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

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 •

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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?

Note names of the English and German System

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.

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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cents:			Frequency ratio:
↓			↓
Frequency ratio			cents

Initial tone:	Hz
Step:	of steps
	Hz

Frequency:		Hz
Note:
Offset in cents:

Frequency 1:	Hz	Frequency 2:	Hz
		↓
	Interval		cents

Frequency:	Hz
Pitch change:	cents
	Hz