(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. 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). 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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[ 2510226, 65628]*) (*NotebookOutlinePosition[ 2511135, 65661]*) (* CellTagsIndexPosition[ 2511058, 65655]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Reverse Conducting Evaluation\n", FontFamily->"Palatino Linotype", FontSize->23], StyleBox["Craig Stuart Sapp \n15 Nov 2005", FontFamily->"Palatino Linotype", FontSize->20] }], "Subtitle"], Cell[TextData[{ "This is a generic ", StyleBox["Mathematica", FontSlant->"Italic"], " notebook used for examining the individual reverse conducting \ performances of Chopin Mazurkas compared to carefully corrected versions of \ the average beat tappings for the performance." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Mazurka in A Minor, Op. 7, No. 2 Chiu 1999\ \>", "Subtitle"], Cell[CellGroupData[{ Cell["Loading the raw data", "Subsection"], Cell["\<\ First load the absolute beat positions for the average beat positions and the \ corrected beat positions:\ \>", "Text"], Cell[BoxData[{ \(\(performance\ = \ "\";\)\), "\[IndentingNewLine]", \(\(pvar\ = \ StringReplace[ performance, \ "\<-\>"\ \[Rule] \ "\"];\)\)}], "Input"], Cell[BoxData[{ \(Get[performance\ \ <> \ "\<.macorrected\>", \ Path \[Rule] "\"]\), "\[IndentingNewLine]", \(\(mcbeats\ = \ ToExpression[pvar\ <> \ "\"];\)\)}], "Input"], Cell[BoxData[{ \(Get[performance\ <> \ "\<.maaverage\>", \ Path \[Rule] "\"]\), "\[IndentingNewLine]", \(\(mabeats\ = \ ToExpression[pvar\ <> \ "\"];\)\)}], "Input"], Cell["\<\ Now measure the time difference between each average and corrected beat. A \ negative value means that the average beat occurs before the corrected beat \ time.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(mdiffs\ = \ \(Transpose[mabeats]\)[\([2]\)]\ - \ \(Transpose[ mcbeats]\)[\([2]\)]\)], "Input"], Cell[BoxData[ \({187, 28, \(-45\), \(-19\), 76, 70, 20, 43, 47, 0, 55, 117, 103, \(-38\), \(-5\), \(-20\), 11, 47, 73, 75, 53, 60, 84, 0, \(-128\), 15, \(-67\), 22, 29, \(-25\), 15, 75, 14, 50, \(-53\), 32, 29, 62, \(-51\), \(-25\), \(-32\), \(-78\), 0, 204, 52, 14, 13, \(-41\), 146, \(-20\), \(-5\), 0, 47, 53, 64, 100, 47, 46, \(-54\), 76, 60, 49, 38, 32, 52, \(-38\), \(-10\), 31, 40, 35, \(-39\), \(-36\), 16, 58, 79, 6, 31, 79, 107, \(-21\), \(-3\), 33, \(-45\), 5, 8, 27, 0, \(-17\), \(-86\), \(-109\), 0, \(-246\), 47, 65, 61, 33, 118, 45, 9, \(-108\), 18, 45, 105, 35, \(-7\), \(-152\), 8, 26, 83, \(-25\), 38, 56, 27, 20, 59, \(-72\), 36, \(-67\), \(-105\), 46, \(-45\), 13, \(-33\), 32, 38, 62, 62, 68, 21, 52, 50, 81, 42, 26, \(-44\), \(-14\), 23, \(-108\), 0, 64, 49, 53, \(-47\), \(-89\), 144, \(-133\), \(-14\), \(-183\), 15, 41, \(-20\), \(-14\), 2, \(-16\), 46, 47, \(-23\), \(-69\), \(-20\), \(-41\), \(-77\), 0, 66, \(-89\), \(-6\), \(-162\), 24, 27, \(-97\), 0, \(-9\), 31, 70, 45, 0, 105, \(-7\), 46, 40, 113, 83, 119, 0, 22, \(-32\), \(-47\), 0, \(-25\), \(-218\), \(-114\), \(-102\), \(-38\), \(-8\), \(-31\), 27, \(-23\), 20, \(-27\), 0, 39, 0, 27, \(-98\), 21, 0, 11, 0, 49, \(-36\), 8, 31, 24, 29, 70, \(-37\), 15, \(-66\), \(-64\), 43, 0, 78, 14, \(-25\), 84, 64, 0, 72, \(-10\), \(-13\), 0, 92, 5, 80, 21, \(-8\), \(-30\), 67, 0, \(-157\), 47, 110, 75, \(-85\), 30, 7, 9, 69, 78, 52, 44, \(-16\), 60, 58, 42, 22, 6, 88, 25, 46, 26, 15, 23, \(-7\), 56, 74, 61, 29, 58, 96, 42, 50, 68, 54, 82, \(-27\), 0, 54, \(-14\), 0, 8, \(-16\), 17, 0, \(-54\), 62, 0, 77, 13, 0, \(-93\), 11, 24, 20, 14, 37, 16, \(-4\), 80, \(-37\), \(-3\), 54, 33, 0, \(-58\), 0, 32, 54, 47, 0, 79, \(-49\), \(-21\), \(-121\), 188, 78, 97, \(-85\), 95, \(-23\), \(-83\), \(-3\), 35, 105, 81, 75, \(-60\), 12, 13, 82, 9, \(-106\), 126, 61, \(-58\), \(-52\), 0, 176, \(-69\), \(-33\), \(-113\), 65, 0, 40, 90, 0, 89, \(-134\), \(-100\), \(-92\), \(-135\), 0, 0, 0, 97, 0, \(-181\), 73, 39, \(-69\), \(-74\), 0}\)], "Output", FontSize->8] }, Open ]], Cell["\<\ The average correction to each beat from the average tap times of all trials \ is typically around 48 milliseconds. This means that, on the average, each \ average tap beat position must be moved 48 milliseconds to align with the \ correct beat time. \ \>", "Text"], Cell[BoxData[ \(<< \ Statistics`ConfidenceIntervals`\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Mean[Abs[mdiffs]]\ // \ N\)], "Input"], Cell[BoxData[ \(48.556786703601105`\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Manual correction of average reverse conducting beat positions\ \>", "Subsection"], Cell["\<\ This section displays the difference between the average reverse conducted \ beat positions and the values derived from manually correcting these values \ by ear using an soundfile editor.\ \>", "Text"], Cell["\<\ This corrected beat duration data was measured by listening to the audio file \ and manually locating the beat positions in the soundfile. The initial \ positions of the average reverse conducting performance were used as a \ baseline, and this baseline was then adjusted so that it sounded as if all \ beats were occuring with the attacks of notes in the performance. There are \ probably a few errors in the corrected due to the tediousness of getting this \ data, and there are a few locations in the audio where the beat positions \ become vague, but overall, this data represents a highly accurate description \ of the pianists' actual beat-by-beat performance tempo, probably an accuracy \ within 10 millseconds for all beats.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(corrected\ = \ \(Transpose[mcbeats]\)[\([2]\)]\)], "Input"], Cell[BoxData[ \({1725, 2529, 3219, 3794, 4355, 4843, 5522, 6246, 6755, 7217, 7758, 8190, 8831, 9591, 10061, 10563, 11048, 11566, 12103, 12602, 13150, 13608, 14132, 14944, 16088, 16721, 17343, 17843, 18371, 18901, 19550, 20219, 20756, 21179, 21737, 22180, 22843, 23543, 24137, 24646, 25205, 26008, 26891, 27478, 28066, 28603, 29193, 30021, 30874, 31605, 32214, 32766, 33313, 33803, 34446, 35112, 35638, 36096, 36721, 37204, 37872, 38548, 38985, 39467, 39959, 40558, 41192, 41753, 42307, 42809, 43496, 44351, 45401, 46086, 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o`030000003oool0oooo00T0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`090?oo o`030000003oool0oooo00T0oooo00<000000?ooo`3oool02P3oool00`000000oooo0?ooo`090?oo o`030000003oool0oooo00T0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`090?oo o`030000003oool0oooo00T0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`090?oo o`030000003oool0oooo00T0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`090?oo o`030000003oool0oooo00T0oooo00<000000?ooo`3oool02P3oool00`000000oooo0?ooo`090?oo o`030000003oool0oooo00T0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`090?oo o`030000003oool0oooo00T0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`090?oo o`030000003oool0oooo00T0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`0?0?oo o`00;@3ooooo00000<`000004@3oool00001\ \>"], ImageRangeCache->{{{0, 520}, {129.25, 0}} -> {-46.8855, -276.01, 0.827458, \ 4.12582}}] }, Open ]], Cell["\<\ The average beats are not quite centered on the corrected beats. 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A score of 1 means 20 ms correction, 2 means 40 ms correction, 3 means \ 80 ms correction, 4, means 160 ms correction, 5 means 360 ms correction, ", StyleBox["etc", FontSlant->"Italic"], ". A score of 0 means there was less than 1 millisecond correction \ necessary, and a score of 0.5 means 10 milliseconds were needed to correct \ the beat location.\n\nQualitatively, a score of 0-1 is an \"A\", 1-2 is a \"B\ \", 2-3 is a \"C\", 3-4 is a \"D\", 4-5 is an \"E\", and 5-6 is an \"F\". A \ score of 6 means the correction was 640 milliseconds, or about\n2/3 of a \ second." }], "Text"], Cell[BoxData[ \(QScore[seq_]\ := \ Module[\ {sign, \ scores}, \[IndentingNewLine]\ \ \ sign\ = \ Map[If[# < 0, \ \(-1\), \ If[# > 0, \ 1, \ 0]] &, \ seq\ ]; \[IndentingNewLine]scores\ = \ Log[2.0, \ Abs[seq]\ /\ 10]\ /. \ \(-Infinity\)\ \[Rule] \ 0; \[IndentingNewLine]scores\ = \ Map[If[#\ < 1, \ \((# + 1)\)/2.0\ , \ #] &, \ scores]; \[IndentingNewLine]scores\ = \ Map[If[# < \ 0, \ 0, \ #] &, \ scores]; \[IndentingNewLine]scores\ \ *\ sign\[IndentingNewLine]]\)], "Input"], Cell["\<\ Mostly the corrections for the average of the tapping trials are evenly \ distributed between A, B, C, and D quality, although \"A\" corrections were \ the most common. The worst case correction was between a value of 4 and 5. \ This occurs on the first beat when there has been no preparation of a \ previous event, so is most likely due to the reaction time of the reverse \ conductor. 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