Re: order of consonance/dissonance (Bill Thompson )

Subject: Re: order of consonance/dissonance
From:    Bill Thompson  <bill.thompson@xxxxxxxx>
Date:    Fri, 1 Apr 2011 10:34:23 +1100

Hi Tom, Check out and do pass on any other info or scripts that you receive. Bill On 31/03/2011, at 11:44 PM, Tom Cochrane wrote: > hi everyone > > I want to use an 'order of tonal consonance' in some musical analysis I am doing where all the intervals are given a value based on their degree of consonance. I know that there is still quite a lot of debate about this, but I am working on the assumption that listener's subjective judgements are at least related to the mathematical properties of the frequency relations. Anyway, it would be good to compare different theories. > > My main problem is that while lots of theories specify a rough order for a few of the intervals, they don't systematically produce a table for all of them, so I don't have any basis for systematic comparison. I am particularly interested in the method of Plomp & Levelt, or Kameoka & Kuriyagawa's refinement of this, based on critical bands and the overlapping of harmonic partials. But while some authors place the equal temperament frequencies in the x axis for this graph (e.g. <> )- I haven't been able to find an explicit quantified table for where exactly on the y axis the 12 equal temperament semitones sit. > > I am aware that these values can change depending on what frequency is taken as fundamental. I am also aware that by this method (as well as the Helmholtz method it is inspired by) intervals greater than an octave will not necessarily have the same consonance as their analogue intervals smaller than an octave (e.g. the 10th versus the 3rd). But has anyone actually produced data for intervals above an octave? Or even more ideally, does anyone know an equation I can plug into Matlab to produce the graph for a given fundamental frequency myself (across several octaves)? > > your help would be much appreciated! > > Tom Cochrane > Sonic Arts Research Centre > Queen's University Belfast > > p.s. does anyone have a pdf copy of Kameoka & Kuriyagawa's paper Consonance Theory Part II: Consonance of Complex Tones and Its Calculation Method?? Bill Thompson Professor and Head Department of Psychology Macquarie University NSW 2109, Australia Work: 02-9850-4083

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