.23%
 Minor third \sqrt[12]{2^3} = \sqrt[12]{8} 1.189207 6/5 = 1.200000 -0.91%
 Major third \sqrt[12]{2^4} = \sqrt[3]{2} 1.259921 5/4 = 1.250000 +0.79%
 Perfect fourth \sqrt[12]{2^5} = \sqrt[12]{32} 1.334840 4/3 = 1.333333 +0.11%
 Diminished fifth \sqrt[12]{2^6} = \sqrt{2} 1.414214 7/5 = 1.400000 +1.02%
 Perfect fifth \sqrt[12]{2^7} = \sqrt[12]{128} 1.498307 3/2 = 1.500000 -0.11%
 Minor sixth \sqrt[12]{2^8} = \sqrt[3]{4} 1.587401 8/5 = 1.600000 -0.79%
 Major sixth \sqrt[12]{2^9} = \sqrt[4]{8} 1.681793 5/3 = 1.666667 +0.90%
 Minor seventh \sqrt[12]{2^{10}} = \sqrt[6]{32} 1.781797 16/9 = 1.777778 +0.23%
 Major seventh \sqrt[12]{2^{11}} = \sqrt[12]{2048} 1.887749 15/8 = 1.875000 +0.68%
 Octave \sqrt[12]{2^{12}} = {2} 2.000000 2/1 = 2.000000 0.00%

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