Fast Fourier Transform for Guitar Tuner Synchronization

The guitar is a musical instrument that has strings where the strings have a tone with a certain frequency. Tuning is the process of changing the frequency of a musical instrument to create the desired song arrangement. The tuning process can be confusing for new guitarists, especially since there are many different ways to tune a guitar. Every time a string on the guitar is plucked, this tuner can output tone parameters. However, the cost of tuners on the market is generally rather high. Using mobile applications can make it simpler for beginners to use and receive it for free. The Fast Fourier Transform (FFT) method is used in the working concept to convert the input time domain signal to a frequency domain.

Hasan and Islam [1] developed an acoustic guitar tuner and graphical user interface (GUI) using MATLAB as part of prior research on the guitar tuning procedure in this fundamental frequency research obtained through the Fast Fourier Transform (FFT) method. Venkataramanan et al. [2] designed a Sasando tuner application that has a high level of accuracy in detecting the fundamental frequency of the 32-string Sasando type using the Fast Fourier Algorithm Transform (FFT) and Harmonic Product Spectrum (HPS). Zhuo [3] presents the state-of-the-art for stringed instrument tuning tools, examines the issues, and suggests an automatic tuning system based on wireless sensor networks using those tools for widely used stringed instruments. Tampubolon and Nasution [4] designed an automatic guitar tuner using an 8-bit microcontroller. In this research, they developed an automatic tuner that uses an Arduino Uno to process audio signals. Processing the data from the ADC of the Arduino Uno to measure the time it takes to complete one full wave is how the frequency reading is calculated. To ensure the frequency is accurate, the frequency of the nearest string is calculated after the frequency value is obtained. The stepper motor will rotate in several steps if it is found that the frequency is off. According to the research, this tool works better when the frequency read is greater than the reference frequency, but it can tune successfully when the frequency is lower than the reference frequency.

Šarga and Demečko [5] made a guitar tuner based on MyRIO, which works in the LabVIEW environment. Thakuria et al. [6] developed a musical instrument tuner using audio signal processing techniques to determine if a musical note is flat or sharp. It emphasizes the importance of identifying the fundamental frequencies of musical audio signals for tuning. Melo et al. [7] explore the use of a NAO robot to aid children in learning acoustic guitar by implementing a guitar tuner and song performance evaluation system. Key aspects include optimizing note detection through analysis of window length and employing Goertzel's algorithm for real-time pitch detection. The system also evaluates song performance with a metronome and was tested successfully, even in noisy environments, although challenges were noted with detecting notes around 680 Hz. Pradana et al. [8] created an automatic guitar tuner based on the open-tuning approach.

Branta et al. [9] made musical instrument tuning with the Yin Algorithm using a microphone, piezoelectric transducer, and line input. Although the cost is low, it turns out that the precision of the tools produced is quite high at 1%. Stange et al. [10] successfully constructed a tuning procedure by implementing a dynamic adaptive scheme. This procedure is realized through a program called Just Intonation. Kumar et al. [11] made guitar tuning using MATLAB where to improve accuracy; before entering the FFT process, the signal is first filtered using the Finite Impulse Response (FIR) technique. introduces an automatic tuning system designed for multi-string musical instruments, focusing on the Thai hammered dulcimer. The system features a one-to-many micro actuating mechanism that uses a single motor to independently and simultaneously adjust the tension of multiple strings to achieve a target frequency. It employs pickup sensors to monitor string vibrations and the Goertzel algorithm for frequency detection, alongside a tuning time predictor to optimize the process. The goal is to simplify the tuning process for both beginners and professionals, which traditionally requires significant expertise and time [12].

Even though there are currently many guitars tuning applications on Android, in the tuning process, the user has to turn the string knobs manually. The main objective of the research conducted by Kumar was to identify the key characteristics that must be considered when designing guitar tuners. This research used a note played, and the program determines if the pitch needs to go up, down, or is correct. The FFT expertise, windowing, filters, identification of pitches and their relationship to basic frequency, MATLAB, and Simulink were all used in the algorithm. Their design could only be adjusted to a restricted number of notes, only six (E2, A2, D3, G3, B3, E4) [11]. Besides that, Becchi [23] created an automated technique for tuning acoustic-electric guitars in 2017. It processed input data using a 32-bit ARM processor on the Arduino Due platform, which it utilized to operate motors to fine-tune the instrument. However, from the result, it could not obtain precise readings and modifications because of the board's restrictions when doing FFT computations. Becchi stated that 0.5 Hz was the maximum acceptable error value for the apparatus. Despite this, the obtained value was above the ideal, at about 4Hz.

This research explores previous studies on frequency analysis methods. As in Shin et al. [24] which focuses on the comparison of Multiple-Measurement Sparse Bayesian Learning (SBL) with Fast Fourier Transform (FFT) for frequency analysis, especially in passive solar systems. This research uses SBL to exploit multiple measurements in the space and time domains, improving frequency detection by utilizing sparse estimation techniques. This approach is compared to the FFT, which is traditionally used for frequency analysis but often suffers from noise and low resolution due to its reliance on a limited signal length. Findings show that SBL significantly improves frequency detection by providing higher resolution and reduced noise compared to FFT. However from the findings, the computation of FFT is more efficient than SBL, this efficiency is due to its ability to compute the Discrete Fourier Transform (DFT) in \(O(N \log N)\) time, which is significantly faster than the computational complexity involved in SBL. Research Hamdan et al also about frequency spectrum and time-frequency analysis for the need or objective tools to evaluate the acoustic properties of violins, which is crucial for parents, novices, and instructors in selecting quality instruments. The research employs time-frequency analysis (TFA) using two main tools: PicoScope oscilloscopes for Fourier spectra and Adobe Audition for spectrogram analysis. These methods were used to analyze the fundamental frequencies and harmonic overtones of the G, D, A, and E strings from four violins manufactured by Eurostring, Stentor, and Suzuki. The research results indicate significant variations in harmonic patterns and overtone intensities among the violins analyzed. In this research, the Fast Fourier Transform (FFT) is used to extract spectral features from the musical signals of violins. FFT is a popular frequency analysis technique, particularly for non-stationary signals where statistical properties vary with time. It helps in identifying the fundamental and overtone frequencies, which are crucial for distinguishing the unique sound characteristics of each instrument. While Time-frequency analysis (TFA) refers to a method that describes the sound in the time-frequency plane. It allows for the identification of dominant frequencies at specific times, offering a detailed view of how frequency content evolves. TFA is particularly useful for analyzing complex tones where individual harmonics are difficult to distinguish by ear [25].

So, from the previous research on frequency analysis, the FFT algorithm was chosen because FFT provides a comprehensive frequency spectrum of the entire signal, which is useful for identifying the fundamental frequencies and harmonics present in the sound. This is particularly beneficial for stationary signals where the frequency content does not change significantly over time. Besides that, FFT can process signal transformations from the time domain to the frequency domain, this algorithm can be used to perform fast and efficient sound transformations. FFT was chosen because the process of changing the signal into frequency involves a decimation process, namely decimation in time (DIT) and decimation in frequency (DIF).

Based on the existing problems, a tool is made that can carry out the tuning process automatically (the string knob rotates according to the desired tone), and the results are fast and accurate according to standard guitar string tone frequencies. Various problems encountered in this tuning process are presented visually through a fishbone diagram in Figure 1.

This research was carried out in the following stages:

(1) Observation: by exploring similar guitar tuner applications.

(2) Interviews with target users, namely beginners who will learn guitar instruments. Interviews are important because they are a source of information by the author in making interface design and guitar learning material suitable for beginner levels.

(3) System analysis and design, namely designing the interface of the application and designing the database structure in the application. Analysis of the sound inputted by the user will be converted into frequency waves (Hz) using the Fast Fourier Transform algorithm.

(4) Implementation of the system, namely testing the installation of applications on Android-based mobile devices.

(5) Test and evaluation, namely testing the application evaluating the errors in the application, and making improvements so that the application can be more effective.

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Figure 2. Use case diagram of the learn guitar chords application for tuning

After the interview, to better understand the design and workflow of the system, a use case diagram was created as shown in Figure 2.

In Figure 2, it is explained that one user actor can choose the metronome, tuner, chord library, mini-game, or custom pitch & beat menu. Users can choose the tuner menu to adjust the pitch of each string on the guitar; in this menu, the user will pluck the guitar strings alternately and adjust the pitch. In the metronome menu, users can practice guitar playing on beat by setting the beat per minute (bpm) and beat as desired. The system will display the existing chord dictionary and the chord's sound in the chord library menu. In the mini-game menu, users can choose to practice chord diagrams and chord sounds or practice with a guitar by sounding certain chords. In the pitch & beat custom menu, the user will select a song from the device, and then the user can also set the song beat and the pitch used in the song.

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Figure 3. Tuner flowchart

In Figure 3, the user will provide input in the form of sound by strumming a guitar string, after which the system will perform windowing to reduce spectral leakage that can arise due to low sample rate (Fs). After that, FFT is carried out, which aims to convert the signal from the time domain into the frequency domain; the number series in the time domain f(x) is converted into the frequency domain f(u), after that if it is detected, the system will display the results of matching the standard guitar tuning frequency if the system will not reprocess. Here is the formula for window hamming:

$w(n)=0,54+0,46 \cdot \cos +\frac{n \pi}{M},-M \leq n \leq M$

The FFT algorithm will be used to convert the signal from the time domain to the frequency domain following windowing. The length of the symmetrical spectrum produced by the FFT technique is equal to the value of the sampling frequency. After passing the calculation process with equation FFT has been successfully calculated, the frequency value that corresponds to the target is obtained. For instance, to identify tone A, it will determine whether or not the detected frequency corresponds to 110Hz. The presence of the detected frequency in comparison to the target tone's range yields the match. The following equation yields the range for any tone:

$x=f_{n-1}+\left(\frac{f n-f n-1}{2}\right)$

$y=f_n+\left(\frac{f n+1-f n}{2}\right)$

with:

f_n=target tone frequency (A)

f_n-1=frequency of the note before the target (e.g., 82)

f_n+1=the frequency of the tone after the target tone (e.g., 146)

x=upper limit

y=lower limit

With a target tone frequency of 110 and using the matching formula, we obtained:

$x=82+\left(\frac{110-82}{2}\right)=96$

$y=110+\left(\frac{146-110}{2}\right)=128$

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Figure 4. The frequency range that represents tone A

So, if we are going to measure tone A, then the range is depicted in Figure 4. The following is the Fast Fourier Transform equation:

$f \cdot(u)=\sum_{x=0}^{x=N-1} f(x)\left(\cos \frac{2 \pi u x}{N}+j \sin \frac{2 \pi u x}{N}\right)$

When open the application, the first page that appears is the tuner menu, where the user can see the tone matches on the guitar strings that are plucked, and the user can choose the sequence of string numbers to match the tone. At the top is a picture showing the tone match indicator in the tuning process; at the bottom is a picture of a guitar with the tone of each string with standard rules. In this menu, the user can provide sound input by hacking guitar strings; then, the system will process the sound signal and provide the user with a frequency-matching result.

The design interface must also be considered so that users can understand better and not get bored easily. This sub-chapter will provide an overview of the interface design in the application. When opening the application, the first page that appears is the tuner menu, as in Figure 5, where the user can see the tone match on a plucked guitar string, and the user can choose the sequence of string numbers to match the tone. At the top is a picture showing the tone match indicator in the tuning process; at the bottom is a picture of a guitar with the tone of each string with standard rules. In this menu, the user can provide sound. input by hacking guitar strings, the system will process the sound signal and give it to the user a frequency-matching result.

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Figure 5. Main display (tuner menu)