musiktheorietheorie/musiktheorietheorie.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "cellView": "code",
    "id": "at5_o2QCg6YY"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy.fft import fft, ifft\n",
    "from IPython.display import Audio, display\n",
    "from scipy.io import wavfile\n",
    "from ipywidgets import widgets\n",
    "from functools import partial\n",
    "import pandas as pd\n",
    "from fractions import Fraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "id": "C2t7WxG-jJac"
   },
   "outputs": [],
   "source": [
    "def create_signal(frequency, amplitude, delay, phase=0, sampling=44100, seconds=1.0):\n",
    "  timesteps = np.linspace(0,seconds, int(seconds * sampling))\n",
    "  # return np.sum(amplitude * np.sin(frequency * 2*np.pi * (timesteps[:, np.newaxis]-delay)*(timesteps[:, np.newaxis]-delay > 0)), axis=1), timesteps\n",
    "  return np.sum(amplitude * triangle(frequency, (timesteps[:, np.newaxis]-delay)*(timesteps[:, np.newaxis]-delay > 0)), axis=1), timesteps\n",
    "\n",
    "def create_waves(frequency, amplitude, phase=0, sampling=44100, seconds=1.0):\n",
    "  timesteps = np.linspace(0,seconds, int(seconds * sampling))\n",
    "  # return amplitude * np.sin(frequency * 2*np.pi * timesteps[:, np.newaxis]), timesteps\n",
    "  return amplitude * triangle(frequency, timesteps[:, np.newaxis]), timesteps\n",
    "\n",
    "def triangle(frequency, t):\n",
    "  phase = (t * frequency + 0.25) % 1 - 0.25\n",
    "  return (phase <= 0.25) * phase + (phase > 0.25) * (0.5 - phase)\n",
    "\n",
    "def nonlinearity(x, param=1.0): # param for scaling of argument; higher values = more nonlinearity\n",
    "  #return np.exp(x*param)\n",
    "  return np.sign(x)*np.log(1+np.abs(x*param))\n",
    "\n",
    "def myAudio(signal, rate=44100, autoplay=False, time_fade=0.2):\n",
    "  length = signal.shape[0]\n",
    "  print(length)\n",
    "  fade = np.minimum(np.ones(length),np.arange(length)/(time_fade * rate))\n",
    "  return Audio(signal * fade * fade[::-1],rate=rate,autoplay=autoplay)\n",
    "\n",
    "def toEDO(ratio, n=12):\n",
    "    return 2**((np.round(np.log(ratio) * n / np.log(2)))/n)\n",
    "\n",
    "def ratio2freq(ratio, base=220):\n",
    "    return base * ratio\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
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     "base_uri": "https://localhost:8080/",
     "height": 897
    },
    "id": "yfTtI-OVmXIo",
    "outputId": "24995b1b-a7f5-486a-abe3-865685474314"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "88200\n"
     ]
    },
    {
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       "                    <source src=\"data:audio/wav;base64,UklGRjSxAgBXQVZFZm10IBAAAAABAAEARKwAAIhYAQACABAAZGF0YRCxAgAAAAAAAAAAAAAAAAABAAEAAgADAAMABAAFAAYABwAIAAoACwAMAA4ADwARABMAFQAWABgAGgAdAB8AIQAjACYAKAArAC4AMAAzADYAOAA4ADgANwA3ADcANgA2ADUANAA0ADMAMgAxADAALgAtACwAKgApACcAJgAkACIAIAAeABwAGgAYABUAEwAQAA4ACwAJAAYAAwAAAP7/+//4//T/8f/u/+r/5//j/9//2//X/9P/z//L/8f/w/++/7r/tf+x/6z/p/+i/53/mP+T/47/if+D/37/ef9z/23/aP9i/1z/WP9b/17/Yf9l/2j/bP9v/3P/dv96/37/gv+G/4r/jv+T/5f/m/+g/6T/qf+u/7P/uP+9/8L/x//M/9H/1//c/+L/5//t//P/+f/+/wMACgAQABYAHAAjACkAMAA2AD0ARABLAFIAWQBgAGcAbwB2AH0AhQCNAJQAnACkAKwAtAC8AMQAzADVAN0A5gDuAPcA/wAIAREBGQETAQ0BBwEAAfoA9ADtAOYA4ADZANIAywDEAL0AtgCvAKcAoACYAJEAiQCCAHoAcgBqAGIAWgBSAEkAQQA4ADAAJwAfABYADQAEAPz/8//q/+H/1//O/8T/u/+x/6f/nv+U/4r/gP92/2v/Yf9X/0z/Qv83/y3/Iv8X/wz/Af/2/uv+4P7U/sn+vf6y/qb+m/6P/oP+d/5+/of+kP6a/qP+rP62/r/+yf7T/t3+5/7x/vv+Bf8P/xn/JP8u/zn/Q/9O/1n/ZP9v/3r/hf+Q/5v/p/+y/77/yf/V/+H/7P/4/wMADwAcACgANABAAE0AWQBmAHMAgACMAJkApgC0AMEAzgDbAOkA9gAEARIBHwEtATsBSQFXAWUBcwGCAZABnwGtAbwBygHZAegB9wHyAeYB2gHOAcEBtQGoAZwBjwGCAXYBaQFcAU8BQQE0AScBGgEMAf8A8QDjANYAyAC6AKwAngCPAIEAcwBkAFYARwA5ACoAGwAMAP7/7//g/9H/wv+y/6P/k/+E/3T/ZP9U/0T/NP8k/xT/BP/z/uP+0/7C/rH+of6Q/n/+bv5d/kz+O/4p/hj+Bv71/eP90v3A/a79nP2d/az9u/3K/dr96f34/Qj+GP4n/jf+R/5X/mf+d/6H/pj+qP64/sn+2v7q/vv+DP8d/y7/P/9Q/2H/c/+E/5b/p/+5/8r/3P/u/wAAEQAjADUASABaAG0AfwCSAKQAtwDKAN0A8AADARYBKQE9AVABZAF3AYsBnwGyAcYB2gHuAQICFgIrAj8CVAJoAn0CkQKmArsC0ALVAsMCsQKfAo0CegJoAlUCQwIwAh0CCgL3AeQB0QG+AasBlwGEAXABXQFJATUBIgEOAfoA5gDRAL0AqQCUAIAAawBXAEIALQAYAAQA7//a/8X/sP+b/4X/cP9a/0T/L/8Z/wP/7f7X/sH+qv6U/n7+Z/5R/jr+I/4N/vb93/3I/bH9mf2C/Wv9U/08/ST9Df31/N38xfy3/Mz84vz3/Az9If03/Uz9Yv14/Y79o/25/c/95f38/RL+KP4//lX+bP6C/pn+sP7H/t7+9f4M/yP/O/9S/2n/gf+Z/7D/yP/g//j/DwAnAD8AVwBwAIgAoQC5ANIA6wADARwBNQFOAWcBgQGaAbMBzQHmAQACGgIzAk0CZwKBApsCtQLQAuoCBAMfAzoDVANvA4oDpQO9A6UDjQN0A1wDRAMrAxMD+gLiAskCsAKXAn4CZQJMAjICGQIAAuYBzQGzAZkBgAFmAUwBMgEXAf0A4wDJAK4AlAB5AF4ARAApAA4A9P/Z/77/ov+H/2z/UP81/xn//f7h/sb+qv6O/nH+Vf45/h3+AP7k/cf9qv2O/XH9VP03/Rr9/fzf/ML8pfyH/Gr8TPwu/BD88/vV++n7BPwf/Dv8Vvxx/I38qPzE/OD8/PwY/TT9UP1s/Yj9pP3B/d39+v0W/jP+UP5t/or+p/7E/uH+/v4c/zn/V/90/5L/sP/O/+v/CAAnAEUAYwCBAKAAvgDdAPsAGgE5AVgBdwGWAbUB1AHzARMCMgJRAnECkQKwAtAC8AIQAzADUANxA5EDsQPSA/IDEwQ0BFQEdQSWBIoEbAROBDAEEQTzA9QDtgOXA3gDWgM7AxwD/QLeAr4CnwKAAmACQQIhAgEC4gHCAaIBggFiAUEBIQEBAeAAwACfAH8AXgA9ABwA/P/b/7r/mf94/1b/Nf8T//L+0P6u/oz+av5I/ib+BP7i/b/9nf16/Vj9Nf0T/fD8zfyq/If8ZPxA/B38+vvW+7P7j/tr+0j7JPsA+wH7I/tE+2X7hvuo+8n76/sM/C78UPxy/JT8tvzY/Pr8Hf0//WH9hP2m/cn97P0P/jL+Vf54/pv+vv7i/gX/KP9M/3D/k/+3/9v///8iAEYAagCPALMA1wD8ACEBRQFqAY8BtAHZAf4BIwJIAm4CkwK5At4CBAMpA08DdQObA8ED5wMNBDQEWgSBBKcEzgT0BBsFQgVpBXQFUAUsBQcF4wS/BJoEdgRRBCwEBwTjA74DmQNzA04DKQMEA94CuQKTAm0CSAIiAvwB1gGwAYoBYwE9ARcB8ADKAKMAfABWAC8ACADi/7v/k/9s/0X/Hf/2/s7+p/5//lf+L/4H/t/9t/2P/Wb9Pv0V/e38xPyc/HP8Svwh/Pj7z/um+3z7U/sq+wD71/qt+oP6Wfov+hb6Pfpk+ov6s/ra+gH7KftR+3j7oPvI+/D7GPxA/Gj8kfy5/OH8Cv0y/Vv9hP2t/dX9/v0o/lH+ev6j/s3+9v4g/0n/c/+d/8f/8P8ZAEQAbgCYAMIA7QAXAUIBbQGXAcIB7QEYAkMCbgKZAsUC8AIbA0cDcwOeA8oD9gMiBE4EegSmBNIE/wQrBVgFhAWxBd4FCgY3BmEGNwYNBuMFuQWOBWQFOQUPBeQEuQSOBGQEOQQNBOIDtwOMA2ADNQMJA94CsgKGAloCLgICAtYBqgF9AVEBJQH4AMwAnwByAEUAGADs/7//kv9l/zf/Cv/d/q/+gf5U/ib++P3K/Zz9bv1A/RH94/y1/Ib8V/wp/Pr7y/uc+237PvsP++D6sPqB+lL6Ivry+cP5k/lj+TP5U/mA+a752/kI+jb6Y/qR+r767Poa+0j7dvuk+9L7APwv/F38jPy6/On8GP1G/XX9pP3T/QL+Mv5h/pD+wP7v/h//Tv9+/67/3v8NAD0AbQCdAM4A/gAuAV8BkAHAAfEBIgJTAoQCtQLmAhgDSQN6A6wD3QMPBEEEcwSlBNcECQU7BW0FnwXSBQQGNwZpBpwGzwYCBzUHIwfzBsMGkwZiBjIGAQbRBaAFbwU+BQ4F3QSrBHoESQQYBOYDtQODA1IDIAPuArwCiwJYAiYC9AHCAZABXQErAfgAxQCTAGAALQD7/8j/lf9i/y7/+/7H/pT+YP4t/vn9xf2R/V39Kf31/MD8jPxY/CP87/u6+4X7UPsc++f6sfp8+kf6Evrc+af5cfk8+Qb50Pib+GX4ZviZ+Mz4//gy+Wb5mfnN+QD6NPpo+pz60PoE+zj7bPuh+9X7Cfw+/HP8p/zc/BH9Rv17/bD95f0a/lD+hf67/vD+Jv9b/5H/x//9/zIAaACfANUACwFCAXgBrwHlARwCUwKKAsEC+AIvA2YDngPVAw0ERAR8BLQE6wQjBVsFkwXLBQQGPAZ0Bq0G5QYeB1cHjwfIBwEIEwjdB6cHcAc6BwQHzQaXBmAGKQbyBbwFhQVOBRYF3wSoBHEEOQQCBMoDkgNbAyMD6wKzAnsCQwIKAtIBmgFhASkB8AC3AH8ARgANANX/nP9i/yn/8P62/n3+Q/4K/tD9lv1c/SL96Pyu/HT8Ofz/+8T7ivtP+xX72vqf+mT6Kfru+bP5d/k8+QH5xfiJ+E74EvjW95r3dPet9+b3H/hY+JL4y/gF+T75ePmy+ez5Jvpg+pr61PoO+0n7g/u++/j7M/xu/Kj
       "                    Your browser does not support the audio element.\n",
       "                </audio>\n",
       "              "
      ],
      "text/plain": [
       "<IPython.lib.display.Audio object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 2880x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#frequency = np.array([100., 200., 300, 400])\n",
    "\n",
    "#frequency_edo12 = 220 * 2**(np.array([5,8,12,14])/12)\n",
    "#frequency_edo53 = 220 * 2**(np.array([22,36,53,62])/53)\n",
    "#frequency_edo53 = 220 * 2**(np.array([22,34,53,61])/53)\n",
    "#frequency_rein1 = 220 * 4/3 * np.array([1, 7/6, 9/6, 10/6])\n",
    "#frequency_rein2 = 220 * 4/3 * np.array([1, 12/10, 15/10, 17/10])\n",
    "dursept = 4/3*np.array([1,5/4,6/4,7/4])\n",
    "\n",
    "dursept_edo12 = 220 * toEDO(dursept, 12) # Durseptakkord in EDO12\n",
    "\n",
    "\n",
    "dursept_edo53 = 220 * toEDO(dursept, 53) # Dursept in EDO53\n",
    "\n",
    "dursept_rein = 220 * dursept # Dursept rein\n",
    "\n",
    "mollsept = 4/3 * np.array([1,12/10, 15/10, 17/10])\n",
    "mollsept_edo12 = 220 * toEDO(mollsept, 12) # Mollseptakkord in EDO12\n",
    "mollsept_edo53 = 220 * toEDO(mollsept, 53) # Mollseptakkord in EDO53\n",
    "mollsept_rein = 220 * mollsept # Mollsept rein\n",
    "\n",
    "doppeltritone = 4/3 * np.array([1, 12/10, 14/10, 17/10])\n",
    "doppeltritone_rein = 220 * doppeltritone # doppeltritone rein\n",
    "doppeltritone_edo12 = 220* toEDO(doppeltritone, 12)\n",
    "doppeltritone_edo53 = 220 * toEDO(doppeltritone, 53) # doppeltritone in EDO53\n",
    "\n",
    "amplitude = np.array([1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0])\n",
    "delay = np.array([0.0,0.2,0.4,0.6,0.8,1.0,1.2])\n",
    "\n",
    "# list of chords to display.\n",
    "# chords = [dursept_edo12, dursept_edo53, dursept_rein, ]\n",
    "# chords = [mollsept_edo12, mollsept_edo53, mollsept_rein, ]\n",
    "chords = [mollsept_edo12, mollsept_edo53, mollsept_rein ]\n",
    "\n",
    "to_display = []\n",
    "for chord in chords:\n",
    "    notes = len(chord)\n",
    "    signal, timesteps = create_signal(frequency=chord, amplitude=amplitude[:notes], delay=delay[:notes], phase=0, sampling=44100, seconds=5.0)\n",
    "    to_display.append(signal)\n",
    "\n",
    "max_play_time = 2.0\n",
    "for signal in to_display:\n",
    "    display(myAudio(signal[timesteps < max_play_time],rate=44100, autoplay=False))\n",
    "\n",
    "plot_time = 1.0\n",
    "\n",
    "plt.figure(1, figsize=(20,6))\n",
    "plt.xlabel(\"time [s]\")\n",
    "for signal in to_display:\n",
    "    plt.plot(timesteps[timesteps < plot_time], (1*signal[timesteps < plot_time]))\n",
    "\n",
    "plt.figure(2, figsize=(40,6))\n",
    "plt.subplot(111, xscale='log', yscale='log')\n",
    "plt.xlabel(\"Frequenz [Hz]\")\n",
    "plt.xlim(200,5000)\n",
    "plt.ylim(bottom=1e-1, top=1e4)\n",
    "for signal in to_display:\n",
    "    plt.plot(np.abs(fft(nonlinearity(signal[timesteps > 1.0], 0.1))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uj1KsDoBQkym"
   },
   "source": [
    "A = 100, B = 152\n",
    "B-A = 52, 2*A-B = 48\n",
    "A = 100, 2*B-2*A = 104, 4*A-2*B=96\n",
    "2*A = 200, 2*B-A = 204, 4*B-4*A = 208"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "id": "mGVxOys101H8",
    "outputId": "987a6b57-7b4a-49dc-bcb1-4970f7d664a9"
   },
   "source": [
    "#print((3/2)**3) #3 Quinten\n",
    "#print(2**2) #2 Oktaven\n",
    "81/80 #syntonisches Komma\n",
    "128/125 #Diesis\n",
    "(3/2)^12/2^7 #pythagoräisches Komma\n",
    "#print(6/5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EImFLStM4Cya"
   },
   "source": [
    "1 (C) 9/8 (D)   6/5 (Es)   5/4 (E)    4/3 (F)  3/2 (G) 8/5 (As) 5/3 (A) 15/8 (H) 2/1 (C) --> 5-limit tuning\n",
    "Ganztöne?\n",
    "C - D: 9/8\n",
    "D - E: 10/9\n",
    "Es - F: 10/9\n",
    "F - G: 9/8\n",
    "G - A: 10/9\n",
    "A - H: 9/8\n",
    "\n",
    "Halbtöne? 16/15, 25/24, 16/15, 16/15, 25/24, 16/15\n",
    "Große Terzen? 5/4, 5/4, 32/25, 5/4, 5/4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3-MNtcii-OMi"
   },
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 72
    },
    "id": "TtnU4FRY_p8f",
    "outputId": "8fdcbdec-f213-40f2-ea53-0cebd30d7eaa"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.125 1.122462048309373\n",
      "1.25 1.2599210498948732\n",
      "1.75 1.7817974362806785\n"
     ]
    }
   ],
   "source": [
    "print(9/8, 2**(2/12))\n",
    "print(5/4, 2**(4/12))\n",
    "print(7/4, 2**(10/12))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5mZHNFRO_xgZ"
   },
   "source": [
    "(3/2)**a = 2**b \n",
    "a * ln(3/2) = b * ln(2)\n",
    "a/b = ln(2) / ln(3/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "85VfR2WxHAx9"
   },
   "source": [
    "[1; 1, 2, 2, 3, 1, 5, 2, 23, 2, 2, 1, 1, 55, 1, 4, 3, 1, 1, 15, 1, 9, 2, 5, 7, 1, 1, 4, 8, 1, 1, ...]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "id": "61-Z8SsfHCe3",
    "outputId": "da53b747-99e4-4277-fc5f-27413ec67962"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7096774193548385"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 + 1/(1+1/2) #--> a=5, b=3\n",
    "1 + 1/(1+1/(2+1/2)) #--> a=12, b=7\n",
    "1 + 1/(1+1/(2+1/(2+1/3))) #--> a=41, b=24\n",
    "1 + 1/(1+1/(2+1/(2+1/(3+1)))) #--> a=53, b=31"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "iGJ4mYrSHF59",
    "outputId": "92fe9b7d-7542-43b7-f410-0213308084d2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.5\n",
      "1.515716566510398\n",
      "1.4983070768766815\n",
      "1.4937589616544857\n",
      "1.5004194330574077\n",
      "1.4999409030781112\n"
     ]
    }
   ],
   "source": [
    "print(3/2)\n",
    "print(2**(3/5))\n",
    "print(2**(7/12))\n",
    "print(2**(11/19))\n",
    "print(2**(24/41))\n",
    "print(2**(31/53))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "WNsx7Md7UqM2"
   },
   "outputs": [],
   "source": []
  }
 ],
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  "colab": {
   "collapsed_sections": [],
   "name": "Akkorde",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.3"
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