back to list

RE: Reply to Neil from Paul

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

2/18/1997 4:37:09 PM
From: PAULE

I wrote,

>>" 19 consistently represents the harmonic series only
>>through the 9th harmonic (though in your music, you tend to use the
>>diatonic, rather than harmonic, dom7th), and 34 consistently represents
the

>>harmonic series only through the 5th harmonic. "


Gary wrote,

>I probably ought to let Neil speak for himself, but I suspect that he meant
>less specifically than the harmonic series itself, but JI in general.

I see no difference here. I could say, "19 consistenly represents 9-limit JI
and 34 consistenly represents 5-limit JI," but I didn't want to start the
odd vs. prime debate on the definition of "limit" again.

Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Wed, 19 Feb 1997 01:42 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA11051; Wed, 19 Feb 1997 01:42:04 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA11047
Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
id QAA07741; Tue, 18 Feb 1997 16:39:56 -0800
Date: Tue, 18 Feb 1997 16:39:56 -0800
Message-Id: <009B017A99238E2B.2E94@vbv40.ezh.nl>
Errors-To: madole@mills.edu
Reply-To: tuning@ella.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@ella.mills.edu

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

2/19/1997 7:47:50 AM
From: PAULE

An error in my post:

I wrote

>If you use a weighted mean, with weights inversely
>proportional to the limit (following Partch who said higher-limit intervals
>need to be tuned more accurately in proportion to their limit), you get a
>perfect fifth of 696.019 cents.

"Inversely proportional to the limit" should be "proportional to the square
of the limit," the square being used since we are dealing with squared
error. Notice how close this result is to the equal-weighted result,
696.165, even though the assumptions seem quite different. One can imagine
many different criteria between these two weighting schemes would lead to
results within this very narrow range.

Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Wed, 19 Feb 1997 23:15 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA11865; Wed, 19 Feb 1997 23:15:47 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA11857
Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
id OAA27935; Wed, 19 Feb 1997 14:09:13 -0800
Date: Wed, 19 Feb 1997 14:09:13 -0800
Message-Id:
Errors-To: madole@mills.edu
Reply-To: tuning@ella.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@ella.mills.edu