Metric Analysis of Tapping Accuracy for Triple Meter in Chopin Mazurkas
Craig Stuart Sapp <craig@ccrma.stanford.edu> 9-10 Jan 2006
This Mathematica notebook examines the accuracy at which each type of metrical beat is tapped when reverse conducting to particular performances of Chopin Mazurkas. The tapping accuracy for four performances of two mazurkas are analyzed below: (1) Mazurka in A minor, Op. 7, No. 2 performed by Frederic Chiu in 1999 (2) Mazurka in A minor, Op. 7, No. 2 performance by Ignaz Friedman in 1930 (3) Mazurka in F minor, Op. 7, No. 3 performed by Ignaz Friedman in 1930 (4) Mazurka in F minor, Op. 7, No. 3 performed by Charles Rosen in 1989
Necessary packages to load first:
![[Graphics:Images/index_gr_1.gif]](Images/index_gr_1.gif)
![[Graphics:Images/index_gr_2.gif]](Images/index_gr_2.gif)
![[Graphics:Images/index_gr_3.gif]](Images/index_gr_3.gif)
Tapping accuracy for each beat (20-trial average)
Mazurka in A minor, Op. 7, No. 2; Chiu 1999
![[Graphics:Images/index_gr_4.gif]](Images/index_gr_4.gif)
![[Graphics:Images/index_gr_5.gif]](Images/index_gr_5.gif)
Calculate the differences between the average tap times and the corrected data, removing the extremities:
![[Graphics:Images/index_gr_6.gif]](Images/index_gr_6.gif)
First display a histogram of all metrical beat displacements.
![[Graphics:Images/index_gr_7.gif]](Images/index_gr_7.gif)
![[Graphics:Images/index_gr_8.gif]](Images/index_gr_8.gif)
Now display separate histograms for individual metrical position in the meter:
![[Graphics:Images/index_gr_9.gif]](Images/index_gr_9.gif)
![[Graphics:Images/index_gr_10.gif]](Images/index_gr_10.gif)
![[Graphics:Images/index_gr_11.gif]](Images/index_gr_11.gif)
![[Graphics:Images/index_gr_12.gif]](Images/index_gr_12.gif)
![[Graphics:Images/index_gr_13.gif]](Images/index_gr_13.gif)
![[Graphics:Images/index_gr_14.gif]](Images/index_gr_14.gif)
![[Graphics:Images/index_gr_15.gif]](Images/index_gr_15.gif)
![[Graphics:Images/index_gr_16.gif]](Images/index_gr_16.gif)
![[Graphics:Images/index_gr_17.gif]](Images/index_gr_17.gif)
![[Graphics:Images/index_gr_24.gif]](Images/index_gr_24.gif)
Here is a table of the average deviation from the correct beat position, and the standard deviation for each beat:
![[Graphics:Images/index_gr_43.gif]](Images/index_gr_43.gif)
1
|
56.09594943981614`
|
72.19152430424515`
|
2
|
36.08014938236139`
|
49.42462218656611`
|
3
|
47.31513932777937`
|
63.36261131630003`
|
Mazurka in A minor, Op. 7, No. 2; Friedman 1930
![[Graphics:Images/index_gr_44.gif]](Images/index_gr_44.gif)
![[Graphics:Images/index_gr_45.gif]](Images/index_gr_45.gif)
Calculate the differences between the average tap times and the corrected data, removing the extremities:
![[Graphics:Images/index_gr_46.gif]](Images/index_gr_46.gif)
First display a histogram of all metrical beat displacements.
![[Graphics:Images/index_gr_47.gif]](Images/index_gr_47.gif)
![[Graphics:Images/index_gr_48.gif]](Images/index_gr_48.gif)
Now display separate histograms for individual metrical position in the meter:
![[Graphics:Images/index_gr_49.gif]](Images/index_gr_49.gif)
![[Graphics:Images/index_gr_50.gif]](Images/index_gr_50.gif)
![[Graphics:Images/index_gr_51.gif]](Images/index_gr_51.gif)
![[Graphics:Images/index_gr_52.gif]](Images/index_gr_52.gif)
![[Graphics:Images/index_gr_53.gif]](Images/index_gr_53.gif)
![[Graphics:Images/index_gr_54.gif]](Images/index_gr_54.gif)
![[Graphics:Images/index_gr_55.gif]](Images/index_gr_55.gif)
![[Graphics:Images/index_gr_56.gif]](Images/index_gr_56.gif)
![[Graphics:Images/index_gr_57.gif]](Images/index_gr_57.gif)
![[Graphics:Images/index_gr_64.gif]](Images/index_gr_64.gif)
Here is a table of the average deviation from the correct beat position, and the standard deviation for each beat:
![[Graphics:Images/index_gr_83.gif]](Images/index_gr_83.gif)
1
|
64.62360630526717`
|
88.89038138590399`
|
2
|
37.88831218762012`
|
50.24796695267493`
|
3
|
45.69236191208512`
|
59.821919932795005`
|
Mazurka in F minor, Op. 7, No. 3; Friedman 1930
![[Graphics:Images/index_gr_84.gif]](Images/index_gr_84.gif)
![[Graphics:Images/index_gr_85.gif]](Images/index_gr_85.gif)
Calculate the differences between the average tap times and the corrected data, removing the extremities:
![[Graphics:Images/index_gr_86.gif]](Images/index_gr_86.gif)
First display a histogram of all metrical beat displacements.
![[Graphics:Images/index_gr_87.gif]](Images/index_gr_87.gif)
![[Graphics:Images/index_gr_88.gif]](Images/index_gr_88.gif)
Now display separate histograms for individual metrical position in the meter:
![[Graphics:Images/index_gr_89.gif]](Images/index_gr_89.gif)
![[Graphics:Images/index_gr_90.gif]](Images/index_gr_90.gif)
![[Graphics:Images/index_gr_91.gif]](Images/index_gr_91.gif)
![[Graphics:Images/index_gr_92.gif]](Images/index_gr_92.gif)
![[Graphics:Images/index_gr_93.gif]](Images/index_gr_93.gif)
![[Graphics:Images/index_gr_94.gif]](Images/index_gr_94.gif)
![[Graphics:Images/index_gr_95.gif]](Images/index_gr_95.gif)
![[Graphics:Images/index_gr_96.gif]](Images/index_gr_96.gif)
![[Graphics:Images/index_gr_97.gif]](Images/index_gr_97.gif)
![[Graphics:Images/index_gr_104.gif]](Images/index_gr_104.gif)
Here is a table of the average deviation from the correct beat position, and the standard deviation for each beat:
![[Graphics:Images/index_gr_123.gif]](Images/index_gr_123.gif)
1
|
34.34313633078833`
|
44.03731133532124`
|
2
|
48.961416407452774`
|
66.28629159815702`
|
3
|
40.47085807647596`
|
60.92569116471904`
|
Mazurka in F minor, Op. 7, No. 3; Rosen 1989
![[Graphics:Images/index_gr_124.gif]](Images/index_gr_124.gif)
![[Graphics:Images/index_gr_125.gif]](Images/index_gr_125.gif)
Calculate the differences between the average tap times and the corrected data, removing the extremities:
![[Graphics:Images/index_gr_126.gif]](Images/index_gr_126.gif)
First display a histogram of all metrical beat displacements.
![[Graphics:Images/index_gr_127.gif]](Images/index_gr_127.gif)
![[Graphics:Images/index_gr_128.gif]](Images/index_gr_128.gif)
Now display separate histograms for individual metrical position in the meter:
![[Graphics:Images/index_gr_129.gif]](Images/index_gr_129.gif)
![[Graphics:Images/index_gr_130.gif]](Images/index_gr_130.gif)
![[Graphics:Images/index_gr_131.gif]](Images/index_gr_131.gif)
![[Graphics:Images/index_gr_132.gif]](Images/index_gr_132.gif)
![[Graphics:Images/index_gr_133.gif]](Images/index_gr_133.gif)
![[Graphics:Images/index_gr_134.gif]](Images/index_gr_134.gif)
![[Graphics:Images/index_gr_135.gif]](Images/index_gr_135.gif)
![[Graphics:Images/index_gr_136.gif]](Images/index_gr_136.gif)
![[Graphics:Images/index_gr_137.gif]](Images/index_gr_137.gif)
![[Graphics:Images/index_gr_144.gif]](Images/index_gr_144.gif)
Here is a table of the average deviation from the correct beat position, and the standard deviation for each beat:
![[Graphics:Images/index_gr_163.gif]](Images/index_gr_163.gif)
1
|
47.754453765670654`
|
60.82833885236838`
|
2
|
46.01263078518237`
|
60.30715529064485`
|
3
|
49.977723316680795`
|
70.63600816937988`
|
Accuracy summary for all beats of the four performances of two mazurkas:
![[Graphics:Images/index_gr_164.gif]](Images/index_gr_164.gif)
![[Graphics:Images/index_gr_165.gif]](Images/index_gr_165.gif)
![[Graphics:Images/index_gr_166.gif]](Images/index_gr_166.gif)
![[Graphics:Images/index_gr_167.gif]](Images/index_gr_167.gif)
![[Graphics:Images/index_gr_168.gif]](Images/index_gr_168.gif)
![[Graphics:Images/index_gr_169.gif]](Images/index_gr_169.gif)
![[Graphics:Images/index_gr_170.gif]](Images/index_gr_170.gif)
![[Graphics:Images/index_gr_171.gif]](Images/index_gr_171.gif)
![[Graphics:Images/index_gr_172.gif]](Images/index_gr_172.gif)
![[Graphics:Images/index_gr_173.gif]](Images/index_gr_173.gif)
![[Graphics:Images/index_gr_174.gif]](Images/index_gr_174.gif)
![[Graphics:Images/index_gr_175.gif]](Images/index_gr_175.gif)
![[Graphics:Images/index_gr_182.gif]](Images/index_gr_182.gif)
Here is a table of the average deviation from the correct beat position, the absolute average deviation, and the standard deviation for each beat:
![[Graphics:Images/index_gr_201.gif]](Images/index_gr_201.gif)
1
|
6.655712050078253`
|
50.861459288664`
|
68.736875976145`
|
2
|
1.8082942097026669`
|
42.0290899791017`
|
56.57681414794406`
|
3
|
|
45.91551934085868`
|
64.07037524839832`
|
Tapping accuracy for individual trials
Examine the accuracy of beat tapping for Charles Rosen's 1989 peformance of Mazurka Op. 7, No. 3. Raw data is from http://mazurka.org.uk/info/revcond/pid52932-05/pid52932-05-abs.ma
![[Graphics:Images/index_gr_203.gif]](Images/index_gr_203.gif)
![[Graphics:Images/index_gr_204.gif]](Images/index_gr_204.gif)
![[Graphics:Images/index_gr_205.gif]](Images/index_gr_205.gif)
Mazurka in F minor, Op. 7, No. 3; Rosen 1989
Calculate the differences between the average tap times and the corrected data, removing the extremities:
![[Graphics:Images/index_gr_206.gif]](Images/index_gr_206.gif)
First display a histogram of all metrical beat displacements.
![[Graphics:Images/index_gr_207.gif]](Images/index_gr_207.gif)
![[Graphics:Images/index_gr_208.gif]](Images/index_gr_208.gif)
Now display separate histograms for individual metrical position in the meter, doing one beat at a time.
![[Graphics:Images/index_gr_209.gif]](Images/index_gr_209.gif)
![[Graphics:Images/index_gr_210.gif]](Images/index_gr_210.gif)
![[Graphics:Images/index_gr_211.gif]](Images/index_gr_211.gif)
![[Graphics:Images/index_gr_212.gif]](Images/index_gr_212.gif)
![[Graphics:Images/index_gr_213.gif]](Images/index_gr_213.gif)
![[Graphics:Images/index_gr_214.gif]](Images/index_gr_214.gif)
![[Graphics:Images/index_gr_215.gif]](Images/index_gr_215.gif)
1
|
|
2
|
|
3
|
|
4
|
|
5
|
|
6
|
|
7
|
|
8
|
|
9
|
|
10
|
|
11
|
|
12
|
|
13
|
|
14
|
|
15
|
|
16
|
|
17
|
|
18
|
|
19
|
|
20
|
|
![[Graphics:Images/index_gr_336.gif]](Images/index_gr_336.gif)
Here is a table of the average deviation from the correct beat position, and the standard deviation for each beat:
![[Graphics:Images/index_gr_697.gif]](Images/index_gr_697.gif)
|
10.773462783171464`
|
3.5695792880258366`
|
|
|
64.58035630125354`
|
58.019825933955495`
|
60.8729066515853`
|
|
80.37779630574715`
|
81.5882683716494`
|
86.43192704414385`
|
|
|
12.980582524271847`
|
|
|
|
60.85125836553871`
|
57.96361579790744`
|
62.13809030068812`
|
|
73.38378886582395`
|
76.56143756280213`
|
84.82897206844618`
|
|
|
6.59870550161813`
|
1.8802588996763823`
|
|
|
63.82753636849212`
|
61.56442643038928`
|
56.53696546956985`
|
|
82.67809751603578`
|
78.52614236811823`
|
77.17985033377727`
|
|
|
10.440129449838183`
|
1.8867313915857549`
|
|
|
58.29057089892231`
|
50.5123008766142`
|
60.75580481980709`
|
|
74.15639520589826`
|
75.06964847790758`
|
83.07567782880957`
|
|
|
13.139158576051724`
|
0.41100323624591534`
|
|
|
60.827787727401166`
|
52.16957300405313`
|
60.65457001916592`
|
|
76.41805924762645`
|
68.34251817569995`
|
80.92406539104181`
|
|
|
8.524271844660237`
|
1.223300970873824`
|
|
|
52.30106513337745`
|
51.02460175322813`
|
58.64643227448385`
|
|
68.00097422623261`
|
66.35043740964146`
|
78.99147397164595`
|
|
|
14.300970873786364`
|
|
|
|
53.54538599302476`
|
49.22132151946495`
|
57.418229804882856`
|
|
68.6335185645479`
|
62.89035418515022`
|
78.02487192962579`
|
|
|
13.776699029126178`
|
1.1747572815533565`
|
|
|
52.23027618060102`
|
50.63012536525605`
|
55.50589122443216`
|
|
65.85841090897007`
|
67.07059196183393`
|
75.25300051950275`
|
|
|
11.485436893203934`
|
1.2912621359223804`
|
|
|
59.45546234329379`
|
54.89047035535859`
|
59.511358280704904`
|
|
71.7764670498543`
|
72.47409325955036`
|
82.74539676213234`
|
|
|
14.029126213592244`
|
0.7281553398058359`
|
|
|
52.83900461871991`
|
52.12545951550565`
|
55.01140541050048`
|
|
69.53210681249436`
|
64.7917823637335`
|
75.21919109208433`
|
|
|
10.236245954692514`
|
2.0711974110031868`
|
|
|
49.76180601376188`
|
48.22364658937384`
|
57.61061362993702`
|
|
65.19100054797605`
|
67.34618096532981`
|
78.39732815759832`
|
|
|
10.433656957928818`
|
3.1423948220064837`
|
|
|
50.328463254469476`
|
53.87692839413077`
|
53.0138875797279`
|
|
62.531227302594814`
|
68.01735061563782`
|
72.0236704116234`
|
|
|
11.689320388349525`
|
0.4951456310679672`
|
|
|
51.550193232161334`
|
54.2123668583278`
|
58.613347158073296`
|
|
66.18273337964648`
|
66.10304101340768`
|
79.97289422770397`
|
|
|
7.074433656957962`
|
3.5695792880259387`
|
|
|
53.28350142960389`
|
46.890344675904124`
|
49.00930027963658`
|
|
67.13876484213097`
|
57.94084762686635`
|
69.07957046056505`
|
|
|
8.190938511326845`
|
1.5113268608414243`
|
|
|
60.760517799352776`
|
55.01941747572819`
|
58.006472491909406`
|
|
77.38987680926249`
|
68.53663072123325`
|
76.95198277347924`
|
|
|
7.300970873786374`
|
2.009708737864044`
|
|
|
51.65048543689309`
|
46.281553398058215`
|
54.66990291262143`
|
|
66.45163875455421`
|
59.85398821144943`
|
73.51497501526059`
|
|
|
7.113268608414277`
|
3.190938511326898`
|
|
|
51.95268168536156`
|
43.31397869733251`
|
55.419737958337144`
|
|
70.48682122564024`
|
59.22135794311619`
|
73.55852018543715`
|
|
|
8.72168284789648`
|
1.012944983818821`
|
|
|
51.330034247651426`
|
50.18522009614481`
|
53.28230747478543`
|
|
63.70140821015959`
|
66.63551908959928`
|
70.03310250454105`
|
|
|
8.249190938511285`
|
|
|
|
55.51516008420515`
|
49.536871209978926`
|
52.95249316617981`
|
|
69.91512762906007`
|
65.9726347805057`
|
70.15251124107088`
|
|
|
3.896440129449842`
|
1.906148867313919`
|
|
|
46.23860244446541`
|
46.57168441888966`
|
54.00782354604584`
|
|
62.53853181171626`
|
62.18437456571747`
|
75.38967744119117`
|
|
Checking the relation to pre-beat event durations
Macurka in A minor, Op. 7, No. 2
![[Graphics:Images/index_gr_721.gif]](Images/index_gr_721.gif)
![[Graphics:Images/index_gr_722.gif]](Images/index_gr_722.gif)
![[Graphics:Images/index_gr_723.gif]](Images/index_gr_723.gif)
![[Graphics:Images/index_gr_724.gif]](Images/index_gr_724.gif)
![[Graphics:Images/index_gr_725.gif]](Images/index_gr_725.gif)
![[Graphics:Images/index_gr_726.gif]](Images/index_gr_726.gif)
![[Graphics:Images/index_gr_727.gif]](Images/index_gr_727.gif)
![[Graphics:Images/index_gr_728.gif]](Images/index_gr_728.gif)
![[Graphics:Images/index_gr_729.gif]](Images/index_gr_729.gif)
![[Graphics:Images/index_gr_730.gif]](Images/index_gr_730.gif)
![[Graphics:Images/index_gr_731.gif]](Images/index_gr_731.gif)
![[Graphics:Images/index_gr_732.gif]](Images/index_gr_732.gif)
![[Graphics:Images/index_gr_733.gif]](Images/index_gr_733.gif)
![[Graphics:Images/index_gr_734.gif]](Images/index_gr_734.gif)
![[Graphics:Images/index_gr_735.gif]](Images/index_gr_735.gif)
![[Graphics:Images/index_gr_736.gif]](Images/index_gr_736.gif)
![[Graphics:Images/index_gr_737.gif]](Images/index_gr_737.gif)
![[Graphics:Images/index_gr_738.gif]](Images/index_gr_738.gif)
Mazurka in F minor, Op. 7, No 3
Beat 1:
![[Graphics:Images/index_gr_739.gif]](Images/index_gr_739.gif)
![[Graphics:Images/index_gr_740.gif]](Images/index_gr_740.gif)
![[Graphics:Images/index_gr_741.gif]](Images/index_gr_741.gif)
![[Graphics:Images/index_gr_742.gif]](Images/index_gr_742.gif)
![[Graphics:Images/index_gr_743.gif]](Images/index_gr_743.gif)
Beat 2:
![[Graphics:Images/index_gr_744.gif]](Images/index_gr_744.gif)
![[Graphics:Images/index_gr_745.gif]](Images/index_gr_745.gif)
![[Graphics:Images/index_gr_746.gif]](Images/index_gr_746.gif)
![[Graphics:Images/index_gr_747.gif]](Images/index_gr_747.gif)
![[Graphics:Images/index_gr_748.gif]](Images/index_gr_748.gif)
Beat 3:
![[Graphics:Images/index_gr_749.gif]](Images/index_gr_749.gif)
![[Graphics:Images/index_gr_750.gif]](Images/index_gr_750.gif)
![[Graphics:Images/index_gr_751.gif]](Images/index_gr_751.gif)
![[Graphics:Images/index_gr_752.gif]](Images/index_gr_752.gif)
![[Graphics:Images/index_gr_753.gif]](Images/index_gr_753.gif)
![[Graphics:Images/index_gr_754.gif]](Images/index_gr_754.gif)
![[Graphics:Images/index_gr_755.gif]](Images/index_gr_755.gif)
Beat durations for each beat
This section measures the average beat duration for each beat in the triple meter of the Mazurkas. Averaging for the "exact" performance by the pianists, and the average uncorrected reverse conducted taps of a listener. Durations are averaged over one measure to compensate for long-term tempo changes, but short-term tempo changes within a measures are more difficult to remove so they are ignored.
Mazurka in A minor, Op. 7, No. 2; Chiu 1999
corrected timing data
![[Graphics:Images/index_gr_756.gif]](Images/index_gr_756.gif)
![[Graphics:Images/index_gr_757.gif]](Images/index_gr_757.gif)
![[Graphics:Images/index_gr_758.gif]](Images/index_gr_758.gif)
![[Graphics:Images/index_gr_759.gif]](Images/index_gr_759.gif)
![[Graphics:Images/index_gr_760.gif]](Images/index_gr_760.gif)
![[Graphics:Images/index_gr_761.gif]](Images/index_gr_761.gif)
![[Graphics:Images/index_gr_762.gif]](Images/index_gr_762.gif)
![[Graphics:Images/index_gr_763.gif]](Images/index_gr_763.gif)
![[Graphics:Images/index_gr_764.gif]](Images/index_gr_764.gif)
![[Graphics:Images/index_gr_765.gif]](Images/index_gr_765.gif)
![[Graphics:Images/index_gr_766.gif]](Images/index_gr_766.gif)
![[Graphics:Images/index_gr_767.gif]](Images/index_gr_767.gif)
![[Graphics:Images/index_gr_768.gif]](Images/index_gr_768.gif)
![[Graphics:Images/index_gr_769.gif]](Images/index_gr_769.gif)
![[Graphics:Images/index_gr_770.gif]](Images/index_gr_770.gif)
![[Graphics:Images/index_gr_771.gif]](Images/index_gr_771.gif)
![[Graphics:Images/index_gr_772.gif]](Images/index_gr_772.gif)
![[Graphics:Images/index_gr_773.gif]](Images/index_gr_773.gif)
![[Graphics:Images/index_gr_774.gif]](Images/index_gr_774.gif)
![[Graphics:Images/index_gr_775.gif]](Images/index_gr_775.gif)
uncorrected average tapping data
![[Graphics:Images/index_gr_794.gif]](Images/index_gr_794.gif)
![[Graphics:Images/index_gr_795.gif]](Images/index_gr_795.gif)
![[Graphics:Images/index_gr_796.gif]](Images/index_gr_796.gif)
![[Graphics:Images/index_gr_797.gif]](Images/index_gr_797.gif)
![[Graphics:Images/index_gr_798.gif]](Images/index_gr_798.gif)
![[Graphics:Images/index_gr_799.gif]](Images/index_gr_799.gif)
![[Graphics:Images/index_gr_800.gif]](Images/index_gr_800.gif)
000oooo0?ooo`0]0?ooo`040000003o
ool0oooo00000080oooo00@000000?ooo`3oool000000P3oool010000000oooo0?ooo`0000090?oo
o`00C@3oool2000000@0oooo0P0000040?ooo`800000=03oool2000003P0oooo0P0000040?ooo`80
0000103oool200000340ooo
![[Graphics:Images/index_gr_801.gif]](Images/index_gr_801.gif)
![[Graphics:Images/index_gr_802.gif]](Images/index_gr_802.gif)
![[Graphics:Images/index_gr_803.gif]](Images/index_gr_803.gif)
![[Graphics:Images/index_gr_804.gif]](Images/index_gr_804.gif)
![[Graphics:Images/index_gr_805.gif]](Images/index_gr_805.gif)
![[Graphics:Images/index_gr_806.gif]](Images/index_gr_806.gif)
![[Graphics:Images/index_gr_807.gif]](Images/index_gr_807.gif)
![[Graphics:Images/index_gr_808.gif]](Images/index_gr_808.gif)
![[Graphics:Images/index_gr_809.gif]](Images/index_gr_809.gif)
![[Graphics:Images/index_gr_810.gif]](Images/index_gr_810.gif)
![[Graphics:Images/index_gr_811.gif]](Images/index_gr_811.gif)
![[Graphics:Images/index_gr_812.gif]](Images/index_gr_812.gif)
Mazurka in A minor, Op. 7, No. 2; Friedman 1930
corrected timing data
![[Graphics:Images/index_gr_831.gif]](Images/index_gr_831.gif)
![[Graphics:Images/index_gr_832.gif]](Images/index_gr_832.gif)
![[Graphics:Images/index_gr_833.gif]](Images/index_gr_833.gif)
![[Graphics:Images/index_gr_834.gif]](Images/index_gr_834.gif)
![[Graphics:Images/index_gr_835.gif]](Images/index_gr_835.gif)
![[Graphics:Images/index_gr_836.gif]](Images/index_gr_836.gif)
![[Graphics:Images/index_gr_837.gif]](Images/index_gr_837.gif)
![[Graphics:Images/index_gr_838.gif]](Images/index_gr_838.gif)
![[Graphics:Images/index_gr_839.gif]](Images/index_gr_839.gif)
![[Graphics:Images/index_gr_840.gif]](Images/index_gr_840.gif)
![[Graphics:Images/index_gr_841.gif]](Images/index_gr_841.gif)
![[Graphics:Images/index_gr_842.gif]](Images/index_gr_842.gif)
![[Graphics:Images/index_gr_843.gif]](Images/index_gr_843.gif)
![[Graphics:Images/index_gr_844.gif]](Images/index_gr_844.gif)
![[Graphics:Images/index_gr_845.gif]](Images/index_gr_845.gif)
![[Graphics:Images/index_gr_846.gif]](Images/index_gr_846.gif)
![[Graphics:Images/index_gr_847.gif]](Images/index_gr_847.gif)
![[Graphics:Images/index_gr_848.gif]](Images/index_gr_848.gif)
![[Graphics:Images/index_gr_849.gif]](Images/index_gr_849.gif)
![[Graphics:Images/index_gr_850.gif]](Images/index_gr_850.gif)
uncorrected average tapping data
![[Graphics:Images/index_gr_869.gif]](Images/index_gr_869.gif)
![[Graphics:Images/index_gr_870.gif]](Images/index_gr_870.gif)
![[Graphics:Images/index_gr_871.gif]](Images/index_gr_871.gif)
![[Graphics:Images/index_gr_872.gif]](Images/index_gr_872.gif)
![[Graphics:Images/index_gr_873.gif]](Images/index_gr_873.gif)
![[Graphics:Images/index_gr_874.gif]](Images/index_gr_874.gif)
![[Graphics:Images/index_gr_875.gif]](Images/index_gr_875.gif)
![[Graphics:Images/index_gr_876.gif]](Images/index_gr_876.gif)
![[Graphics:Images/index_gr_877.gif]](Images/index_gr_877.gif)
![[Graphics:Images/index_gr_878.gif]](Images/index_gr_878.gif)
![[Graphics:Images/index_gr_879.gif]](Images/index_gr_879.gif)
![[Graphics:Images/index_gr_880.gif]](Images/index_gr_880.gif)
![[Graphics:Images/index_gr_881.gif]](Images/index_gr_881.gif)
![[Graphics:Images/index_gr_882.gif]](Images/index_gr_882.gif)
![[Graphics:Images/index_gr_883.gif]](Images/index_gr_883.gif)
![[Graphics:Images/index_gr_884.gif]](Images/index_gr_884.gif)
![[Graphics:Images/index_gr_885.gif]](Images/index_gr_885.gif)
![[Graphics:Images/index_gr_886.gif]](Images/index_gr_886.gif)
![[Graphics:Images/index_gr_887.gif]](Images/index_gr_887.gif)
![[Graphics:Images/index_gr_888.gif]](Images/index_gr_888.gif)
Mazurka in F minor, Op. 7, No. 3; Friedman 1930
corrected timing data
![[Graphics:Images/index_gr_907.gif]](Images/index_gr_907.gif)
![[Graphics:Images/index_gr_908.gif]](Images/index_gr_908.gif)
![[Graphics:Images/index_gr_909.gif]](Images/index_gr_909.gif)
![[Graphics:Images/index_gr_910.gif]](Images/index_gr_910.gif)
![[Graphics:Images/index_gr_911.gif]](Images/index_gr_911.gif)
![[Graphics:Images/index_gr_912.gif]](Images/index_gr_912.gif)
![[Graphics:Images/index_gr_913.gif]](Images/index_gr_913.gif)
![[Graphics:Images/index_gr_914.gif]](Images/index_gr_914.gif)
![[Graphics:Images/index_gr_915.gif]](Images/index_gr_915.gif)
![[Graphics:Images/index_gr_916.gif]](Images/index_gr_916.gif)
![[Graphics:Images/index_gr_917.gif]](Images/index_gr_917.gif)
![[Graphics:Images/index_gr_918.gif]](Images/index_gr_918.gif)
![[Graphics:Images/index_gr_919.gif]](Images/index_gr_919.gif)
![[Graphics:Images/index_gr_920.gif]](Images/index_gr_920.gif)
![[Graphics:Images/index_gr_921.gif]](Images/index_gr_921.gif)
![[Graphics:Images/index_gr_922.gif]](Images/index_gr_922.gif)
![[Graphics:Images/index_gr_923.gif]](Images/index_gr_923.gif)
![[Graphics:Images/index_gr_924.gif]](Images/index_gr_924.gif)
![[Graphics:Images/index_gr_925.gif]](Images/index_gr_925.gif)
![[Graphics:Images/index_gr_926.gif]](Images/index_gr_926.gif)
uncorrected average tapping data
![[Graphics:Images/index_gr_945.gif]](Images/index_gr_945.gif)
![[Graphics:Images/index_gr_946.gif]](Images/index_gr_946.gif)
![[Graphics:Images/index_gr_947.gif]](Images/index_gr_947.gif)
![[Graphics:Images/index_gr_948.gif]](Images/index_gr_948.gif)
![[Graphics:Images/index_gr_949.gif]](Images/index_gr_949.gif)
![[Graphics:Images/index_gr_950.gif]](Images/index_gr_950.gif)
![[Graphics:Images/index_gr_951.gif]](Images/index_gr_951.gif)
![[Graphics:Images/index_gr_952.gif]](Images/index_gr_952.gif)
![[Graphics:Images/index_gr_953.gif]](Images/index_gr_953.gif)
![[Graphics:Images/index_gr_954.gif]](Images/index_gr_954.gif)
![[Graphics:Images/index_gr_955.gif]](Images/index_gr_955.gif)
![[Graphics:Images/index_gr_956.gif]](Images/index_gr_956.gif)
![[Graphics:Images/index_gr_957.gif]](Images/index_gr_957.gif)
![[Graphics:Images/index_gr_958.gif]](Images/index_gr_958.gif)
![[Graphics:Images/index_gr_959.gif]](Images/index_gr_959.gif)
![[Graphics:Images/index_gr_960.gif]](Images/index_gr_960.gif)
![[Graphics:Images/index_gr_961.gif]](Images/index_gr_961.gif)
![[Graphics:Images/index_gr_962.gif]](Images/index_gr_962.gif)
![[Graphics:Images/index_gr_963.gif]](Images/index_gr_963.gif)
![[Graphics:Images/index_gr_964.gif]](Images/index_gr_964.gif)
Mazurka in F minor, Op. 7, No. 3; Rosen 1989
corrected timing data
![[Graphics:Images/index_gr_983.gif]](Images/index_gr_983.gif)
![[Graphics:Images/index_gr_984.gif]](Images/index_gr_984.gif)
![[Graphics:Images/index_gr_985.gif]](Images/index_gr_985.gif)
![[Graphics:Images/index_gr_986.gif]](Images/index_gr_986.gif)
![[Graphics:Images/index_gr_987.gif]](Images/index_gr_987.gif)
![[Graphics:Images/index_gr_988.gif]](Images/index_gr_988.gif)
![[Graphics:Images/index_gr_989.gif]](Images/index_gr_989.gif)
![[Graphics:Images/index_gr_990.gif]](Images/index_gr_990.gif)
![[Graphics:Images/index_gr_991.gif]](Images/index_gr_991.gif)
![[Graphics:Images/index_gr_992.gif]](Images/index_gr_992.gif)
![[Graphics:Images/index_gr_993.gif]](Images/index_gr_993.gif)
![[Graphics:Images/index_gr_994.gif]](Images/index_gr_994.gif)
![[Graphics:Images/index_gr_995.gif]](Images/index_gr_995.gif)
![[Graphics:Images/index_gr_996.gif]](Images/index_gr_996.gif)
![[Graphics:Images/index_gr_997.gif]](Images/index_gr_997.gif)
![[Graphics:Images/index_gr_998.gif]](Images/index_gr_998.gif)
![[Graphics:Images/index_gr_999.gif]](Images/index_gr_999.gif)
![[Graphics:Images/index_gr_1000.gif]](Images/index_gr_1000.gif)
![[Graphics:Images/index_gr_1001.gif]](Images/index_gr_1001.gif)
![[Graphics:Images/index_gr_1002.gif]](Images/index_gr_1002.gif)
uncorrected average tapping data
![[Graphics:Images/index_gr_1021.gif]](Images/index_gr_1021.gif)
![[Graphics:Images/index_gr_1022.gif]](Images/index_gr_1022.gif)
![[Graphics:Images/index_gr_1023.gif]](Images/index_gr_1023.gif)
![[Graphics:Images/index_gr_1024.gif]](Images/index_gr_1024.gif)
![[Graphics:Images/index_gr_1025.gif]](Images/index_gr_1025.gif)
![[Graphics:Images/index_gr_1026.gif]](Images/index_gr_1026.gif)
![[Graphics:Images/index_gr_1027.gif]](Images/index_gr_1027.gif)
![[Graphics:Images/index_gr_1028.gif]](Images/index_gr_1028.gif)
![[Graphics:Images/index_gr_1029.gif]](Images/index_gr_1029.gif)
![[Graphics:Images/index_gr_1030.gif]](Images/index_gr_1030.gif)
![[Graphics:Images/index_gr_1031.gif]](Images/index_gr_1031.gif)
![[Graphics:Images/index_gr_1032.gif]](Images/index_gr_1032.gif)
![[Graphics:Images/index_gr_1033.gif]](Images/index_gr_1033.gif)
![[Graphics:Images/index_gr_1034.gif]](Images/index_gr_1034.gif)
![[Graphics:Images/index_gr_1035.gif]](Images/index_gr_1035.gif)
![[Graphics:Images/index_gr_1036.gif]](Images/index_gr_1036.gif)
![[Graphics:Images/index_gr_1037.gif]](Images/index_gr_1037.gif)
![[Graphics:Images/index_gr_1038.gif]](Images/index_gr_1038.gif)
![[Graphics:Images/index_gr_1039.gif]](Images/index_gr_1039.gif)
![[Graphics:Images/index_gr_1040.gif]](Images/index_gr_1040.gif)
All pieces
Manually Corrected Data
![[Graphics:Images/index_gr_1059.gif]](Images/index_gr_1059.gif)
![[Graphics:Images/index_gr_1060.gif]](Images/index_gr_1060.gif)
![[Graphics:Images/index_gr_1061.gif]](Images/index_gr_1061.gif)
![[Graphics:Images/index_gr_1062.gif]](Images/index_gr_1062.gif)
![[Graphics:Images/index_gr_1063.gif]](Images/index_gr_1063.gif)
![[Graphics:Images/index_gr_1064.gif]](Images/index_gr_1064.gif)
![[Graphics:Images/index_gr_1065.gif]](Images/index_gr_1065.gif)
![[Graphics:Images/index_gr_1066.gif]](Images/index_gr_1066.gif)
![[Graphics:Images/index_gr_1067.gif]](Images/index_gr_1067.gif)
![[Graphics:Images/index_gr_1068.gif]](Images/index_gr_1068.gif)
![[Graphics:Images/index_gr_1069.gif]](Images/index_gr_1069.gif)
![[Graphics:Images/index_gr_1070.gif]](Images/index_gr_1070.gif)
![[Graphics:Images/index_gr_1071.gif]](Images/index_gr_1071.gif)
![[Graphics:Images/index_gr_1072.gif]](Images/index_gr_1072.gif)
![[Graphics:Images/index_gr_1073.gif]](Images/index_gr_1073.gif)
![[Graphics:Images/index_gr_1074.gif]](Images/index_gr_1074.gif)
![[Graphics:Images/index_gr_1075.gif]](Images/index_gr_1075.gif)
![[Graphics:Images/index_gr_1076.gif]](Images/index_gr_1076.gif)
![[Graphics:Images/index_gr_1077.gif]](Images/index_gr_1077.gif)
![[Graphics:Images/index_gr_1078.gif]](Images/index_gr_1078.gif)
![[Graphics:Images/index_gr_1079.gif]](Images/index_gr_1079.gif)
![[Graphics:Images/index_gr_1080.gif]](Images/index_gr_1080.gif)
![[Graphics:Images/index_gr_1081.gif]](Images/index_gr_1081.gif)
![[Graphics:Images/index_gr_1082.gif]](Images/index_gr_1082.gif)
Raw Tapping Data
![[Graphics:Images/index_gr_1083.gif]](Images/index_gr_1083.gif)
![[Graphics:Images/index_gr_1084.gif]](Images/index_gr_1084.gif)
![[Graphics:Images/index_gr_1085.gif]](Images/index_gr_1085.gif)
![[Graphics:Images/index_gr_1086.gif]](Images/index_gr_1086.gif)
![[Graphics:Images/index_gr_1087.gif]](Images/index_gr_1087.gif)
![[Graphics:Images/index_gr_1088.gif]](Images/index_gr_1088.gif)
![[Graphics:Images/index_gr_1089.gif]](Images/index_gr_1089.gif)
![[Graphics:Images/index_gr_1090.gif]](Images/index_gr_1090.gif)
![[Graphics:Images/index_gr_1091.gif]](Images/index_gr_1091.gif)
![[Graphics:Images/index_gr_1092.gif]](Images/index_gr_1092.gif)
![[Graphics:Images/index_gr_1093.gif]](Images/index_gr_1093.gif)
![[Graphics:Images/index_gr_1094.gif]](Images/index_gr_1094.gif)
![[Graphics:Images/index_gr_1095.gif]](Images/index_gr_1095.gif)
![[Graphics:Images/index_gr_1096.gif]](Images/index_gr_1096.gif)
![[Graphics:Images/index_gr_1097.gif]](Images/index_gr_1097.gif)
![[Graphics:Images/index_gr_1098.gif]](Images/index_gr_1098.gif)
![[Graphics:Images/index_gr_1099.gif]](Images/index_gr_1099.gif)
![[Graphics:Images/index_gr_1100.gif]](Images/index_gr_1100.gif)
![[Graphics:Images/index_gr_1101.gif]](Images/index_gr_1101.gif)
![[Graphics:Images/index_gr_1102.gif]](Images/index_gr_1102.gif)
![[Graphics:Images/index_gr_1103.gif]](Images/index_gr_1103.gif)
![[Graphics:Images/index_gr_1104.gif]](Images/index_gr_1104.gif)
![[Graphics:Images/index_gr_1105.gif]](Images/index_gr_1105.gif)
![[Graphics:Images/index_gr_1106.gif]](Images/index_gr_1106.gif)
![[Graphics:Images/index_gr_1107.gif]](Images/index_gr_1107.gif)
Looking at the relative metric fractions of each beat in sequence
![[Graphics:Images/index_gr_1108.gif]](Images/index_gr_1108.gif)
Mazurka in A minor, Op. 7, No. 2 performed by Chiu 1999
Manually Corrected Data
![[Graphics:Images/index_gr_1109.gif]](Images/index_gr_1109.gif)
![[Graphics:Images/index_gr_1110.gif]](Images/index_gr_1110.gif)
Raw Tapping Data
![[Graphics:Images/index_gr_1111.gif]](Images/index_gr_1111.gif)
![[Graphics:Images/index_gr_1112.gif]](Images/index_gr_1112.gif)
Mazurka in A minor, Op. 7, No. 2 performed by Friedman 1930
Manually Corrected Data
![[Graphics:Images/index_gr_1113.gif]](Images/index_gr_1113.gif)
![[Graphics:Images/index_gr_1114.gif]](Images/index_gr_1114.gif)
Raw Tapping Data
![[Graphics:Images/index_gr_1115.gif]](Images/index_gr_1115.gif)
![[Graphics:Images/index_gr_1116.gif]](Images/index_gr_1116.gif)
Mazurka in F minor, Op. 7, No. 3 performed by Friedman 1930
Manually Corrected Data
![[Graphics:Images/index_gr_1117.gif]](Images/index_gr_1117.gif)
![[Graphics:Images/index_gr_1118.gif]](Images/index_gr_1118.gif)
Raw Tapping Data
![[Graphics:Images/index_gr_1119.gif]](Images/index_gr_1119.gif)
![[Graphics:Images/index_gr_1120.gif]](Images/index_gr_1120.gif)
Mazurka in F minor, Op. 7, No. 3 performed by Rosen 1989
Manually Corrected Data
![[Graphics:Images/index_gr_1121.gif]](Images/index_gr_1121.gif)
![[Graphics:Images/index_gr_1122.gif]](Images/index_gr_1122.gif)
Raw Tapping Data
![[Graphics:Images/index_gr_1123.gif]](Images/index_gr_1123.gif)
![[Graphics:Images/index_gr_1124.gif]](Images/index_gr_1124.gif)
|