code

code/akkorde.py

@@ -0,0 +1,82 @@
+import numpy as np
+from matplotlib import pyplot as plt
+from scipy.fft import fft, ifft
+from IPython.display import Audio, display
+from scipy.io import wavfile
+from ipywidgets import widgets
+from functools import partial
+import pandas as pd
+from fractions import Fraction
+
+def create_signal(frequency, amplitude, delay, phase=0, sampling=44100, seconds=1.0):
+  timesteps = np.linspace(0,seconds, int(seconds * sampling))
+  # return np.sum(amplitude * np.sin(frequency * 2*np.pi * (timesteps[:, np.newaxis]-delay)*(timesteps[:, np.newaxis]-delay > 0)), axis=1), timesteps
+  return np.sum(amplitude * triangle(frequency, (timesteps[:, np.newaxis]-delay)*(timesteps[:, np.newaxis]-delay > 0)), axis=1), timesteps
+
+def create_waves(frequency, amplitude, phase=0, sampling=44100, seconds=1.0):
+  timesteps = np.linspace(0,seconds, int(seconds * sampling))
+  # return amplitude * np.sin(frequency * 2*np.pi * timesteps[:, np.newaxis]), timesteps
+  return amplitude * triangle(frequency, timesteps[:, np.newaxis]), timesteps
+
+def triangle(frequency, t):
+  phase = (t * frequency + 0.25) % 1 - 0.25
+  return (phase <= 0.25) * phase + (phase > 0.25) * (0.5 - phase)
+
+def nonlinearity(x, param=1.0): # param for scaling of argument; higher values = more nonlinearity
+  #return np.exp(x*param)
+  return np.sign(x)*np.log(1+np.abs(x*param))
+
+def myAudio(signal, rate=44100, autoplay=False, time_fade=0.2):
+  length = signal.shape[0]
+  print(length)
+  fade = np.minimum(np.ones(length),np.arange(length)/(time_fade * rate))
+  return Audio(signal * fade * fade[::-1],rate=rate,autoplay=autoplay)
+
+#frequency = np.array([100., 200., 300, 400])
+
+#frequency_edo12 = 220 * 2**(np.array([5,8,12,14])/12)
+#frequency_edo53 = 220 * 2**(np.array([22,36,53,62])/53)
+#frequency_edo53 = 220 * 2**(np.array([22,34,53,61])/53)
+#frequency_rein1 = 220 * 4/3 * np.array([1, 7/6, 9/6, 10/6])
+#frequency_rein2 = 220 * 4/3 * np.array([1, 12/10, 15/10, 17/10])
+dursept_edo12 = 220 * 2**(np.array([5,9,12,15])/12) # Durseptakkord in EDO12
+dursept_edo53 = 220 * 2**(np.array([22,39,53,65])/53) # Dursept in EDO53
+dursept_rein = 220 * 4/3 * np.array([1, 5/4, 6/4, 7/4]) # Dursept rein
+mollsept_edo12 = 220 * 2**(np.array([5,8,12,14])/12) # Mollseptakkord in EDO12
+mollsept_edo53 = 220 * 2**(np.array([22,36,53,63])/53) # Mollseptakkord in EDO53
+mollsept_rein = 220 * 4/3 * np.array([1, 12/10, 15/10, 17/10]) # Mollsept rein
+doppeltritone_rein = 220 * 4/3 * np.array([1, 12/10, 14/10, 17/10]) # doppeltritone rein
+doppeltritone_edo53 = 220 * 2**(np.array([22,36,48,63])/53) # doppeltritone in EDO53
+
+amplitude = np.array([1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0])
+delay = np.array([0.0,0.2,0.4,0.6,0.8,1.0,1.2])
+
+# list of chords to display.
+# chords = [dursept_edo12, dursept_edo53, dursept_rein, ]
+# chords = [mollsept_edo12, mollsept_edo53, mollsept_rein, ]
+chords = [doppeltritone_rein, doppeltritone_edo53, ]
+
+to_display = []
+for chord in chords:
+    notes = len(chord)
+    signal, timesteps = create_signal(frequency=chord, amplitude=amplitude[:notes], delay=delay[:notes], phase=0, sampling=44100, seconds=5.0)
+    to_display.append(signal)
+
+max_play_time = 2.0
+for signal in to_display:
+    display(myAudio(signal[timesteps < max_play_time],rate=44100, autoplay=False))
+
+plot_time = 1.0
+
+plt.figure(1, figsize=(20,6))
+plt.xlabel("time [s]")
+for signal in to_display:
+    plt.plot(timesteps[timesteps < plot_time], (1*signal[timesteps < plot_time]))
+
+plt.figure(2, figsize=(40,6))
+plt.subplot(111, xscale='log', yscale='log')
+plt.xlabel("Frequenz [Hz]")
+plt.xlim(200,5000)
+plt.ylim(bottom=1e-1, top=1e4)
+for signal in to_display:
+    plt.plot(np.abs(fft(nonlinearity(signal[timesteps > 1.0], 0.1))))

inputs/appendix.tex

@@ -1,3 +1 @@
-\begin{listing}
+\lstinputlisting[language=Python]{code/akkorde.py}
-TODO: Code einfügen 
-\end{listing}

musiktheorie.sty

@@ -12,3 +12,28 @@
 \RequirePackage{listing}
 \RequirePackage{wasysym}
 \RequirePackage{cancel}
+\RequirePackage{listings}
+
+\definecolor{KeywordColor}{cmyk}{0.64,0,0.95,0.40} %TODO
+\definecolor{mGray}{rgb}{0.5,0.5,0.5}
+\definecolor{mOrange}{rgb}{0.9,0.53,0.35}
+
+\lstset{
+  language=Python,                             % Code langugage
+  basicstyle=\ttfamily,                   % Code font, Examples: \footnotesize, \ttfamily
+  keywordstyle=\color{KeywordColor},        % Keywords font ('*' = uppercase)
+  commentstyle=\color{mGray},              % Comments font
+  numberstyle=\tiny\color{mGray},
+  stepnumber=1,                           % Step between two line-numbers
+  numbersep=5pt,                          % How far are line-numbers from code
+  frame=none,                             % A frame around the code
+  tabsize=2,                              % Default tab size
+  captionpos=b,                           % Caption-position = bottom
+  breaklines=true,                        % Automatic line breaking?
+  breakatwhitespace=false,                % Automatic breaks only at whitespace?
+  showspaces=false,                       % Dont make spaces visible
+  showtabs=false,                         % Dont make tabls visible
+  columns=flexible,                       % Column format
+  stringstyle=\color{mOrange},
+  escapeinside={/*!}{!*/},
+}