This report is a summary and revision of my thesis at the Cremona International Violin making School. In this paper, academic content and difficult parts, comparative analysis content with Taptone, and content/source related to analysis program development were omitted as much as possible and reorganized to make it easier for beginners to understand. The original title of the thesis is 「Nuovo Metodo di Analisi per Capire le Caratteristiche del Violino (A
New Analytical Method to Understand Violin Characteristics)」.
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Accurately knowing the acoustic characteristics of a violin will be a necessary condition in order to produce a violin with a desired sound. There are many ways to understand the acoustic characteristics of a violin, but currently, the only way to know the unique characteristics of the violin body, excluding strings and accessories, is tap-tone analysis. However, the tap-tone analysis method has a limitation in that it is impossible to know what kind of sound the instrument will make when strings are actually attached.
In this study, a method for calculating the characteristics of the violin body by subtracting the inherent acoustic characteristics of the strings from the acoustic characteristics of a violin equipped with strings is proposed and the method is explained. The vibrations produced by the strings are amplified as they pass through the violin body. Some frequency bands may be amplified and others may be attenuated. This will be different for each violin, and that is the unique characteristic of that violin. Here, the characteristic refers to the frequency characteristic (spectrum) by FFT analysis, and if there is even a slight difference between the two fundamental frequencies during recording, the subtraction result will bring about completely unexpected results. Therefore, in this study, we try to subtract the spectral envelopes instead of the spectrums.
The LPC spectral envelope is used for calculation (hereinafter LPC S.E.). For 4 open strings, check the body characteristics of the experimental violin by subtracting the unique LPC S.E. from the LPC S.E. of the finished violin. The result is defined as 「HIS Characteristic」 or 「HIS Graph」 in this paper, and five elements appearing in 「HIS characteristic」 will be defined. This spectral envelope subtraction method can be used in any case where you want to compare two sounds.
1. Concept and Theory
1.1. Definition of Terms
⃝ The Violin Sound
In this paper, 「Violin sound」 refers to the sound produced when playing a violin with strings attached and tuning completed.
⃝ The String Sound
In this paper, 「String sound」 refers to the sound produced when strings are played while the strings are mounted on a structure such as Figure 4. Therefore, this is the sound of the string itself, which has nothing to do with the sound of the violin, and it means the sound produced by directly vibrating the air.
⃝ HIS Characteristic
The result obtained through the subtraction operation between two different spectral envelopes can be called 「Spectral envelope subtraction characteristics」 or 「Spectral envelope subtraction graph」. Therefore, it can be said that the result obtained by subtracting the spectral envelope of the string from the spectral envelope of the violin sound is 「the spectral envelope subtraction characteristic of the violin body」. In this paper, we will simply
call this 「HIS Characteristic」 or 「HIS graph」. In other words, 「HIS characteristic」 means the characteristics of a violin body as a result obtained by subtracting the spectral envelope of a string from the spectral envelope of a violin sound. However, in this case, the *order used at this time should also be specified along with what technique (LPC or Cepstrum...) was used when calculating the spectral envelope. In addition, both the violin sound and the string sound should be analyzed under the same conditions.
( * explained in next chapter )
This spectral envelope subtraction method can be used more widely because it can be used to find out the characteristics of other parts, such as measuring by changing the thickness of the bridge. Therefore, in that case, it should be specified together with which part to analyze. However, when speaking of 「HIS characteristic」 about violins, it is defined as referring to the characteristics of the violin body obtained by subtracting the spectral envelope of the string from the spectral envelope of the violin sound as above.
1.2. LPC Spectral Envelope
There are various methods to obtain the Spectral Envelope, but there are representative LPC and Cepstrum methods. In the case of Cepstrum, there are many parts that are difficult for beginners to understand, so the description is omitted and only the LPC Spectral Envelope used in this study will be described.
First, LPC (Linear predictive coding) means a linear predictive coefficient, and is a method of acoustically modeling the process by which a human voice is generated, that is, its resonance characteristics. Figure 1 describes the process of acoustically modeling the process by which the human voice is generated, and below is a step-by-step explanation.
1. Vibration of air is created by vibration of the vocal cords of the neck. This vibration of air is the basic sound of the voice, and the loudness and frequency of this vibration determine the volume and pitch of the voice. As the generated basic sound passes through the pharynx, oral cavity, and nasal cavity, the tone is changed by their respective resonance characteristics, and the final voice is emitted through the mouth. Because the vibration characteristics of the vocal cords are different for each person, the volume and pitch of the voice are different for each person. Also, by *changing the shape of the oral cavity and nasal cavity when speaking, the tone changes temporally, that is, it becomes ‘speech’.
( * control of tongue and mouth opening, etc. )
2. Step 1 is schematically illustrated.
3. The vocal cords in step 2 correspond to sound source signals, and the pharynx, oral cavity, and nasal cavity can be thought of as acoustic tubes. This acoustic tube is a tube that reproduces the resonance characteristics of the pharynx and the oral cavity and nasal cavity above. The sound source signal enters the sound tube and its characteristics are changed by the sound tube, and the final sound is emitted.
4. The sound source signal of step 3 is filtered and output by the frequency characteristic (spectral envelope) of the acoustic tube.
5. In digital signal processing, when the characteristics of the sound source signal in step 4 are E(z), the filter characteristics are H(z), and the output signal characteristics are X(z), multiplying E(z) by H(z) gives X(z).
Figure 1 : Speech generation process and acoustic model
Therefore, it can be concluded that LPC is to find the filter characteristic H(z), and the mathematical result is as follows.
This H(z) is the transfer function (characteristic of the filter) indicating the characteristics of the acoustic tube above. Also, a_p corresponds to α_i and is called a linear predictive coefficient. The above expression (1) can be rearranged as follows.
By finding the values of a_1, a_2, · · · , a_p, it is possible to know the transfer function H(z), which is the characteristic (filter characteristic) of the violin body. and it means the spectral envelope of the violin body. This series of processes is called linear predictive analysis, and the resolution of the spectral envelope changes depending on how many orders of a_p, in other words, how much of the value (order) of p.
Figure 2 shows how the spectral envelope changes according to the order of a_p as an LPC analysis of the ‘Mi’ open string sound of the experimental violin*. That is, the degree of 16 means that 16 a were used in the analysis, such as a_1, a_2, · · · , a_16. The higher the value of p, the more backwards the signal is calculated.
( * ’Hwang Ilseok, 2011’ )
Figure 2: LPC Spectral Envelope
1.3. Spectral Envelope Subtraction Method
When noise is recorded together in a recording process, there are cases in which spectums are subtracted in order to remove the noise. It is called spectral subtraction and is used in some signal processing fields besides noise removal. However, we have not yet found an example of subtracting spectral envelopes.
Here, we will learn how to subtract between Spectral Envelopes. This operation is a very simple operation, and it is enough to subtract data of the same order. Therefore, the two signals to be operated must have the same number of data.
When there are two spectral envelopes H(k) and E(k) with k data, H(k) and E(k) are expressed as follows.
The subtraction of these two spectral envelopes can be defined as follows.
Therefore, the result of subtraction X(k) is :
Figure 3 shows the result of subtracting Envelope B from Envelope A. As can be seen from the above equation, the operation subtracts data of the same order. That is, subtract 8.8 of 1 [kHz] value of B from 12.0 of 1 [kHz] value of A.
Figure 3 : Two envelopes and their subtraction result
2. Recording and Programming
2.1. Recording Environment
In principle, recording in an anechoic room was used to exclude the effect of reflected sound, but due to practical difficulties, it had to be carried out in a general room. Therefore, resonance sound in the room may have been included, and this should be considered in advance.
During the recording process, I performed by hand for practical reasons. For the sake of accuracy, the error was tuned to be within ±1.5[Hz], and after recording several times, the one with flat sound, smooth temporal waveform and the least noise was selected.
⃝ Violin for Sound Measurement
The instrument used for the recording was made by me in the past, and the strings used were Evah Pirazzi. In the case of strings, it would be better to use a new product as much as possible, but since this study is not a study on the sound of the strings themselves, any string does not matter. You just have to follow the principle of using the same string in all experiments.
⃝ Structure for measuring string sound
When measuring the sound of the string itself, a measuring structure was manufactured and used ( - Figure 4 - ). The main shape and size of the violin are reproduced as they are, and heavy and hard wood is used to prevent the vibration of the strings or to minimize the absorption of vibrations. The strings and tailpieces used at this time were used for the experimental violin, and this is to conduct the experiment in the same environment as possible.
Figure 4 : Measuring structure equipped with strings
Figure 5 : Size of structure for string sound measurement
In addition, the characteristics of the violin body obtained by subtracting the characteristics of the strings from the characteristics of the violin sound include the characteristics of the bridge used in the violin. This is because, when subtracting, the characteristics of the bridge are not subtracted because the characteristics of the string do not include the characteristics of the actual bridge.
⃝ Recording and Analysis Equipment
Table 1 below lists the equipment and environments used for recording and analysis.
Python was used as the language of the analysis program. In addition, Python-related extension packages such as Numpy, Scipy, Matplotlib and Seaborn were used, and Sound Forgy was used for editing and white noise production.
Table 1 : Recording and Analysis Equipment
2.2. Recording
⃝ Recording of Violin Sound
The microphone is directed toward the center of the bottom of the bridge of the violin and is installed at an angle of 45◦ to the top right when viewed from the front of the violin and 45◦ to the top right when viewed from the bottom. The straight-line distance from the center of the bridge feet is 30 cm.
The recorder settings are 44.1 [kHz], 16 [bit], Mono, and for violins, the band below about 150 [Hz] has no meaning, so LCF is cut-off at 150 [Hz].
Figure 6 : Position of microphone when recording violin sound
⃝ Recording of String Sound
The microphone is directed toward the center of the bottom of the bridge of the structure and is installed at an angle of 45◦ to the top right when viewed from the front of the structure and 45◦ to the top right when viewed from the bottom. The straight-line distance from the center of the bridge feet is 30 cm. The settings of the recorder are the same as those of the violin.
Figure 7: Position of microphone when recording string sound
2.3. Python Programming
The goal of this study is to make a program to obtain the LPC spectral envelope in Python, perform the subtraction operation, and obtain the HIS characteristic. However, since the program coding explanation is quite long and difficult for those who do not know programming, this report omits the content and only describes the result graph after program production is completed and the program option value. Also, the completed program can be downloaded from my website.
2.3.1. LPC Spectral envelope
Create two noises (Noise A and B) using the sound editing tool. First, we generate Noise A (corresponding to string sound) and amplify the 5 [kHz] band of Noise A by 15 [dB] / 0.5 [oct] and the 15 [kHz] band by 10 [dB] / 0.3 [oct]. And save it as Noise B (corresponding to the violin sound) ( - Figure 8 - ). Figure 9 is the result of checking the frequency characteristics of Noise A and Noise B produced by the above method in Sound Forgy. Looking at the time waveform at the top of the figure, it can be seen that the overall amplitude of Noise B is increased, and in the frequency characteristic graph at the bottom, the amplitude is increased around the 5 [kHz] band and the 15 [kHz] band.
Figure 8 : EQ settings
Figure 9 : Characteristics of Noise A and Noise B
After that, the developed program calculates the power spectrum of Noise A and B. Figure 10 is the power spectrum of Noise A and B analyzed with the developed program. Comparing with Figure 9 , it can be confirmed that the program developed this time is operating normally because the results analyzed by Sound Forgy and the results analyzed by the program are almost the same.
Figure 10 : Power spectrum of Noise A and B
Next, we specify the LPC order and obtain the LPC spectral envelope of the power spectrum obtained above. Figure 11 shows the LPC spectral envelope on the power spectrum of Noise A and B shown above. When only the power spectrum was checked in Figure 10, it was difficult to see the entire shape due to the complicated graph lines, but now it is possible to intuitively grasp the characteristics of the power spectrum.
Figure 11 : Logarithmic power spectrum of Noise A, B and LPC spectral envelope (log)
2.3.2. Subtraction of LPC Spectral envelope
Then we perform the LPC spectral envelope subtraction operation. The calculated LPC data is an array type, so if the size is the same, you only need to perform a subtraction operation. Since Noise B is an amplification of Noise A in some frequency bands, Noise A corresponds to a string sound and Noise B corresponds to a violin sound. Since the purpose is to obtain the characteristics of the violin body by subtracting the characteristics of the string sound from the characteristics of the violin sound, in this case, the characteristics of Noise A can be subtracted from the characteristics of Noise B. Figure 12 shows the LPC spectral envelope and their subtraction results. From the result, the amplification status of Noise B can be grasped at a glance.
Figure 12 : LPC spectral envelope and subtraction result
In the above, we learned how to obtain the LPC spectral envelope and how to calculate the subtraction in Python, and what results are actually produced using two noise samples. It can be seen that the results at this stage using the noise sample are quite satisfactory. Therefore, it is judged that it will be sufficiently applicable to the LPC spectral envelope of an actual instrument and its subtraction operation. However, the results change depending on the option value at the time of analysis, so this time, learn about the option value and then analyze the violin and strings.
2.3.3. The decision of acquisitions affecting results
Until now, the LPC order used in the subtraction operation after obtaining the LPC spectral envelope was ‘16’, the FFT size was ‘4,096’, and the analysis sample extracted from the sample file was ‘0.1 seconds’. Since these three factors affect the results, the most appropriate value should be selected during analysis. Here, we will examine how the result is changed by these three factors, and therefore, what value is appropriate.
⃝ LPC order
The LPC order means how many orders of a_p, that is, the value of p. The relationship between the LPC order and the result has already been checked once in Figure 2. However, I have not seen anything about what the result will be when deducting it. So, this time, let’s check the subtraction result together. However, as seen in the previous section, when the order p is greater than about ‘32’, the evnelope becomes sharper and becomes closer to the spectrum itself, so a lower order is suitable. Therefore, this time, we will observe the result while changing the order p around ‘16’. Here, we will analyze the real violin and string sound of 660[Hz].
Figure 13 is the result of changing the order p to 12, 16, 20. It can be seen that when p=20, the envelope becomes very sharp. In the case of p=12, a little lack of resolution is felt. As a result of the above results, p=16 is judged to be the most appropriate, so we will proceed with p=16 in all subsequent analyzes.
Figure 13 : Change of result according to order p
A larger FFT size means higher frequency *resolution, so a larger value is probably better. Let’s see if that’s actually the case.
( * frequency resolution = sampling frequency/FFT size )
Figure 14 is the result of changing the FFT size to 2048, 4096, 8192 (LPC order p is all ‘16’). Looking at the graph, contrary to the initial expectation, the LPC spectral envelope and its subtraction result do not change at all. However, there is a difference only in Spectrum. Spectrum shows a clear difference between 2014 and 4096, and only a slight change can be felt in 4096 and 8192. The larger the value of this FFT size, the greater the load during computer operation, which causes a decrease in speed. Therefore, if there is no qualitative difference, it would be better to set it to a minimum. However, since the resolution of the spectrum is determined by the FFT size, it is better to set it to the maximum in view of such a standard. If the FFT size is low, the frequency resolution is lowered, resulting in lower resolution. However, due to the interpolation of the graph, a sufficiently high resolution can be expected even if the frequency resolution is actually low. However, it should also be taken
into account that the resolution of the spectrum does not play a large role in this analysis. Combining the above, it can be seen that it is appropriate to compromise to the extent that there is no difference between the LPC spectral envelope and the subtraction result and there is no problem in the spectrum analysis. Therefore, in subsequent analysis, we intend to proceed with FFT size=4096.
Figure 14 : Results change according to FFT size (FS)
⃝ Data size
Finally, we look at the number of data to be used for analysis. This program extracts and analyzes the central part of the recorded file, and this data size determines how many seconds to extract. If this time becomes longer, that is, to extract and analyze more sections, it can be seen that the analysis is performed over a wider section. Conversely, as this time becomes shorter, it means that only more localized sections are analyzed. The reason that the spectrum changes depending on the analysis location of a certain sound file is because the sound recorded in the file is not constant. For example, in the case of a violin sound, depending on the intensity of turning on the violin, the pitch can be changed very minutely, and the vibration pattern of the instrument also changes little by little. Therefore, as the number of data increases, it would be better to know the overall contents, but in that case, a load will occur during calculation. So, let’s try to figure out what the best value is. Experiments are conducted for 0.02 sec, 0.10 sec, and 0.30 sec, and all are fixed at LPC order p=16 and FFT size=4096.
Figure 15 is the result of changing the data size to 0.02 sec, 0.1 sec, and 0.3 sec. Looking at the graph, it can be seen that the overall position of the LPC spectral envelope rises as the data size increases. The overall height of the envelope is not an important issue. Next, there is a difference in Spectrum. It is natural that this is different because, as described above, the sample sound does not have a completely constant sound.In this study, which targets sounds with no pitch change, 0.3 seconds is actually a very long time, but if you look at the spectrum, you can see that 0.1 seconds is the most actively analyzed for vibration. Next, there is no significant difference in the subtraction result. Here, only the above three cases are presented. However, further confirmation showed that the case of 0.04 ∼ 0.1 seconds is most suitable. Therefore, in this study, we will proceed with 0.1 second.
Figure 15 : Results change according to Data size(DS)
Appropriate values for three of the above LPC order, FFT size, and data size were investigated. Finally, all subsequent analyzes will proceed with LPC order p = 16, FFT size = 4096, Data size = 0.1[sec], and these option values are expected to be generally used in all cases of comparing two sounds expected.
3. LPC Spectral Envelope and HIS Characteristic
In this chapter, using the Python program created in the previous chapter, we will obtain the LPC spectral envelope of the violin and string sound, and check and analyze the HIS characteristic through the subtraction operation. New findings from the HIS characterization will be described separately. To ensure the visibility of the graph, blue lines were used for all string sounds, purple lines were used for violin sounds, and red lines were used for the HIS characteristic, which is the result of subtraction.
3.1. HIS characteristic of the Violin
Figure 16 ∼ 19 shows the power spectrum, LPC Spectral envelope and HIS characteristic of the violin sound and string sound for 4 strings. Analysis options were the same as in the previous chapter, LPC order p = 16, FFT size = 4096, Data size = 0.1 sec, Hanning window, 50% overlap.
Figure 16 : 4th string open ‘Sol’, 195.6[Hz], G2’
Figure 16 shows the result of 4th string open ‘Sol’. In the HIS characteristic, the amplification becomes more pronounced toward the low frequency with the boundary of about 14 [kHz], and almost no amplification occurs at the high frequency. The peculiar thing is that the attenuation is noticeable in the bands of about 2.7, 9 [kHz]. In particular, in the 9 [kHz] band, the violin sound is smaller than the string sound, and this phenomenon is also occurring in the 14and19[kHz] bands.
Figure 17 : 3rd string open ‘Re’, 293.3[Hz], D3’
Figure 17 shows the result of 3rd string open ‘Re’. The HIS characteristic of this string does not have much amplification in the middle band, and there is amplification at both ends. Interestingly, the attenuation of 2, 6 [kHz] is very large. And in the bands of 6, 15, and18 [kHz], the violin sound is smaller than the string sound as in the case of the previous 4th string open ‘Sol’. In other words, a 「reversal phenomenon」 is taking place.
Figure 18 : 2nd string open ‘La’, 440.0[Hz], A4’
Figure 18 shows the result of 2nd string open ‘La’. In this case, it shows a generally soft characteristic, but there is no significant change except for the low frequency band. However, this also shows a 「reversal phenomenon」 in three places.
Figure 19 : 1st string open ‘Mi’, 660.0[Hz], E4’
Figure 19 shows the result of 1st string open ‘Mi’. The HIS characteristic of this string are broadly amplified overall, and 「reversal phenomenon」 hardly occurs. However, almost no amplification occurs in the band of about 4[kHz], and the amplification is large in the band above 20 [kHz].
For the above four open strings, the characteristics of violin and string sound and HIS characteristic were investigated. In the HIS characteristics, very unusual things are found in common, which is that there is a 「reversal phenomenon」 in which the violin sound is rather small than the string sound. Or there are points where they are not amplified at all. In the next chapter, we will summarize these unusual phenomena.
3.2. Special Point and Special Zone
As we have seen above, there are unusual things to be found in the HIS characteristic of the violin. They can be classified into the following five types.
Amplification section
No change section
Attenuation section
Point of local amplification
Point of local attenuation
Why do these singularities and singular sections exist? It is probably the interference effect caused by the numerous vibrations of the violin interacting with each other. If so, is it absolute or relative? For example, in the 3rd string open ‘Re’, there is a severe attenuation around 2[kHz]. What would happen if you play the 2[kHz] note in the 3rd string open ‘Re’.If it were absolute, then there would be attenuation as well, and the sound would be very weak. However, if they are relative, this attenuation point will be shifted away and there will be no change in loudness. Current projections are of course relative and this damping point will shift. If so, maybe there are some rules for that movement. Knowing the answer will be very important in understanding the characteristics of the violin. Unfortunately, however, it is difficult to elucidate with the current research alone, and it can only be identified in future research.
Like 「HIS characteristic」, the above five types appearing in HIS characteristic are also the first concepts, so define them as Table 2 .
Table 2 : Five types of HIS characteristic in HIS graphs
These names of five types were determined to be the most easily understood terms from the meaning of the words themselves. A point to note about the above 5 types is that there may be a *dead spot in the live zone. Conversely, there may be a live spot in the dead zone as well. In the former case, if attenuation occurs locally at only a certain point in the overall amplification section, it should be regarded as a dead spot even though it is located in the live zone. The latter is the other way around. Therefore, the discrimination of Live/Suspended/Dead zone is based on the symbols +, 0, − of the value [dB] of the section. The discrimination of live/dead spot is not based on the value of the point [dB] but the comparison with the surroundings, that is, whether the shape of the line is pointed upward or downward.
( * The term 「dead spot」 appears occasionally in acoustics. For example, in underwater ballet, players operate while listening to music with an underwater speaker installed inside the swimming pool (under the water). However, when I go to a certain point (under the water), there is a place where the music is suddenly not heard, so there was a request to my school to fix it. This point is called a 「dead spot」 in acoustics. )
Among these 5 types, I personally want to pay attention to the dead zone and dead spot. Dead zone is a section whose value is ‘-’ as defined above. Therefore, it means that the spectral envelope of the violin sound is lower than the spectral envelope of the string sound in this section. In other words, it is a section in which a 「reversal」 occurs. However, the dead spot may or may not be reversed. On the graph, if the dead spot is located above 0[dB], it means that reversal has not occurred, and if it is below, it means that reversal has occurred. However, there is a very important condition here. That is, it is limited to the case where both
violin and string sound were recorded under the same conditions. This means that you have to play the same strings with the same pressure and speed. If not, the live zone becomes the dead zone or vice versa. For example, if you record a small violin sound and a large string sound, the HIS curve will go down further than it is now. Therefore, it is important to keep the same recording environment. However, under the assumption that the sound volume during performance does not change the shape of the spectral envelope itself, the live spot and dead spot will not change even if the playing conditions change when recording violin and
string sound as in the above case. That is, the playing conditions during recording affect the zone but not the spot.
Figure 20 is an example of the previous 3rd string open ‘Re’, and it is difficult to determine the live spot and the dead spot. For example, in the case of Figure 20, is the 18 [kHz] band a dead spot or not? Therefore, a standard such as [a point where Y [dB] or more is attenuated per X oct is called a dead spot] is necessary, and it should be judged using the *Q Factor. In other words, it is necessary to establish a standard of 「When the Q Factor is more than x, it is judged as a live/dead spot」.
( * Quality Factor: A value indicating the sharpness of the graph. The value obtained by dividing the resonance frequency (peak frequency) by 3 [dB] bandwidth. The higher the Q Factor, the sharper it is. )
Figure 20 : Examples of 5 types of HIS characterization
In any case, this study has a significant meaning in itself as the fact that these five peculiarities were known from the HIS characteristic. These five characteristics are very important for future research, so they should be looked at carefully in the future.
4. Conclusions and Considerations
I made a program that compares the two sounds by subtracting the LPC spectral envelope, and investigated how the sound of the completed violin and the sound of the strings themselves differ. In contrast to the section in which the sound is amplified, there is a section in which attenuation occurs, and there is also a section in which there is little change. It was also found that there was a point where the sound was greatly amplified locally and a point where it was attenuated. This phenomenon, or these characteristics, can be said to be a unique characteristic of the violin body.
In a situation where there is no indicator to inform the amplification characteristics of the violin body only, 「HIS characteristic」, which calculates the characteristics of the violin body by subtracting the spectral envelope of the string from the spectral envelope of the violin sound, is considered to be a very meaningful analysis method. Since the case of subtraction between spectral envelopes has not been found yet, in this paper, although it is only a very simple math, the concept is defined. Since the spectral envelope subtraction method has infinite
expandability(For example, when the thickness of the violin bridge is adjusted, the characteristics change before and after adjustment can be easily informed with a single line.) depending on the application, it is thought that it can play many roles in the study of other instruments as well as the characteristics of the violin body.
In fact, it is a great harvest to be able to know and organize the five types of 「Live/Suspended/Dead zone, Live/Dead spot」, which were not expected from the HIS characteristic of the violin. If we observe the changes in the above five characteristics, we have hope that we will soon know their rules and even the rules of the violin.
However, it is a pity that we did not compare other spectral envelopes in terms of early research. The LPC spectral envelope used in this study does not reflect human auditory characteristics, so it is disappointing in that the low-frequency band resolution is different from the human feeling in the low-frequency band. However, it is thought that this problem can be solved by using the Mel-Generalized Cepstrum analysis method considering human auditory characteristics.
Lastly, when recording violin sound and strings, it is very important to play them with the same string pressure and speed. Because due to the difference, the dead zone can become a live zone and vice versa. Therefore, it is necessary to think deeply about the establishment of an environment for accurate experiments.
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