(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 24567, 598]*) (*NotebookOutlinePosition[ 25210, 620]*) (* CellTagsIndexPosition[ 25166, 616]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[StyleBox["Playing Sine Waves", FontColor->RGBColor[1, 0, 0]]], "Subsection", Background->GrayLevel[0.900008]], Cell[TextData[{ "Another standard application studied in trigonometry is sound waves of the \ form ", StyleBox["f ", FontWeight->"Bold", FontSlant->"Italic"], StyleBox["( t ) = A sin [ B t ]", FontWeight->"Bold"], " , where A is the amplitude of the sound (how loud or soft) and B is \ the frequency of the sound (the pitch \[Rule] how high or low the note is). \ The frequency of a musical note is measured in Hertz (or cycles per second). \ ", StyleBox["Mathematica", FontSlant->"Italic"], " can Play notes of the form ", StyleBox["Sin[ B*2\[Pi] t]", FontWeight->"Bold"], " . (I haven't yet figured out how to get ", StyleBox["Mathematica", FontSlant->"Italic"], " to deal with loud or soft.) " }], "Text"], Cell["\<\ by David R. Wood Augustana College March, 2004\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Pure Tones ", "Subsection"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " uses its ", StyleBox["Play", FontWeight->"Bold"], " command to play sounds. Here's what the ", StyleBox["Help Browser", FontWeight->"Bold"], " says about ", StyleBox["Play", FontWeight->"Bold"], ".\n\[FilledSmallSquare] ", StyleBox["Play[", "MR", FontWeight->"Bold"], StyleBox["f", "TI", FontWeight->"Bold"], StyleBox[",", "MR", FontWeight->"Bold"], StyleBox[" ", FontWeight->"Bold"], Cell[BoxData[ \(TraditionalForm\`{\)], "InlineFormula", FontWeight->"Bold"], StyleBox["t", "TI", FontWeight->"Bold"], StyleBox[",", "MR", FontWeight->"Bold"], StyleBox[" ", FontWeight->"Bold"], StyleBox["tmin", "TI", FontWeight->"Bold"], StyleBox[",", "MR", FontWeight->"Bold"], StyleBox[" ", FontWeight->"Bold"], StyleBox["tmax", "TI", FontWeight->"Bold"], Cell[BoxData[ \(TraditionalForm\`}\)], "InlineFormula", FontWeight->"Bold"], StyleBox["]", "MR", FontWeight->"Bold"], " plays a sound whose amplitude is given by ", StyleBox["f", "TI"], " as a function of time ", StyleBox["t", "TI"], " in seconds between ", StyleBox["tmin", "TI"], " and ", StyleBox["tmax", "TI"], ". \nThe following command instructs ", StyleBox["Mathematica", FontSlant->"Italic"], " to play a pure tone with a frequency of 263 Hertz for 0.2 seconds. The \ human ear can hear sounds with frequencies ranging from about: 20 Hertz to \ about 22,000 Hertz. Dogs can hear sounds with much higher frequencies \ (higher pitches). \nThere's another new feature in the command below. The \ part that looks like this \[Rule]", StyleBox[" (* Middle C *)", FontFamily->"Courier New", FontWeight->"Bold"], StyleBox[" is called a comment. ", FontFamily->"Times New Roman"], StyleBox["Mathematica", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[" ignores comments. We put comments into input cells to provide \ explanations for those who read our ", FontFamily->"Times New Roman"], StyleBox["Mathematica", FontFamily->"Times New Roman", FontSlant->"Italic"], StyleBox[" documents. \nThe comment below informs us that the note we hear \ is A below middle C. ", FontFamily->"Times New Roman"] }], "Text"], Cell[BoxData[ \(\(\(Play[Sin[220\ 2 \[Pi]\ t], {t, 0, .2}]\)\(\ \ \ \ \ \)\( (*\ A\ below\ middle\ C\ *) \)\)\)], "Input"], Cell[TextData[{ "The command ", StyleBox["Play", FontWeight->"Bold"], " is analogous to the command ", StyleBox["Plot", FontWeight->"Bold"], ". It takes two arguments. The first is a function defining the sound to \ ", StyleBox["play", FontSlant->"Italic"], ", and the second is an interval of time telling ", StyleBox["Mathematica", FontSlant->"Italic"], " how long to play it. Notice that ", StyleBox["Play", FontWeight->"Bold"], " produces two outputs just like ", StyleBox["Plot", FontWeight->"Bold"], " does. We can suppress the ", StyleBox[" \[SkeletonIndicator]Sound\[SkeletonIndicator] ", Background->GrayLevel[0.900008]], " tag by putting a semicolon at the end of the command. Here's a really \ weird sound without the ", StyleBox[" \[SkeletonIndicator]Sound\[SkeletonIndicator] ", Background->GrayLevel[0.900008]], " tag." }], "Text"], Cell[BoxData[ \(\(Play[Sin[700\ t\ + \ 25\ t\ Sin[350\ \ t]], {t, 0, 4}];\)\)], "Input"], Cell[TextData[{ "Those who study music tell us that a musical octave spans a factor of 2 in \ frequency and that there are twelve notes per octave. The notes are \ separated by the factors of ", Cell[BoxData[ \(TraditionalForm\`\@2\%\(\(12\)\(\ \)\)\)]], " (or approximately ", StyleBox["1.05946", FontFamily->"Courier New"], " ) . If the frequency of A below middle C is 220 Hertz, then the \ frequency of A# (the next note in the octave) is 220 * ", Cell[BoxData[ \(TraditionalForm\`\@2\%\(\(12\)\(\ \)\)\)]], " (or about 233.08 Hertz. The command below defines a very simple, \ eight-note (diatonic) ", StyleBox["C major ", FontSlant->"Italic"], "scale for ", StyleBox["Mathematica. (", FontSlant->"Italic"], "The word ", StyleBox["scale", FontSlant->"Italic"], " comes from the Italian word ", StyleBox["scala", FontSlant->"Italic"], " meaning ", StyleBox["ladder", FontSlant->"Italic"], ".) Notice that we use ", StyleBox["DisplayFunction \[Rule] Identity", FontWeight->"Bold"], " to suppress the sound and the fancy box. These notes all have names that \ are similar. If we don't turn off the ", StyleBox["Mathematica", FontSlant->"Italic"], " feature that checks for misspellings, we would get many, many error \ messages. That's what the first command does \[Rule] suppresses spelling \ errors.\nEnter this command. " }], "Text"], Cell[BoxData[{ \(\(Off[General::spell1];\)\), "\[IndentingNewLine]", \(\(c4 = Play[Sin[2 Pi\ 261.64\ t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(d4 = Play[Sin[2 Pi\ 293.68 t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(e4 = Play[Sin[2 Pi\ 329.64 t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(f4 = Play[Sin[2 Pi\ 349.24\ t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(g4 = Play[Sin[2 Pi\ 392.00\ t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(a4 = Play[Sin[2 Pi\ 440.00 t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(b4 = Play[Sin[2 Pi\ 493.92 t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(cAbove4 = Play[Sin[2 Pi\ 523.28\ t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\)}], "Input"], Cell[TextData[{ " No sound! Now let's define a simple tune for ", StyleBox["Mathematica", FontSlant->"Italic"], " to play. Enter this command." }], "Text"], Cell[BoxData[ \(\(OdeToJoy = {e4, e4, f4, g4, g4, f4, e4, d4, c4, c4, d4, e4, e4, d4, d4, e4, e4, f4, g4, g4, f4, e4, d4, c4, c4, d4, e4, d4, c4, c4};\)\)], "Input"], Cell[TextData[{ "Again, no sound. Now enter the command below. Notice that we execute a \ series a previously produced but suppressed sounds using the ", StyleBox["Show", FontWeight->"Bold"], " command." }], "Text"], Cell[BoxData[ \(\(Show[OdeToJoy];\)\)], "Input"], Cell[TextData[{ "I admit that I'm not much of a musician, but I had fun defining all 12 \ notes in the chromatic scale at each of four note lengths (plus a few extra) \ and then teaching ", StyleBox["Mathematica", FontSlant->"Italic"], " to play a couple of simple tunes. Enter the following functions." }], "Text"], Cell[BoxData[{ \(\(Off[General::spell1];\)\), "\[IndentingNewLine]", \(\(bBelow8 = Play[Sin[2 Pi\ 246.96\ t], {t, 0, 0.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(bBelow4 = Play[Sin[2 Pi\ 246.96\ t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(bBelow2 = Play[Sin[2 Pi\ 246.96\ t], {t, 0, 0.8}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(bBelow1 = Play[Sin[2 Pi\ 246.96\ t], {t, 0, 1.6}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(c8 = Play[Sin[2 Pi\ 261.64\ t], {t, 0, 0.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(c4 = Play[Sin[2 Pi\ 261.64\ t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(c2 = Play[Sin[2 Pi\ 261.64\ t], {t, 0, 0.8}, DisplayFunction \[Rule] Identity]; (*Middle\ C*) \[IndentingNewLine]c1 = Play[Sin[2 Pi\ 261.64\ t], {t, 0, 1.6}, DisplayFunction \[Rule] Identity];\), "\[IndentingNewLine]", \(\(d8 = Play[Sin[2 Pi\ 293.68 t], {t, 0, 0.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(d4 = Play[Sin[2 Pi\ 293.68 t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(d2 = Play[Sin[2 Pi\ 293.68 t], {t, 0, 0.8}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(d1 = Play[Sin[2 Pi\ 293.68 t], {t, 0, 1.6}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(e8 = Play[Sin[2 Pi\ 329.64 t], {t, 0, 0.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(e4 = Play[Sin[2 Pi\ 329.64 t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(e2 = Play[Sin[2 Pi\ 329.64 t], {t, 0, 0.8}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(e2dot = Play[Sin[2 Pi\ 329.64 t], {t, 0, 1.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(e1 = Play[Sin[2 Pi\ 329.64 t], {t, 0, 1.6}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(f8 = Play[Sin[2 Pi\ 349.24\ t], {t, 0, 0.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(f4 = Play[Sin[2 Pi\ 349.24\ t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(f2 = Play[Sin[2 Pi\ 349.24\ t], {t, 0, 0.8}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(f1 = Play[Sin[2 Pi\ 349.24\ t], {t, 0, 1.6}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(g8 = Play[Sin[2 Pi\ 392.00\ t], {t, 0, 0.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(g4 = Play[Sin[2 Pi\ 392.00\ t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(g2 = Play[Sin[2 Pi\ 392.00\ t], {t, 0, 0.8}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(g1 = Play[Sin[2 Pi\ 392.00\ t], {t, 0, 1.6}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(a8 = Play[Sin[2 Pi\ 440.00 t], {t, 0, 0.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(a4 = Play[Sin[2 Pi\ 440.00 t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(a2 = Play[Sin[2 Pi\ 440.00 t], {t, 0, 0.8}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(a1 = Play[Sin[2 Pi\ 440.00 t], {t, 0, 1.6}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(b8 = Play[Sin[2 Pi\ 493.92 t], {t, 0, 0.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(b4 = Play[Sin[2 Pi\ 493.92 t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(b2 = Play[Sin[2 Pi\ 493.92 t], {t, 0, 0.8}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(b1 = Play[Sin[2 Pi\ 493.92 t], {t, 0, 1.6}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(cAbove8 = Play[Sin[2 Pi\ 523.28\ t], {t, 0, 0.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(cAbove4 = Play[Sin[2 Pi\ 523.28\ t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(cAbove4dot = Play[Sin[2 Pi\ 523.28\ t], {t, 0, 0.6}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(cAbove2 = Play[Sin[2 Pi\ 523.28\ t], {t, 0, 0.8}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(cAbove1 = Play[Sin[2 Pi\ 523.28\ t], {t, 0, 1.6}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(dSharpAbove8 = Play[Sin[2 Pi\ 622.24\ t], {t, 0, 0.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(dAbove8 = Play[Sin[2 Pi\ 587.36\ t], {t, 0, 0.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(dAbove4 = Play[Sin[2 Pi\ 587.36\ t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(dAbove2 = Play[Sin[2 Pi\ 587.36\ t], {t, 0, 0.8}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(dAbove1 = Play[Sin[2 Pi\ 587.36\ t], {t, 0, 1.6}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(eAbove8 = Play[Sin[2 Pi\ 659.28\ t], {t, 0, 0.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(eFlatAbove8 = Play[Sin[2 Pi\ 622.24\ t], {t, 0, 0.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(eAbove4 = Play[Sin[2 Pi\ 659.28\ t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(eAbove4dot = Play[Sin[2 Pi\ 659.28\ t], {t, 0, 0.6}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(eAbove2 = Play[Sin[2 Pi\ 659.28\ t], {t, 0, 0.8}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(eAbove1 = Play[Sin[2 Pi\ 659.28\ t], {t, 0, 1.6}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(fAbove8 = Play[Sin[2 Pi\ 698.48\ t], {t, 0, 0.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(fAbove4 = Play[Sin[2 Pi\ 698.48\ t], {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(fAbove2 = Play[Sin[2 Pi\ 698.48\ t], {t, 0, 0.8}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(fAbove1 = Play[Sin[2 Pi\ 698.48\ t], {t, 0, 1.6}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(rest8 = Play[0, {t, 0, 0.2}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(rest4 = Play[0, {t, 0, 0.4}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(rest2 = Play[0, {t, 0, 0.8}, DisplayFunction \[Rule] Identity];\)\), "\[IndentingNewLine]", \(\(rest1 = Play[0, {t, 0, 1.6}, DisplayFunction \[Rule] Identity];\)\)}], "Input"], Cell[BoxData[ \(\(PollyWollyDoodle = {c8, d8, \[IndentingNewLine]e4, e4, c4, c8, d8, \[IndentingNewLine]e4, e4, c4, c4, \[IndentingNewLine]e8, e8, e8, e8, f8, f8, e8, e8, \[IndentingNewLine]d2, rest4, bBelow8, c8, \[IndentingNewLine]d4, d4, bBelow4, bBelow4, \[IndentingNewLine]d4, d4, bBelow4, d4, \[IndentingNewLine]g8, g8, g8, g8, f8, f8, d8, d8, \[IndentingNewLine]c2, rest4, c8, d8, \[IndentingNewLine]e2dot, c8, d8, \[IndentingNewLine]e2dot, c8, d8, \[IndentingNewLine]e4, e4, f4, e4, \[IndentingNewLine]d2, rest4, bBelow8, c8, \[IndentingNewLine]d8, d8, d8, d8, bBelow8, bBelow8, bBelow8, c8, \[IndentingNewLine]d8, d8, d8, d8, bBelow8, bBelow8, d4, \[IndentingNewLine]g8, g8, g8, g8, f8, f8, d4, \[IndentingNewLine]c2, rest4};\)\)], "Input"], Cell[BoxData[ \(\(RockIslandLine = {g8, a8, \[IndentingNewLine]cAbove8, cAbove8, a8, cAbove4, cAbove8, cAbove8, cAbove8, \[IndentingNewLine]eFlatAbove8, eAbove8, cAbove8, eAbove4dot, g8, a8, \[IndentingNewLine]cAbove8, cAbove8, a8, cAbove4, \ cAbove8, cAbove8, cAbove8, \[IndentingNewLine]dAbove4, b4, g4, g8, a8, \[IndentingNewLine]cAbove8, cAbove8, a8, cAbove4, cAbove8, cAbove8, cAbove8, \[IndentingNewLine]eFlatAbove8, eAbove8, cAbove8, eAbove8, eAbove4dot, cAbove8, a8, \[IndentingNewLine]cAbove4dot, a8, cAbove8, dAbove8, cAbove8, a8, \[IndentingNewLine]cAbove8, dAbove8, cAbove8, a8, cAbove8, dAbove8, cAbove8, a8, \[IndentingNewLine]cAbove8, dAbove8, cAbove8, a8, cAbove8, dAbove8, cAbove8, a8, \[IndentingNewLine]g8, a8, b8, cAbove4dot, rest4\[IndentingNewLine]};\)\)], "Input"], Cell[BoxData[ \(\(Show[PollyWollyDoodle];\)\)], "Input"], Cell[BoxData[ \(\(Show[RockIslandLine];\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Chords", "Subsection"], Cell[TextData[{ "We can also get ", StyleBox["Mathematica", FontSlant->"Italic"], " to play more than one note at a time." }], "Text"], Cell[BoxData[ \(\(cChord\ = Play[{Sin[2 Pi\ 261.64\ t]\ (*C*) , \ \ Sin[ 2 Pi\ 329.64 t]\ (*E*) , Sin[2 Pi\ 392.00\ t] (*G*) \ }, {t, 0, 2}];\)\)], "Input"], Cell[BoxData[ \(\(gChord\ = Play[{Sin[2 Pi\ 392.00\ t] (*G*) , \ \ Sin[ 2 Pi\ 493.92 t]\ (*B*) , Sin[2 Pi\ 587.36\ t] (*D*) \ }, {t, 0, 2}];\)\)], "Input"], Cell[TextData[{ Cell[GraphicsData["Metafile", "\<\ CF5dJ6E]HGAYHf4PEfU^I6mgLb15CDHPAVmbKF5d0@0000[T0@0006`000000000000002<0000Q0000 00000000001X10008P@00215CDH00040i0X000d000010000000000000000000000@0000300100@00 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1}, {0, 1}}], " The musicians among us are invited to make some music. The rest of you \ can make up your own sounds." }], "Text"] }, Open ]] }, FrontEndVersion->"5.0 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 681}}, WindowSize->{905, 508}, WindowMargins->{{0, Automatic}, {Automatic, 0}} ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1776, 53, 127, 2, 54, "Subsection"], Cell[1906, 57, 767, 21, 71, "Text"], Cell[2676, 80, 70, 4, 71, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[2783, 89, 33, 0, 38, "Subsection"], Cell[2819, 91, 2338, 76, 149, "Text"], Cell[5160, 169, 135, 2, 30, "Input"], Cell[5298, 173, 921, 28, 71, "Text"], Cell[6222, 203, 93, 1, 30, "Input"], Cell[6318, 206, 1437, 39, 155, "Text"], Cell[7758, 247, 1169, 25, 190, "Input"], Cell[8930, 274, 167, 5, 33, "Text"], Cell[9100, 281, 191, 3, 50, "Input"], Cell[9294, 286, 227, 6, 33, "Text"], Cell[9524, 294, 52, 1, 30, "Input"], Cell[9579, 297, 326, 7, 52, "Text"], Cell[9908, 306, 7981, 171, 1170, "Input"], Cell[17892, 479, 885, 13, 350, "Input"], Cell[18780, 494, 923, 13, 250, "Input"], Cell[19706, 509, 60, 1, 30, "Input"], Cell[19769, 512, 58, 1, 30, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[19864, 518, 28, 0, 38, "Subsection"], Cell[19895, 520, 144, 5, 33, "Text"], Cell[20042, 527, 203, 4, 30, "Input"], Cell[20248, 533, 201, 4, 30, "Input"], Cell[20452, 539, 4099, 56, 49, "Text"] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)