source file: mills2.txt Date: Thu, 2 Jan 1997 16:35:45 -0800 Subject: RE: Paul Erlich's "tonalness" algorithm From: PAULE Thanks to Brian for a fine summary of the historical developments in the theory of pitch perception. I certainly agree that the issue is complex and that we are very far from understanding the complexities of the ear-brain system. However, this from Brian himself: >Among the three popular pitch theories only >the optimum processor theory [Goldstein's] >is able to account for most of the data >[in] a quantitative sense. It is no coincidence that I chose to highlight, and cite results from, Goldstein's work, and only mentioned Terhardt and Wightmann due to some overall similarities between their theories. Goldstein's theory can be viewed as a first approximation to the problem, to which corrections will no doubt be added by more sophisticated theories. In trying to understand Van Eck's work, I carefully studied Goldstein's paper and found that the form of Goldstein's theory was strongly suggested by the data, and was not merely a preconceived construct to which the data was fitted. This impressed me enough to inspire a reconstruction and correction of Van Eck's procedure, which is the "algorithm" I posted. It seems a simple enough construct to merit consideration, especially where no reasonable alternatives are apparant. Far too many writers on tuning, etc. interpret chords cavalierly and end up unknowingly contradicting themselves. A first step is to recognize that any SWNR interval will tolerate some mistuning. A second step is to attempt a consistent description of how an arbitrary interval will be heard. This is what I have done, and although refinements are no doubt possible, much useful information can be gleaned from this model. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 3 Jan 1997 02:04 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01098; Fri, 3 Jan 1997 02:07:32 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA01096 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id RAA14058; Thu, 2 Jan 1997 17:07:30 -0800 Date: Thu, 2 Jan 1997 17:07:30 -0800 Message-Id: <199701022005_MC1-E20-4A58@compuserve.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu