1. A density calculating apparatus comprising: an image data acquisition section that acquires print image data representing a print image to be printed by a printing system, the printing system setting print densities of color materials having a plurality of colors and printing an image based on the image data by using the color materials in the print densities; a place designating section that designates a place on the print image represented by the print image data acquired by the image data acquisition section; a target color acquisition section that acquires a target color of a color of the place; a color guess section that guesses a print color of the place to be printed by the printing system on the basis of a corresponding relationship between print densities and colors of patches, the patches being obtained by printing in each print density by the printing system based on chart image data a chart image which is represented by the chart image data and on which the patches having a plurality of colors line up while the print density of each of the color materials having the plurality of colors is changed to a series of print densities, as well as on the basis of a tentative print density that is designated for each of the color materials having the plurality of colors, the printing system producing the print color of the place based on the print image data and the tentative print density; a density calculation section that calculates the print densities of the color materials having the plurality of colors by using the color guess section so that the target color acquired by the target color acquisition section is achieved at the place by the printing system based on the print image data; and a storage section that stores a reference color of each patch which is obtained by printing the chart image while setting the print density of the printing system to a standard print density when a print color of an image printed on the basis of a predetermined image data becomes a predetermined standard color, as well as stores a corresponding relationship between a color difference and a density difference, the color difference being a difference between the reference color and a color of each patch obtained by printing the chart image while setting the print density of the printing system to a series of print densities changed from the standard print density for each of the color materials having the plurality of colors, and the density difference being a difference between the print density and the standard print density, wherein the color guess section receives the designation of the tentative print density of each of the color materials having the plurality of colors and the place, acquires a relating portion according to the place of the corresponding relationship stored in the storage section, and guesses a print color at the place by interpolation processing using the reference color of each patch and the relation portion, wherein the interpolation processing includes calculation according to: print color R of a patch approximately obtained as follows: 
 R=R (std)+ RΔC+RΔM+RΔY+RΔK (1) wherein R(std) is print color of the standard print density, a difference between the colorimetric value of the patch when print density of only C color ink is changed and the colorimetric value of the patch printed with the standard print density is R ΔC , a difference between the colorimetric value of the patch when the print density of only M color ink is changed and the colorimetric value of the patch printed with the standard print density is R ΔM , a difference between the colorimetric value of the patch when the print density of only Y color ink is changed and the colorimetric value of the patch printed with the standard print density is R ΔY , and a difference between the colorimetric value of the patch when the print density of only K color ink is changed and the colorimetric value of the patch printed with the standard print density is R ΔK .