1 import numpy as np
  2 
  3 
  4 #
  5 # see details: https://en.wikipedia.org/wiki/MIDI_tuning_standard
  6 #
  7 _SCALES_L = ["C", "C#/Db", "D", "D#/Eb", "E", "F", "F#/Gb", "G", "G#/Ab", "A", "A#/Bb", "B"]
  8 
  9 def _nn2scale(d):
 10     return int(d / 12) - 2, _SCALES_L[int(d) % 12]
 11 
 12 def _nn2freq(d):
 13     return np.power(2, (d - 69) / 12.) * 440
 14 
 15 def _freq2nn(f):
 16     return 69 + 12 * np.log2(f / 440.)
 17 
 18 #############################################################
 19 #
 20 # matplotlib's custom scale implementation for MTS scales.
 21 #
 22 from numpy import ma
 23 from matplotlib import scale as mscale
 24 from matplotlib import transforms as mtransforms
 25 import matplotlib.ticker as ticker
 26 
 27 
 28 class MTSScaleScale(mscale.ScaleBase):
 29     name = 'midituningstandardscale'
 30 
 31     def __init__(self, axis, **kwargs):
 32         mscale.ScaleBase.__init__(self)
 33 
 34     def get_transform(self):
 35         return self.MTSScaleTransform()
 36 
 37     def set_default_locators_and_formatters(self, axis):
 38         class _nnformat(ticker.Formatter):
 39             def __init__(self, minor):
 40                 ticker.Formatter.__init__(self)
 41                 if minor:
 42                     self._fmt = lambda oc, sc: sc
 43                 else:
 44                     self._fmt = lambda oc, sc: "%s%d    -" % (sc, oc)
 45         
 46             def __call__(self, f, pos=None):
 47                 if f > 0:
 48                     nn = _freq2nn(f)
 49                     if nn - int(nn) < 1e-2:
 50                         oc, sc = _nn2scale(nn)
 51                         return self._fmt(oc, sc)
 52                 return ""
 53 
 54         _all = np.arange(-24, 168)
 55         _maj = np.array([v for v in _all if v % 12 == 0])
 56         _min = np.array([v for v in _all if v % 12 in (2, 4, 5, 7, 9, 11)])
 57         axis.set_major_locator(ticker.FixedLocator(_nn2freq(_maj)))
 58         axis.set_minor_locator(ticker.FixedLocator(_nn2freq(_min)))
 59         axis.set_major_formatter(ticker.FuncFormatter(_nnformat(False)))
 60         axis.set_minor_formatter(ticker.FuncFormatter(_nnformat(True)))
 61 
 62     def limit_range_for_scale(self, vmin, vmax, minpos):
 63         return max(_nn2freq(-2), vmin), max(_nn2freq(-2), vmax)
 64 
 65     class MTSScaleTransform(mtransforms.Transform):
 66         input_dims = 1
 67         output_dims = 1
 68         is_separable = True
 69 
 70         def __init__(self):
 71             mtransforms.Transform.__init__(self)
 72 
 73         def transform_non_affine(self, f):
 74             masked = ma.masked_where((f == 0), f)
 75             if masked.mask.any():
 76                 return 69 + 12 * ma.log2(f / 440.)
 77             else:
 78                 return 69 + 12 * np.log2(f / 440.)
 79 
 80         def inverted(self):
 81             return MTSScaleScale.InvertedMTSScaleTransform()
 82 
 83     class InvertedMTSScaleTransform(mtransforms.Transform):
 84         input_dims = 1
 85         output_dims = 1
 86         is_separable = True
 87 
 88         def __init__(self):
 89             mtransforms.Transform.__init__(self)
 90 
 91         def transform_non_affine(self, d):
 92             return _nn2freq(d)
 93 
 94         def inverted(self):
 95             return MTSScaleScale.MTSScaleTransform()
 96 
 97 mscale.register_scale(MTSScaleScale)
 98 #############################################################
 99 
100 if __name__ == '__main__':
101     # to display as text
102     print("<table>")
103     print("<thead><tr><th>Note Number</th><th>Scale + Octave</th><th>Freq. (in Hz)</th></td></thead>")
104     for i in range(0, 132, 12):
105         for d in range(i, i + 12):
106             print("<tr><td>{:3d}</td><td>{:5s}{:-2d}</td><td>{:8.2f}</td></tr>".format(
107                     d, _SCALES_L[d % 12], d // 12 - 2, _nn2freq(d)))
108     print("</table>")
109 
110     # graphical display
111     import matplotlib.pyplot as plt
112     f = np.arange(44100)
113 
114     fig, ax = plt.subplots()
115     fig.set_size_inches(11.69, 16.53)
116     ax.plot(f, f, '-', lw=2)
117     ax.set_yscale('midituningstandardscale')
118     ax.grid(True)
119 
120     ax.set_xlabel("Hz")
121     ax.set_ylabel("MIDI Tuning Standard Scales")
122     #plt.show()
123     fig.tight_layout()
124     fig.savefig("MTS_Scales.jpg")

 1 import math
 2 
 3 #
 4 # see details: https://en.wikipedia.org/wiki/MIDI_tuning_standard
 5 #
 6 _SCALES_L = ["C", "C#/Db", "D", "D#/Eb", "E", "F", "F#/Gb", "G", "G#/Ab", "A", "A#/Bb", "B"]
 7 
 8 def _nn2scale(d):
 9     ##return int(d / 12) - 2, _SCALES_L[int(d) % 12]
10     return int(d / 12) - 1, _SCALES_L[int(d) % 12]
11 
12 def _nn2freq(d):
13     return math.pow(2, (d - 69) / 12.) * 440
14 
15 def _freq2nn(f):
16     return 69 + 12 * math.log(f / 440., 2)