[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
order of consonance/dissonance
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.
<http://sethares.engr.wisc.edu/paperspdf/consonance.pdf> )- 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
your help would be much appreciated!
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