The independence of extremities in drumming

• Drumming is a complex psychomotor activity that requires simultaneous bimanual and bipedal co-ordination.
  
• Different rhythmic patterns have to be played on the instruments of a drumset with different extremities at a time. This is referred to as polymetric shifting.
  
• Independence is an important criterion for assessing a drummer's performance.
  
• independence can be assessed rather objectively, unlike, for example the 'feel' or 'groove' of a drum part.

Systematic problem construction

• In the case of drumming, the four `components' of each problem are a drummer's extremities. The attributes of each of these components are the note values.
  
• Figure 1 shows the components (extremities) and the linear order of their attributes (note values). Note that only one cymbal (a), snare (b) and bass drums (c), and the hi-hat (d) were considered.

  
  Figure 1: Ordering within components (Note: nu = not used)

• The smaller the note value, the more difficult it is to play
  
• The cymbal should be played most easily, since it is played with the right hand. Dominance of hands over feet: the left hand - which plays the snare drum - should rank above the right foot. The hi-hat should be most difficult to play.
  
• Four attributes were not taken into consideration.
• Pool of problems is the Cartesian product of all components' attributes. An example problem derived from the diagram above is a5b2c3d2, which means that sixteenths had to be played with the right hand on the cymbal, quarter notes with the left hand on the snare drum, eighths with the right foot on the bass drum, and quarter notes with the left foot on the hi-hat.
• 5 (cymbal) X 5 (snare drum) X 4 (bass drum) X 3 (hi-hat) = 300 problems
  
• Problem a1b1c1d1 excluded because of a floor effect.
  
• From the pool of 299 problems, we drew a sample of 38 problems that were representative of the demands of independent drumming.

Sampling criteria:

1. Note value ratios between the extremities: odd ratios more difficult than even ones; difficulty increases with the note values for an extremity. These criteria lead to the following order of time ratios
2. Rations with *:1 should be excluded in the future.

   
   
                                            Order of time ratios.

3. Same note value is more difficult to play with one's feet that with one's hands.
   
4. Right-handed drummers play the same note value more easily with their right hand than with their left hand, they play more easily with their right foot than with their left foot. The opposite holds for left-handed players.
   
5. side equality principle:
   
6. The more extremities are involved, the greater the attentional demands.

Method

• Participants
  
  • 68 drummers
    
  • The sample included drummers with four different levels of practice.

Procedure

• Recordings were made with a four-channel tape recorder.
  
• Tempo of the problems was indicated by a metronome.
  
• Participants played on their own drum sets in their usual surroundings.
  
• The metronome speed was set to 80 beats per minute for all problems.
  
• Five minutes to `warm up'
  
• Two practice problems.
  
• Problems that had been played incorrectly within the first block could be repeated after the third block.

Results

• Performance rating
  
  
  • Assessment with regard to the quality of solution: Ratings
    
  • Tempo
    
  • Regularity of beats
    
  • By combining the criteria of tempo and regularity, we obtained 16 paired criteria
    
  • Two ways of rating problems as correctly played: moderate assessment, Strict assessment
    
  • Objectivity: two raters
    
    
    
• Knowledge space and symmetric distances
  
  
  • Knowledge space for the 38 drumming problems contained 1.6 million knowledge states.
    
  • Symmetrical distance is computed as .
    
  • Moderately and strictly assessed problems were analysed; In addition: analyses were conducted with and without repetitions.
    
    
• Table 1: Average symmetrical distances and standard deviations
  
  

  Type of analysis
  Moderate, repetitions		Strict, repetitions		Moderate, no rep`s		Strict, no rep`s
  Distance	SD	Distance	SD	Distance	SD	Distance	SD
  .16	.41	.44	.67	.22	.45	.54	.79

Solution frequencies

• Calculated across participants for each of the 38 problems
  
  
• Table 2: Solution frequencies of 5 out of the 38 problems for all four types of assessment.
  
  

  Problem attributes	Type of analysis
  	Moderate, repetitions	Strict, repetitions	Moderate, no repetitions	Strict, no repetitions
  a2b3c4d5	0	0	0	0
  a5b4c3d2	17	17	17	11
  a3b5c4d2	9	9	9	8
  a5b4c3d1	19	19	21	17
  a1b5c4d2	16	16	16	14

Discussion

• Neither floor nor ceiling effects contributed to that result:
  
• For the moderate analysis with repetitions, results on solution frequencies are compatible both with the hypotheses on the vertical (ordering within components) and the horizontal differentiation (a to d).
  
• Theory of knowledge spaces provides an adequate tool for the assessment of independence in drumming.

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