{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# 1. Literate Computing for Art and Science" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Douglas Blank
\n", "Associate Processor, Computer Science
\n", "Bryn Mawr College
\n", "

\n", "\n", "http://goo.gl/hNNMY8" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## 1.1 Literate Computing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Literate Computing**: _a style of computation that can be enjoyably read by anyone._\n", "\n", "> \"The focus of **literate programming** is to document a program. In this manner, it is an inward-facing document, designed to explain itself. On the other hand, **literate computing** is meant to focus on the computational goals, rather than on the specific details of the program. The goal of literate computing is not to explain the workings of a program to programmers, but to explain a computational problem to a wide audience.\" - O'Hara, Blank, and Marshall (2015)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1.1 What?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Literate computing is not new. But new tools better integrate computation with writing. \n", "\n", "* One could manually construct a document with embedded code, equations, and media. \n", "* Mathematica notebook \n", "\n", "\n", "\n", "* Jupyter, an open source, language agnostic, project that includes notebook\n", "* You are looking at a Jupyter Notebook using the Python3 kernel" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1.2 Why?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Makes results reproducible\n", "\n", "> To convince someone of a particular result, those results should be reproducible. With the rise of \"data-driven journalism\" replication of results is critical. \n", "\n", "> Consider Reinhart and Rogoff's Growth in a Time of Debt. This paper has had a large impact in the way that we view the effectiveness of austerity in fiscal policy. However, Herndon, Ash, and Pollin reportedly found \"spreadsheet errors, omission of available data, weighting, and transcription\" in this paper. Corrected data significantly alter the results of the original findings.\n", "\n", "* Can explain computation effectively\n", "* Empowers the reader\n", "* Excellent uses in education: assignments, lectures, flipped classroom\n", "* Jupyter has thriving development, including over 40 programming languages, slideshow viewer, integration with github, and much more." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## 1.2 Sonification" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "format": "tab", "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline\n", "import math\n", "import random\n", "from IPython.display import IFrame" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "format": "tab" }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "IFrame(\"https://en.wikipedia.org/wiki/Sonification\", width=\"100%\", height=400)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# 2. Experiments" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.1 Sound via Functions" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "format": "tab", "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This cell defines the Audio class.\n" ] } ], "source": [ "from IPython.display import DisplayObject\n", "\n", "class Audio(DisplayObject):\n", " _read_flags = 'rb'\n", " \n", " def __init__(self, data=None, filename=None, url=None, embed=None, rate=None, autoplay=False, maxvalue=None):\n", " if filename is None and url is None and data is None:\n", " raise ValueError(\"No image data found. Expecting filename, url, or data.\")\n", " if embed is False and url is None:\n", " raise ValueError(\"No url found. Expecting url when embed=False\")\n", "\n", " if url is not None and embed is not True:\n", " self.embed = False\n", " else:\n", " self.embed = True\n", " self.autoplay = autoplay\n", " self.maxvalue = maxvalue\n", " super(Audio, self).__init__(data=data, url=url, filename=filename)\n", "\n", " if self.data is not None and not isinstance(self.data, bytes):\n", " self.data = self._make_wav(data,rate)\n", "\n", " def reload(self):\n", " \"\"\"Reload the raw data from file or URL.\"\"\"\n", " import mimetypes\n", " if self.embed:\n", " super(Audio, self).reload()\n", "\n", " if self.filename is not None:\n", " self.mimetype = mimetypes.guess_type(self.filename)[0]\n", " elif self.url is not None:\n", " self.mimetype = mimetypes.guess_type(self.url)[0]\n", " else:\n", " self.mimetype = \"audio/wav\"\n", "\n", " def _make_wav(self, data, rate):\n", " \"\"\" Transform a numpy array to a PCM bytestring \"\"\"\n", " import struct\n", " from io import BytesIO\n", " import wave\n", "\n", " try:\n", " import numpy as np\n", "\n", " data = np.array(data, dtype=float)\n", " if len(data.shape) == 1:\n", " nchan = 1\n", " elif len(data.shape) == 2:\n", " # In wave files,channels are interleaved. E.g.,\n", " # \"L1R1L2R2...\" for stereo. See\n", " # http://msdn.microsoft.com/en-us/library/windows/hardware/dn653308(v=vs.85).aspx\n", " # for channel ordering\n", " nchan = data.shape[0]\n", " data = data.T.ravel()\n", " else:\n", " raise ValueError('Array audio input must be a 1D or 2D array')\n", " if self.maxvalue is None:\n", " maxvalue = np.max(np.abs(data))\n", " else:\n", " maxvalue = self.maxvalue\n", " scaled = np.int16(data/maxvalue * 32767).tolist()\n", " except ImportError:\n", " # check that it is a \"1D\" list\n", " idata = iter(data) # fails if not an iterable\n", " try:\n", " iter(idata.next())\n", " raise TypeError('Only lists of mono audio are '\n", " 'supported if numpy is not installed')\n", " except TypeError:\n", " # this means it's not a nested list, which is what we want\n", " pass\n", " if self.maxvalue is None:\n", " maxvalue = float(max([abs(x) for x in data]))\n", " else:\n", " maxvalue = self.maxvalue\n", " scaled = [int(x/maxvalue * 32767) for x in data]\n", " nchan = 1\n", "\n", " fp = BytesIO()\n", " waveobj = wave.open(fp,mode='wb')\n", " waveobj.setnchannels(nchan)\n", " waveobj.setframerate(rate)\n", " waveobj.setsampwidth(2)\n", " waveobj.setcomptype('NONE','NONE')\n", " waveobj.writeframes(b''.join([struct.pack('\n", " \n", " Your browser does not support the audio element.\n", " \n", " \"\"\"\n", " return src.format(src=self.src_attr(),type=self.mimetype, autoplay=self.autoplay_attr())\n", "\n", " def src_attr(self):\n", " import base64\n", " if self.embed and (self.data is not None):\n", " data = base64=base64.b64encode(self.data).decode('ascii')\n", " return \"\"\"data:{type};base64,{base64}\"\"\".format(type=self.mimetype,\n", " base64=data)\n", " elif self.url is not None:\n", " return self.url\n", " else:\n", " return \"\"\n", "\n", " def autoplay_attr(self):\n", " if(self.autoplay):\n", " return 'autoplay=\"autoplay\"'\n", " else:\n", " return ''\n", " \n", "print(\"This cell defines the Audio class.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1.1 White Noise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For these first experiments, we will create a series of functions that take a time argument and return a value representing sound at that time.\n", "\n", "For example, here are a couple of functions that will generate noise at a couple of different volumes (note that t is ignored):" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def noise50(t):\n", " return 0.5 * random.uniform(-1, 1)\n", "\n", "def noise75(t):\n", " return 0.75 * random.uniform(-1, 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's test these out:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-0.25963995967660586" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "noise75(576457465476)" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-0.12930471751048123" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "noise50(0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now have a couple of functions that give random values between -amplitude and +amplitude." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, even before we begin to use these, we notice that there is a lot of repeated code. We could actually use our computational skills to abstract these into a function that creates functions:" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def make_noise(amplitude=0.5):\n", " def f(t):\n", " return amplitude * random.uniform(-1, 1)\n", " return f" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we can use the function `make_noise` to create our functions for us:" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": true }, "outputs": [], "source": [ "noise50 = make_noise(0.5)\n", "noise10 = make_noise(0.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we can interactively test these as before." ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.4566795868363519" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "noise50(0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's make a lot of noise!\n", "\n", "We will use the standard of 44,100 data values per second, as most hardware can support that format.\n", "\n", "We use Python's list comprehension to make a list of random values:" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false }, "outputs": [], "source": [ "data = [noise10(t) for t in arange(0, 5, 1/44100)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, let's take a look at some of the data, the first 100 values (the plot command is part of matplotlib we we activated using `%pylab inline` magic):" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEACAYAAAC3adEgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", 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"metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "<__main__.Audio object>" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Audio(data, rate=44100, maxvalue=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Audio can also take a two-dimensional array of numbers to create stereo audio." ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": true }, "outputs": [], "source": [ "data2 = [noise50(t) for t in arange(0, 5, 1/44100)]" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "<__main__.Audio object>" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Audio([data, data2], rate=44100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Does it sound fundamentally different from mono noise?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1.2 Perlin Noise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This next code won an Academy Award for Technical Acheivement." ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "IFrame(\"https://en.wikipedia.org/wiki/Perlin_noise\", width=\"100%\", height=\"400\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We're going to use use open source code for generating the Perlin Noise. In fact, we will automate getting the code in this notebook as well. We use the `!` symbol to indicate that this is a shell command:" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--2015-07-09 15:44:11-- https://raw.githubusercontent.com/caseman/noise/master/perlin.py\n", "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 23.235.46.133\n", "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|23.235.46.133|:443... connected.\n", "HTTP request sent, awaiting response... 200 OK\n", "Length: 11694 (11K) [text/plain]\n", "Saving to: ‘perlin.py.1’\n", "\n", "100%[======================================>] 11,694 --.-K/s in 0s \n", "\n", "2015-07-09 15:44:11 (298 MB/s) - ‘perlin.py.1’ saved [11694/11694]\n", "\n" ] } ], "source": [ "! wget https://raw.githubusercontent.com/caseman/noise/master/perlin.py " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have that code, we can simply import it, and use it:" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from perlin import *" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false }, "outputs": [], "source": [ "ngen = SimplexNoise()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I played around with the resolution to find values that would give good values for random sounds:" ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 6.41 s, sys: 0 ns, total: 6.41 s\n", "Wall time: 6.41 s\n" ] } ], "source": [ "%%time\n", "data = [ngen.noise2(t/200, 0) for t in arange(0, 44100 * 5)]" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" }, { "data": { 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"data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "<__main__.Audio object>" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Audio(data, rate=44100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1.3 Tones" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We made some noise, but now let's make music.\n", "\n", "Tones are generated by creating waves at a particular frequency.\n", "\n", "First, as before, we define a function that can make functions:" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "def make_tone(frequency):\n", " def f(t):\n", " return math.sin(2 * math.pi * frequency * t)\n", " return f" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "tone440 = make_tone(440)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's take a look at 1/100 of a second of this tone:" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYAAAAEACAYAAAC6d6FnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJztnXm0XdV93z9b8zwBmgVPIMQswNgYY2NkBzvgNNhukzrp\n", "YC+nSd02TrJcpx5T+7X1alKnTrJS145TO6uu09pJm8QlMdTGgDyAwQYkwIBAAj3NA4MkBBKgYfeP\n", "fe7T1dUdzj1nz+f3WUtL7917hp9+2nt/9++3JxAEQRAEQRAEQRAEQRAEQRAEQRAEQRAEQRAEQRAE\n", "QRAayp8Be4FH+lzzx8Am4CHgSh9GCYIgCO65DtOo9xKAdwC3Fj+/HrjXh1GCIAiCH0boLQB/Aryn\n", "7feNwCLXBgmCIAj9meDhHcuA7W2/7wCWe3ivIAiC0AcfAgCgOn7Xnt4rCIIg9GCSh3fsBFa0/b68\n", "+KyTzcB5HuwRBEHIiaeAVSENGKHcIPA19B4ErhEV6F8FfQ/oicXv54B+FvTK6s8EYLTm/S4YrX6r\n", 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"execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Audio([tone440(t) for t in arange(0, 5, 1/44100)], rate=44100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1.4 Binaural beats" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import IFrame\n", "IFrame(\"http://en.wikipedia.org/wiki/Binaural_beats\", width=\"100%\", height=\"400\")" ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": true }, "outputs": [], "source": [ "tone220 = make_tone(220)\n", "tone221 = make_tone(221)\n", "data220 = [tone220(t) for t in arange(0, 5, 1/44100)]\n", "data221 = [tone221(t) for t in arange(0, 5, 1/44100)]" ] }, { "cell_type": "code", "execution_count": 85, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "<__main__.Audio object>" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Audio([data220, data221], rate=44100)" ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def array_add(a1, a2):\n", " return [a1[i] + a2[i] for i in range(len(a1))]" ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "<__main__.Audio object>" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Audio(array_add(data220, data221), rate=44100)" ] }, { "cell_type": "code", "execution_count": 89, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# (6.0, 4.0)\n", "rcParams[\"figure.figsize\"] = (12.0, 4.0)" ] }, { "cell_type": "code", "execution_count": 90, "metadata": 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object>" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Audio([data300, data310], rate=44100)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "Audio(array_add(data300, data310), rate=44100)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 2.2 Array-based Mathematics" ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "collapsed": true }, "outputs": [], "source": [ "framerate = 44100\n", "t = np.linspace(0, 5, framerate * 5)\n", "tone = np.sin(2 * np.pi * 440 * t)" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYAAAAEACAYAAAC6d6FnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", 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"execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Audio(tone + antitone, rate=framerate, maxvalue=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2.1 Sequence of Tones" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the following code:" ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "collapsed": false }, "outputs": [], "source": [ "framerate = 44100\n", "t = np.linspace(0, 5, framerate * 5)\n", "chunk = np.sin(2 * np.pi * 440 * t)\n", "data = np.array(0)\n", "for i in range((44100 * 5)//870 + 1):\n", " data = np.append(data, chunk[:870])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that we interrupt the tone after 870 data points to restart the tone again at zero. Here is what that looks like at one of the interruptions:" ] }, { "cell_type": "code", "execution_count": 104, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYAAAAEACAYAAAC6d6FnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJztnXnQXcV14H9Xn/YFCbEIIQkkIQRCCxJiEQjMhzFG4AWb\n", "BNtMnGRsj2NX7IyT2WySSUVVMzWLXVNJeeyxXfG4hsTjpRKPCQ4YGzCYxSDAaAEJoQUkJCEksYhF\n", "AiHQmT+636fve3rbfa/v7eWeX9VX31vu7T73dd8+t885fRoURVEURVEURVEURVEURVEURVEURVEU\n", "RVEURVEURVGUivI9YA/wRItjvg5sBtYCS8oQSlEURSmeyzCDejMFcC1wu319EfBwGUIpiqIo5TCT\n", "5grg28DHB73fCEwpWiBFURSlNcNKqGMasGPQ+53A9BLqVRRFUVpQhgIAyOreS0n1KoqiKE0YXkId\n", "u4AZg95Pt5/VswU4owR5FEVRUmIrMMenADPpzAm8jOZO4JJmBfJxkG0gs+o+nwSyBuTPC6p4ZUHl\n", "hsDK8qqSvwR5BGRy3eezQZ4z7euclQWUWRLyRyCbQKbVfT4VZD3IF4n6+jpipW8Buke+BvIAyLi6\n", 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smooth transitions between two tones (or even the same tone) we need to keep track of where we are in the sin curve. " ] }, { "cell_type": "code", "execution_count": 106, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def make_tone(t, frequency):\n", " return math.sin(2 * math.pi * frequency * t)\n", "\n", "data = []\n", "freq = 220\n", "for t in arange(0, 5, 1/44100):\n", " if t % 1.0 == 0:\n", " freq = freq * 2\n", " data.append(make_tone(t, freq))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we look at the transition point between two tones:" ] }, { "cell_type": "code", "execution_count": 107, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYAAAAEACAYAAAC6d6FnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJztnXmwZUd93z9nVs2mGc1o9hlphBas0QICIzZhxixmiyGk\n", "jDFJlRXjcigTcKqcEDYnqFKpsuOqVFIO4JAEEpJygYNtiGJ2HMQmEBJoQBKSRoM0aJ0ZzaLR7Nvr\n", 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Notice that doubling the frequency exactly raises the tone to the next octave." ] }, { "cell_type": "code", "execution_count": 108, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "<__main__.Audio object>" ] }, "execution_count": 108, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Audio(data, rate=44100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just as a double check, we can look at the spectrogram of the resulting sound:" ] }, { "cell_type": "code", "execution_count": 109, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEACAYAAAC+gnFaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzsvWusJdl1HvZV1bmvfkwPyREpiRyKpERTkhHYjh3RiuG4\n", "EQmIYsBQ/kSCAgSwkR9KAOZH/sSBg0QTIA8YSALHUAATjuIfBmIlSGJYASIJARzBgCElJmA51oMS\n", "KVJ8ipRmONM93X1fp2rnx65V61trr111Tt/b9/LePqtx+5zaj7XWftR67ccBdrCDHexgBzvYwQ52\n", 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The DFT is defined by the formula\n", "\n", "$ X_k = \\sum_{n=0}^{N-1} x_n e^{-{i 2\\pi k \\frac{n}{N}}} \\qquad k = 0,\\dots,N-1. $\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2.2 Random Tones" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We return to Perlin Noise to make music that no human would ever create." ] }, { "cell_type": "code", "execution_count": 110, "metadata": { "collapsed": false }, "outputs": [], "source": [ "ngen = SimplexNoise()\n", "\n", "data = []\n", "for t in arange(0, 44100 * 5):\n", " freq = ngen.noise2(t/700000, 0) * 800 + 800\n", " data.append(make_tone(t, freq))" ] }, { "cell_type": "code", "execution_count": 111, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "<__main__.Audio object>" ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Audio(data, rate=44100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What do you think of that? Could a computer ever create music as beautiful as Bach? Maybe, but obviously not in this manner.\n", "\n", "Here is that \"music\" as seen in a spectrogram:" ] }, { "cell_type": "code", "execution_count": 112, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEACAYAAAC+gnFaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzsvXusNllW3vfbe1e9l3POd+3ume7puQNmgAmWjS0MBjy2\n", "E0dGYEuOnIBx7JCLZIvYwrYS5SIbkSgRkYL/iGI7jgEjJZFjBycBKwQRiFBkkMNEIO7DMDMwM/T0\n", "/buc2/u+VbX3yh/P2rvqfAMWooeW0nm3dHTOeS9Vu3ZVrWet51lrFRzHcRzHcRzHcRzHcRzHcRzH\n", "cRzHcRzHcRzHcRzHcRzHcRzHcRzHcRzHcRzHcRzHcRzHcRzHcRzHcRzHcRzHcdwY3wO8DPzcP+cz\n", "/xXwK8DPAL/nzZjUcRzHcRzHcbx546uRcf/NgOBrgR/0v78c+GdvxqSO4ziO4ziO480d7+U3B4L/\n", "BvjXFv9/BHj77/SEjuM4juM4juNzM+LnYBvPA59e/P/rwDs/B9s9juM4juM4jjdhfC6AACA88b99\n", "jrZ7HMdxHMdxHL/Do/scbOMF4F2L/9/pr90Y74/YJ8rnYG/HcRzHcRz//xofBz7/d3IHn4uI4AeA\n", "P+d//wHgEcoyujE+UcD+LEzvgs8k2L0NHq4g/3E4fBDsnfDyGuxPwvUz8HoH5X2wuw3DHf223wXX\n", 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Our goal is to listen to climate change.\n", "\n", "First, we use Rhine's data from a spreadsheet representing the years and global average temperature." ] }, { "cell_type": "code", "execution_count": 115, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import csv" ] }, { "cell_type": "code", "execution_count": 119, "metadata": { "collapsed": false }, "outputs": [], "source": [ "data = []\n", "with open(\"nasa climate data four.csv\") as fp:\n", " for row in csv.reader(fp):\n", " data.append(row)" ] }, { "cell_type": "code", "execution_count": 120, "metadata": { "collapsed": false }, "outputs": [], "source": [ "time = [int(row[0]) for row in data]" ] }, { "cell_type": "code", "execution_count": 121, "metadata": { "collapsed": true }, "outputs": [], "source": [ "temps = [float(row[3]) for row in data]" ] }, { "cell_type": "code", "execution_count": 122, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 122, 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[ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(time, temps)" ] }, { "cell_type": "code", "execution_count": 123, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "50" ] }, "execution_count": 123, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(temps)" ] }, { "cell_type": "code", "execution_count": 124, "metadata": { "collapsed": false }, "outputs": [], "source": [ "data = []\n", "for t in arange(0, 5, 1/44100):\n", " temp_index = floor(t/5.0 * len(temps))\n", " ratio = (temps[temp_index] - min(temps))/(max(temps) - min(temps))\n", " data.append(make_tone(t, ratio * 16000 + 400)) " ] }, { "cell_type": "code", "execution_count": 125, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "<__main__.Audio object>" ] }, "execution_count": 125, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Audio(data, rate=44100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And again, a double check to make sure that we have the data correct:" ] }, { "cell_type": "code", "execution_count": 126, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEACAYAAAC+gnFaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzsvXnQbctV2Pfrvc/5vu/eN/OenmZLoNEYCwlsJBMrvAIS\n", "CAZTGRwKp5yqVCVxksKVxKlKlfOHUVJJqlzlxJDYrqiMk7jsOPxBBlPYDEkIhMSAmQRmEEhCEpqe\n", "nvQkveHebzhnd+eP3mv36t5r7XPO1dW9vI+zbn1377OH7tW9u9fcq+EIRzjCEY5whCMc4QhHOMIR\n", "jnCEIxzhCEc4whGOcIQjHOEIRzjCEY5whCMc4QhHOMIRjnCEIxzhCEeo4L8HPg3804Vn/hvgA8Cv\n", "Au+4F0gd4QhHOMIR7h28m0zcPUbwbcA/Gs/fCfzcvUDqCEc4whGOcG/h9fiM4L8Dvkv9fj/w8i81\n", "Qkc4whGOcIS7A91dKOPVwMfU748Dr7kL5R7hCEc4whHuAdwNRgAQmt/pLpV7hCMc4QhH+BLD6i6U\n", "8Qngter3a8ZrFZy94RXp4kNP34XqjnCEIxzhDxR8CHjjl7KCu8EIfhj4HuAHgXcBXyBHGVVw8aGn\n", "+c709xnoOeOSDWsCiQ/yRl7B0zzG5+mI9Gx5jkd4ks/wNn6NX+Jr+Vp+iffxdt7O+/gPfui9/Ov/\n", 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Reflection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Could sonification be used to make data more understandable?" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "

References

\n", "\n", "Keith J. O’Hara, Douglas Blank, and James Marshall. [Computational Notebooks for AI Education](https://www.researchgate.net/publication/271446724_Computational_Notebooks_for_AI_Education). Proceedings of the Twenty-Eighth International Florida Artificial Intelligence Research Society Conference, FLAIRS 2015, Hollywood, Florida. May 2015. \n", "\n", "[Rhine Singleton](http://www.franklinpierce.edu/academics/bios/singleton.htm). http://www.ecologyandevolution.org/sonification.html" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.4.0" } }, "nbformat": 4, "nbformat_minor": 0 }