source file: mills2.txt Date: Wed, 6 Nov 1996 10:53:18 -0800 Subject: Consonance coefficient From: Antonio The motive for which I have needed a list of the intervals was tied up to the type of software that I am preparing. He, once you give the notes of a chord, produces all his possible inversions on guitar keyboard. The number of inversions is so high that it requires a filter that allows to rearrange it with various criterions. These are essentially of two types: a) technical difficulty (fingering) b) level of consonance Naturally the point b is a problem so vast and open from seem me often a pure utopia. My objective would be that of establish a "consonance coefficient" that gathers in a number the problematic that the concept of "consonance" implies (beating, harmonics series and many other things that I don't know but that surely anybody of you knows well...) Naively I've thought that this number could be synthesized in a value to give to the various intervals that each inversion requires. For instance: octave=3D 12 P5=3D 11 P4=3D 10 M6=3D 9 M3=3D 8 m3=3D 7 m6=3D 6 m7=3D 5 4+=3D 4 M2=3D 3 M7=3D 2 m2=3D 1 This is only an example based upon my instinctive list of the intervals. A triad of C would get the followings "scores": Root position: M3, m3, P5=3D 8+ 7+ 11=3D 26 First inversion: m3, P4, m6=3D 7+ 10+ 6=3D 23 Second inversion: P4, M3, M6=3D 10+ 8+ 9=3D 27 The fact that the second inversion is, in according to this strange "score", more consonant than root position is strange but, in effects, in the harmonics series it appears before. In short the principal problem is that of establish the values in the intervals list correctly. I don't know if my method is too na=EFve, let m= e know. Ciao. --Lorenzo Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 6 Nov 1996 21:26 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05965; Wed, 6 Nov 1996 21:27:36 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA05918 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id MAA11344; Wed, 6 Nov 1996 12:27:34 -0800 Date: Wed, 6 Nov 1996 12:27:34 -0800 Message-Id: <199611062026.UAA02698@freenet3.carleton.ca> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu