Daughter love in lunch box

   Today, in wechat, my friend sent me an interesting video . This video demonstrates a fresh and elegant plucking music ： Daughter love From the nine rubber bands on the lunch box , People can't help feeling ： Flying flowers and picking leaves can hurt people , Grass, wood, bamboo and stone are all swords , I will not deceive you .

▲ chart 1 Music played with lunch boxes

   As a pentatonic, you enjoy music while , Not just ask ： Although the tune is good , But is the tone of this lunch box plucking instrument accurate ？

   Of course, answer this question , With the help of a little knowledge of signal processing .

   utilize How to go from MP4 Extract from video files MP3 Audio ？ The method introduced is to download from wechat MP4 Extract the corresponding audio from the video . Because the volume in the original video is relatively small , Use Audacity The software has preliminarily processed the audio , Increased audio data volume .

Time waveform

   The following is the music time waveform in the video , Obviously, this just tells us the general trend of sound over time , But if you want to answer the quality of lunch box instruments （ tone 、 timbre ） problem , There is no direct answer .

▲ chart 2 Waveform of music data

Spectrum waveform

   The tone of the instrument is reflected in the spectrum of the data . The following is the time-varying waveform of the spectrum of music data obtained by short-sighted Fourier transform .

short-term FFT Parameters ：

frequency range ：10~2000Hz
Length of time ：100ms

▲ chart 2.1 How the audio spectrum changes over time

   From the change of spectrum, we can see the fundamental frequency corresponding to syllables in music and the Gaussian harmonics contained . In order to get the change of its fundamental frequency as the music progresses , Use scipy.signal.spectrogram Draw the time-frequency joint distribution of music , As shown in the figure below .

   The abscissa in the figure below is the duration of the music , The ordinate corresponds to a period of time （100ms） The spectrum of . In order to highlight the small frequency component of audio , The spectral amplitude is saturated .

▲ chart 2.2 Time frequency joint distribution of music

   In the above figure, we can see the syllable distribution structure in the lunch box musical instrument . Rich high-frequency components add to the appeal of musical instruments .

   In order to evaluate whether the tone of the lunch box is accurate , You need to get the main fundamental frequency at every moment . Let's go through the following FFT Search for frequency peaks , The corresponding frequency peak parameters of each segment can be obtained （ Frequency value and amplitude value ）、

▲ chart 2.3 Frequency and amplitude corresponding to spectrum peak

   The blue curve above represents the fundamental frequency of the music at the corresponding time , The red curve indicates the fundamental frequency amplitude . From the change of fundamental frequency amplitude , This is in line with the law of oscillation exponential attenuation of plucked instruments , Each fluctuation lasts only about 0.3 second , Fast attenuation is not very beneficial to the performance of melodious songs , So in playing , The method of continuous dialing is used to realize the continuity of sound .

   Now there's only one question left ： Is the frequency of each syllable accurate ？

   Histogram statistics of the amplitude of the frequency curve obtained above , You can see the syllable distribution in the whole performance process .

▲ chart 2.4 Histogram of peak spectrum

   In the diagram above , For all below 250Hz The frequency components of all belong to the frequency corresponding to the background noise . higher than 1000Hz The frequency component of should belong to the harmonic component of the fundamental frequency . Let's put the frequency at 350Hz ~ 1000Hz The classification of .

   according to “ Daughter love ” tune , The fundamental frequency distribution contained in the spectrum of music is marked . From low frequency to high frequency, it corresponds to the first string To The vibration fundamental frequency of the ninth string , The notes in the corresponding song are also given below .

▲ chart 2.5 Give the frequency component of the corresponding string according to the music melody

   It's amazing , In the strings that seem to be evenly spaced , There are two chromatic scales （7-1、3-4） The corresponding frequency component actually roughly conforms to the value of syllable . Why ？

   To determine whether the tuning of the strings is accurate , We also need to draw the syllable frequency at the same time . In the spectrum 3 The highest range , With its corresponding frequency f3=695.9Hz Benchmarking , according to The law of twelve averages Calculate the corresponding frequency of the other eight tones . As shown in the figure below .

   by force of contrast , You can see in the nine strings of the instrument , Bass 6 、7 The corresponding frequency deviation is relatively large , Other strings are actually very close to normal syllables .

▲ chart 2.7 Calculate the corresponding frequency of all strings according to the twelve average law

   So far, we have analyzed the frequency of each syllable in the above lunch box music , We can see that the frequency of the string in an octave range roughly conforms to the distribution of the twelve mean law , This is the basis of elegant melody performance .

   Seemingly evenly distributed strings , The structure of the two chromatic scales is roughly accurate , This is surprising . You can't see it structurally （7、4） What's special about the two strings .

▲ chart 2.6 The syllable frequency corresponding to each string of the lunch box

   The reason why lunch box music moved us , It's not its accurate intonation and rich timbre , But the soul with rich emotions behind the fingers that pluck the strings , This emotion is accompanied by “ Mohe dance hall ” Your music can jump out of the past and this life forever .

---

■ Links to related literature :

• How to go from MP4 Extract from video files MP3 Audio ？
• The law of twelve averages

● Related chart Links :

• chart 1 Music played with lunch boxes
• chart 2 Waveform of music data
• chart 2.1 How the audio spectrum changes over time
• chart 2.2 Time frequency joint distribution of music
• chart 2.3 Frequency and amplitude corresponding to spectrum peak
• chart 2.4 Histogram of peak spectrum
• chart 2.5 Give the frequency component of the corresponding string according to the music melody
• chart 2.7 Calculate the corresponding frequency of all strings according to the twelve average law
• chart 2.6 The syllable frequency corresponding to each string of the lunch box