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How to find Frequency of Any Music note (Formula + Examples)

how to find frequency of music notes

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 in a certain octave 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)

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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 : A4A#4B4C5C#5D5. 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 : D4D#4E4F4F#4G4G#4A4. 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.

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Music Theory: From Beginner to Expert; The Ultimate Step-by-Step Guide to Understanding and Learning Music Theory Effortlessly (Paperback)

Unique, Simple and Straightforward Way to Learn Music Theory and Become a Better Musician, Even if You’re a Total Beginner!
* Updated and massively Expanded edition with Audio examples, new Exercises, and over 150 pages of NEW content! *** On a special promo price for a limited time! **Have you ever wanted:

  • To know how understanding music theory can make you a better player (on any instrument)?
  • To unlock the mysteries of notes, intervals, music scales, modes, keys, circle of fifths, chords and chord progressions, and other important concepts in music, and how they all relate to one another?
  • To get a deep understanding of scales, modes and chords, where they come from, what are the different types that exist, how they’re built, and how to use any chord or scale in your playing?
  • To learn how rhythm works and how to master your rhythm and time skills that will make you sound like a pro?
  • To know what’s the magic behind all the beautiful music that you love and how you can (re)create it?
  • To get a broad perspective of tonal harmony, and how melody, harmony, and rhythm work together?
  • Understand advanced concepts (such as modal playing, atonality, polytonality, free music, etc.) that usually only advanced jazz musicians use?

But…

  • Have you ever been put off by music theory or thought that it wasn’t necessary, boring or too hard to learn?

If you find yourself in any of this, then this book is what you need. It covers pretty much everything that anyone who plays or wants to play music, and wishes to become a better musician, should know.
This is one of the most comprehensive and straightforward, evergreen books on music theory that you can find, and you will wish to study it often and keep it forever.
The book is structured in a way that is very easy to follow and internalize all the concepts that are explained. You don’t have to be a college degree music student in order to understand and use any of this – anyone can do it, even a total beginner! It also doesn’t matter what instrument(s) you play nor what is your level of knowledge or playing ability, because music theory is universal and all about what sounds good together! It explains the WHY and HOW, and it is your roadmap, a skill and a tool – guided by your ears – for creating beautiful music
This book will give you what is necessary to become a true expert in music theory without frustration and feeling overwhelmed in the process, and this in-turn will have immense benefits to your playing and musicianship!
Just use the look inside feature by clicking on the book cover to get a sneak peak of what you’ll learn inside…
Get this book now and solve all your problems with music theory, and become proficient in this field!
Pick up your copy by clicking on the BUY now button at the top of this page.


Features:  Createspace Independent Publishing Platform
By (author):  Nicolas Carter

List Price: INR 831.00
New From: INR 831.00 INR In Stock
Used from: Out of Stock
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Theory of Music Workbook Grade 2 (2007) (Trinity Guildhall Theory of Music) (Sheet music)

This theory workbook contains worked examples and sample exercises for Trinity College London Theory Grade 2 examinations from 2007. This is suitable for use in lessons or at home, for private study.

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