Musical Istruments Signal Study Based On The Bayesian Algorithm

Computer recognition and intelligent creation of music is the fundamental objective of computer music study, in our country, computer creation fields of music is only the beginning. With the fast development of computer technology and audio multi-media technology, computer applications in the field of plucked string instrument have a new start. In the real life, because of people's energy is often limited, the traditional artificial creation and composition methods can not meet the demand for music creation and music compose. People don't trust the computer creation of music because they believe the music is so complicated and difficult of access. They believe that the beautiful music depends entirely on the intellectual level, the nature of instruments music is the voice of the natural world. The voice includes voice pitch, amplitude, length and frequency characteristics. The organized voice is created by these continuous changes of these elements. The basic unit of music is note, the music depend on the value and frequency of the note. In a sense, computer simulation to the instruments music has its unique characteristics and advantages, the development of computer audio technology is slower than other computer technology, but with the development of the audio technology and computer technology, computer music is developed recently. Today, with the development of the computer simulation technology, the music technology itself, as well as hardware and software level, musical instruments model simulation become possible. The emergence of computer simulation music make the music creation itself has so great changes. People can compose by computer models, in order to achieve the purpose of music listening. We find the some parameters of instruments music by computer, create the computer music model which can simulate real instruments music, then people can compose on their own preferences efficiently.This paper mainly studies the audio models which can be used for music creation. There are some computer audio models: harmonic model and inharmonic model. For plucked string Instruments, the string wires have diameter, also have the hardness, so while voice on the half length of the wire length. Although the intermediate transformation node is vacant, because the wire has physical size, it will stop the totally free rotation of the wire in the node. This will cause the length of the wire's voice is shorten slightly. In other word., the frequency of the secondary partial is twice the audio fundamental frequency add a little bit, this is the inharmonicity of musical instruments. This paper mainly study on the inharmonicity of the musical instruments audio, in order to provide a more accurate audio to the creation, the purpose of this paper is to prove that the inharmonic model is better than the harmonic model while it reflects the characteristics of the instruments audio. This paper make the inharmonic model apply to the study on the guitar and harpsichord audio, in which we first using Bayesian algorithm to join the prior information and sample information in order to obtain the posterior distribution, then estimate parameters of the posterior distribution by MCMC iteration methods, at last analysis the fitting effect of the models. In this paper, the specific work is as follows.(1).Study the plucked string instruments, the concept of harmonic, the causes of the inharmonicity, music computer creation.(2).Analysis the Markov chain Monte Carlo method which application to Bayesian theory. First establish the inharmonic model which used to the guitar single plucked string audio, then use Bayesian algorithm and MCMC method to estimate model parameters, compare fitting data with the original audio data, at last study the accuracy of the estimate and the results of model fitting effect.(3).Establish the inharmonic model which used to the harpsichord single plucked string audio, then estimate model parameters such as inharmonicity, the fundamental frequency, number of the partials. Then fit the harpsichord fixed pitch audio using the harmonic model and the inharmonic model. At last analysis the advantage and estimate accuracy of the two models.(4).Music Computer creation is the fundamental goal of computer music technology, the significance of this study is to establish a more accurately model to creation which need make the instrument's signal to the notation. But what this paper study is mainly the single plucked string audio, the model is also single-audio model. This paper study the single plucked string audio using the single-audio model, but in real life there is so much polyphonic audio case, in order to truly realize the computer automatically we need study the polyphonic audio using the harmonic model. This is our future work.This paper gets the following conclusions by the computer simulations. Through establishing the harmonic model to the guitar audio, estimating parameters we found that the parameters all converge to a value around. Through comparing the fitting audio data with the original audio data we found that the model is fitting the original data accurately.Establish the inharmonic model to the harpsichord audio, use Bayesian algorithm and MCMC method to estimate parameters of the inharmonic model. The parameters such as inharmonicity, the fundamental frequency, number of the partials are convergence to a value. Here the harmonic model is the inharmonic model with B=0. Then fit the harpsichord fixed pitch audio using the harmonic model and the inharmonic model. We find that the inharmonic model fitting the high frequency peak with very high accuracy in the spectrum while the harmonic model misses the high frequency peak altogether. The miss-fitting of peaks as done by the harmonic model will inevitably lead to errors when the models are used to the computer automatic compose. It shows that the inharmonic model is more accurate than harmonic model while fitting the instruments audio. However, we only prove the advantages of the new model in the computer simulations, but we don't make the new inharmonic model applied to the music computer creation, this is our future work.