合成音符聲音 ( 鋼琴 Do Re Mi Fa So )

這篇文章會參考國外作者「Nishu Jain」的文章，使用 numpy 產生音符的聲音 ( 鋼琴的 Do Re Mi Fa So )，最後透過 scipy.io.wavfile 將音符組合成音樂輸出成 wav 檔案。

• 參考：How to Play Music Using Mathematics in Python
• 本篇使用的 Python 版本為 3.7.12，所有範例可使用 Google Colab 實作，不用安裝任何軟體 ( 參考：使用 Google Colab )

安裝 numpy 和 scipy

輸入下列指令安裝 numpy 和 scipy，根據個人環境使用 pip 或 pip3 ( Colab 或 Anaconda Jupyter 可能已經內建 )。

pip install numpy

pip install scipy

合成音符聲音

下方的程式碼執行後，會將定義好的音樂，按照音符的順序產生對應的頻率，然後輸出成為 wav 檔案，詳細說明寫在程式碼的註解中。

import numpy as np

samplerate = 44100    # 取樣頻率

def get_wave(freq, duration=0.5):
    amplitude = 4096      # 震幅 ( 音量大小 )
    t = np.linspace(0, duration, int(samplerate * duration)) # 使用等差級數，在指定時間長度裡，根據取樣頻率建立區間
    wave = amplitude * np.sin(2 * np.pi * freq * t)          # 在每個區間裡放入指定頻率的波形
    return wave

def get_piano_notes():
    octave = ['C', 'c', 'D', 'd', 'E', 'F', 'f', 'G', 'g', 'A', 'a', 'B']  # 建立音符英文字對照表
    base_freq = 261.63    # 預設為 C4 的頻率
    note_freqs = {octave[i]: base_freq * pow(2,(i/12)) for i in range(len(octave))} # 產生頻率和英文字的對照
    note_freqs[''] = 0.0  # 如果是空值則為 0 ( 無聲音 )
    return note_freqs

def get_song_data(music_notes):
    note_freqs = get_piano_notes()   # 取的英文與音符對照表
    song = [get_wave(note_freqs[note]) for note in music_notes.split('-')]  # 根據音樂的音符，對應到對照表產生指定串列
    song = np.concatenate(song)      # 連接為新陣列
    return song

# 音樂的音符表
music_notes = 'C-C-G-G-A-A-G--F-F-E-E-D-D-C--G-G-F-F-E-E-D--G-G-F-F-E-E-D--C-C-G-G-A-A-G--F-F-E-E-D-D-C'
data = get_song_data(music_notes)   # 轉換成頻率對照表
data = data * (16300/np.max(data))  # 調整震幅 ( 音量大小 )

from scipy.io.wavfile import write
write('twinkle-twinkle.wav', samplerate, data.astype(np.int16))  # 寫入檔案

音符與頻率對照表

下方列出八組八度音符 ( Note )、頻率 ( Frequency，單位 Hz ) 和波長 ( Wavelength，單位 cm ) 的對照表，基本上往下八度是除以 2，往上八度是乘以 2，例如 C4 的頻率為 261.63，C3 就是 130.81 ( 261.63/2 )，C5 就是 523.25 ( 261.63x2 )。

音符對照的字典格式如下：

{
  A0: {frequency: "27.50", wavelength: "1254.55"},
  A1: {frequency: "55.00", wavelength: "627.27"},
  A2: {frequency: "110.00", wavelength: "313.64"},
  A3: {frequency: "220.00", wavelength: "156.82"},
  A4: {frequency: "440.00", wavelength: "78.41"},
  A5: {frequency: "880.00", wavelength: "39.20"},
  A6: {frequency: "1760.00", wavelength: "19.60"},
  A7: {frequency: "3520.00", wavelength: "9.80"},
  A8: {frequency: "7040.00", wavelength: "4.90"},
  B0: {frequency: "30.87", wavelength: "1117.67"},
  B1: {frequency: "61.74", wavelength: "558.84"},
  B2: {frequency: "123.47", wavelength: "279.42"},
  B3: {frequency: "246.94", wavelength: "139.71"},
  B4: {frequency: "493.88", wavelength: "69.85"},
  B5: {frequency: "987.77", wavelength: "34.93"},
  B6: {frequency: "1975.53", wavelength: "17.46"},
  B7: {frequency: "3951.07", wavelength: "8.73"},
  B8: {frequency: "7902.13", wavelength: "4.37"},
  C0: {frequency: "16.35", wavelength: "2109.89"},
  C1: {frequency: "32.70", wavelength: "1054.94"},
  C2: {frequency: "65.41", wavelength: "527.47"},
  C3: {frequency: "130.81", wavelength: "263.74"},
  C4: {frequency: "261.63", wavelength: "131.87"},
  C5: {frequency: "523.25", wavelength: "65.93"},
  C6: {frequency: "1046.50", wavelength: "32.97"},
  C7: {frequency: "2093.00", wavelength: "16.48"},
  C8: {frequency: "4186.01", wavelength: "8.24"},
  D0: {frequency: "18.35", wavelength: "1879.69"},
  D1: {frequency: "36.71", wavelength: "939.85"},
  D2: {frequency: "73.42", wavelength: "469.92"},
  D3: {frequency: "146.83", wavelength: "234.96"},
  D4: {frequency: "293.66", wavelength: "117.48"},
  D5: {frequency: "587.33", wavelength: "58.74"},
  D6: {frequency: "1174.66", wavelength: "29.37"},
  D7: {frequency: "2349.32", wavelength: "14.69"},
  D8: {frequency: "4698.63", wavelength: "7.34"},
  E0: {frequency: "20.60", wavelength: "1674.62"},
  E1: {frequency: "41.20", wavelength: "837.31"},
  E2: {frequency: "82.41", wavelength: "418.65"},
  E3: {frequency: "164.81", wavelength: "209.33"},
  E4: {frequency: "329.63", wavelength: "104.66"},
  E5: {frequency: "659.25", wavelength: "52.33"},
  E6: {frequency: "1318.51", wavelength: "26.17"},
  E7: {frequency: "2637.02", wavelength: "13.08"},
  E8: {frequency: "5274.04", wavelength: "6.54"},
  F0: {frequency: "21.83", wavelength: "1580.63"},
  F1: {frequency: "43.65", wavelength: "790.31"},
  F2: {frequency: "87.31", wavelength: "395.16"},
  F3: {frequency: "174.61", wavelength: "197.58"},
  F4: {frequency: "349.23", wavelength: "98.79"},
  F5: {frequency: "698.46", wavelength: "49.39"},
  F6: {frequency: "1396.91", wavelength: "24.70"},
  F7: {frequency: "2793.83", wavelength: "12.35"},
  F8: {frequency: "5587.65", wavelength: "6.17"},
  G0: {frequency: "24.50", wavelength: "1408.18"},
  G1: {frequency: "49.00", wavelength: "704.09"},
  G2: {frequency: "98.00", wavelength: "352.04"},
  G3: {frequency: "196.00", wavelength: "176.02"},
  G4: {frequency: "392.00", wavelength: "88.01"},
  G5: {frequency: "783.99", wavelength: "44.01"},
  G6: {frequency: "1567.98", wavelength: "22.00"},
  G7: {frequency: "3135.96", wavelength: "11.00"},
  G8: {frequency: "6271.93", wavelength: "5.50"},
  "A#0": {frequency: "29.14", wavelength: "1184.13"},
  "Bb0": {frequency: "29.14", wavelength: "1184.13"},
  "A#1": {frequency: "58.27", wavelength: "592.07"},
  "Bb1": {frequency: "58.27", wavelength: "592.07"},
  "A#2": {frequency: "116.54", wavelength: "296.03"},
  "Bb2": {frequency: "116.54", wavelength: "296.03"},
  "A#3": {frequency: "233.08", wavelength: "148.02"},
  "Bb3": {frequency: "233.08", wavelength: "148.02"},
  "A#4": {frequency: "466.16", wavelength: "74.01"},
  "Bb4": {frequency: "466.16", wavelength: "74.01"},
  "A#5": {frequency: "932.33", wavelength: "37.00"},
  "Bb5": {frequency: "932.33", wavelength: "37.00"},
  "A#6": {frequency: "1864.66", wavelength: "18.50"},
  "Bb6": {frequency: "1864.66", wavelength: "18.50"},
  "A#7": {frequency: "3729.31", wavelength: "9.25"},
  "Bb7": {frequency: "3729.31", wavelength: "9.25"},
  "A#8": {frequency: "7458.62", wavelength: "4.63"},
  "Bb8": {frequency: "7458.62", wavelength: "4.63"},
  "C#0": {frequency: "17.32", wavelength: "1991.47"},
  "Db0": {frequency: "17.32", wavelength: "1991.47"},
  "C#1": {frequency: "34.65", wavelength: "995.73"},
  "Db1": {frequency: "34.65", wavelength: "995.73"},
  "C#2": {frequency: "69.30", wavelength: "497.87"},
  "Db2": {frequency: "69.30", wavelength: "497.87"},
  "C#3": {frequency: "138.59", wavelength: "248.93"},
  "Db3": {frequency: "138.59", wavelength: "248.93"},
  "C#4": {frequency: "277.18", wavelength: "124.47"},
  "Db4": {frequency: "277.18", wavelength: "124.47"},
  "C#5": {frequency: "554.37", wavelength: "62.23"},
  "Db5": {frequency: "554.37", wavelength: "62.23"},
  "C#6": {frequency: "1108.73", wavelength: "31.12"},
  "Db6": {frequency: "1108.73", wavelength: "31.12"},
  "C#7": {frequency: "2217.46", wavelength: "15.56"},
  "Db7": {frequency: "2217.46", wavelength: "15.56"},
  "C#8": {frequency: "4434.92", wavelength: "7.78"},
  "Db8": {frequency: "4434.92", wavelength: "7.78"},
  "D#0": {frequency: "19.45", wavelength: "1774.20"},
  "Eb0": {frequency: "19.45", wavelength: "1774.20"},
  "D#1": {frequency: "38.89", wavelength: "887.10"},
  "Eb1": {frequency: "38.89", wavelength: "887.10"},
  "D#2": {frequency: "77.78", wavelength: "443.55"},
  "Eb2": {frequency: "77.78", wavelength: "443.55"},
  "D#3": {frequency: "155.56", wavelength: "221.77"},
  "Eb3": {frequency: "155.56", wavelength: "221.77"},
  "D#4": {frequency: "311.13", wavelength: "110.89"},
  "Eb4": {frequency: "311.13", wavelength: "110.89"},
  "D#5": {frequency: "622.25", wavelength: "55.44"},
  "Eb5": {frequency: "622.25", wavelength: "55.44"},
  "D#6": {frequency: "1244.51", wavelength: "27.72"},
  "Eb6": {frequency: "1244.51", wavelength: "27.72"},
  "D#7": {frequency: "2489.02", wavelength: "13.86"},
  "Eb7": {frequency: "2489.02", wavelength: "13.86"},
  "D#8": {frequency: "4978.03", wavelength: "6.93"},
  "Eb8": {frequency: "4978.03", wavelength: "6.93"},
  "F#0": {frequency: "23.12", wavelength: "1491.91"},
  "Gb0": {frequency: "23.12", wavelength: "1491.91"},
  "F#1": {frequency: "46.25", wavelength: "745.96"},
  "Gb1": {frequency: "46.25", wavelength: "745.96"},
  "F#2": {frequency: "92.50", wavelength: "372.98"},
  "Gb2": {frequency: "92.50", wavelength: "372.98"},
  "F#3": {frequency: "185.00", wavelength: "186.49"},
  "Gb3": {frequency: "185.00", wavelength: "186.49"},
  "F#4": {frequency: "369.99", wavelength: "93.24"},
  "Gb4": {frequency: "369.99", wavelength: "93.24"},
  "F#5": {frequency: "739.99", wavelength: "46.62"},
  "Gb5": {frequency: "739.99", wavelength: "46.62"},
  "F#6": {frequency: "1479.98", wavelength: "23.31"},
  "Gb6": {frequency: "1479.98", wavelength: "23.31"},
  "F#7": {frequency: "2959.96", wavelength: "11.66"},
  "Gb7": {frequency: "2959.96", wavelength: "11.66"},
  "F#8": {frequency: "5919.91", wavelength: "5.83"},
  "Gb8": {frequency: "5919.91", wavelength: "5.83"},
  "G#0": {frequency: "25.96", wavelength: "1329.14"},
  "Ab0": {frequency: "25.96", wavelength: "1329.14"},
  "G#1": {frequency: "51.91", wavelength: "664.57"},
  "Ab1": {frequency: "51.91", wavelength: "664.57"},
  "G#2": {frequency: "103.83", wavelength: "332.29"},
  "Ab2": {frequency: "103.83", wavelength: "332.29"},
  "G#3": {frequency: "207.65", wavelength: "166.14"},
  "Ab3": {frequency: "207.65", wavelength: "166.14"},
  "G#4": {frequency: "415.30", wavelength: "83.07"},
  "Ab4": {frequency: "415.30", wavelength: "83.07"},
  "G#5": {frequency: "830.61", wavelength: "41.54"},
  "Ab5": {frequency: "830.61", wavelength: "41.54"},
  "G#6": {frequency: "1661.22", wavelength: "20.77"},
  "Ab6": {frequency: "1661.22", wavelength: "20.77"},
  "G#7": {frequency: "3322.44", wavelength: "10.38"},
  "Ab7": {frequency: "3322.44", wavelength: "10.38"},
  "G#8": {frequency: "6644.88", wavelength: "5.19"},
  "Ab8": {frequency: "6644.88", wavelength: "5.19"}
}

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