musiktheorietheorie/code/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": {
    "colab": {
     "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"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "                <audio  controls=\"controls\" >\n",
       "                    <source src=\"data:audio/wav;base64,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
       "                    Your browser does not support the audio element.\n",
       "                </audio>\n",
       "              "
      ],
      "text/plain": [
       "<IPython.lib.display.Audio object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "88200\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "                <audio  controls=\"controls\" >\n",
       "                    <source src=\"data:audio/wav;base64,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
       "                    Your browser does not support the audio element.\n",
       "                </audio>\n",
       "              "
      ],
      "text/plain": [
       "<IPython.lib.display.Audio object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "88200\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "                <audio  controls=\"controls\" >\n",
       "                    <source src=\"data:audio/wav;base64,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
       "                    Your browser does not support the audio element.\n",
       "                </audio>\n",
       "              "
      ],
      "text/plain": [
       "<IPython.lib.display.Audio object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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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": []
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "Akkorde",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}