Click here to Skip to main content
Click here to Skip to main content

FFT Guitar Tuner

, 10 Aug 2010 MIT
Rate this:
Please Sign up or sign in to vote.
Using a Fast Fourier Transform to calculate the fundamental frequency of the captured audio sound

Introduction

This article shows how to use a Fast Fourier Transform (FFT) algorithm to calculate the fundamental frequency of a captured audio sound. Also, we will see how to apply the algorithm to analyze live sound to build a simple guitar tuner: the code provides a solution to the problem of calculation of the fundamental frequency of the played pitch.

Background

The computer can capture live sound/music using a microphone that is connected to the sound card. Modern sound cards can capture digital signals. A digital signal is a set of quantized sound values that were taken in uniformly spaced times. The digital signal does not provide any information about frequencies that are present in the sound. To determine that, the data need to be analyzed.

The Short-Time Fourier Transform (STFT) makes representation of the phase and magnitude of the signal. The result of the STFT can be used to produce the spectrogram of the signal: the magnitude squared over time and frequencies. We will use a Fast Fourier Transform (FFT) to generate the spectrogram of the signal of short periods of time. After the spectrogram is calculated, the fundamental frequency can be determined by finding the index of the maximum value of the magnitude squared. The improved algorithm finds several such places, candidate frequency bins, with the magnitude squared in the top of the maximum values, and further analyzes them to verify the candidate fundamental frequencies by using the signal data.

When a note is played on a musical instrument, the sound waves are generated by strings, air, or the speaker - an instrument generates a musical note. One of the characteristics of a musical note is a pitch (fundamental frequency). Traditionally musical alphabet frequencies are divided by octaves, and then by semitones. An octave has 12 named pitches: C (prime), C#, D, D#, E, F, F#, G, G#, A, A#, and B. Octaves also have names: great, small, one-lined, two-lined, etc. The "standard pitch" (A one-lined or A4) has a fundamental frequency of its sound waves equals to 440 Hz. The frequencies of two neighboring notes are different by 21/12, and frequencies of the notes with the same name in two neighboring octaves are different by 2.

Table: Notes and Their Fundamental Frequencies
Note Name Traditional Octave Names (Scientific), Hz
Great (2) Small (3) One-lined (4) Two-lined (5)
C 65.4064 130.8128 261.6256 523.2511
C# 69.2957 138.5913 277.1826 554.3653
D 73.4162 146.8324 293.6648 587.3295
D# 77.7817 155.5635 311.1270 622.2540
E 82.4069 164.8138 329.6276 659.2551
F 87.3071 174.6141 349.2282 698.4565
F# 92.4986 184.9972 369.9944 739.9888
G 97.9989 195.9977 391.9954 783.9909
G# 103.8262 207.6523 415.3047 830.6094
A 110.0000 220.0000 440.0000 880.0000
A# 116.5409 233.0819 466.1638 932.3275
B 123.4708 246.9417 493.8833 987.7666

The typical (six string) guitar normally plays pitches of great through two-lined octaves. The pitches of the open strings (E2, A2, D3, G3, B3, and E4) are selected in the table in bold.

Using the Code

The solution contains three projects: the main windows application (FftGuitarTuner), the sound analysis library (SoundAnalysis), and the sound capture library (SoundCapture). The heart of the solution and the SoundAnalysis project is the FFT algorithm (see the Calculate method of the SoundAnalysis.FftAlgorithm class):

// bit reversal
ComplexNumber[] data = new ComplexNumber[length];
for (int i = 0; i < x.Length; i++)
{
    int j = ReverseBits(i, bitsInLength);
    data[j] = new ComplexNumber(x[i]);
}

// Cooley-Tukey 
for (int i = 0; i < bitsInLength; i++)
{
    int m = 1 << i;
    int n = m * 2;
    double alpha = -(2 * Math.PI / n);

    for (int k = 0; k < m; k++)
    {
        // e^(-2*pi/N*k)
        ComplexNumber oddPartMultiplier = 
           new ComplexNumber(0, alpha * k).PoweredE();

        for (int j = k; j < length; j += n)
        {
            ComplexNumber evenPart = data[j];
            ComplexNumber oddPart = oddPartMultiplier * data[j + m];
            data[j] = evenPart + oddPart;
            data[j + m] = evenPart - oddPart;
        }
    }
}

// calculate spectrogram
double[] spectrogram = new double[length];
for (int i = 0; i < spectrogram.Length; i++)
{
    spectrogram[i] = data[i].AbsPower2();
}

The data for the algorithm is provided from the sound card capture buffer. The abstract SoundCapture.SoundCaptureBase utility class is an adapter for DirectSound's Capture and CaptureBuffer classes, that helps to encapsulate buffering and setting up the audio format parameters. The application requires Microsoft DirectX 9 runtime components for the live sound capture from the microphone.

Main Application Form

Figure: Main Application Form

After the application is started, select the sound device and play a note. The application will capture the live sound and will calculate the current fundamental frequency of the signal. The information can be used to tune the guitar.

Points of Interest

To calculate the Fast Fourier Transform, the Cooley-Tukey algorithm was used. It gives good performance for the required task. To challenge the algorithm, the application analyses about 22,000 sample blocks in real time: the sound is captured at a 44,100 Hz rate and a 16 bits sample size, and the analysis is performed twice a second.

The sound analysis library can be used for tone, background noise, sound, or speech detection. Series of the spectrogram of the continued sound can be displayed as a 2D (or 3D) image to present it visually.

References

  1. "Musical Note", Wikipedia
  2. "Short-Time Fourier Transform", Wikipedia
  3. "Fast Fourier Transform", Wikipedia
  4. "Cooley-Tukey FFT Algorithm", Wikipedia

History

  • 1st January, 2009: Initial version
  • 2nd January, 2009: Added algorithm code snippet
  • 3rd August, 2010: Corrected article typos; new frequency detection algorithm

License

This article, along with any associated source code and files, is licensed under The MIT License

Share

About the Author

notmasteryet
Software Developer
United States United States
No Biography provided
Follow on   Twitter

Comments and Discussions

 
QuestionHow to get the sound of line 2? PinmemberTheJediMaster27-Jul-11 6:36 
GeneralGuitar Tuner (macro and micro tuning) - The Dark Side of the Force. (please test) PinmemberTheJediMaster16-Jul-11 11:10 
GeneralRe: Guitar Tuner (macro and micro tuning) - The Dark Side of the Force. (please test) Pinmemberfullcharged247-Feb-12 18:58 
Questionjust one more thing PinmemberTheJediMaster14-Jul-11 15:12 
AnswerRe: just one more thing Pinmembernotmasteryet14-Jul-11 15:57 
GeneralRe: just one more thing PinmemberTheJediMaster14-Jul-11 16:24 
QuestionIs there any advantage if I increase or decrease the value of BufferSeconds? PinmemberTheJediMaster12-Jul-11 13:40 
AnswerRe: Is there any advantage if I increase or decrease the value of BufferSeconds? Pinmembernotmasteryet12-Jul-11 15:58 
It depends on your hardware: smaller buffer gives less latency but more CPU usage.
 
I recommend to experiment with NotifyPointsInSecond, increasing this amount will give you smaller amount of data that need to processed by the FFT.
GeneralRe: Is there any advantage if I increase or decrease the value of BufferSeconds? PinmemberTheJediMaster13-Jul-11 12:17 
QuestionWhat about win7 Pinmemberamersaw10-Jul-11 15:42 
AnswerRe: What about win7 PinmemberTheJediMaster11-Jul-11 11:44 
AnswerRe: What about win7 Pinmemberbmac20-Jul-13 7:02 
SuggestionHere is how to display the name of the note and octave for the note. PinmemberTheJediMaster8-Jul-11 4:43 
Question"frequencyTextBox" update PinmemberTheJediMaster8-Jul-11 2:09 
AnswerRe: "frequencyTextBox" update PinmemberTheJediMaster12-Jul-11 13:42 
GeneralRe: "frequencyTextBox" update Pinmembernotmasteryet12-Jul-11 16:00 
QuestionI made some changes: Voice tuner PinmemberTheJediMaster7-Jul-11 9:17 
QuestionFundamental frequency algoritm PinmemberKvanttt1-Jul-11 9:46 
BugI'm having problems using the VB .Net version, running on Windows 7 64-bit PinmemberTheJediMaster30-Jun-11 15:24 
GeneralRe: I'm having problems using the VB .Net version, running on Windows 7 64-bit Pinmembernotmasteryet30-Jun-11 15:26 
GeneralRe: I'm having problems using the VB .Net version, running on Windows 7 64-bit PinmemberTheJediMaster5-Jul-11 12:23 
GeneralRe: I'm having problems using the VB .Net version, running on Windows 7 64-bit PinmemberMember 826810726-Sep-11 11:41 
GeneralRe: I'm having problems using the VB .Net version, running on Windows 7 64-bit PinmemberMember 766644016-Dec-11 7:26 
GeneralRe: I'm having problems using the VB .Net version, running on Windows 7 64-bit Pinmemberbmac20-Jul-13 7:05 
QuestionIs it easy to convert to VB. Net? PinmemberTheJediMaster30-Jun-11 6:23 

General General    News News    Suggestion Suggestion    Question Question    Bug Bug    Answer Answer    Joke Joke    Rant Rant    Admin Admin   

Use Ctrl+Left/Right to switch messages, Ctrl+Up/Down to switch threads, Ctrl+Shift+Left/Right to switch pages.

| Advertise | Privacy | Terms of Use | Mobile
Web02 | 2.8.141223.1 | Last Updated 10 Aug 2010
Article Copyright 2009 by notmasteryet
Everything else Copyright © CodeProject, 1999-2014
Layout: fixed | fluid