[从头学声学] 第207节 声学的原理

剧情提要：
[机器小伟]在[工程师阿伟]的陪同下进行着声学神通的修炼。
这次要研究的是[声学的原理]。

正剧开始：

星历2016年05月06日 13:54:48, 银河系厄尔斯星球中华帝国江南行省。
[工程师阿伟]正在和[机器小伟]一起研究[声学的原理]。

这个音高频率表是这样算出来的：

[32.703, 34.648, 36.708, 38.891, 41.203, 43.654, 46.249, 48.999, 51.913, 55.0, 58.27, 61.735, 65.406, 69.296, 73.416, 77.782, 82.407, 87.307, 92.499, 97.999, 103.826, 110.0, 116.541, 123.471, 130.813, 138.591, 146.832, 155.563, 164.814, 174.614, 184.997, 195.998, 207.652, 220.0, 233.082, 246.942, 261.626, 277.183, 293.665, 311.127, 329.628, 349.228, 369.994, 391.995, 415.305, 440.0, 466.164, 493.883, 523.251, 554.365, 587.33, 622.254, 659.255, 698.456, 739.989, 783.991, 830.609, 880.0, 932.328, 987.767, 1046.502, 1108.731, 1174.659, 1244.508, 1318.51, 1396.913, 1479.978, 1567.982, 1661.219, 1760.0, 1864.655, 1975.533, 2093.005, 2217.461, 2349.318, 2489.016, 2637.02, 2793.826, 2959.955, 3135.963, 3322.438, 3520.0, 3729.31, 3951.066]def tmp():    #公比 半音    q = 2**(1/12);    #A4 = (+9)    A4 = 440;    #C1 = (-36)    C1 = A4/q**45;    toneFrequence = [];    for i in range(-36, 48):        toneFrequence.append(round(A4*q**(i-9), 3));    print(toneFrequence);

>>> 203.91*5+90.221109.77>>> 203.91*5+90.22*21199.99>>> [440, 469.865, 495.0, 528.598, 556.875, 594.672, 626.484, 669.006, 704.795, 752.632, 792.894, 846.711, 892.006]#三分损益法（黄钟大吕音)def tmp():    #公比 半音    q = 2**(1/1200);    #A4 = (+9)    A4 = 440;    tmpfreq  = A4;        toneFrequence = [];    for i in range(13):                toneFrequence.append(round(tmpfreq, 3));        if (i%2==0):            tmpfreq *= q**(113.69);        else:            tmpfreq *= q**(90.22);    print(toneFrequence);

阿伟给小伟做了一个乐音遍历工具，可以听出国际谱中的所有音符。

本来可以传到酷狗的，但想了想，还是传优酷了，尽管很短，

还要看很长时间的广告。

点击打开链接 -- 乐音音符

idleWave = [b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00', b'\x00'];#把十进制数按照小尾字节序切割def littleEndian(number, byte = 4):    result = [0]*byte;    for i in range(byte):        result[i] = number%256;        number//=256;    return result;    #把UltraEdit中的值字串转化为hex序列组def hexExpr(string):    resultString = '';    size = len(string);    for i in range(size):        if (i == 0 ):            resultString += '0x'+string[i];        elif (string[i] == ' '):            resultString += ', 0x';        else:            resultString += string[i];    print(resultString);#### @usage   写.wav文件，能把声波数据阵列用二进制写成.wav。# @author  mw# @date    2016年04月28日  星期四  14:31:34 # @param# @return####def writeWav(index , filename):        byteArray = [];    dataArray = [];    mode = 2;        #样本数据阵列    sampleArray = [];    if mode == 1:        sampleArray = waveDataChoose(index, filename);    elif mode == 2:        sampleArray = waveDataChoose_2(filename);    #样本数据点数    N = len(sampleArray);    times = 2;    dataSize = N*times;        fileSize = dataSize+44; #44为格式头部分所用字节数        #RIFF WAVE CHUNK    RIFF_ID = [0x52, 0x49, 0x46, 0x46];  #'RIFF'    RIFF_Size = littleEndian(fileSize-8, 4); #文件总字节数减去8    RIFF_Type = [0x57, 0x41,0x56, 0x45, 0x66, 0x6D, 0x74, 0x20]; #'WAVEfat '    #Format Chunk    Format_10_17 = [0x10, 0x00, 0x00, 0x00, 0x01, 0x00, 0x01, 0x00];#过滤4+格式2+声道2=8个字节    Format_18_1B = [0x11, 0x2B, 0x00, 0x00]; #采样频率0x2B11 = 11025    Format_1C_1F = [0x22, 0x56, 0x00, 0x00]; #比持率 = 频率*通道*样本位 = 22050    Format_20_23 = [0x02, 0x00, 0x10, 0x00]; #块对齐 = 通道数* 样本位数 = 1*2 = 2        #Fact Chunk(optional)    #Data Chunk    Data_24_27 = [0x64, 0x61, 0x74, 0x61]; #'DATA'标记    Data_Size = littleEndian(fileSize-44, 4); #下面的Data部分的字节数，文件总字节数-44    #RIFF WAVE CHUNK    '''    for i in range(4):        byte = struct.pack('B', RIFF_ID[i]);        byteArray.append(byte);    '''    RIFF = [b'R', b'I', b'F', b'F'];    for i in range(4):        byteArray.append(RIFF[i]);    for i in range(4):        byte = struct.pack('B', RIFF_Size[i]);        byteArray.append(byte);    '''    for i in range(8):        byte = struct.pack('B', RIFF_Type[i]);        byteArray.append(byte);    #Format Chunk    for i in range(8):        byte = struct.pack('B', Format_10_17[i]);        byteArray.append(byte);    for i in range(4):        byte = struct.pack('B', Format_18_1B[i]);        byteArray.append(byte);    for i in range(4):        byte = struct.pack('B', Format_1C_1F[i]);        byteArray.append(byte);    for i in range(4):        byte = struct.pack('B', Format_20_23[i]);        byteArray.append(byte);        #Data Chunk    for i in range(4):        byte = struct.pack('B', Data_24_27[i]);        byteArray.append(byte);    '''    #Format_28_2B是数据块大小，formatHead是它前面的所有部分    formatHead = [b'W', b'A', b'V', b'E', b'f', b'm', b't', b' ', \                  b'\x10', b'\x00', b'\x00', b'\x00', b'\x01', b'\x00', b'\x01', b'\x00', \                  b'\x11', b'+', b'\x00', b'\x00', \                  b'"', b'V', b'\x00', b'\x00', \                  b'\x02', b'\x00', b'\x10', b'\x00', \                  b'd', b'a', b't', b'a'];    for i in range(len(formatHead)):        byteArray.append(formatHead[i]);    for i in range(4):        byte = struct.pack('B', Data_Size[i]);        byteArray.append(byte);    #写出到文件    print('文件写入开始。>>>');    s = '';    if mode == 1:        s = filename[index]+'.wav';    elif mode == 2:        s = 'randMusic'+str(index)+'.wav';            fout= open(s, 'wb');    size = len(byteArray);        for i in range(size):        fout.write(byteArray[i]);               size = len(sampleArray);    sizeIdle = len(idleWave);            for j in range(times):        for i in range(size):            fout.write(sampleArray[i]);    fout.close();    print('文件写入完毕。');#生成声音样本，返回样本矩阵def sampleGen(N, freq):    #设立20000个数值点，约可听2秒    sampleArray = [];    coef = 2*math.pi*freq/11025;    #音色调节    weight = [1, 2.55, 2.13, 1.98, 1.57, 1.23];    total = sum(weight);           for i in range(N):        xvalue = coef*i;                yvalue = (weight[0]*math.sin(xvalue) + weight[1]*math.sin(xvalue*2)+ weight[2]*math.sin(xvalue*3) +\                 weight[3]*math.sin(xvalue*4) + weight[4]*math.sin(xvalue*5)+ weight[5]*math.sin(xvalue*6))/total;        if (yvalue < 0):            yvalue *= 32768;        else:            yvalue *= 32767;        sampleArray.append(round(yvalue));    return sampleArray;def waveDataGen(freq):    N = 200;    sampleArray = sampleGen(N, freq);    dataArray = [];        for i in range(N):        value = littleEndian(sampleArray[i], 2);        for j in range(2):            byte = struct.pack('B', value[j]);            dataArray.append(byte);        return dataArray;def genIdle():    dataArray = [];        for i in range(200):        value = littleEndian(0, 2);        for j in range(2):            byte = struct.pack('B', value[j]);            dataArray.append(byte);        print(dataArray);#波形选择def waveDataChoose(index, filename):    import wavedata;        tmpdata = eval('wavedata.'+filename[index]);    sampledata = [];    for i in range(1, 21):        for j in range(15):            sampledata += idleWave;        for j in range(i):            sampledata += tmpdata;        for j in range(15):            sampledata += idleWave;    return sampledata; def waveDataChoose_2(filename):    import wavedata;    size = len(filename);        sampledata = [];        for i in range(300):        #index_1 = random.randint(24, size-1-36);        idleCircle = random.randint(2, 8);        longIdleCircle = random.randint(8, 20);        musicCircle = random.randint(2, 15);                tmpdata = eval('wavedata.'+filename[i%size]);        for j in range(musicCircle):            sampledata += tmpdata;        for j in range(idleCircle):            sampledata += idleWave;        if (i%longIdleCircle == 0):            for j in range(longIdleCircle):                sampledata += idleWave;    for i in range(30):        sampledata += idleWave;            return sampledata;    #调用入口, 生成wav文件def tmp(filename):    size = len(filename);        for i in range(size):        if i > 300:            break;                writeWav(i, filename);def tmp_2(index, filename):    writeWav(index, filename);#生成声波数据def tmp2():    print('生成波形开始。>>>');        fout= open('output.txt', 'w');    frequence = [32.703, 34.648, 36.708, 38.891, 41.203, 43.654, 46.249, 48.999, 51.913, 55.0, 58.27, 61.735, \                65.406, 69.296, 73.416, 77.782, 82.407, 87.307, 92.499, 97.999, 103.826, 110.0, 116.541, 123.471, \                130.813, 138.591, 146.832, 155.563, 164.814, 174.614, 184.997, 195.998, 207.652, 220.0, 233.082, 246.942, \                261.626, 277.183, 293.665, 311.127, 329.628, 349.228, 369.994, 391.995, 415.305, 440.0, 466.164, 493.883, \                523.251, 554.365, 587.33, 622.254, 659.255, 698.456, 739.989, 783.991, 830.609, 880.0, 932.328, 987.767, \                1046.502, 1108.731, 1174.659, 1244.508, 1318.51, 1396.913, 1479.978, 1567.982, 1661.219, 1760.0, 1864.655, 1975.533, \                2093.005, 2217.461, 2349.318, 2489.016, 2637.02, 2793.826, 2959.955, 3135.963, 3322.438, 3520.0, 3729.31, 3951.066];    size = len(frequence);        for i in range(size):        dataStr = 'musicfreq_'+str(frequence[i]).replace('.', 'p') + ' = [';        fout.write(dataStr);        data = waveDataGen(frequence[i]);        size_1 = len(data);        for n in range(size_1):            fout.write(str(data[n]));            if (n < size_1-1):                fout.write(', ');        fout.write('];');                    fout.write('\r\n');    fout.close();    print('生成波形结束，请到output.txt查收。');#打印文件名             def tmp3():    filename = [];        frequence = [32.703, 34.648, 36.708, 38.891, 41.203, 43.654, 46.249, 48.999, 51.913, 55.0, 58.27, 61.735, \            65.406, 69.296, 73.416, 77.782, 82.407, 87.307, 92.499, 97.999, 103.826, 110.0, 116.541, 123.471, \            130.813, 138.591, 146.832, 155.563, 164.814, 174.614, 184.997, 195.998, 207.652, 220.0, 233.082, 246.942, \            261.626, 277.183, 293.665, 311.127, 329.628, 349.228, 369.994, 391.995, 415.305, 440.0, 466.164, 493.883, \            523.251, 554.365, 587.33, 622.254, 659.255, 698.456, 739.989, 783.991, 830.609, 880.0, 932.328, 987.767, \            1046.502, 1108.731, 1174.659, 1244.508, 1318.51, 1396.913, 1479.978, 1567.982, 1661.219, 1760.0, 1864.655, 1975.533, \            2093.005, 2217.461, 2349.318, 2489.016, 2637.02, 2793.826, 2959.955, 3135.963, 3322.438, 3520.0, 3729.31, 3951.066];    size = len(frequence);        for i in range(size):        dataStr = 'musicfreq_'+str(frequence[i]).replace('.', 'p');        filename.append(dataStr);    print(filename);if __name__ == '__main__':        part = 1;    if (part == 3):        tmp3();    elif (part == 2):        tmp2();    elif (part == 1):        import wavename;        filename = wavename.wavename;                tmp_2(3, filename);        

点击打开链接 -- 元音发音

#生成声音样本，返回样本矩阵def sampleGen_2(N, freq1, freq2):    #设立20000个数值点，约可听2秒    sampleArray = [];    coef = 2*math.pi/11025;    #音色调节    weight = [1.53, 1];    total = sum(weight);        for i in range(N):        xcoef_1 = coef*i*freq1;        xcoef_2 = coef*i*freq2;                yvalue = (weight[0]*math.sin(xcoef_1)+ weight[1]*math.sin(xcoef_2))/total;                if (yvalue < 0):            yvalue *= 32768;        else:            yvalue *= 32767;        sampleArray.append(round(yvalue));    return sampleArray;def waveDataGen_2(freq1, freq2):    N = 200;    sampleArray = sampleGen_2(N, freq1, freq2);    dataArray = [];        for i in range(N):        value = littleEndian(sampleArray[i], 2);        for j in range(2):            byte = struct.pack('B', value[j]);            dataArray.append(byte);        return dataArray;                                                          #生成声波数据def tmp2_2():    print('生成波形开始。>>>');        fout= open('output.txt', 'w');    frequence = [[240,2400],                 [235,2100],                 [390,2300],                 [370,1900],                 [610,1900],                 [585,1710],                 [850, 1610],                 [820, 1530],                 [750, 940],                 [700, 760],                 [600, 1170],                 [500, 700],                 [460, 1310],                 [360, 640],                 [300, 1390],                 [250, 595]];                size = len(frequence);        for i in range(size):        dataStr = 'primaryTone_'+ str(frequence[i][0])+'_'+str(frequence[i][1]) + ' = [';                                                                       fout.write(dataStr);        data = waveDataGen_2(frequence[i][0], frequence[i][1]);        size_1 = len(data);        for n in range(size_1):            fout.write(str(data[n]));            if (n < size_1-1):                fout.write(', ');        fout.write('];');                    fout.write('\r\n');    fout.close();    print('生成波形结束，请到output.txt查收。');    #生成声波数据def tmp3_2():    filename = [];    frequence = [[240,2400],                 [235,2100],                 [390,2300],                 [370,1900],                 [610,1900],                 [585,1710],                 [850, 1610],                 [820, 1530],                 [750, 940],                 [700, 760],                 [600, 1170],                 [500, 700],                 [460, 1310],                 [360, 640],                 [300, 1390],                 [250, 595]];            size = len(frequence);        for i in range(size):        dataStr = 'primaryTone_'+ str(frequence[i][0])+'_'+str(frequence[i][1]);                                                                       filename.append(dataStr);        print(filename);    if __name__ == '__main__':        part = 1;    if (part == 3):        tmp3_2();    elif (part == 2):        tmp2_2();    elif (part == 1):        import wavename;        filename = wavename.wavename;                tmp_2(5, filename);

本节到此结束，欲知后事如何，请看下回分解。