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by Marshall Hampton {{{ |
by Marshall Hampton. When the two frequencies are well separated, we hear the right hand side of the identity. When they start getting close, we hear the higher-pitched factor in the left-hand side modulated by the lower-pitched envelope. {{{#!sagecell |
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def sinsound(freq_ratio = slider(0,1,1/144,1/12)): | def sinsound(freq_ratio = slider(1/144,1,1/144,1/12)): |
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s2str = '' for x in s2f: s2str += wave.struct.pack('h',x) lab=str(float(freq_ratio)) |
s2str = ''.join(wave.struct.pack('h',x) for x in s2f) lab="%1.2f"%float(freq_ratio) |
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html('<embed src="https:./test'+ lab +'.wav" width="200" height="100"></embed>') | html('<embed src="cell://test'+ lab +'.wav" width="200" height="100"></embed>') |
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== Karplus-Strong algorithm for plucked and percussive sound generation == by Marshall Hampton {{{#!sagecell import wave class SoundFile: def __init__(self, signal,lab=''): self.file = wave.open('./test' + lab + '.wav', 'wb') self.signal = signal self.sr = 44100 def write(self): self.file.setparams((1, 2, self.sr, 44100*4, 'NONE', 'noncompressed')) self.file.writeframes(self.signal) self.file.close() mypi = float(pi) from math import sin def ks(delay,length,blend = 0,filler=None,stretch=0): if filler == None: filler = [randint(-16383,16383) for q in range(delay+1)] outsig = filler[:] index = len(filler) while len(outsig) < length: s = random() if s > stretch: b = random() if b < 1-blend: newvalue = (outsig[index-delay]+outsig[index-delay-1])*.5 else: newvalue = -(outsig[index-delay]+outsig[index-delay-1])*.5 else: newvalue = outsig[index-delay] outsig.append(newvalue) index += 1 return [int(round(x)) for x in outsig] @interact def sinsound(delay = slider([int(2^i) for i in range(2,10)], default=100, label="initial delay"), blend=slider(srange(0,1,.01,include_endpoint=True),default=0,label="blend factor"), stretch=slider(srange(0,1,.01,include_endpoint=True),default=0,label="stretch factor")): s2f = ks(delay,int(44100*(1/2)),blend=blend,stretch=stretch) for i in range(12): s2f = s2f + ks(int(2^((12+i)/12.0)*delay),int(44100*(1/2)),blend=blend, stretch=stretch) html("Karplus-Strong algorithm with blending and delay stretching") html("<br>K. Karplus and A. Strong, <em>Digital synthesis of plucked string and drum timbres</em>, \nComputer Music Journal 7 (2) (1983), 43–55.<br>") html("Initial waveform:") show(list_plot(s2f[0:2000],plotjoined=True), figsize = [7,3.5]) html("Waveform after stabilization:") show(list_plot(s2f[20000:22000],plotjoined=True), figsize = [7,3.5]) s2str = ''.join(wave.struct.pack('h',x) for x in s2f) lab="" f = SoundFile(s2str,lab=lab) f.write() html('<embed src="cell://test'+ lab +'.wav" width="200" height="100"></embed>') }}} {{attachment:KarplusStrong.png}} |
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{{{ | {{{#!sagecell |
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XY = X.intersection(Y) XZ = X.intersection(Z) YZ = Y.intersection(Z) XYZ = XY.intersection(Z) |
XY = X & Y XZ = X & Z YZ = Y & Z XYZ = XY & Z |
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Z = set(S[i]).intersection(S[(i+1)%3]).difference(set(XYZ)) | Z = (set(S[i]) & S[(i+1)%3]) - set(XYZ) |
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{{{ | {{{#!sagecell |
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{{{ | {{{#!sagecell |
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print "<html>" # trick to avoid word wrap | |
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cProfile.run(cmd) | cProfile.runctx(cmd,globals(), locals()) |
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profile.run(cmd) print "</html>" |
profile.runctx(cmd,globals(), locals()) |
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{{{ | {{{#!sagecell |
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== A Random Walk == by William Stein {{{ html('<h1>A Random Walk</h1>') vv = []; nn = 0 @interact def foo(pts = checkbox(True, "Show points"), refresh = checkbox(False, "New random walk every time"), steps = (50,(10..500))): # We cache the walk in the global variable vv, so that # checking or unchecking the points checkbox doesn't change # the random walk. html("<h2>%s steps</h2>"%steps) global vv if refresh or len(vv) == 0: s = 0; v = [(0,0)] for i in range(steps): s += random() - 0.5 v.append((i, s)) vv = v elif len(vv) != steps: # Add or subtract some points s = vv[-1][1]; j = len(vv) for i in range(steps - len(vv)): s += random() - 0.5 vv.append((i+j,s)) v = vv[:steps] else: v = vv L = line(v, rgbcolor='#4a8de2') if pts: L += points(v, pointsize=10, rgbcolor='red') show(L, xmin=0, figsize=[8,3]) }}} {{attachment:randomwalk.png}} == 3D Random Walk == {{{ @interact def rwalk3d(n=(50,1000), frame=True): pnt = [0,0,0] v = [copy(pnt)] for i in range(n): pnt[0] += random()-0.5 pnt[1] += random()-0.5 pnt[2] += random()-0.5 v.append(copy(pnt)) show(line3d(v,color='black'),aspect_ratio=[1,1,1],frame=frame) }}} {{attachment:randomwalk3d.png}} |
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{{{ | {{{#!sagecell |
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edge_lines = edge_lines + line([verts[an_edge[0]], verts[an_edge[1][0]]]) edge_lines = edge_lines + line([verts[an_edge[0]], verts[an_edge[1][1]]]) |
edge_lines += line([verts[an_edge[0]], verts[an_edge[1][0]]]) edge_lines += line([verts[an_edge[0]], verts[an_edge[1][1]]]) |
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triangle_sum = triangle_sum + polygon(temp_list, alpha = .5, rgbcolor = (1,0,0)) | triangle_sum += polygon(temp_list, alpha = .5, rgbcolor = (1,0,0)) |
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kite_sum = kite_sum + polygon(temp_list, alpha = .3,rgbcolor = (0,0,1)) | kite_sum += polygon(temp_list, alpha = .3,rgbcolor = (0,0,1)) |
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labels = labels + text('=', (-.2,.5), rgbcolor = (0,0,0)) | labels += text('=', (-.2,.5), rgbcolor = (0,0,0)) |
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== Cellular Automata == by Pablo Angulo, Eviatar Bach {{{#!sagecell %python from numpy import zeros from random import randint def cellular(rule, N, initial='Single-cell'): '''Yields a matrix showing the evolution of a Wolfram's cellular automaton rule: determines how a cell's value is updated, depending on its neighbors N: number of iterations initial: starting condition; can be either single-cell or a random binary row ''' M=zeros( (N,2*N+2), dtype=int) if initial=='Single-cell': M[0,N]=1 else: M[0]=[randint(0,1) for a in range(0,2*N+2)] for j in range(1,N): for k in range(0,2*N): l = 4*M[j-1,k-1] + 2*M[j-1,k] + M[j-1,k+1] M[j,k]=rule[ l ] return M[:,:-1] def num2rule(number): if not 0 <= number <= 255: raise Exception('Invalid rule number') binary_digits = number.digits(base=2) return binary_digits + [0]*(8-len(binary_digits)) }}} Put in separate cell: {{{#!sagecell @interact def _( initial=selector(['Single-cell', 'Random'], label='Starting condition'), N=input_box(label='Number of iterations',default=100), rule_number=input_box(label='Rule number',default=110), size = slider(1, 11, label= 'Size', step_size=1, default=6 ), auto_update=False): rule = num2rule(rule_number) M = cellular(rule, N, initial) plot_M = matrix_plot(M, cmap='binary') plot_M.show( figsize=[size,size]) }}} {{attachment:cellular2.png}} |
Sage Interactions - Miscellaneous
goto interact main page
Contents
Hearing a trigonometric identity
by Marshall Hampton. When the two frequencies are well separated, we hear the right hand side of the identity. When they start getting close, we hear the higher-pitched factor in the left-hand side modulated by the lower-pitched envelope.
Karplus-Strong algorithm for plucked and percussive sound generation
by Marshall Hampton
An Interactive Venn Diagram
Unreadable code
by Igor Tolkov
Profile a snippet of code
Evaluate a bit of code in a given system
by William Stein (there is no way yet to make the text box big):
Minkowski Sum
by Marshall Hampton
Cellular Automata
by Pablo Angulo, Eviatar Bach
Put in separate cell: