Standard canvas and stretcher sizes satisfying golden and silver ratios as well as optimal use of material

The sizes of canvases and stretchers for oil painting have been standardized in France in 19th century and widely accepted in many countries in Europe as well as in Japan so far. These standard sizes do not follow the golden ratio and porte d'harmonie number as has been often claimed. In this work, a general formula is derived to calculate the sizes of painting canvases and stretchers, which satisfy exactly the golden ratio and the porte d'harmonie number as well as the rule for optimal use of material in their mass production. Based on this formula new canvas and stretcher sizes are calculated for all three figure, landscape and marine formats.