harmonic entropy stuff, van Eck's model

Paul, could you post values for, say, the top 20 ratios, with s=1.0? I'm
having trouble getting good numbers off the charts.

Also, could somebody check my work? I've written a program that spits
out the "widest" ratios less than an 8ve from a Farey series of a given
order. Here's the top 20 of order 100. Shouldn't be too far off,
since it's ordered by denominator. (Note: this isn't harmonic entropy,
this is just van Eck's model.)

0.02856915219677081 (2 1)
0.01414622188897297 (3 2)
0.00943001718010761 (4 3)
0.00938378761226610 (5 3)
0.00703880692699749 (5 4)
0.00687217101688342 (7 4)
0.00568569821800397 (7 5)
0.00565828749191405 (6 5)
0.00557915549283261 (9 5)
0.00555376330850399 (8 5)
0.00460731642550794 (11 6)
0.00458047281019133 (7 6)
0.00404149818474608 (12 7)
0.00398271703938879 (9 7)
0.00396481195162146 (13 7)
0.00396386924443387 (8 7)
0.00394661620776649 (11 7)
0.00392722983563987 (10 7)
0.00345207718096036 (11 8)
0.00343615857784640 (15 8)

-Carl

[Carl Lumma, archive 12402:]
>Also, could somebody check my work? I've written a program that spits
>out the "widest" ratios less than an 8ve from a Farey series of a given
>order. Here's the top 20 of order 100. Shouldn't be too far off,
>since it's ordered by denominator. (Note: this isn't harmonic entropy,
>this is just van Eck's model.)

>0.02856915219677081 (2 1)
>0.01414622188897297 (3 2)
>0.00943001718010761 (4 3)
>0.00938378761226610 (5 3)
>0.00703880692699749 (5 4)

Carl, I'm not getting quite the same results. For example, for 3/2,
I have the interval nestled between 100/67 and 98/65, which, if I'm
understanding the "rules" involved here, means that the influence
spans between (100+3)/(67+2) and (98+3)/(65+2), i.e., between 103/69
and 101/67, or between 1.49275 and 1.50746, or 0.014709 total range.

Paul E, wanna jump in here? Anyone else?

JdL

>>0.02856915219677081 (2 1)
>>0.01414622188897297 (3 2)
>>0.00943001718010761 (4 3)
>>0.00938378761226610 (5 3)
>>0.00703880692699749 (5 4)
>
>Carl, I'm not getting quite the same results. For example, for 3/2,
>I have the interval nestled between 100/67 and 98/65, which, if I'm
>understanding the "rules" involved here, means that the influence
>spans between (100+3)/(67+2) and (98+3)/(65+2), i.e., between 103/69
>and 101/67, or between 1.49275 and 1.50746, or 0.014709 total range.

Heya John, thanks for the help!

You're results and mine agree, I'm just using log widths. The real
question is, are you getting a different ordering?

-Carl

[Paul Erlich:]
>John, the "range" must be measured logarithmically. So
>1.50746/1.49275=1.0098543, and log(1.0098543)/log(2) agrees with Carl's
>result.

OK, gotcha. Now I'm matching Carl's numbers.

[Carl Lumma:]
>You're results and mine agree, I'm just using log widths. The real
>question is, are you getting a different ordering?

Same ordering, except that I'm showing 1/1 at the top of the list.

JdL

>>Paul, could you post values for, say, the top 20 ratios, with s=1.0? I'm
>>having trouble getting good numbers off the charts.
>
>top 20 ratios?

Sorry for not being more clear. Could you show the 20 ratios, from the
farey series used, with the lowest harmonic entropy?

Incidentally, how do you determine which ratios 'cause' local minima?

>>Also, could somebody check my work?
>
>right (although what I call s=1% becomes, in your units, s=1%/log(2)=1.4427.

Eh? How does s apply to what I did?

-Carl

>>You're results and mine agree, I'm just using log widths. The real
>>question is, are you getting a different ordering?
>
>Same ordering, except that I'm showing 1/1 at the top of the list.

I chopped it off.

-Carl

>>Sorry for not being more clear. Could you show the 20 ratios, from the
>>farey series used, with the lowest harmonic entropy?
>
>I've only calculated the harmonic entropy at cents values.

Can you ask it about the cents values represented by the ratios of a given
farey order?

>>>right (although what I call s=1% becomes, in your units,
>>>s=1%/log(2)=1.4427.
>
>>Eh? How does s apply to what I did?
>
>It doesn't, but if you're going to proceed to calculate harmonic entropy,
>it'll be good to have this straight.

Ah, thanks. I think I'll need to go over to something a little higher-level
than LISP before I calculate harmonic entropy. I have Maple V, but perhaps
I should start with Mathematica or Matlab...

-Carl