Metronome Accuracy Test

0. Time Calibration

  1. Recorder: Zoom H2n (Analog input to 24bit 44.1kHz wav file)
  2. Reference time: telephone service 60bpm click and voice (Japanese Standard Time by dial 117)
    In the US https://www.nist.gov/pml/time-and-frequency-division/services/telephone-time-day-ttds
  3. Onset Detection: aubioonset -i input.wav
  4. My metronome written in JavaScript: http://goto920.github.io/demos/metronome
  5. Source code: metronome in https://github.com/goto920/nodejs/metronome 
Onset of Reference click(telephone service)
14.929614 # 0 sec of a minute
15.926462
(omit)
73.949501
74.947960 # 0 sec of the next minute
# 74.947960 - 14.929614 = 60.018346 (18.3 m sec longer than exact 60 second)
The internal clock of H2n is a little too fast. 
Time is fixed so that the mean difference to the theoretical playback time becames minimal. 
timefix = 0.999634855237734 is used in the following recorded metronome sound samples.


# seq time diff interval timefix = 0.999634855237734
0 0 0 
1 0.996484006174024 -0.00351599382597578 0.996484006174024
(omit)
59 58.9983361973924 -0.00166380260760945 0.998636220017346
60 59.9964306153182 -0.00356938468180346 0.998094417925806
# Diff mean = 1.24943037397666e-11, cv = N/A
# Interval mean = 0.999940510255303, cv = 0.0119367472143475
# Note: cv is Coefficient of Variation (std. deviation/mean)
# std. deviation is sqrt(variance)

1. 4/4 beat (at 60, 120, 180, 240bpm)

Here BPM(beat/minutes) is based on quarter note. Therefore, there are 60 notes in a minutes at 60bpm. Note that accuracy internal clock depends on device hardware and environment. It may also different in individual PCs or telephones Clocks of all my devices seems a little too fast.

Tested Metronomes

  1. (Best) Roland RMP5 (mesh head snare pad) as an example of good metronome
  2. (Excellent except for 180bpm) TempoApp on Android as an example of smartphone App
  3. The JavaScript metronome
    1. (The first note delays) Old Linux PC (developement PC)
    2. (Good) Windows 10 (Microsoft Surface Pro3, latest Win10 release)
    3. (Surprisingly good enough) Android phone (Sony SO-02H, compact but good one. Purchased in Nov. 2015)

Fig.1-1 60bpm (60sec)
X: note number, Y (actual playback time) - (theoretical ideal time) in sec 
RolandRMP5
# seq time diff interval timefix = 0.999634855237734
0 0 # first note (will be omitted here after)
1 0.998478277710223 -0.00152172228977654 0.998478277710223
(omit)
# Diff mean = -0.00399574043086079, cv = -0.465593719286576
# Interval mean = 0.999880815393865, cv = 0


TempoAndroid
# seq time diff interval timefix = 0.999634855237734
1 1.00178806871592 0.00178806871591553 1.00178806871592
(omit)
60 59.9840521369058 -0.0159478630942118 0.998411302174915
# Diff mean = -0.00732362482743205, cv = -0.670160375389208
# Interval mean = 0.999734202281763, cv = 0


Android-SO-02H
# seq time diff interval timefix = 0.999634855237734
1 0.999385946158779 -0.000614053841220819 0.999385946158779
(omit)
60 59.9783642145795 -0.0216357854205071 0.998502268946744
# Diff mean = -0.0105865662795749, cv = -0.60193780467709
# Interval mean = 0.999639403576325, cv = 0


Windows10-Edge
# seq time diff interval timefix = 0.999634855237734
1 0.996960831999972 -0.00303916800002779 0.996960831999972
(omit)
60 59.9733310530834 -0.0266689469166295 0.998636220017353
# Diff mean = -0.0149234154567007, cv = -0.44246669142329
# Interval mean = 0.999555517551389, cv = 0


Linux-Firefox-oldThinkpad
# seq time diff interval timefix = 0.999634855237734
# 1st note delayed 
then 2nd note was played earlier and interval became short
1 0.883986099200425 -0.116013900799575 0.883986099200425
(omit)
60 59.8623985742931 -0.137601425706926 0.998391309477817
# Diff mean = -0.126155334867884, cv = -0.049050851570485
# Interval mean = 0.997706642904885, cv = 0

Fig.1-2 120bpm(60sec)
RolandRMP5
# seq time diff interval timefix = 0.999634855237734
1 0.499386584996259 -0.000613415003740514 0.499386584996259
(omit)
120 59.9939815099229 -0.00601849007713184 0.501948649130235
# Diff mean = -0.00389274185190754, cv = -0.472071705421503
# Interval mean = 0.499949845916024, cv = 0


TempoAndroid
# seq time diff interval timefix = 0.999634855237734
1 0.499885402789023 -0.000114597210976897 0.499885402789023
(omit)
120 59.9862073496537 -0.0137926503463106 0.499523534971431
# Diff mean = -0.00671629380343126, cv = -0.507799546618484
# Interval mean = 0.499885061247114, cv = 0


Windows10-Edge
# seq time diff interval timefix = 0.999634855237734
1 0.494921216097913 -0.00507878390208749 0.494921216097913
(omit)
120 59.9735569705607 -0.0264430294393492 0.499431568564738
# Diff mean = -0.0149188475898261, cv = -0.443203466794944
# Interval mean = 0.499779641421339, cv = 0


Android-SO-02H
# seq time diff interval timefix = 0.999634855237734
1 0.499205651087461 -0.000794348912538545 0.499205651087461
(omit)
120 59.9783422226127 -0.0216577773873254 0.499298617128993
# Diff mean = -0.0111270743083914, cv = -0.573180370647238
# Interval mean = 0.499819518521772, cv = 0


Linux-Firefox-oldThinkpad
# seq time diff interval timefix = 0.999634855237734
1 0.37154228372505 -0.12845771627495 0.37154228372505
(omit)
120 59.8508357979225 -0.149164202077465 0.499226643419419
# Diff mean = -0.138350602334498, cv = -0.0450205118242414
# Interval mean = 0.498756964982688, cv = 0

Fig.1-3 180bpm(60sec)
Similar except for TempoAndroid. TempoApp played the beat a little too fast only at 180bpm. Reason is unknown.

Fig.1-4 240bpm(60sec)
TempoAndroid was OK at 240bpm.

2. 8/8 swing beat

  1. 8 swing notes in a bar(measure)
    |o-oo-oo-oo-o|o-oo-oo-oo-o|o-oo-oo-oo-o|o-oo-oo-oo-o| (4 bars)
  2. 120, 240, 360, 480 notes per minutes at 60, 120, 180, 240 bpm respectively.
  3. The results are similar to 4/4 beat test.

Fig.2-1 60bpm(1 min)

Fig.2-2 120bpm(1 min)

Fig.2-3 180bpm(1min, quite fast)
Fig.2-4 240bpm(1min, very fast)
goto at kmgoto.jp