Differences between revisions 18 and 19

Sage Interactions - Miscellaneous

Contents

Sage Interactions - Miscellaneous

Hearing a trigonometric identity

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.

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

@interact
def sinsound(freq_ratio =  slider(0,1,1/144,1/12)):
    hz1 = 440.0
    hz2 = float(440.0*2^freq_ratio)
    html('$\cos(\omega t) - \cos(\omega_0 t) = 2 \sin(\\frac{\omega + \omega_0}{2}t) \sin(\\frac{\omega - \omega_0}{2}t)$')
    s2 = [sin(hz1*x*mypi*2)+sin(hz2*x*mypi*2) for x in srange(0,4,1/44100.0)]
    s2m = max(s2)
    s2f = [16384*x/s2m for x in s2]
    s2str = ''.join(wave.struct.pack('h',x) for x in s2f)
    lab="%1.2f"%float(freq_ratio)
    f = SoundFile(s2str,lab=lab)
    f.write()
    pnum = 1500+int(500/freq_ratio)
    show(list_plot(s2[0:pnum],plotjoined=True))
    html('<embed src="https:./test'+ lab +'.wav" width="200" height="100"></embed>')
    html('Frequencies: '+ '$\omega_0 = ' + str(hz1) + ' $, $\omega = '+latex(hz2) + '$')

Karplus-Strong algorithm for plucked and percussive sound generation

by Marshall Hampton

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="https:./test'+ lab +'.wav" width="200" height="100"></embed>')

An Interactive Venn Diagram

def f(s, braces=True): 
    t = ', '.join(sorted(list(s)))
    if braces: return '{' + t + '}'
    return t
def g(s): return set(str(s).replace(',',' ').split())

@interact
def _(X='1,2,3,a', Y='2,a,3,4,apple', Z='a,b,10,apple'):
    S = [g(X), g(Y), g(Z)]
    X,Y,Z = S
    XY = X & Y
    XZ = X & Z
    YZ = Y & Z
    XYZ = XY & Z
    html('<center>')
    html("$X \cap Y$ = %s"%f(XY))
    html("$X \cap Z$ = %s"%f(XZ))
    html("$Y \cap Z$ = %s"%f(YZ))
    html("$X \cap Y \cap Z$ = %s"%f(XYZ))
    html('</center>')
    centers = [(cos(n*2*pi/3), sin(n*2*pi/3)) for n in [0,1,2]]
    scale = 1.7
    clr = ['yellow', 'blue', 'green']
    G = Graphics()
    for i in range(len(S)):
        G += circle(centers[i], scale, rgbcolor=clr[i], 
             fill=True, alpha=0.3)
    for i in range(len(S)):
        G += circle(centers[i], scale, rgbcolor='black')

    # Plot what is in one but neither other
    for i in range(len(S)):
        Z = set(S[i])
        for j in range(1,len(S)):
            Z = Z.difference(S[(i+j)%3])
        G += text(f(Z,braces=False), (1.5*centers[i][0],1.7*centers[i][1]), rgbcolor='black')


    # Plot pairs of intersections
    for i in range(len(S)):
        Z = (set(S[i]) & S[(i+1)%3]) - set(XYZ)
        C = (1.3*cos(i*2*pi/3 + pi/3), 1.3*sin(i*2*pi/3 + pi/3))
        G += text(f(Z,braces=False), C, rgbcolor='black')

    # Plot intersection of all three
    G += text(f(XYZ,braces=False), (0,0), rgbcolor='black')

    # Show it
    G.show(aspect_ratio=1, axes=False)

Unreadable code

by Igor Tolkov

@interact
def _(h=(20,(1,36,1))):
    print (lambda f:f(0,f))(
        lambda n,f:'%s\n%s'%(
            ('*'*(2*n+1)).join([' '*(h-n-1)]*2),
            ((n<h-1 and f(n+1,f)) or '')
        )
    )

Profile a snippet of code

html('<h2>Profile the given input</h2>')
import cProfile; import profile
@interact
def _(cmd = ("Statement", '2 + 2'), 
      do_preparse=("Preparse?", True), cprof =("cProfile?", False)):
    if do_preparse: cmd = preparse(cmd)
    print "<html>"  # trick to avoid word wrap
    if cprof:
        cProfile.run(cmd)
    else:
        profile.run(cmd)
    print "</html>"

Evaluate a bit of code in a given system

by William Stein (there is no way yet to make the text box big):

@interact
def _(system=selector([('sage0', 'Sage'), ('gp', 'PARI'), ('magma', 'Magma')]), code='2+2'):
    print globals()[system].eval(code)

Minkowski Sum