{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def saut_quinte(n, freq_ref):\n",
      "    return freq_ref * (3./2) ** n\n",
      "        "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "saut_quinte(-1, 660)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "440.0"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ints = arange(-6, 6)\n",
      "ints "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "array([-6, -5, -4, -3, -2, -1,  0,  1,  2,  3,  4,  5])"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "freqs_iter = map(lambda s: saut_quinte(s, 440), ints)\n",
      "freqs_iter"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "[38.628257887517144,\n",
        " 57.942386831275726,\n",
        " 86.913580246913568,\n",
        " 130.37037037037035,\n",
        " 195.55555555555554,\n",
        " 293.33333333333331,\n",
        " 440.0,\n",
        " 660.0,\n",
        " 990.0,\n",
        " 1485.0,\n",
        " 2227.5,\n",
        " 3341.25]"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def back_to_ref(freq, freq_ref):\n",
      "    if freq < freq_ref:\n",
      "        while freq < freq_ref:\n",
      "            freq = freq * 2.\n",
      "        return freq\n",
      "    elif freq > 2 * freq_ref:\n",
      "        while freq > 2 * freq_ref:\n",
      "            freq = freq / 2.\n",
      "        return freq\n",
      "    else:\n",
      "        return freq"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "back_to_ref(57, 440)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "456.0"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c_scale = map(lambda s: back_to_ref(s, 440), freqs_iter)\n",
      "c_scale"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "[618.0521262002743,\n",
        " 463.53909465020581,\n",
        " 695.30864197530855,\n",
        " 521.48148148148141,\n",
        " 782.22222222222217,\n",
        " 586.66666666666663,\n",
        " 440.0,\n",
        " 660.0,\n",
        " 495.0,\n",
        " 742.5,\n",
        " 556.875,\n",
        " 835.3125]"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "len(c_scale)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "12"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def get_scale(n):\n",
      "    total_scale = c_scale + c_scale + c_scale\n",
      "    return total_scale[12 + n - 1: 12 + n + 6]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "get_scale(6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "[586.66666666666663, 440.0, 660.0, 495.0, 742.5, 556.875, 835.3125]"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "get_scale(7)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "[440.0, 660.0, 495.0, 742.5, 556.875, 835.3125, 618.0521262002743]"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "map(lambda s: back_to_ref(s, 660), get_scale(7))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "[880.0, 660.0, 990.0, 742.5, 1113.75, 835.3125, 1236.1042524005486]"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def calc_ratio(seq):\n",
      "    seq = map(lambda s: back_to_ref(s, seq[1]), seq)\n",
      "    ratios = map(lambda s: s/seq[1], seq)\n",
      "    ratios.sort()\n",
      "    return ratios"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "calc_ratio(get_scale(6))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "[1.0, 1.125, 1.265625, 1.3333333333333333, 1.5, 1.6875, 1.8984375]"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "calc_ratio(get_scale(7))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "[1.0, 1.125, 1.265625, 1.3333333333333333, 1.5, 1.6875, 1.8728852309099222]"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "calc_ratio(get_scale(2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 42,
       "text": [
        "[1.0,\n",
        " 1.125,\n",
        " 1.2656250000000002,\n",
        " 1.3333333333333337,\n",
        " 1.5,\n",
        " 1.6875000000000002,\n",
        " 1.8984375000000002]"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ratio_diff(n):\n",
      "    ref = calc_ratio(get_scale(6))\n",
      "    diff = array(calc_ratio(get_scale(n))) - array(ref)\n",
      "    return diff"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ratio_diff(0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": [
        "array([  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "         1.81910197e-02,   2.22044605e-16,   0.00000000e+00,\n",
        "         0.00000000e+00])"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ratio_diff(7)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "array([ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
        "        0.        , -0.02555227])"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(10, 10))\n",
      "for i in range(12):\n",
      "    plot(ratio_diff(i),label='%i' % i)\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 44,
       "text": [
        "<matplotlib.legend.Legend at 0xac0088c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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fwMGDppOIuE/nzp2ZPXs2ubm5HD58mM8++4y//e1vbru/VjuK+IBBgyApCR59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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xac065cc>"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "i = 7\n",
      "plot(range(i, i + 7), ratio_diff(i))\n",
      "i = 8\n",
      "plot(range(i, i + 7), ratio_diff(i))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "[<matplotlib.lines.Line2D at 0xac5f7ac>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wbNkyAEBQUBC2bNmCrKwsqNVqrFixAvHx8QCA3bt3Izo6GseOHcOyZcuwZMkS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\nnKIiQQghxCkqEoQQQpz6/531vgC02iEaAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xaa7f26c>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mat = zeros((12, 12+7))\n",
      "for i in range(12):\n",
      "    mat[i, i:i+7] = ratio_diff(i)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "matshow(mat)\n",
      "colorbar()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 47,
       "text": [
        "<matplotlib.colorbar.Colorbar instance at 0xb147e2c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ffHPUOt3d3VitoTeditsY/oRsUXYZ0vcUHn1PkWiMdwCmEs4eIoWFhXg8Hrq6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\ngKtugwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb11c0ac>"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ratio_diff(10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "array([ 0.        , -0.01514209, -0.01703485,  0.        ,  0.        ,\n",
        "       -0.02271313, -0.02555227])"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}