Cents to frequency ratios conversion and convert frequency ratio to cent interval pitch change fraction tuning TET calculator ¢ semitone convert hertz to semitones equation

$Cents to frequency ratios conversion and convert frequency ratio to cent interval pitch change fraction tuning TET calculator ¢ convert hertz to semitones equation - sengpielaudio$ Checker

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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.

c = 1200 × log₂ (f₂ / f₁)
log 2 = 0.301029995

Formula for converting the interval frequency ratio f₁ / f₂ to cents (c or ¢).

This formula employs a log 2, or logarithm base 2, function. This formula can also be
written using a log10 function,available on most scientific calculators via the log button:

c = 1200 × 3.322038403 log₁₀ (f₂ / f₁)
1/log 2 = 1/0.301029995 = 3.322038403

The formula expressed using log 10, rather than log 2.

3.322038403 is a conversion factor that converts base 2 logarithms to base 10 logarithms.

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.

Thanks to Christopher J. Struck for his kind help to correct this program.
The original got 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

Masterclock calculator

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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%

TET 12 - an equal temperament semitone (1/2 tone) has the frequency ratio of ¹²√2 = 2^1/12 = 1.059463094
TET 24 - an equal temperament quarter tone (1/4 tone) has the frequency ratio of ²⁴√2 = 2^1/24 = 1.029302237
TET 48 - an equal temperament eighth tone (1/8 tone) has the frequency ratio of ⁴⁸√2 = 2^1/48= 1.014545335

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Reference wordclock 48.0 kHz Piano tuning f: Hz	↔	Reference frequency 440 Hz Studio wordclock f_s: kHz

Reference wordclock 44.1 kHz Piano tuningf: Hz	↔	Reference frequency 440 Hz Studio wordclock f_s: kHz