back to list

RE: Meaner tones again (Paul E)

🔗Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul)

3/12/1997 10:16:33 AM
From: PAULE

>Paul E: The weights I used were 3, 5, and 5. My error function
>was thus 3*(F-X)^2 + 5*(TM-4*X+2*OCT)^2 + 5*(MS-3*X+0CT)^2.
>(F=cents(3/2), TM=Cents(5/4), MS= cents(5/3), OCT= 1200)
>Your weights are 9 25 25, the squares of these. I weighted
>the derivatives, you the squared errors themselves. I'm not
>sure which is more correct mathematically, but your unweighted
>gives a slightly lower sum of sq'ed errors.

A slightly lower unweighted sum of sq'ed errors, duh, by definition.

My weighting scheme is based on Partch's "Observation One" which claims that
the field of attraction, in cents, of an interval is inversely proportional
to the (odd-number) limit of the interval. Therefore the errors must be
multiplied by the limit to get the error in units of the field of
attraction. Your weighting scheme can be seen as a compromise between this
and equal-weighting. I think leaning towards equal weighting is appropriate
when the music tends to use complete chords and the various intervals
reinforce one another.

Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Wed, 12 Mar 1997 19:40 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA03550; Wed, 12 Mar 1997 19:40:41 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA03548
Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
id KAA21966; Wed, 12 Mar 1997 10:39:03 -0800
Date: Wed, 12 Mar 1997 10:39:03 -0800
Message-Id:
Errors-To: madole@mills.edu
Reply-To: tuning@ella.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@ella.mills.edu