Hello Guys,

In this article, we will learn a method of finding out the frequency of any note from any music scale. We know that music note is nothing but a music sound frequency which is generated by vibrations. So when some one says that a note is being played, then, it means that a particular frequency is generated from that instrument.

## What is the audible frequency range of a human ear?

We all have studied that human ear can listen any frequency between 20 Hertz to 20,000 Hertz. So any frequency between these numbers can be listened by a human being. All music we listen, (in fact, everything we listen from our ears) is between 20 Hz and 20 KHz (20000 Hz).

## Does musical notes have fixed frequency?

Answer is Yes! Every note comes in a certain octave and every note has its fixed frequency. For example A Note of 4th octave has 440 Hz frequency. (Frequency of A4=440 Hz). Like wise, frequency of A5 (A note of 5th octave) is 880 Hz. So the same note in the consecutive higher octave have just double frequency then the previous. It means:

Frequency of A6 Note = 2 X Frequency of A5 Note = 2 X 880 Hz = 1760 Hz.

So by musical frequency law, an octave has 12 notes, which are equally spaced from its lower and higher nearest notes.

It means:-

A5/G#5 (1 semitone difference notes) = G#5/G5 (1 semitone difference notes) (The ratio will be same with reference to the steps)

## How to find Frequency Relation from a Known Musical Note?

Okay, now we have seen that when an octave is completed; the frequency get doubled. So how to find the formula for the increment of the frequency in the octave (divide the increment in the each half step equally so that the ratio remains same for two consecutive notes). You can understand it better from following steps:

Since the frequency is doubled after one octave (after 12 notes or half steps or semitones), we have to find out the increment in such a way that the ratio of any two consecutive note’s frequency, remain same in all the octaves. It means we have to find out 12th root of the number 2, because the frequency is doubled just after 12 notes, Understand this in the way:

[12th root of 2] if, multiplied 12 times to self = results in 2 (it means ((2^^{(1 ÷ 12)})^^{12}) = 2)

12th root of 2 = 1.05946309436 (Lets say its 1.059463)

It means 1.059463 multiplied to self 12 times = 2 ((1.059463^^{12})=2)

Hence any note’s frequency from a known note frequency will be: *f(n) = f(0) * (a) ^{n}*

Where f(0) = Frequency of any known note o

f(n) = Required and unknown frequency of any note which is n half steps away from f(o)

n = number of half steps between f(n) and f(0) (it may be in minus too if f(n)<f(0))

a= 12th root of 2 or 1.059463 (this is the approximate ratio of two consecutive notes anywhere in music)

## Example of finding out Frequency of any Musical Note from Above Formula

#### Example I (frequency of any note above a known frequency note)

Lets say, we know the frequency of A4 note which is 440 Hz.

Consider that, we have to find out the frequency of D5 note.

So f(n) = f(D5)

f(0) = f(A4) = 440 Hz

n = number of half-steps between A4 and D5

So let us accend in the order : A4—A#4—B4—C5—C#5—D5. So there are total 5 Half Steps between D5 and A4.

hence n = +5 (because f(n)>f(o))

And a = constant = 1.059463

So lets put all the values together in the formula:

*f(n) = f(0) * (a) ^{n}*

f(D5) = 440 * (1.059463)^^{5}

f(D5) = 440 * 1.33483925974 = 587.329274287 OR 587.329 Hz approximately **ANSWER**

#### Example II (frequency of any note below a known frequency note)

Lets say, we know the frequency of A4 note which is 440 Hz.

Consider that, we have to find out the frequency of D4 note.

So f(n) = f(D4)

f(0) = f(A4) = 440 Hz

n = number of half-steps between A4 and D4

So let us ascend in the order : D4—D#4—E4—F4—F#4—G4—G#4—A4. So there are total 7 Half Steps between D4 and A4.

hence n = -7 (because f(n)<f(o))

And a = constant = 1.059463

So lets put all the values together in the formula:

*f(n) = f(0) * (a) ^{n}*

f(D4) = 440 * (1.059463)^^{-7}

f(D4) = 440 * 0.66742034318 = 293.664951001 OR 293.665 Hz approximately **ANSWER**

So you can find out any notes frequency from the above given formula, provided that you have a reference note frequency.

Please write in comments if you have any further query. You can also purchase top home recording gadgets from THIS PAGE for building your studio! If you want to learn music theory in deep you can also purchase the following books which are available on amazon.