Suppose a density is defined by measuring the amount of information. Why does the first list having three pitches result in lower density than the second list comprising two pitches?

 

(density-analysis '((c4 d4 g4) (d4 a4)))

=> (0.2916667 0.5833334)

 

Thank you!

The bigger the interval the lower the density.

 

(density-analysis '((c4 d4) (c4 a4)))
=> (0.16666667 0.75)

(density-analysis '((c4 d4 e4 f4) (c4 a4 g5 c7)))
=> (0.1388889 0.86111116)

 

Thank you! And with length density, is it correct to say that the longer the duration the lower the density?

(density-analysis '((h q q) (e s)))
=> (0.19 0.67)

 

Yes
 

(density-analysis '((h q e =) (e = = = = = = =)))
=> (0.25 0.5)

(density-analysis '((h q e =) (s = t =)))
=> (0.25 1.0)

 

My apologies for continuing questions...

 

Given that longer durations result in lower density, and if I understand it right, the density value of 1.0 indicates the lowest density, why are the longer durations resulting in higher density estimation:

 

(density-analysis '((h q) (e s)))

=> (0.17 0.67)

 

Thank you for your patience!

1.0 is the highest density.

Thanks for clarifying. It makes sense that 1.0 is the highest density; that was what my initial understanding was.

 

Going back to my pitch density question from earlier, where we attested that "the bigger the interval, the lower the density," should the density be lower for a major sixth and higher for a major second, the former being a larger interval? The example below and others I tested, produce higher density for larger intervals.

(density-analysis '((c4 a4) (c4 d4)))
=> (0.75 0.16666667)

 

I'm sorry if I'm not looking at this the wrong way! The length density is clear now.

The density increases with the size of the interval/s.

For example (cs2 g7) is more dense than (cs2 g2). The more difficult (complex) is to recognise the intervals the more dense is the pitch sequence.

 

(density-analysis '((cs2 g7) (cs2 g2)))
=> (1.0 0.5)