FRactal GEOmetry of Music

This library provides functionality for computing Hausdorff dimension over excerpts of music in MIDI format. The fragem executable provides a rudimentary command line interface.

The notion of scalling is modelled by metrics, which tells us which notes to consider at each given scalling factor.

Installing

Run stack build

Usage of fragem

Run stack exec fragem -- --options --to --fragem --come --here.

Examples:

Get the fractal dimension of the prelude to Bach's Cello suite number 1. The measures are grouped 2 by 2:

$ stack exec fragem -- "dataset/jsbach/cellosui/01prelud.mid"
0.178850387616
0.158114378584
0.109915367425
0.143308151141
0.122156915346
0.129072754513
0.097805716386
0.123414766481
0.143280562736
0.117777582496
0.131543326263
0.086578741273
0.112061820095
0.104881646668
0.097654886808
0.138884555284
0.118860785174
0.089003949420
0.239329990569
0.221046594345
1.551035438443

Now, lets say one wants to get the dimensions on by jumping from scaling factor 3 to 5 and group the measures 4 by 4:

$ stack exec fragem -- --group=4 --zoom=3,5 "dataset/jsbach/cellosui/01prelud.mid"
0.320504698703
0.317546489356
0.316865532637
0.316786378126
0.319154811106
0.318082602743
0.317389643893
0.316978561089
0.316091297338
0.316034983039

Now, lets say we are only interested in the first 8 measures:

$ stack exec fragem -- --interval=0,8 --group=4 --zoom=3,5 "dataset/jsbach/cellosui/01prelud.mid"
0.320504698703
0.317546489356

We can also see information about how many voices and how many sections are in a given piece of music with the --verbose or -v flag:

$ stack exec fragem -- -v -i 0,8 -g 4 -z 3,5 "dataset/jsbach/cellosui/01prelud.mid"
Midi Information: 
Voice: 
---------------
  timesig:         4/4
  ticks-per-beat:  240
  measures length: 42

0.320504698703
0.317546489356

This is usefull to learn how many voices and what the time-signature of each part of the midi file"

$ stack exec fragem -- -v --voice=1 "dataset/jsbach/sinfon/sinfon1.mid" 
Midi Information: 
Voice: 
---------------
timesig:         4/4
ticks-per-beat:  240
measures length: 21
Voice: 
---------------
timesig:         4/4
ticks-per-beat:  240
measures length: 20
Voice: 
---------------
timesig:         4/4
ticks-per-beat:  240
measures length: 21

1.243953157132
3.223508271268
0.023169562229
0.260019133590
0.297888639573
0.585230193007
1.671102048247
0.404998187800
0.026212211104
1.872974745471

The -d or --debug flag displays some additional information about the internals:

$ stack exec fragem -- -v -d --interval=0,2 --group=2 --zoom=1,5 -v "dataset/jsbach/cellosui/01prelud.mid"
Midi Information: 
Voice: 
---------------
timesig:         4/4
ticks-per-beat:  240
measures length: 42

max metric zoom level: 5
Notes at: 5
43 |--      |        |        |        |--      |

Notes at: 1
60 |        |        |        |        |    --  |--  --  |    --  |--  --  |
   |    --  |--  --  |    --  |--  --  |      --|        |      --|        |
   |        |        |        |        |        |        |        |        |
   |      --|        |      --|        |        |        |        |        |
   |        |        |        |        |        |        |        |        |
   |        |        |        |        |        |        |        |        |
   |        |        |        |        |        |        |        |        |
   |        |        |        |        |        |        |        |        |
   |        |        |        |        |  --    |  --  --|  --    |  --  --|
   |        |        |        |        |        |        |        |        |
   |  --    |  --  --|  --    |  --  --|        |        |        |        |
   |        |        |        |        |        |        |        |        |
   |        |        |        |        |        |        |        |        |
   |        |        |        |        |        |        |        |        |
   |        |        |        |        |        |        |        |        |
   |        |        |        |        |        |        |        |        |
   |        |        |        |        |        |        |        |        |
43 |--      |        |--      |        |--      |        |--      |        |

1.057535219047