Cents to frequency ratios conversion and convert frequency ratio to cent interval pitch change

Deutsche Version

Interval conversions

• Frequency ratio to cents and cents to frequency ratio •

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Cent value of an interval

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

Frequency calculation for different octave intervals

Changing of the frequency about a cent value

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

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?

Table: Frequencies of equal temperament and Note names

Masterclock calculator

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click the mouse in an empty area of the page to update the result.
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.

Note names: English and German System by comparison.

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.

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%