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| by Marshall Hampton. When the two frequencies are well seperated, 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. {{{ |
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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| 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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| {{{ | {{{#!sagecell |
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| {{{ | {{{#!sagecell |
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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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| by Pablo Angulo {{{ %cython |
by Pablo Angulo, Eviatar Bach {{{#!sagecell %python |
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def cellular(rule, int N): |
from random import randint def cellular(rule, N, initial='Single-cell'): |
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| initial: starting condition; can be either single-cell or a random binary row | |
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| cdef int j,k,l M=zeros( (N,2*N+1), dtype=int) M[0,N]=1 |
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)] |
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| for k in range(N-j,N+j+1): | for k in range(0,2*N): |
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| return M }}} {{{ |
return M[:,:-1] |
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@interact def _( N=input_box(label='Number of iterations',default=100), |
}}} Put in separate cell: {{{#!sagecell @interact def _( initial=selector(['Single-cell', 'Random'], label='Starting condition'), N=input_box(label='Number of iterations',default=100), |
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| size = slider(1, 11, step_size=1, default=6 ) ): | size = slider(1, 11, label= 'Size', step_size=1, default=6 ), auto_update=False): |
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| M = cellular(rule, N) plot_M = matrix_plot(M) |
M = cellular(rule, N, initial) plot_M = matrix_plot(M, cmap='binary') |
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| {{attachment:cellular.png}} | {{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:
