Re: buckets...

> From: paul@stretch-music.com
> Subject: Re: mistuning of octave considered good
>
< summarizing the differences between Pauls Harmonic Entropy
and my 'hacked psuedo harmonic entropy calculation' >

HE HPHEC
2/1 1200+-42 1200+-30
3/2 702+-35 702+-18

> > Basically, I gave my tool sharper ears than 'typical resolution'.
>
> Not necessarily! The range I gave doesn't correspond to the "width
> of the bucket" -- would that be the distance between the two
> nearest local maxima?

Yes, I am referring to the width of the bucket up to the local
maxima. Somewhere around 1230 the walls of the bucket rising up
from 33/16 are lower than those from the 2/1, hence it stops
being a bruised octave and starts being some distinct identity.

An interesting observation in this thread is that some microtonal
useage really IS to have, for instance, a 'range' of 5/4's. So
a scale that contains a 9/7, 24/19 and 5/4 may just want a
major third, spicy major third and very spicy major third. I
have built my code to assume that a spicy major third may want
to sink on some RI identity.

Note that with the current bucket shape, I am filling the
HPHEC chart all the way up to the 1111 limit, however, the
ratios that appear in the table turn out to be limited to
around 33 limit (with this bucket tuning).

The complexity calculation I use gives some fudge factor
to otonal ratios since I didn't like 5/3 beinlg less complex
than 5/4 and is :

comlexity = numerator * denominator;
if ( is_power_of_2( denominator ) )
complexity = complexity / 2;

I build the buckets linearly up in either direction from this
point (and carry it to infinity, there is no saturation) and
have played with the steepness. If I decrease the
steepness the buckets become wider and the maximum included
limit is decreased. Of course the opposite can be done as well.

Bob Valentine