Any distinction in principle between qualitative and quantitative characters disappeared long ago, although in the early days of Mendelism it was often conjectured that they might be inherited according to fundamentally different laws.
If it is still convenient to call some characters qualitative and others quantitative, it is only to denote that the former naturally have a discontinuous and the latter a continuous distribution, or that the former are not easily measured on a familiar metrical scale. Colors are an example. Differences between colors can be measured in terms of length of light waves, hue, brilliance etc., but most of us find it difficult to compare those measurements with our own visual impressions.
Most quantitative characters are affected by many pairs of genes and also importantly by environmental variations. It is rarely possible to identify the pertinent genes in a Mendelian way or to map the chromosomal position of any of them. Fortunately this inability to identify and describe the genes individually is almost no handicap to the breeder of economic plants or animals. What he would actually do if he knew the details about all the genes which affect a quantitative character in that population differs little from what he will do if he merely knows how heritable it is and whether much of the hereditary variance comes from dominance or overdominance, and from epistatic interactions between the genes.
(That last part might not always be true anymore, but it still remained on point for more than half the time that genetics as a discipline has existed.)
Jay L Lush (1949) Heritability of quantitative characters in farm animals