Subject: Beware of circles From: "Bruno L. Giordano" <bruno.giordano@xxxxxxxx> Date: Wed, 24 Mar 2010 17:46:55 -0400 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>Hello, I can't resist writing a methodological note about circles and wheels. In the original posting by Michael, the wheel was conceived as a morphing strategy. Stating the obvious, and following up on Richard's note, for the psychologist the circle can happen to be a concise and visually elegant model of how humans organize a particular sensory/perceptual/cognitive domain. Such a representation is often grounded in the construct of similarity (objects that are close/far within the representation are similar/different). Now, my note is about those cases where circular representations are extracted from the multidimensional scaling (MDS) analysis of behavioral estimates of similarity. I have seen several of these. What I have rarely seen pointed out is that popular MDS algorithms under specific but not uncommon circumstances are prone to representing the data as a circular (2D) or spherical (3D) structure, independently of whether a circle/sphere is there or not. From my understanding, this MDS modeling bias takes the name of "annular bias". A similar bias takes the name of "horseshoe effect". So, circles can be attractive, but there are times when we should beware of them. Bruno ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Bruno L. Giordano, Ph.D. Postdoctoral Research Fellow CIRMMT - Schulich School of Music 555 Sherbrooke Street West Montréal, QC H3A1E3 Canada +1 514 398 4535, Ext. 00900 (voice) +1 514 398 2962 (fax) http://www.music.mcgill.ca/~bruno Richard E Pastore wrote: > What is the reasonable goal of finding an auditory circle analogy to the > visual color circle? > Although the discussion has focused on finding an auditory analogue > to the color wheel, the discussion really has focused on the wheel. > Color is an artifical system that represents wavelength, with a > resulting representation of artificial "nonspectral hues" that do not > correspond to wavelengths in the visible spectrum. Color space was > defined using color mixing findings. The typical figure from those data > is essentially a triangle with rounded corners. The three primary > colors are at the three corners outside the space. If 400 and 700 nm > ("blue" and "red") at maximum saturation are along the abscissa and > roughly 520 nm at the apex of the triangle, the wavelengths of the > visible spectrum runs along the outside from the 400 nm corner (blue) > through the apex (green) to the 700 nm corner (red). The abscissa maps > the non-spectral hues that are an artificial by-product of mixing the > long and short wavelengths. The space is populated from the edge to the > non-central region of total desaturation (white) by systematic > decreasing saturation or spectral purity. Complimentary colors are the > opposite ends of any line through "white." This 2-dimensional space is > actually a cross-section of a 3-D representation, with the 3rd dimension > being intensity or brightness. > The edge from the apex to the long wavelength corner (700 nm) > represents the opponent processing interaction between the long (red) > and middle (green) primaries. The space becomes populated with the > addition of the opponent processing between the short wavelength primary > (Blue) and the combined long and middle primaries (Yellow = Red + > Green). Because of the opponent neural coding that is driven by the > breakdown of the light sensitive photopigments, the afterimages are the > complimentary color of the original. > The "classic color circle" is a simplified, stylizied version of the > outer edge of the 2-D cross-section. It is round (a circle) that is > unpopulated and with a gap to represent the non-spectral hue portion of > color space - the circle is NOT complete. > Now, back to the original question that prompted the discussion: > What is the "auditory" circle intended to represent and in what way is > it analogous to the color circle? > > Dick Pastore > -- > Richard E Pastore > Distinguished Service Professor > Department of Psychology > Binghamton University > Binghamton, NY 13902-6000 > Office: (607) 777-2539